path planning, guidance and control for a uav forced landing

Path Planning, Guidance and Controlfor a

UAV Forced Landing

by

Pillar C. S. EngBEng (AeroAv)(Hons1), GradIEAust

A thesis submitted in fulfillment of the requirementsfor the degree of

Doctor of Philosophy

at the

Australian Research Centre for Aerospace AutomationSchool of Engineering Systems

Queensland University of Technology

2011

Statement of Authorship

The work contained in this thesis has not been previously submitted to meet require-

ments for an award at this or any other higher education institution. To the best

of my knowledge and belief, the thesis contains no material previously published or

written by another person except where due reference is made.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Author

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Date

iii

“There are two critical points in every aerial flight — its beginning and its end.”

Alexander Graham Bell, 1906

v

Abstract

A forced landing is an unscheduled event in flight requiring an emergency landing,

and is most commonly attributed to engine failure, failure of avionics or adverse

weather. Since the ability to conduct a successful forced landing is the primary in-

dicator for safety in the aviation industry, automating this capability for unmanned

aerial vehicles (UAVs) will help facilitate their integration into, and subsequent rou-

tine operations over civilian airspace. Currently, there is no commercial system

available to perform this task; however, a team at the Australian Research Cen-

tre for Aerospace Automation (ARCAA) is working towards developing such an

automated forced landing system. This system, codenamed Flight Guardian, will

operate onboard the aircraft and use machine vision for site identification, artificial

intelligence for data assessment and evaluation, and path planning, guidance and

control techniques to actualize the landing. This thesis focuses on research specific

to the third category, and presents the design, testing and evaluation of a Trajectory

Generation and Guidance System (TGGS) that navigates the aircraft to land at a

chosen site, following an engine failure.

Firstly, two algorithms are developed that adapts manned aircraft forced landing

techniques to suit the UAV planning problem. Algorithm 1 allows the UAV to select

a route (from a library) based on a fixed glide range and the ambient wind conditions,

while Algorithm 2 uses a series of adjustable waypoints to cater for changing winds.

A comparison of both algorithms in over 200 simulated forced landings found that

using Algorithm 2, twice as many landings were within the designated area, with

an average lateral miss distance of 200 m at the aimpoint. These results present a

baseline for further refinements to the planning algorithms.

A significant contribution is seen in the design of the 3-D Dubins Curves planning

algorithm, which extends the elementary concepts underlying 2-D Dubins paths to

account for powerless flight in three dimensions. This has also resulted in the devel-

opment of new methods in testing for path traversability, in losing excess altitude,

and in the actual path formation to ensure aircraft stability. Simulations using this

algorithm have demonstrated lateral and vertical miss distances of under 20 m at

the approach point, in wind speeds of up to 9 m/s. This is greater than a tenfold

improvement on Algorithm 2 and emulates the performance of manned, powered

aircraft.

The lateral guidance algorithm originally developed by Park, Deyst, and How

(2007) is enhanced to include wind information in the guidance logic. A simple

assumption is also made that reduces the complexity of the algorithm in following

a circular path, yet without sacrificing performance. Finally, a specific method of

supplying the correct turning direction is also used. Simulations have shown that

this new algorithm, named the Enhanced Nonlinear Guidance (ENG) algorithm,

vii

ABSTRACT

performs much better in changing winds, with cross-track errors at the approach

point within 2 m, compared to over 10 m using Park’s algorithm.

A fourth contribution is made in designing the Flight Path Following Guidance

(FPFG) algorithm, which uses path angle calculations and the MacCready theory to

determine the optimal speed to fly in winds. This algorithm also uses proportional-

integral-derivative (PID) gain schedules to finely tune the tracking accuracies, and

has demonstrated in simulation vertical miss distances of under 2 m in changing

winds.

A fifth contribution is made in designing the Modified Proportional Navigation

(MPN) algorithm, which uses principles from proportional navigation and the ENG

algorithm, as well as methods specifically its own, to calculate the required pitch to

fly. This algorithm is robust to wind changes, and is easily adaptable to any aircraft

type. Tracking accuracies obtained with this algorithm are also comparable to those

obtained using the FPFG algorithm.

For all three preceding guidance algorithms, a novel method utilising the geo-

metric and time relationship between aircraft and path is also employed to ensure

that the aircraft is still able to track the desired path to completion in strong winds,

while remaining stabilised.

Finally, a derived contribution is made in modifying the 3-D Dubins Curves

algorithm to suit helicopter flight dynamics. This modification allows a helicopter

to autonomously track both stationary and moving targets in flight, and is highly

advantageous for applications such as traffic surveillance, police pursuit, security or

payload delivery.

Each of these achievements serves to enhance the on-board autonomy and safety

of a UAV, which in turn will help facilitate the integration of UAVs into civilian-

airspace for a wider appreciation of the good that they can provide. The automated

UAV forced landing planning and guidance strategies presented in this thesis will

allow the progression of this technology from the design and developmental stages,

through to a prototype system that can demonstrate its effectiveness to the UAV

research and operations community.

viii

Acknowledgments

Firstly, I wish to thank my supervisors Prof. Rodney Walker, A/Prof. Duncan

Campbell, Dr. Luis Mejias-Alvarez and Dr. Daniel Fitzgerald at ARCAA for the

guidance and support they provided throughout my candidature, and the constant

incitement to push myself further. In particular, I wish to thank Dr. Mejias for

being a valuable sounding board for my ideas, and for patiently sitting with me to

work through some of the more difficult problems encountered.

I am also grateful to my fellow peers Dr. Paul Wu and Dr. Troy Bruggemann for

their advice, as well as for allowing me to learn and even to benefit from their own

research experiences, and to Mr. Richard Glassock and Mr. Scott McNamara for

providing great technical support during flight trials — all of whom are also great

friends.

Further, I am indebted to Prof. Pascual Campoy, Mr. Ivan Mondragon, Mrs.

Carol Martınez and Mr. Miguel Olivares-Mendez for affording me the invaluable

opportunity to work with their wonderful team at the Universidad Politecnica de

Madrid (UPM), and for the great hospitality they extended to me during my three-

and-a-half months research stay in Spain.

Finally, I would like to thank my family for their love, support and understand-

ing. This thesis would not have been possible without them.

The work carried out in this thesis was sponsored by the Australian Postgraduate

Award, the QUT Vice-Chancellor Scholarship Top-Up Award and the CSIRO Top-

Up Scholarship, and partly by the Australian Academy of Science International

Research Staff Exchange Scheme (IRSES) award.

ix

Contents

Statement of Authorship iii

v

Abstract vii

Acknowledgments ix

List of Figures xxi

List of Tables xxiii

List of Algorithms xxv

1 Introduction 1

1.1 Research Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Phase 1 - Literature Review . . . . . . . . . . . . . . . . . . . 7

1.2.2 Phase 2 - Forced Landing Simulation Environment . . . . . . 7

1.2.3 Phase 3 - Development of Path Planning and Guidance Algo-

rithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.4 Phase 4 - Testing and Verification . . . . . . . . . . . . . . . 9

1.3 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . 9

1.3.1 Primary Contributions . . . . . . . . . . . . . . . . . . . . . . 9

1.3.2 Derived Contribution . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Related Work 15

2.1 Path Planning Techniques . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Global Path Planning Techniques . . . . . . . . . . . . . . . . 16

2.1.1.1 Graph Search Algorithms . . . . . . . . . . . . . . . 16

2.1.1.2 Evolutionary Algorithms . . . . . . . . . . . . . . . 23

2.1.2 Local Path Planning Techniques . . . . . . . . . . . . . . . . 25

2.1.2.1 Heuristic-based Path Planning . . . . . . . . . . . . 25

2.1.2.2 Trajectory Generation Techniques . . . . . . . . . . 25

2.1.2.3 Dealing with Wind . . . . . . . . . . . . . . . . . . 35

2.2 Guidance Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Manned Aircraft Forced Landing Procedures . . . . . . . . . . . . . 41

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

xi

CONTENTS

3 Path Planning for a Fixed-Wing UAV 47

3.1 Algorithms based on Piloted Forced Landing Procedures . . . . . . . 47

3.1.1 Algorithm 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.1.2 Algorithm 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.2 3-D Dubins Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2.1 The 2-D Dubins Path . . . . . . . . . . . . . . . . . . . . . . 55

3.2.1.1 Determining Path Traversability . . . . . . . . . . . 58

3.2.2 The 3-D Dubins Path . . . . . . . . . . . . . . . . . . . . . . 62

3.2.2.1 Dealing with Excess Altitude . . . . . . . . . . . . . 64

3.2.2.2 Additional Waypoint for Post-Approach Point Gliding 67

3.2.2.3 Replanning . . . . . . . . . . . . . . . . . . . . . . . 68

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4 Guidance and Control for a Fixed-Wing UAV 71

4.1 Great-Circle Navigation, Guidance and Control . . . . . . . . . . . . 71

4.1.1 Waypoint Navigation . . . . . . . . . . . . . . . . . . . . . . . 72

4.1.2 Wind Correction . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.3 Waypoint Tracking . . . . . . . . . . . . . . . . . . . . . . . . 74

4.1.4 Flight Control . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2 3-D Nonlinear Guidance and Control . . . . . . . . . . . . . . . . . . 76

4.2.1 The Enhanced Nonlinear Guidance (ENG) Algorithm . . . . 77

4.2.1.1 Line Following . . . . . . . . . . . . . . . . . . . . . 78

4.2.1.2 Arc Following . . . . . . . . . . . . . . . . . . . . . 80

4.2.1.3 Calculating Roll Angle from Acceleration . . . . . . 81

4.2.1.4 Determining the Correct Turning Direction . . . . . 82

4.2.2 The Flight Path Following Guidance (FPFG) Algorithm . . . 83

4.2.3 The Modified Proportional Navigation (MPN) Algorithm . . 84

4.2.4 Ensuring Smooth Transition between Waypoints . . . . . . . 89

4.2.5 Control for Flight Stability . . . . . . . . . . . . . . . . . . . 90

4.2.5.1 Lateral Control . . . . . . . . . . . . . . . . . . . . . 91

4.2.5.2 Longitudinal Control . . . . . . . . . . . . . . . . . 95

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5 The Forced Landing Simulation Environment 101

5.1 Aerosonde UAV Model . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.2 Boomerang UAV model . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

xii

CONTENTS

6 Flight Experiment Setup 107

6.1 Overview of the Unmanned Aircraft System . . . . . . . . . . . . . . 107

6.2 Hardware Description . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.3 Software Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.4 Procedures for Testing the Forced Landing Software in Flight . . . . 118

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7 Discussion of Results 123

7.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.1.1 Results from Algorithms based On Piloted Forced Landing

Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.1.2 Results from Algorithms based on Nonlinear Planning and

Guidance Techniques . . . . . . . . . . . . . . . . . . . . . . . 127

7.1.2.1 Initial Results obtained using the 3-D Dubins Curves,

ENG and FPFG Algorithms . . . . . . . . . . . . . 127

7.1.2.2 Improved Results obtained using the 3-D Dubins Curves,

ENG and MPN Algorithms . . . . . . . . . . . . . . 132

7.1.2.3 Results demonstrating Path Replanning using the 3-

D Dubins Curves, ENG and MPN Algorithms . . . 134

7.1.3 Results from Simulations using the HORIZONmp Simulator . 135

7.2 Results from Flight Experiments . . . . . . . . . . . . . . . . . . . . 137

7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

8 Conclusions 143

8.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

9 149

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

A State-Space Model of Boomerang UAV 157

A.1 Lateral Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

A.2 Longitudinal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

B MATLAB® Simulink Models 163

B.1 The Aerosonde UAV Model . . . . . . . . . . . . . . . . . . . . . . . 163

B.2 The Boomerang UAV Model . . . . . . . . . . . . . . . . . . . . . . 164

C Path Planning for Target Tracking Using an Autonomous Heli-

copter 165

C.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

C.2 Path Planning for Target Tracking . . . . . . . . . . . . . . . . . . . 168

xiii

CONTENTS

C.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

C.3.1 Simple Path Following . . . . . . . . . . . . . . . . . . . . . . 171

C.3.2 Replanning with Shifting Target . . . . . . . . . . . . . . . . 171

C.3.3 Replanning with Moving Target . . . . . . . . . . . . . . . . 172

C.3.4 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

xiv

List of Figures

1.1 The Flight Guardian automated UAV forced landing system architec-

ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Stages of flight in a UAV forced landing . . . . . . . . . . . . . . . . 7

2.1 Schematic diagram showing how a flight trajectory is generated using

Pettersson and Doherty’s method . . . . . . . . . . . . . . . . . . . . 18

2.2 Example of Frazzoli’s RRT two-dimensional tree-expansion proce-

dure. Note that the paths have already been smoothed (Source: Fraz-

zoli, Dahleh, & Feron, 2002) . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Visual example of Frazzoli’s manoeuvre generation system (Source:

Frazzoli, Dahleh, & Feron, 2005) . . . . . . . . . . . . . . . . . . . . 21

2.4 Griffith’s collision avoidance manoeuvre (Source: Griffiths et al., 2006) 21

2.5 Overview of evolutionary search algorithms . . . . . . . . . . . . . . 23

2.6 (a) Potential field contour plot (b) Skeleton (Source: Barraquand et

al., 1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.7 Simple 2-D Dubins curves showing both CSC and CCC type paths.

Initial and target headings are indicated by ωi and ωt respectively. . 29

2.8 3-D CSC Dubins curves constructed using Hota’s analytical method.

Initial and target headings are indicated by the red and black arrows

respectively. (Source: Hota and Ghose, 2010) . . . . . . . . . . . . . 30

2.9 Examples of clothoid curves or Cornu spirals. . . . . . . . . . . . . . 31

2.10 Smooth trajectory formed by a symmetrical clothoid arc used to tran-

sition between arcs and lines in a Dubins path (Source: Liu et al.,

2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.11 Flyable paths and their curvature profiles (Source: Shanmugavel et

al., 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.12 A lane change manoeuvre using paths of minimum curvature and

sharpness (Source: Wilde, 2009) . . . . . . . . . . . . . . . . . . . . 33

2.13 Four quintic PH splines solving a planning problem. The most ap-

propriate solution is the curve with the least bending energy (solid

black line). (Source: Bruyninckx and Reynaerts, 1997) . . . . . . . . 34

2.14 3-D Pythagorean-hodograph space curve with bounded climb angle

(Source: Neto and Campos, 2009) . . . . . . . . . . . . . . . . . . . 35

2.15 Path planning with sliding surface control and virtual target - (a)

Forming the virtual target, (b) Example ground path created through

multiple waypoints (Source: McGee & Hedrick, 2006) . . . . . . . . 37

xv

LIST OF FIGURES

2.16 (a) Strategy 1 - Arctan nonlinear control, (b) Strategy 2 - Velocity

ratio control (Source: Frew et al., 2004) . . . . . . . . . . . . . . . . 39

2.17 Illustration of the curve to be tracked and the connecting contour

(Source: Rathinam et al., 2006) . . . . . . . . . . . . . . . . . . . . . 40

2.18 Illustrating the vector field concept for linear and circular path fol-

lowing. The desired course of the UAV is specified by the direction

of the vector field. (Source: D. R. Nelson et al., 2007) . . . . . . . . 41

2.19 The forced landing circuit pattern (Source: Civil Aviation Safety Au-

thority of Australia (CASA), 2007) . . . . . . . . . . . . . . . . . . . 43

2.20 Path planning on final approach (Source: Brandon, 2007) . . . . . . 43

3.1 Determination of glide range and waypoints for a forced landing . . 48

3.2 Standard RHC forced landing pattern . . . . . . . . . . . . . . . . . 49

3.3 Modified RHC forced landing pattern . . . . . . . . . . . . . . . . . 51

3.4 State transition diagram for Algorithm 1 . . . . . . . . . . . . . . . . 52

3.5 Altitude prediction for Algorithm 2 . . . . . . . . . . . . . . . . . . . 53

3.6 State transition diagram for Algorithm 2 . . . . . . . . . . . . . . . . 54

3.7 Speed polar diagram for a Boomerang-60 UAV using simulated data,

showing how the best glide speed Vbg is obtained. . . . . . . . . . . . 57

3.8 Speed polar diagram for a Boomerang-60 UAV using flight data, show-

ing how the best glide speed Vbg is estimated from a smooth curve

fitted to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.9 (a)Step 1 of generating the 2-D path. (b)Step 2 of generating the 2-D

path. (c) Step 3 of generating the 2-D path. Four plausible paths are

obtained; the optimal path is path no.1 . . . . . . . . . . . . . . . . 59

3.10 Diagram showing how path traversability is determined from the geo-

metric construction of the 2-D Dubins curve, and the initial and final

positions of the UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.11 Relationship between elements of the generated 3-D flight path. The

generated path is Γarc0 ∪ Γline ∪ Γarcf . . . . . . . . . . . . . . . . . . 63

3.12 Forced landing flight path example showing the use of extra helix

spirals, Γex and a connecting contour Γjoin to form a feasible path. . 66

3.13 Derivation of an additional waypoint to track to improve path follow-

ing performance in strong headwinds . . . . . . . . . . . . . . . . . . 67

3.14 Forced landing flight path example showing path replanning. Path 2

is the new path that connects to the breaking point at Point C, where

the unflown portion of the original path (CB) is removed from Path 1. 68

4.1 Wind triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

xvi

LIST OF FIGURES

4.2 Flight path tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.3 Simple lateral controller for the Aerosonde UAV . . . . . . . . . . . 75

4.4 Simple longitudinal controller for the Aerosonde UAV . . . . . . . . 75

4.5 Lateral controller response for the Aerosonde UAV, showing good

tracking of the commanded roll angle, φcmd. The yaw angle, ψ changes

synchronously with the roll angle, φ to provide a coordinated response

with a minimal side slip, β. Both the ailerons and rudder are working

synchronously to provide a coordinated turn. . . . . . . . . . . . . . 76

4.6 Airspeed controller for the Aerosonde UAV, showing the desired Vbg

of 19 m/s is able to be maintained throughout the forced landing

descent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.7 Diagram showing the lateral guidance law . . . . . . . . . . . . . . . 78

4.8 Vehicle kinematics for straight line following, showing (a) the rela-

tionship between the aircraft velocity V and the expected/average

wind velocity W , and (b) the relationship between the aircraft bear-

ing ψ(t), the path bearing ψ12 , the wind bearing ψw , and the angle

η. In addition, the relationship between the cross-track error d, the

hypotenuse d1 and the look-ahead distance L1 is also shown. . . . . 79

4.9 Vehicle kinematics for circular path following . . . . . . . . . . . . . 80

4.10 Vehicle kinematics showing how roll angle is derived from acceleration 82

4.11 Geometric relationship between aircraft and path . . . . . . . . . . . 83

4.12 Using the speed polar diagram to determine the required speed-to-fly

while gliding in winds (Source: Brandon, 2007) . . . . . . . . . . . . 85

4.13 Cross-sectional view of vehicle kinematics for vertical path tracking . 85

4.14 Components of vehicle kinematics for vertical path tracking . . . . . 86

4.15 Diagram showing the relative position between the aircraft and the

start of the second arc in the Dubins path. The relative position is

used for more accurate path following. . . . . . . . . . . . . . . . . . 90

4.16 Root locus plot of the Boomerang lateral control autopilot using just

the ailerons. The pole locations indicate a very well-damped response. 91

4.17 Transfer function of the washout filter for the Boomerang-60 UAV

showing the magnitude response . . . . . . . . . . . . . . . . . . . . 92

4.18 Root locus plot of the Boomerang lateral control autopilot using both

the ailerons and rudder. The pole and zero locations indicate a very

well-damped response. . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.19 Aileron controller response of the Boomerang-60 UAV to a 15 deg roll

command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.20 Rudder controller response of the Boomerang-60 UAV to a 15 deg roll

command, showing negligible sideslips . . . . . . . . . . . . . . . . . 93

xvii

LIST OF FIGURES

4.21 Simulated lateral controller for the Boomerang UAV, showing a two-

stage control process for the roll angle, and a yaw damper to correct

for any undesirable aircraft yawing motion. The same controller is

employed by both the FPFG and MPN algorithms. . . . . . . . . . . 94

4.22 Good tracking of commanded roll during a simulated forced landing,

with negligible sideslips . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.23 Root locus plot of the Boomerang longitudinal control autopilot using

elevators to control pitch. The pole and zero locations indicate a very

well-damped response. . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.24 Elevator controller response of the Boomerang-60 UAV to a -6 deg

pitch command. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.25 Longitudinal controller for the FPFG algorithm - the reference signal

is selected from either θde or θdewind and passed to a lower-level pitch-

to-elevator controller. . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.26 Longitudinal controller for the MPN algorithm - the reference signal is

chosen from a velocity-to-pitch angle lookup table before being passed

to a lower-level pitch-to-elevator controller. . . . . . . . . . . . . . . 97

4.27 Good tracking of commanded pitch during a simulated forced landing

with constant manoeuvring . . . . . . . . . . . . . . . . . . . . . . . 98

5.1 Screen capture of a simulated forced landing in FlightGear, showing

the planned path (orange), the incident wind vector and the desired

landing site. The generic Cessna skin with an actual model of an

Aerosonde aircraft is used. The model is constructed using the classic

coefficient build-up method (Nelson, 1998) and is available inside the

MATLAB® AeroSim blockset. . . . . . . . . . . . . . . . . . . . . . 102

5.2 Simplified Simulink model of Aerosonde UAV . . . . . . . . . . . . . 103

5.3 Model of simulation world . . . . . . . . . . . . . . . . . . . . . . . . 103

5.4 Wind components (WN : Blue, WE : Green, WD: Red). These com-

ponents were used to compute the resultant wind vector incident on

the UAV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.5 An example of simulated wind turbulence experienced by the aircraft

during a forced landing, with gusting applied in the longitudinal,

lateral and vertical directions. . . . . . . . . . . . . . . . . . . . . . . 105

5.6 Simplified Simulink model of Boomerang UAV . . . . . . . . . . . . 106

6.1 Boomerang-60 avionics architecture . . . . . . . . . . . . . . . . . . . 108

6.2 Clockwise from top: The MicroPilot autopilot box; the flight com-

puter stack and interface plate; location of avionics inside the fuselage.112

xviii

LIST OF FIGURES

6.3 Location of avionics outside the Boomerang UAV . . . . . . . . . . . 113

6.4 PID loop structure of the MicroPilot MP2128g autopilot (Source: Mi-

croPilot Autopilot Installation & Operation, Stony Mountain, Mani-

toba Canada, 2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.5 Diagram showing how the Pitch From Airspeed and Roll From Head-

ing PID loops of the MicroPilot autopilot interface with the aircraft

flight control system . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.6 Plot showing the relationship between the desired (black) and actual

(blue) pitch values over one second. The actual pitch values were

obtained using a linear mapping of the airspeed to a pitch value. . . 117

6.7 Aerial view of the Burrandowan test site. The two candidate landing

sites are labeled as Site A and Site B, and have their preferred di-

rection of approach indicated by the blue arrows. Shown also is the

reference point for translating between different coordinate systems,

the approach point and aimpoint for each site, as well as the starting

waypoint for all forced landing descents (Source: Google Earth). . . 119

6.8 Schematic diagram of the procedures followed in conducting the UAV

forced landing flight tests . . . . . . . . . . . . . . . . . . . . . . . . 120

6.9 Screen capture of the Horizonmp simulator program. This simula-

tor allows an operator on the ground to keep track of the aircraft

throughout the flight, as well as issue any telecommands if required. 121

7.1 Forced landing results for a single case, for (A)-Algorithm 1, and

(B)-Algorithm 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.2 Monte Carlo simulation results — Algorithm 2 produces more land-

ings within the designated landing site and closer to the aim point

(≤ 200m) than Algorithm 1 (≤ 400m) . . . . . . . . . . . . . . . . . 126

7.3 Path planning and following for a forced landing from a high initial

altitude in nil wind conditions . . . . . . . . . . . . . . . . . . . . . . 129

7.4 Path planning and following in ambient winds, showing (a) Aircraft

response in 6 m/s wind from SSW; (b) Aircraft response in 0-9 m/s

changing winds from NNE and SSW; (c) Horizontal and vertical track

errors for case a; and (d) Horizontal and vertical track errors for case b.130

7.5 Input winds for the scenario in Figure 7.4b, showing changes in wind

speed over time, and the errors between the expected (cyan) and

actual (magenta) north and east wind component values. . . . . . . 131

7.6 Wind turbulence for the scenario in Figure 7.4b, showing examples of

gusts and lulls in the longitudinal, lateral and vertical directions. . . 131

xix

LIST OF FIGURES

7.7 Path planning and following for a forced landing from a high initial

altitude in nil wind conditions, with improved path planning and

tracking algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.8 Path planning and following in ambient winds using improved plan-

ning and tracking algorithms, showing (a) Aircraft response in 0-9

m/s changing winds from NNE and SSW; and (b) Horizontal and

vertical track errors for case a. . . . . . . . . . . . . . . . . . . . . . 134

7.9 Path replanning and tracking in ambient winds using improved plan-

ning and tracking algorithms, showing (a) Top view of the aircraft

response in 0-9 m/s changing winds from the NNE and SSW; and (b)

An oblique view of the same. . . . . . . . . . . . . . . . . . . . . . . 135

7.10 Path replanning and tracking in nil winds using the HORIZONmp

Simulator, showing (a) Top view of the aircraft response, and (b)

An oblique view of the same. These results are comparable to those

obtained using the MATLAB® Simulink models. . . . . . . . . . . . 136

7.11 Aircraft control response from a simulated forced landing descent in

the HORIZONmp Simulator, showing good tracking of the input com-

mands in (a) Roll and (b) Pitch. . . . . . . . . . . . . . . . . . . . . 136

7.12 Flight activities. Clockwise from top: The Boomerang-60 UAV in

flight; the pilot, who is on standby for takeoff and landing, as well

as any emergencies; the ground operator, who communicates with

the pilot via UHF radio and constantly monitors the progress of the

flight, and finally, the MOC which houses the ground operator and

associated computing and communications equipment. . . . . . . . . 138

7.13 Results from flight test example 1. (a) Top view of flight path; (b)

Oblique view of the same; (c) Roll performance; (d) Pitch performance139

7.14 Results from flight test example 2. (a) Top view of flight path; (b)

Oblique view of the same; (c) Roll performance; (d) Pitch performance141

B.1 Simulink diagram of the Aerosonde UAV model . . . . . . . . . . . . 163

B.2 Simulink diagram of the Boomerang UAV model . . . . . . . . . . . 164

C.1 Helipad target used for obtaining the image homographies. (Source:

CVG Image Repository) . . . . . . . . . . . . . . . . . . . . . . . . . 166

C.2 Rotomotion electric helicopter UAV used for pose estimation flight

experiments. The helicopter is carrying an Xscale-based flight com-

puter, a pan-tilt camera system and a VIA mini-ITX 1.5 GHz on-

board computer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

xx

LIST OF FIGURES

C.3 UAV on-board visual control system employing a dynamic look-and-

move architecture. (Source: CVG Image Repository) . . . . . . . . . 167

C.4 Relationship between the helipad, camera and UAV coordinate sys-

tems (Source: CVG Image Repository) . . . . . . . . . . . . . . . . . 168

C.5 Desired and actual helicopter flightpath while tracking a stationary

target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

C.6 Desired and actual helicopter flightpath while tracking a shifting tar-

get, showing (a) Top view of the aircraft response, and (b) An oblique

view of the same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

C.7 Desired and actual helicopter flightpath while tracking a moving tar-

get, showing (a) Top view of the aircraft response, and (b) An oblique

view of the same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

xxi

List of Tables

2.1 Suitability of various PRM planners to different types of regions . . 17

3.1 Standard RHC Waypoint Coordinates . . . . . . . . . . . . . . . . . 50

3.2 Sink rates at different airspeeds for the Boomerang-60 UAV . . . . . 57

4.1 Look-up table relating commanded airspeed to desired pitch angle for

Boomerang UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.1 Power budget for avionics (The power consumptions are under typical

operating conditions) . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.1 Sample test data for the path planning and guidance algorithms. Ta-

ble 7.1a shows the desired initial and final aircraft positions and atti-

tudes for a descent from 1640 ft to 500 ft in nil wind conditions, while

Table 7.1b presents the desired initial and final aircraft positions and

attitudes for a descent from 850 ft to 500 ft in winds. . . . . . . . . . 128

C.1 Initial conditions for autonomous helicopter path planning . . . . . . 170

xxiii

List of Algorithms

3.1 Determining Path Traversability . . . . . . . . . . . . . . . . . . . . . 61

4.1 Determining the Correct Turning Direction . . . . . . . . . . . . . . . 84

xxv

Nomenclature

AGL The altitude Above Ground Level

API Application Programming Interface

ARCAA Australian Research Centre for Aerospace Automation

CASA The Civil Aviation Safety Authority of Australia

CSSS Candidate Site Selection System

EA The Evolutionary Algorithm

ENG The Enhanced Nonlinear Guidance algorithm

ENU The East-North-Up coordinate reference frame

FPFG The Flight Path Following Guidance algorithm

GA General Aviation

GIS Graphical Information System

GPS Global Positioning System

ICPUAS International Cooperative Program for Unmanned Aircraft Systems

INS Inertial Navigation System

LIDAR Light Detection and Ranging

MDMS Multi-Criteria Decision Making System

MOC Mobile Operations Centre

MPC The Model Predictive Control guidance algorithm

MPN The Modified Proportional Navigation algorithm

NAS National Airspace System

NED The North-East-Down coordinate reference frame

PBVS Position-Based Visual Servoing

PID Proportional-Integral-Derivative control

PRM The Probabilistic Roadmap planning algorithm

PWM Pulse Width Modulated

xxvii

NOMENCLATURE

QUT Queensland University of Technology

RC Radio-controlled

RDT The Rapidly exploring Dense Tree planning algorithm

RF Radio Frequency

RRT The Rapidly exploring Random Tree planning algorithm

SDK Software Development Kit

TAS True Airspeed

TCP Transmission Control Protocol

TGGS Trajectory Generation and Guidance System

UAS Unmanned Aircraft System

UAV Unmanned Aerial Vehicle

UDP User Datagram Protocol

UPM Universidad Politecnica de Madrid

xxviii

1Introduction

IN recent years, unmanned aerial vehicles (UAVs) have been widely used in com-

bat, and their potential applications in civil and commercial roles are also receiv-

ing considerable attention by industry and the research community. There are nu-

merous, published reports of UAVs used in earth science missions (Cobleigh, 2006),

fire-fighting (Velinov, 2008) and border security (Wise, 2009; Tyrrell, 2008) trials,

with other speculative deployments including applications in agriculture, communi-

cations and traffic monitoring (Wong, 2001). The use of UAVs, with their unique

flexibility and response time, not only reduces costs compared to existing methods

(such as with manned aircraft or satellites), but also enables information to be ac-

quired in a time frame previously unrealisable (Wegener et al., 2004). In addition,

ongoing advancements in control and communications, manufacturing and propul-

sion technologies mean that UAVs have a very promising future, with a recent Teal

Group study estimating the worldwide UAV market to exceed $USD54 billion by

2017 (Corporation, n.d.).

Yet, despite these seeming advantages, a significant challenge remains - that of in-

tegrating UAVs within the national airspace system (NAS) (see report by DeGarmo

(2004)). Since many of the proposed missions for civilian UAVs will involve flying

over populated areas and in airspace occupied by manned aircraft, UAVs flying in

such areas must be able to interact with these aircraft and air traffic control (ATC),

as well as manage flight plans and handle emergency situations. They must possess

a higher degree of onboard autonomy to replicate certain capabilities of a human

pilot, such as navigation and decision making. In fact, it has been stipulated by the

Federal Aviation Authority (FAA) and other civil aviation regulatory bodies around

the world, including Australia, that UAVs must demonstrate an equivalent level of

safety (ELOS) to that of manned aircraft (DeGarmo, 2004; Fitzgerald, Mejias, Eng,

& Liu, 2007). This is due to the fact that UAV/NAS policy makers are conscious

of the repercussions that a major UAV accident could have on public acceptance of

this technology. This may be arguably the main factor which has prevented these

1

CHAPTER 1. Introduction

UAV trials from becoming full-scale commercial operations, as well as restricted

operations of civilian UAVs to only within segregated airspace. In light of this,

much research is underway in developing technologies to enhance UAV autonomy

and safety, including collision avoidance (Debadeepta, Geyer, Singh, & Digioia, July

14-15, 2009; Geyer, Debadeepta, & Singh, May, 2009; Lai, Mejias, & Ford, 2010),

health monitoring (Bethke, How, & Vian, 2008; Tanwer, Hussain, & Reel, 2010),

mission management (McManus, 2004; Wu, 2009) and more recently, forced landing

systems (Fitzgerald, 2007; Eng, Mejias, Fitzgerald, & Walker, 2007; Eng, Mejias,

Walker, & Fitzgerald, 2010).

A forced landing is an unscheduled event in flight which requires the aircraft to

perform an emergency landing, and is most commonly attributed to engine failure

and adverse weather. There must still be some degree of flight control so that the

aircraft is able to manoeuvre to a desired landing site. During a piloted forced

landing, a complex decision trade-off must be continously made on the airspeed,

angle of attack and descent rate for continued flight. This is further complicated by

the fact that the pilot must locate a suitable landing site within the gliding range

of the aircraft, which is constantly affected by changing wind conditions, and with

limited time to make decisions. On final approach to land, the pilot must also avoid

trees, power lines, buildings and other obstacles in the descent path which may or

may not have been detected from the air. The landing itself is a controlled descent

that, if successful, results in no harm to the pilot, aircraft or persons and property

on the ground (CASA, 2007).

To date, the most commonly employed method to allay the severity of a UAV

forced landing is the use of parachutes or parafoils to retard the rate of descent,

while still providing some degree of controllability for the aircraft (Redelinghuys,

2007). Whilst this concept is attractive in that it still enables limited vehicle con-

trollability even when both the engine and control surfaces have failed, it is highly

susceptible to wind gusts and other atmospheric effects which may adversely affect

the final impact point. Having a parachute or parafoil onboard also adds to the

weight and complexity of the aircraft. Another solution which has seen recent op-

eration at the 2009 UAV Outback Challenge held in Australia requires the UAV to

deflect its control surfaces such that the aircraft will spiral into the ground, follow-

ing an engine or communications failure (Airborne Delivery Challenge and Search

and Rescue Challenge: Mission, Rules and Regulations, Judging and Scoring Cri-

teria, 2009). Although this solution has been proven to successfully terminate the

flight and also contain the crash site within a limited area, it is hardly desirable

for operations over populated areas. Other safety systems currently available allow

the UAV to fly towards a pre-defined safe ditching area selected from a database of

such, known locations (D. R. Nelson, Barber, McLain, & Beard, 2007). To date,

2

the only reported successful UAV forced landing involves the U.S. Air Force Global

Hawk, which performed a gliding descent under remotely-piloted control (RPC) to

an emergency airstrip in 2006 (Froeschner, n.d.).

As the ability to execute a successful forced landing remains the primary in-

dicator for safety in the manned aviation industry, automating this capability for

UAVs will facilitate their integration into, and subsequent routine operations over

civilian airspace. Currently, there is no commercial system available to perform this

task; however, a team at the Australian Research Centre for Aerospace Automation

(ARCAA) is working towards developing such an automated forced landing system.

This system, codenamed Flight Guardian, will operate onboard the aircraft and will

use a natural sensing modality that aims to emulate human pilot performance (Eng

et al., 2007; Fitzgerald et al., 2007; Fitzgerald, 2007). Primarily, this includes the

use of machine vision for navigation and guidance, as well as artificial intelligence for

data assessment and evaluation. More specifically, there are three main components

of an onboard forced landing system which will need to operate seamlessly together

for a successful landing. These include:

1. A Candidate Site Selection System (CSSS) responsible for identifying areas

on the ground that are large enough for the aircraft to land, are free of ob-

stacles and whose surface types can be accurately classified. A commercially

viable approach for small UAVs (similar to those used for flight testing in

this research) is the use of video camera data to enhance a priori graphical

information system (GIS) raster maps. This will produce an accurate map of

the landing area, from which hazards and safe landing locations can be iden-

tified. The benefits of using machine vision, rather than sensing systems such

as those employing radar or light detection and ranging (LIDAR) techniques,

are that cameras are much smaller, lighter, have lower power consumption

and are significantly cheaper. As such, they can be easily integrated with

existing onboard navigation systems such as the global positioning system

(GPS) and the aircraft inertial navigation system (INS). Of course, given a

larger aircraft capable of lifting heavier loads, the use of radar and LIDAR

will need to be considered since these are more accurate sensors that also add

a measure of safety to the costly payloads likely to be housed onboard.

2. A Multi-Criteria Decision Making System (MDMS) that assesses multiple

attributes, such as wind velocity and the geometry of the landing site, to

identify the most suitable landing area, while simultaneously attempting to

satisfy as many of the mission objectives as possible. These objectives are

arranged in order of priority and include minimizing human casualty and

property damage, as well as maximizing both aircraft and payload survival.

3


In many cases these objectives may be conflicting, and thus compromises

must be made such that the most critical objective is achieved, and finally,

3. A Trajectory Generation and Guidance System (TGGS) that navigates the

aircraft to land at the chosen site. The inputs to this system are the desired

approach and landing GPS coordinates, as calculated by the MDMS, as well

as the current aircraft position. This system assesses the variable wind con-

ditions which can greatly affect an unpowered aircraft descent, and attempts

to output the most feasible trajectory to the landing site that is within the

limits of the aircraft dynamics. Should the proposed trajectory be unsuit-

able due to various reasons, the system can also output alternate paths in

real-time. Finally, due to uncertainties in a priori information concerning

the operating environment and uncertainties in the aircraft state, this sys-

tem may also need to utilise information from an additional sensor, such as

a video camera or laser scanner to provide more accurate, real-time updates

of the outside aircraft environment and to augment coarse GIS data.

Since current UAVs in operation are heavily reliant on remote monitoring and

control by human pilots, having an onboard system will greatly enhance UAV auton-

omy and reduce the need for human intervention. This in turn decreases operational

cost, operator workload and susceptibility to loss of aircraft due to communications

failure.

1.1 Research Problem

A conceptual UAV forced landing system is depicted in Figure 1.1. Note that the

Secondary System (shown in green in Figure 1.1), to be deployed should the aircraft

become uncontrollable, has been included merely for completeness and will not be

the focus of any of the forced landing research described above at this stage, since

these studies are mainly concerned with the “heart” of the forced landing problem,

that is, the precision landing of a UAV on an identified safe location.

The selection of candidate landing sites and multi-criteria decision making are

currently under investigation by Daniel Fitzgerald, Luis Mejias and Xi Liu at AR-

CAA (Fitzgerald, 2007; Fitzgerald et al., 2007; Mejias, Fitzgerald, Eng, & Liu,

2009), and it is assumed that these algorithms will function as designed for the UAV

forced landing problem. This thesis deals with the problem of generating the de-

scent trajectory for a UAV forced landing, and will address the following key research

questions:

1. Can an automated, reconfigurable flight path be generated that accounts for

4

1.1. RESEARCH PROBLEM

Figure 1.1: The Flight Guardian automated UAV forced landing system architecture

the dynamics of the gliding aircraft during the forced landing descent?

The research will mainly deal with fixed-wing UAVs, as these platforms repre-

sent the most difficult forced landing planning problem (there are more options for

a fixed-wing than a rotary-wing aircraft forced landing). However, this does not

exclude the fact that the research outcomes can also be applied to rotary-wing or

even hybrid aircraft, such as a tiltrotor. The term ”reconfigurable” implies that

the planned trajectory can be adjusted to accommodate unforeseen events, such as

favourable wind conditions at a lower altitude which could facilitate the descent

plan. In addition, the dynamic and structural limitations of the aircraft can be

accommodated by imposing geometric constraints on the planned path. To further

limit the research scope, the descent trajectory will only be generated from the point

of failure to final approach, that is, from an upper altitude limit of 10000 ft above

ground level (AGL) to where the aircraft will be at a nominal altitude of 500 ft

AGL, aligned with the length of the runway/landing site and approximately 0.5 nm

out from the runway/landing site threshold. The 10000 ft limit represents the upper

bound of Class G airspace, which is the highest altitude that general aviation (GA)

and recreational aircraft (and possibly UAVs for the near future) are allowed to fly

in uncontrolled airspace (CASA, 2007). For this research, it is assumed that GPS,

a low quality inertial navigation system (INS), air data and a magnetometer are

available, and that there are feasible landing areas that can be physically attained

by the aircraft. It is also assumed that the terrain is generally flat, although possi-

bly containing natural and man-made obstacles such as trees, fences and powerlines.

The objective is that the proposed trajectory generation method will operate inde-

pendently of human input and will always find a viable solution within realistic wind

change conditions. In addition, the flight trajectories flown by human pilots when

5


conducting a forced landing will be analysed to see how they can be incorporated

into a machine-flown trajectory.

Seeing that wind conditions will ultimately have the greatest impact on the

success or failure of a forced landing, regardless of how well-planned the initial

trajectory is, this research will also consider a second question:

3. Can automated guidance algorithms be designed that would enable the gliding

aircraft to intercept the desired path and follow it with acceptable cross-track

errors in winds?

Once an automated path is formed, suitable guidance strategies must be em-

ployed which will allow continuous path following regardless of the ambient wind

conditions. It is assumed that the aircraft primary flight control surfaces (ailerons,

elevators, rudder) are still intact even though the engine has failed, meaning that

the gliding aircraft is still fully controllable. In addition, it is assumed that no ob-

stacles are to be avoided during descent to the approach point, and that the aircraft

is aligned with the longest portion of the selected landing site and facing into the

wind at this point. The desired bearing, airspeed and position of the aircraft at

the approach point (such that the preceding conditions are fulfilled) is determined

beforehand by the MDMS using GIS and other available sensor data, and is passed

as an input into the planning algorithm. Once past the approach point however,

the aircraft may need to deal with obstacles such as those described in Question 1,

however, this problem is beyond the scope of this research. Finally, it is assumed

that wind velocities can be estimated using onboard instruments such as a compass,

a GPS unit and the INS, and that this estimation is accurate enough to create a

robust guidance algorithm. Perhaps a more accurate estimate of the wind conditions

can be obtained by building a statistical model from meteorological data, and aug-

mented by updates from onboard wind estimates and weather forecasts. However,

a thorough investigation into this area is once again outside the research scope, and

it is expected that the robustness of the algorithm to be employed would negate

the need for these alternative methods in most cases. Finally, for test purposes,

the required path following performance will be specified as having a horizontal

(lateral) and vertical (longitudinal) cross-track error at the approach point of no

greater than 10 m (approximately 30 ft), and a maximum vertical and horizontal

deviation of no greater than 30 m (approximately 100 ft) on average. These upper

and lower bounds are commonly accepted as the performance standard for general

aviation aircraft (CASA, 2007).

By addressing the two research questions defined above, this thesis will provide a

significant contribution to the field of UAV forced landing research, as well as supply

6

1.2. RESEARCH METHODOLOGY

a methodological framework model for future research in this area. Figure 1.2 depicts

the various stages of flight in a UAV forced landing, including that investigated in

this research (shown shaded). Note that the Landing Phase, from the approach

point to the aimpoint, is an area of research outside the scope of this thesis.

Figure 1.2: Stages of flight in a UAV forced landing

1.2 Research Methodology

An iterative approach to design and development has been adopted in which an

increased functionality of the proposed solution can be progressively realized. In

this way, feedback from previous stages can be used to refine the methodology for

subsequent iterations, and the proposed solution can be verified at each stage of

development.

1.2.1 Phase 1 - Literature Review

In the first phase, a comprehensive review of existing work in the fields of robotics

path planning and trajectory generation, as well as manned aircraft forced landing

procedures has been conducted and the findings documented in Chapter 2. These

findings direct the development of the forced landing path planning and guidance

algorithms presented in this thesis.

1.2.2 Phase 2 - Forced Landing Simulation Environment

In the second phase, the trajectory generation and guidance algorithms are imple-

mented at a basic level in a computer simulation environment. The MATLAB®

7


Simulink programming software has been used to allow rapid development of non-

linear aircraft models, wind conditions and the underlying terrain. The simulation

includes only one landing site and assumes that all wind conditions and terrain

information are known. The aircraft model used is that of an Aerosonde UAV,

which is provided with basic manoeuvring capabilities to track the desired path to

the landing site, using manned aircraft forced landing procedures (Section 2.3). By

studying this model, a more in-depth understanding of the forced landing problem

can be obtained, which in turn aids in the development of new planning and guid-

ance strategies with improved performance. To reduce complexity and to comply

with control functions implemented in most commercial-off-the-self (COTS) hard-

ware, all low-level stabilizing control actions are governed by simple PID control

laws.

1.2.3 Phase 3 - Development of Path Planning and Guidance Al-

gorithms

In the third phase, trajectory generation and guidance techniques derived from the

robotics literature are implemented and tested in simulation, initially without con-

sideration of wind effects. However, once performance is demonstrated with accept-

able results, wind effects are incorporated.

Concurrent with the development of the software algorithms, initial flight testing

with a suitable UAV is also conducted to obtain real-world sensor data, as well

as to test the functionality of hardware and software both onboard and on the

ground. The sensor data provides valuable feedback on the behaviour of the aircraft

system in its operating environment, and is used to refine the trajectory generation

and guidance (including wind estimation) algorithms. The UAV platform chosen

for these experiments is an almost-ready-to-fly Boomerang 60 size model aircraft.

This UAV is controlled by a MicroPilot MP2128g flight control computer, which is

capable of guiding the aircraft autonomously between waypoints using GPS and an

INS suite while ensuring stability. The ground component comprises COTS software

that allows both telemetry and telecommand operations.

Once the trajectory generation and guidance algorithms have been developed and

refined to a high level of integrity in MATLAB®, using a model of the Boomerang

aircraft, they are converted into the C programming language and implemented on

embedded computers located onboard the aircraft. These computers are used to

provide higher level commands to the UAV in flight, as well as to store data for

post-flight analysis. They also interact with the Micropilot autopilot which oversees

the lower-level aircraft stabilising controls. In this way, the flight tests provide better

understanding of how the software algorithms perform in a real-world scenario, and

8

1.3. CONTRIBUTIONS OF THE RESEARCH

are used to further refine the algorithms.

1.2.4 Phase 4 - Testing and Verification

Once all software algorithms have been tested to a sufficiently high level of confidence

in Phase 3, all hardware associated with these algorithms are transferred onboard

the UAV for final flight testing. A modified Boomerang 60 UAV with a larger cargo

bay and carrying the MicroPilot MP2128 Heli flight control computer is used. This is

similar to the MP2128g but with greater processing power and more storage capacity.

However, the UAV is still required to transmit each intended course of action, and

any relevant sensor data to an operator on the ground so that he/she will be able

to override the machine decision and fly the aircraft should it be necessary to do so.

This is an added safety feature which may be required for public acceptance of the

technology and for certification purposes.

Throughout the research process, significant results have also been published

in selected peer-reviewed conference, journal and book articles. This ensures that

the quality of research is maintained at a high standard, and stimulates valuable

collaboration with industry and academia.

1.3 Contributions of the Research

The contributions of the research carried out as part of this thesis are divided into

two categories: Primary and secondary. These contributions are highlighted below.

1.3.1 Primary Contributions

The primary contributions of this thesis is in the design of path planning and guid-

ance strategies for an autonomous aircraft landing during an emergency caused by

engine failure. Specifically, these contributions are:

• Algorithms 1 and 2 — Two algorithms that utilize piloted forced landing

techniques to plan a path from the point of failure to the landing site;

• The 3-D Dubins Curves — A path planner that caters for the dynamics of

powerless flight using simple geometric shapes;

• The Enhanced Nonlinear Guidance (ENG) algorithm — A lateral guidance

algorithm that accounts for wind and sideslips in the guidance logic;

• The Flight Path Following Guidance (FPFG) algorithm — A vertical guidance

algorithm that seeks to optimise the airspeed for gliding flight in winds, rising

or sinking air;

9


• The Modified Proportional Navigation (MPN) algorithm — A robust vertical

guidance algorithm that calculates the required pitch to fly, and is also easily

adaptable to any aircraft type, and;

• A novel method for ensuring smooth transition between waypoints in the

generated path.

Each of these contributions is described in further detail below.

Firstly, in designing a path planner that adapts techniques from manned aircraft

forced landing procedures, two algorithms were trialled. Algorithm 1 uses a library

of preplanned routes and allows the UAV to select a route at run-time based on a

fixed glide range and the ambient wind conditions, while Algorithm 2 uses a series

of waypoints that can be adjusted in flight to cater for changing glide slopes due

to winds. A comparison of both algorithms in over 200 simulated forced landings

found that using Algorithm 2, twice as many landings were within the designated

area, with an average lateral miss distance of 200 m at the aimpoint. Although these

results are not exemplary, they do present a baseline for further refinements to the

planning algorithms.

Secondly, in designing the 3-D Dubins Curves path planning algorithm, the el-

ementary concepts underlying 2-D Dubins paths (commonly used in robotics path

planning) was extended to cater for the dynamics of powerless flight in the 3-D do-

main. This has also resulted in the development of new methods in testing for path

traversability, in losing excess altitude, and in the actual path formation to ensure

aircraft stability. Simulations using this algorithm have demonstrated lateral and

vertical miss distances of under 20 m at the approach point, in wind speeds of up

to 9 m/s. This is greater than a tenfold improvement on Algorithm 2, and emulates

the performance of manned, powered aircraft.

Thirdly, in designing the ENG algorithm, an enhancement to the lateral guidance

algorithm originally developed by Park et al. (2007) was made to include wind infor-

mation in the guidance logic, rather than treating wind as an adaptive element for

the control system. A simple assumption was also made that reduces the complexity

of the algorithm in following a circular path, yet without sacrificing performance.

Finally, a specific method of supplying the correct turning direction is also used.

Simulations have shown that the ENG algorithm performs much better in changing

winds, with cross-track errors at the approach point of less than 2 m, compared to

over 10 m using Park’s algorithm.

Next, in designing the FPFG algorithm, the error of the flightpath angle and

the MacCready theory were used to determine the optimal speed to fly in winds.

This algorithm uses PID gain schedules to finely tune the tracking accuracies, and

10

1.4. PUBLICATIONS

vertical miss distances of under 2 m in changing winds have been demonstrated in

simulations.

Following this, in designing the MPN algorithm, principles from proportional

navigation and the ENG algorithm, as well as certain techniques specific to this al-

gorithm, were used to calculate the required pitch to fly. The MPN algorithm is more

robust than the FPFG algorithm, in that it does not require the tuning of multiple

gain schedules, and is adaptable to any aircraft type with minimal changes. Track-

ing accuracies obtained with this algorithm are also comparable to those obtained

using the FPFG algorithm.

Finally, for the ENG, FPFG and MPN algorithms, a novel method utilising the

geometric and time relationship between aircraft and path was employed to ensure

that the former is still able to track the desired path to completion in strong winds,

while remaining stabilised.

1.3.2 Derived Contribution

A derived contribution is made in modifying the 3-D Dubins Curves algorithm de-

signed in this research to suit the flight dynamics of a helicopter. This modification

allows an autonomous helicopter to track both a stationary and moving target in

flight, and further details are provided in Appendix C. The decision to extend the

planning algorithm to helicopters was made after validating the algorithm for fixed-

wing aircraft, with the results suggesting that the algorithm is also robust enough

to function on different flight platforms.

1.4 Publications

A number of refereed publications were produced during the course of this research

program and these are listed below. The contents of these publications are included

in Chapters 3 to 7.

Book Chapter

Mejias, L., Fitzgerald, D., Eng, P. and Liu, X. (2009). Forced Landing Technologies

for Unmanned Aerial Vehicles: Towards Safer Operations. In M. L. Thanh (Ed.),

Aerial Vehicles (p. 415-440). In-Tech Education and Publishing, Kirchengasse,

Austria.

Conference Papers

Eng, P., Mejias, L., Fitzgerald, D. and Walker, R. (2007, December). Simulation

of a fixed-wing UAV forced landing with dynamic path planning. In Australasian

11


Conference on Robotics and Automation. Brisbane, Australia.

Fitzgerald, D., Mejias, L., Eng, P. and Liu, X. (2007, December). Towards flight

trials for an autonomous UAV emergency landing using machine vision. In Aus-

tralasian Conference on Robotics and Automation. Brisbane, Australia.

Journal Papers

Eng, P., Mejias, L., Walker, R. and Fitzgerald, D. (2010). Guided Chaos - Path

Planning and Control for a UAV Forced Landing. IEEE Robotics and Automation

Magazine, 17 (2), 90-98.

Eng, P., Mejias, L., Liu, X. and Walker, R. (2010) Automating human thought

processes for a UAV forced landing. Journal of Intelligent and Robotic Systems, 57,

329-349.

1.5 Thesis Outline

This thesis is structured as follows. Chapter 2 presents a review of robotics path

planning, trajectory generation and aircraft guidance techniques in the literature,

and aims to identify algorithms suitable to this research. For global, more gen-

eralised planning, four topics are covered. These include Probabilistic Roadmaps

(PRM), Rapidly exploring Dense/Random Trees (RDT/RRT), cell decomposition

and the Evolutionary Algorithm (EA). For local, more specific planning, topics cov-

ered include heuristic-based search algorithms, trajectory generation utilising po-

tential fields, finite horizon planning and manoeuvre generation techniques, as well

as how wind is accounted for in the planning process. Following this, aircraft guid-

ance techniques using receding waypoints, cross and along-track velocities, vector

fields and the geometric relationship between vehicle and path is discussed. Finally,

the manned aircraft forced landing procedure is presented. This is a combination

of path planning, trajectory generation and guidance methodologies, and contains

many concepts applicable to this research.

Chapter 3 presents two classes of planning algorithms investigated in this re-

search. The first class of algorithms are based on piloted forced landing procedures,

and include two similar, albeit different techniques that utilise the aircraft glide

range to form the descent path. These algorithms are aptly named Algorithm 1

and Algorithm 2. The second class of algorithms extend Dubins curves to 3-D, and

incorporates the dynamic constraints of a gliding aircraft in the planning process.

This class of algorithms is named the 3-D Dubins Curves.

Chapter 4 details the design of two sets of guidance and control techniques tri-

alled in this research. The first set of guidance algorithms combines the great-circle

12

1.5. THESIS OUTLINE

navigation and wind correction methods employed by pilots with a simple lateral

path tracker. The system then uses a series of Proportional-Integral-Derivative

(PID) controllers to control the airspeed and roll angle. In the second set of al-

gorithms, a lateral guidance and control algorithm and two longitudinal guidance

and control algorithms are presented. These are namely the ENG, FPFG and MPN

algorithms, and utilize line-of-sight guidance principles as well as PID controllers to

stabilize the aircraft.

Chapter 5 describes the design of the MATLAB® simulation environment used

to test the path planning, guidance and control algorithms. The design uses the

AeroSim software plug-in, which enables rapid construction of aircraft models as

well as the modelling of sensor errors, winds and atmospheric effects.

In Chapter 6, the software and hardware setup for flight experiments is described,

as well as the test procedure to be followed in conducting the flight trials.

Chapter 7 presents first the results of the MATLAB® simulations, where the

performances of the different path planning, guidance and control algorithms in-

vestigated in this research are compared and analysed. Next, results from actual

flight experiments are presented, and these results are then compared against the

simulated results.

Finally, Chapter 8 draws conclusions and presents limitations and recommen-

dations for further research. Appendix A contains the state-space models for the

guidance and control algorithms described in Chapter 4, Appendix B contains the

full MATLAB® aircraft models used for simulation, and Appendix C describes the

work that was carried out at UPM, Spain as part of the ICPUAS Project, in which

the 3-D Dubins planning algorithm used in this research was demonstrated to be

applicable also to rotary-wing aircraft tasked with target tracking and pursuit.

13

2Related Work

THIS chapter will first present an overview of existing methods for robotics

path planning and trajectory generation in the literature, and will identify

algorithms and methodologies that are suitable to this research. Following this,

techniques used by human pilots to steer an unpowered aircraft to a chosen site

during a forced landing will be presented, and the knowledge gained from examining

these differing disciplines are reflected in the development of the proposed TGGS

system.

2.1 Path Planning Techniques

Path planning is a term widely used in robotics and commonly involves the construc-

tion of a path that avoids obstacles, or incurs the minimal cost from a start state

to a goal state (LaValle, 2006). A planning algorithm is complete if it will always

find a path in finite time when one exists, or will alert the user in finite time if no

path exists. The path planning algorithms presented in this review were originally

developed for ground (mobile) robots and robotic manipulators, but many have also

been modified for unmanned aircraft applications.

In the robotics literature, path planning has been classified by Barraquand, Lan-

glois, and Latombe (1992) as either global or local. Global planning first constructs

a roadmap or graph that represents the connectivity of the free space; a search is

then performed on this roadmap to find the best path that links the start and goal

states. Examples of global path planning methods include roadmap based tech-

niques and cell decomposition techniques. On the other hand, local planning does

not create a roadmap but instead searches the world space directly by overlaying

a search grid over the entire world space. This type of planning is also concerned

with constructing a feasible path between waypoints provided by the global path

planning system, described in the literature as trajectory or manoeuvre generation.

Potential field methods are a form of local search. It is important to note that

15

CHAPTER 2. Related Work

although both global and local planners carry out their searches within a graph,

the graph in a global planner contains only traversable nodes whereas some of the

nodes in the local planner’s graph may be non-traversable. A common approach is

to combine an approximate global planner which ignores the constraints of vehicle

dynamics, with an accurate local planner (Ferguson & Stentz, 2006). For the UAV

forced landing problem, it is desirable that the path planner will produce a solution

within a real-time deadline; even if the solution is suboptimal. If the path planner

cannot fulfill this requirement, it should generate a partially complete solution so

that the trajectory generation layer can still construct a smooth trajectory to guide

the UAV.

2.1.1 Global Path Planning Techniques

In this section, commonly used global path planning methods in the robotics com-

munity are presented, namely: Graph search and evolutionary search algorithms.

These methods can be either directly applied to or modified to suit the forced land-

ing descent path planning problem.

2.1.1.1 Graph Search Algorithms

A widely used path planning algorithm that uses the graph search method is the

Probabilistic Roadmap (PRM). Developed by Kavraki, Svestka, Latombe, and Over-

mars (1996), this algorithm is a two-phase method for solving the robot motion

planning problem in static workspaces. In the preprocessing phase, a roadmap con-

sisting of a collection of configurations (nodes) randomly sampled across the free

configuration space (C-space) is constructed. In the query phase, the roadmap is

consulted to find a sequence of collision-free robot configurations which interpolate

the path from a start to a goal robot configuration. Querying is often conducted by

employing heuristic-based local path planners such as Dijkstra’s algorithm. While

building the roadmap, the PRM planner heuristically identifies difficult regions in

the free C-space and generates additional configurations in those regions to increase

the connectivity of the roadmap graph. Hence, the final distribution of configu-

rations is not uniform across the free C-space, but is denser in regions considered

difficult by the heuristic function. This helps to overcome the problem of navigating

through a cluttered workspace, for example. PRM planners are also probabilisti-

cally complete; meaning that as the number of samples of the configuration space

approaches infinity, the probability of finding a path through the space (if one exists)

approaches one.

Since its inception in the early 90’s, many promising variants of PRM have

been proposed, each with their own strengths and weaknesses. Dale and Amato

16

2.1. PATH PLANNING TECHNIQUES

(2001) proposed a meta-planner that combines several PRM planners to create a

roadmap. This method works by first decomposing the workspace into different

types of regions, and then assigning a suitable PRM planner to generate nodes

and add them to the roadmap (see Table 2.1). The process terminates when it is

evident that the entire workspace has been mapped satisfactorily or when no more

progress is made, or when computation time expires. To help reduce the tendency

to over-sample the workspace and hence decrease the computation time required to

construct and analyse the roadmap, filtering is used to limit the number of robot

configurations generated and to delete redundant nodes and edges in the roadmap.

However, since a situation requiring a forced landing can occur at any time during a

flight, using a meta-planner may not be suitable to the UAV forced landing problem.

This is because the computation time required to iteratively construct and analyse

the roadmap may exceed the limited time available for planning and executing the

descent to a selected landing area.

Table 2.1: Suitability of various PRM planners to different types of regions

In work done at the Linkoping University in Sweden, Pettersson and Doherty

(2006) used a modified PRM technique to enable a helicopter UAV to navigate be-

tween several building structures and take photographs of each of the buildings’

faade. A very accurate three-dimensional (3-D) polygonal model of the test location

was supplied to the onboard geographical information system (GIS), and was used

by the PRM planner to generate random helicopter configurations offline. These

configurations were then checked for collisions with obstacles in the model using the

oriented bounding box-tree algorithm. The Oriented Bounding Box Tree (OBBT)

algorithm constructs a tree of bounding boxes around the obstacles in the environ-

ment by including all polygons in the root-box and then recursively dividing the

polygons into smaller and smaller boxes (Pettersson & Doherty, 2006). The orien-

tations of the bounding boxes are determined by conducting a principal component

17


analysis on the vertices. Following the preprocessing stage, an A* search was used

during flight to connect collision-free configurations and generate a multi-segmented

helicopter trajectory. The resulting straight lines were then smoothed, where pos-

sible, using cubic spline curves more suited to high speed flight (Cao, Dodds, &

Irwin, 1997). This research also employed a delayed handling of constraints, such

as maximum and minimum altitudes, no-fly zones and limits on ascent and descent

rates, to the query phase at runtime rather than at the prepossessing stage. This

procedure was found to be greatly beneficial to UAV missions in the field, and is

depicted in Figure 2.1.

Figure 2.1: Schematic diagram showing how a flight trajectory is generated using Petterssonand Doherty’s method

Although Pettersson and Doherty’s method has been proven to work well in

actual practice, it nevertheless requires a very accurate model of the UAV operating

environment to be constructed. Should this information be not readily available,

the UAV will need to rely on other sensors, such as machine vision to prevent

collisions. Since the UAV descent considered in this thesis occurs in airspace that

is relatively free of obstacles, using a PRM planner may not be necessary, however,

using spline curves to smooth the flightpath as well as allocating the handling of

certain constraints to the online phase are worthy of further investigation.

Another path planning algorithm that uses the graph search method is the

Rapidly exploring Dense Tree (RDT). Assuming that a dense sequence of sam-

18


ples is available in C-space, RDT begins with a single seed configuration. The

algorithm then iteratively chooses a new configuration that is the shortest distance

away from the current seed and connects them together (branching), thus forming

tree-like structures. RDTs that use random means of selecting new configurations

are known as Rapidly exploring Random Trees (RRT). As with other incremental

sampling and search methods, it is necessary to check for collisions when joining

two configurations together, and specific collision checking algorithms are available

(LaValle, 2006). It is also possible to encode aircraft dynamics into the planning

algorithm by changing the geometry of the branches and to incrementally build two

search trees rooted at the start and goal configurations. The trees explore space

around them and also advance towards each other by using a greedy heuristic. An

advantage of RDT/RRT algorithms is that they can converge to a solution within

a given deadline. Another advantage of using RDTs/RRTs is that no preprocessing

of the environment is necessary; however, the resultant plan can include many spu-

rious turns due to the nature in which branches are created (LaValle, 2006; Hrabar,

2006). Additionally, the RDT/RRT algorithms are inherently designed for single-

query problems, whereas a UAV forced landing would be posed as a multiple query

problem to deal with changing landing site locations.

Frazzoli, Dahleh, and Feron (2002) present a two-dimensional (2-D) randomized,

incremental roadmap building algorithm which is able to effectively deal with the

system’s dynamics, in an environment containing both static and dynamic obsta-

cles. This algorithm assumes that an obstacle-free guidance loop is available, which

is able to steer the UAV from any state (including configuration and velocity) to

any desired configuration at rest, assuming that there are no obstacles in the en-

vironment. This guidance loop enables uniform sampling of the workspace while

generating trajectories that are executable by the dynamic system. To find a path

through the obstacles, a generalized RRT algorithm is used, in which all nodes are

tested for expansion during the tree expansion phase instead of just the closest node.

Obstacles are circumnavigated by generating random points around the obstacle and

seeing if the current path can be connected to these points (see Figure 2.2).

If a solution is found ahead of schedule, then the remaining time is used for fur-

ther path optimisation. The linear paths generated by the RRT algorithm are then

replaced with predefined manoeuvres chosen from a library of trajectory primitives,

such that the resultant path is a smooth curve (see Figure 2.3). This is possible as

Frazzoli has proven that any two manoeuvres can be concatenated together given the

existence of a trim primitive (trim flight manoeuvre) of finite length to separate the

two manoeuvres (Frazzoli, Dahleh, & Feron, 2005). Combining trim primitives to

form feasible manoeuvres will be further investigated in the forced landing research.

However, the use of RDT/RRT algorithms may not be suitable for this research, for

19


Figure 2.2: Example of Frazzoli’s RRT two-dimensional tree-expansion procedure. Notethat the paths have already been smoothed (Source: Frazzoli, Dahleh, & Feron, 2002)

the reasons given above.

Griffiths et al. (2006) present a system that plans nominal paths for a miniature

aerial vehicle (MAV) through city or mountainous terrain. An RRT algorithm is

used to build a tree of traversable paths through an environment modelled using a

priori data. Branches in the tree are then checked to ensure that they satisfy turn

radius and climb rate constraints and are also collision free. While on course, the

MAV avoids frontal threats via data from a forward-pointing laser, and uses flow

field information from three optic flow cameras to negotiate rough terrain. Since

detected obstacles, or parts thereof, are modelled as cylinders with radii equal to

the minimum turning radius of the vehicle, once an obstacle is detected, the MAV

executes a sequence of maximum roll manoeuvres designed to carry it pass the

threat and intersect its intended course (Figure 2.4). The authors also present an

alternative approach to path tracking, where the focus is to remain on the path

rather than be at a specific point that evolves with time. This is accomplished

through the use of vector fields and groundspeed commands that drive the MAV

back to the desired path (ground track) after a disturbance (such as from wind).

An advantage of using ground speed and course commands, rather than bearing and

airspeed, is that rejection of wind disturbances is greatly improved (D. R. Nelson et

al., 2007), however, the authors also assume that the MAV can instantaneously roll

between positive and negative bank angles to avoid obstacles, which is not true for

20


Figure 2.3: Visual example of Frazzoli’s manoeuvre generation system (Source: Frazzoli,Dahleh, & Feron, 2005)

real aircraft as there is always a transition lag associated with such manoeuvres.

Figure 2.4: Griffith’s collision avoidance manoeuvre (Source: Griffiths et al., 2006)

A hybrid path planner capable of both single-mission path planning in known

environments, as well as path replanning in uncertain and dynamic environments

is presented by Ping, Mingyue, Chengping, and Changwen (2004). Initially, the

planner uses Dijkstra’s algorithm to find a minimum cost path inside a 2-D grid

representation of the battlefield. By using a grid map, sampling the C-space can

be avoided, which in turn reduces the computational complexity. In the roadmap

grid, UAV kinodynamic (kinematic and dynamic) constraints, such as minimum

flying altitude, as well as battlefield threats are represented as cost functions that

penalize the cost of the path to prevent the UAV from traversing an undesirable flight

path. Other kinodynamic constraints such as maximum climbing, diving and turning

angles are incorporated into placement of nodes in the roadmap. The sparse roadmap

produced in the initial phase is then further refined during mission execution by using

a dynamic sparse A* search (DSAS), which maintains a search tree of extended nodes

21


in memory so that a new path can be found in real-time when new threats appear

(path replanning). To help accelerate the construction of the DSAS search tree, a

heuristic distance measure is used to eliminate nodes that are too far away from

the currently extended node on the search tree. The technique of combining both a

global and local path planner to sample the robotic world space while addressing the

UAV kinodynamic constraints, is well suited to the UAV forced landing problem.

During a forced landing, replanning is necessary when a more favourable landing

site is detected. In addition, kinodynamic constraints have to be taken into account

to reduce excessive stress on the airframe.

Other global planning methods such as those described by Latombe (1991),

Rippel, Bar-Gill, and Shimkin (2005) and Ferguson and Stentz (2006) first de-

compose the C-space into cells or grids, then construct a path by joining nodes

inside these cells. A search for the optimal path is then made using any num-

ber of local, heuristic-based algorithms such as A* or D*. The kinodynamic con-

straints of the aircraft are subsequently addressed by using any number of different

path smoothing techniques, such as splines, judicious placement of nodes and mul-

tiple linear-interpolation. While these algorithms are well-suited to planning within

an obstacle-filled environment, they will overcomplicate the forced landing descent

problem addressed in this thesis (see Section 1.1) and hence will not be considered

further.

Inevitably, there is a need to deal with uncertainty in any type of UAV path

planning. Uncertainty in the current state (internal and external) of the aircraft can

stem from numerous sources. Saffiotti (1997) describes four sources of uncertainty:

1. A priori knowledge of the world is incomplete;

2. Sensor data is unreliable and uncertain;

3. There are moving obstacles, and;

4. Control actions do not necessarily produce the desired state transition.

Gonzalez and Stentz (2005, 2007) present a path planner for autonomous ground

vehicles (AGVs) that calculates optimal paths while considering uncertainty in po-

sition, and uses landmarks obtained from a priori map data to localize the vehicle

as part of the planning process. Uncertainty in vehicle position is combined with

the error in map registration to give a total uncertainty in the position of the robot,

and this uncertainty is shown to be appropriately modelled as a Gaussian distribu-

tion. Cost values are assigned to grid maps overlaid onto aerial photographs, and

landmarks (electric poles) are combined with the estimated vehicle position such

that they are uniquely identifiable within the detection range of the robot’s laser

sensor. These landmarks are used to help localize the robot. A modified version

of the A* algorithm in 3-D is then used to plan the optimal path while ensuring

that the uncertainty in the robot’s position does not compromise its safety or the

22


reachability of the goal. For the UAV forced landing problem, uncertainties in the

UAV position, winds and sensor data will need to be modelled and simulated to

determine their effects on the performances of the planning, guidance and control

algorithms. The method described above to model uncertainties can be analysed

further to determine its suitability to the forced landing problem.

2.1.1.2 Evolutionary Algorithms

An Evolutionary Algorithm (EA) is a biologically inspired path planner that at-

tempts to mimic genetic systems. This algorithm firstly specifies an initial popula-

tion of potential vehicle paths, which is then subjected to a series of evolutionary

processes that include mutation and propagation operations. A cost function is then

used to score the fitness of all members of the larger population and, based on those

scores, the population is culled to its initial size. The difference is that now the

new population will contain more paths that measure well against goodness objec-

tives such as vehicle goals and constraints (Rathbun, Kragelund, Pongpunwattana,

& Capozzi, 2002). A diagram showing the EA process is given in Figure 2.5.

Figure 2.5: Overview of evolutionary search algorithms

Rathbun et al. (2002) employed an EA path planner to help solve the problem

of navigating a UAV through static and dynamic obstacles, to a goal location. After

planning the most probabilistically successful path (made up of a series of arcs and

straight lines) the UAV moves along the path a finite distance before replanning

occurs again. During replanning, the estimates of the obstacle and UAV position

and velocity are updated. A circle representing the uncertainty of each obstacle’s

position continues to grow until their positions and velocities have been updated.

The centre of the circle is derived from the current location and velocity of the

23


obstacle with random noise added to simulate estimation error. The population

is then repeatedly subjected to a series of mutation operations which attempt to

connect paths that satisfy the given kinodynamic, fuel and collision constraints.

The iterative process terminates when a feasible path is found, or when a time

limit has been exceeded. This algorithm has been demonstrated to work well in

simulation, in which a UAV was able to successfully avoid two other UAVs crossing

its flight path and also navigate to a goal location.

Nikolos, Valavanis, Tsourveloudis, and Kostaras (2003) extended the use of EA

techniques to develop an offline/online path planner capable of negotiating moun-

tainous terrain. Given a known 3-D mountainous environment, the offline planner

generates a single, continuous 3-D B-Spline curve (Ozaki, Lin, & Shimogawa, 1999)

which connects the start and goal points while avoiding known obstacles. The use

of B-Spline curves allowed the vehicle dynamic constraints, as well as other enforced

constraints such as maximum flight altitude to be addressed. During mission execu-

tion, the online planner uses acquired information from onboard radar to update the

offline plan, generating a series of smoothly connected B-spline curves to the goal

position. A potential field is also used to drive the path line to bypass obstacles lying

between the UAV and its final destination, and an additional EA-based procedure

is introduced to force the UAV to bypass concave obstacles and avoid local optima.

The advantages of EA algorithms lie in their high robustness compared to other

directed search methods, and their ease of implementation in optimization problems

with a relatively high number of constraints, including geometric avoidance, time-

based dynamics and vehicle performance limitations. Another desirable feature is

that EA algorithms improve over an internal state, which allows the conditions at the

end of one planning cycle to more easily be used to initialize the next cycle. However,

the use of EA-based planners has its limitations. Due to the probabilistic nature of

genetic algorithms, a feasible solution will be found if enough initial path segments

are chosen, however, increasing the number of path segments results invariably in

longer processing time. In addition, it is difficult to accurately predict the time

required to converge to an acceptable solution, or if a solution does indeed exist.

Finally, due to the inherent stochastic nature of EA planners, no two solutions

formulated by such a planner can be guaranteed to be the same, even though the

operating environment remains unchanged. This can present a significant problem

to aerospace certification processes. Hence, EA path planners are not suitable for

this research.

24


2.1.2 Local Path Planning Techniques

As alluded to earlier, in many planning scenarios it is highly desirable to have both

a global and local planner working in concert, in order to capitalize on the inherent

advantages that each present. The local planners considered as part of this review

include both heuristic-based searching and trajectory generation techniques, as well

as how wind effects are incorporated into the planning process.

2.1.2.1 Heuristic-based Path Planning

A common approach for robotics path planning consists of representing the envi-

ronment (configuration space or world space) of the robot as a graph G = (S,E),

where S is the set of possible robot locations and E is a set of edges that represent

transitions between these locations. Assuming that this graph has been previously

constructed using a suitable global planner such as those presented in Section 2.1.1,

the cost of each edge is then the cost of transitioning between the two endpoint

locations and planning a path for navigation can be cast as a search problem on this

graph (Ferguson & Stentz, 2006). A number of heuristic-based search algorithms

have been developed for this task, and the more commonly used algorithms include

Dijkstra’s algorithm, A*, D* and D* Lite (Hart, Nilsson, & Rafael, 1968; Stentz,

1994; Koenig & Likhachev, 2002). However, these algorithms presuppose that the

C-space is divided into regions or cells with linear paths connecting any number of

nodes and, as mentioned earlier in Section 2.1.1, such division of the C-space result

in unnecessary complication of the UAV descent planning problem. In addition,

these algorithms devote much of their energy to computing the optimal path (be

it in terms of cost, time, reachability or other constraints) as well as in repairing

previously generated solutions.

For a UAV forced landing, computing the optimal path may be infeasible due

to the sheer number of states required to be processed to obtain such a path. In

this situation, one must be satisfied with the best solution that can be generated in

the time available. It may also be more efficient to replan afresh rather than try to

repair suboptimal paths, due to the ever decreasing time available for planning and

manoeuvring as the aircraft nears the ground. Hence, in light of this, heuristic-based

local planning algorithms are not considered further in this research.

2.1.2.2 Trajectory Generation Techniques

Trajectory generation is a part of the local path planning process, and is primarily

concerned with constructing a traversable path between two or more waypoints, such

as those connected by a local graph search technique. One early implementation of

trajectory generation techniques uses the principles of potential fields.

25


A potential field algorithm models the world by a field function, where obsta-

cles act as repulsive poles while the goal acts as an attractive pole. To plan a

path through the world, the algorithm follows the steepest slope of the field func-

tion towards the goal. A representative example of this method is in the work of

Barraquand et al. (1992). Here the workspace is divided into cells and the minimal

length distance d from a cell to each obstacle is calculated using wavefront expansion.

The potential field strength around an obstacle is then a function that varies linearly

with d. The intersection of the potential fields (wavefronts) around each obstacle

forms a skeleton path along which the robot navigates (Figure 2.6). Although it has

been assumed that there are no obstacles in the UAV forced landing descent path,

the concept of potential fields can still be applied to the UAV forced landing prob-

lem. For instance, if wind conditions cause the UAV to head initially in the wrong

direction, a potential field can be used to “drive” the UAV back onto the correct

path. Notwithstanding, the greatest weakness of potential field methods is that they

tend to become trapped in local minima. One method used to escape local minima

is to conduct a best first search to “fill up” local minima when one is encountered

(Latombe, 1991). The problem with this approach is that it can become very com-

putationally expensive for high-dimensional problems. Another widely used method

is to execute a random walk when a local minima is encountered (LaValle, 2006;

Latombe, 1991). However, this method is not guaranteed to be complete and also

makes the planner non-deterministic and therefore, care must be taken when using

potential fields in this research.

Figure 2.6: (a) Potential field contour plot (b) Skeleton (Source: Barraquand et al., 1992)

Model Predictive Control (MPC) is a nonlinear control technique that uses a

dynamic model of a plant and a history of its past control moves to optimise its

future states over a finite time period (also referred to as receding horizon control

for this reason) and for a defined cost function (Garcia, Prett, & Morari, 1989).

For generating UAV trajectory, the dynamic model is the UAV and its response to

internal and external forces. The future states of the UAV include all variables used

26


to describe its orientation and location, such as position, velocity and attitude, at

any specified time. The cost function is dependant on a particular constraint, or

combination of constraints to be minimised, which can include constraints due to

distance, timing or control effort. A visual technique used to model the cost function

is a spline curve (piecewise polynomial) defined by a set of control points. The spline

curves used include cubic splines (3rd order polynomial) and Basis Splines (B-Spline)

but are not limited to these. B-splines are commonly chosen as every spline function

of a given degree, smoothness and domain partition can be represented as a linear

combination of B-splines of that same degree and smoothness.

Singh and Fuller (2001) presented a 2-D MPC based method for UAV flight

navigation and control in an urban setting. The algorithm assumes that waypoints

are provided by an offline path planning layer, with potential errors such as map

inaccuracies which must be addressed in the trajectory generation phase. The algo-

rithm assumes further that scene analysis software is available which localizes threat

obstacles as a function of the vehicle’s position. Perturbation analysis was used to

linearize the nonlinear vehicle model about a nominal trajectory and thus formulate

a convex optimization (or quadratic programming) problem. The nominal trajec-

tory is initially generated as a spline containing vehicle coordinates expressed as a

polynomial series. If at anytime the generated trajectory falls outside the convex

feasible space, a new waypoint is positioned in the middle of the feasible set and

the spline based trajectory recomputed using MPC techniques. A nominal control

sequence to track the trajectory is then formulated based on the assumption that the

UAV possesses differentially flat characteristics. In this implementation the planning

horizon for the MPC controller was kept constant, and there was no requirement for

the algorithm to satisfy any real-time deadline since all calculations were conducted

offline. It is important to note that offline processing is only feasible if the UAV

stores highly accurate maps onboard and the environment remains static.

Shim, Hoam, and Sastry (2006) combined MPC-based obstacle avoidance with

online obstacle map building to produce a 3-D navigation system suitable for ex-

ploring partially known or unknown urban environments. A 3-D local map of the

environment is generated using an onboard LADAR scanner. This information is re-

layed to a ground station via a radio communications link. The ground station MPC

algorithm then generates an optimal safe-vehicle path, using a cost function that pe-

nalizes the proximity of the UAV to the nearest vehicle. The adjusted trajectory is

relayed back to the onboard flight management system responsible for UAV attitude

control. Potential fields are also used as part of the overall planning strategy. A

disadvantage of Shim et al.’s system is that since the MPC algorithm is processed on

the ground, the UAV must remain within communications range at all times which

decreases its mission capacity and flexibility. The system may also be subjected to

27


signal interference, propagation delays or even complete communications failure if

operated within a “busy” urban environment.

Another class of manoeuvre generation techniques, developed by Frazzoli et al.

(2005) and known as Manoeuvre Automata, uses a finite set of manoeuvres to con-

struct a continuous trajectory though predefined waypoints. The manoeuvres are

generated offline and are classed as either motion primitives or trim primitives. Trim

primitives are manoeuvres of constant velocity and turn rates that satisfy the vehicle

dynamic constraints, while motion primitives can represent any type of manoeuvre

that is feasible within the UAV kinodynamic constraints. Frazzoli has mathemat-

ically proven that two motion primitives can be concatenated together by a trim

primitive of finite length (which can approach a null value if desired) between the

two motion primitives. This provides for an extremely robust trajectory generation

technique where any number of manoeuvres can be concatenated together to form

a smooth trajectory through a predefined set of waypoints.

Still another class of manoeuvre generation techniques, known as Dubins curves

(Dubins, 1957), allows the construction of optimal planar paths to move a vehicle

(such as a car or aircraft flying at constant altitude) from an initial to a goal location

defined in terms of position and heading. Paths are formed using a combination of

curves of maximum curvature (C) and with/without straight lines tangential to the

curves (S), where the optimal solution is shown to be of a bang-bang form. This is a

type of control method where the controller begins operations only when a discrete

threshold value is exceeded. The geometric construction of the solution assumes that

the vehicle can effectively transition between either a CCC or CSC path type using

an external guidance or control algorithm, and does not account for obstacles or cost

functions other than minimum time (see Figure 2.7). Further, as with other classes

of optimal plans, the shortest path does not permit a margin for execution error

as the constraints are kept at their limits (steering is always applied at maximum

lock), and also possesses abrupt curvature discontinuities and direction reversals

that require infinitely fast steering and acceleration to track at finite speeds (Triggs,

2010). However, Dubins curves are still attractive in that they are easily constructed

and do not require expensive computation to calculate the path length. In addition,

by relaxing the steering constraint and allowing the vehicle a small margin of error

when tracing the path, the problems with discontinuities can be overcome.

An interesting application of 2-D Dubins curves to a 3-D motion planning prob-

lem is described by M. Hwangbo and Kanade (2007). Here, the UAV is tasked to

navigate in a complex 3-D air slalom environment with stationary and/or moving

obstacles. Initially, the environment is divided into 3-D grid cells and a coarse A*

search performed to link the start and goal states. As the aircraft traverses the path,

a finer level of motion planning is activated to account for any changes to the en-

28


Figure 2.7: Simple 2-D Dubins curves showing both CSC and CCC type paths. Initial andtarget headings are indicated by ωi and ωt respectively.

vironment, such as obstacles moving into the flight path. This lower-level planning

generates a reachable set of motion primitives (similar to the concept introduced by

Frazzoli et al. (2005) in front of the aircraft and utilises 2-D Dubins curves projected

in both the horizontal and vertical planes to estimate the distance to the goal loca-

tion, thus finding the optimal set of primitives. The use of two Dubins curves helps

to satisfy the yaw angle, turn radius and pitch angle requirements, and allows the

aircraft to execute complex manoeuvres to avoid obstacles.

The use of Dubins curves to form the 3-D path actually traversed by the aircraft

is presented by Ambrosino et al. (2006, 2009). Initially, Dubins’ algorithm is used

to form an optimal path between two waypoints on the xy-plane that satisfies the

aircraft minimum turn radius constraints. The trajectory is then extended to 3-D

space by connecting one of the generated arcs with another positioned at a lower

vertical plane (different altitude), by a line tangential to both arcs. The vertical

separation between the two arcs is chosen to satisfy an aircraft pitch angle require-

ment, and the horizontal offset distance between the two arcs is selected to account

for the desired aircraft heading. A line-of-sight guidance algorithm is then applied

causing the UAV flight path to converge on the desired track to fly. Since the prin-

ciples described here are ideally suited to UAVs flying in clutter-free regions of the

sky, they can be used to model a set of manoeuvres which, when concatenated with

other manoeuvres, form the complete system of forced landing descent manoeuvres

required in this research.

Another method of extending the 2-D Dubins curves to three dimensions is

presented in the work of Chitsaz and LaValle (2007), where the path is characterized

as a four-dimensional system consisting of the aircraft coordinates in 3-D Euclidean

space, and the angle between the z-axis and the longitudinal axis in the x − y

plane. Time-optimality is then obtained by using Pontryagin’s Maximum Principle

(Pontryagin, 1986) to solve a cost function that incorporates the initial and final

constraints of the path. This gives for low and high final altitudes, respectively,

a path consisting of the Dubins curve with unsaturated altitude velocity, and the

29


Figure 2.8: 3-D CSC Dubins curves constructed using Hota’s analytical method. Initialand target headings are indicated by the red and black arrows respectively. (Source: Hotaand Ghose, 2010)

Dubins curve followed by a helix with saturated altitude velocity. For medium

final altitudes, the time-optimal trajectory is either a Dubins extremal (not the

shortest) with unsaturated altitude velocity or a Dubins path of certain length with

saturated altitude velocity. Although the authors employ great lengths to prove

time-optimality in the path, this formulation nevertheless requires the saturation of

controls to achieve two extremes, that is, a minimum turning radius and a maximum

altitude velocity. As mentioned earlier, keeping the controls always at their limits

leaves no margin for error, and can be detrimental to a gliding aircraft during a

forced landing.

Finally, Hota and Ghose (2010) proposed a method where the optimal, CSC-

type 3-D Dubins path is constructed by analysing the geometry of the path and

solving for a set of vector equations (Figure 2.8). Due to its simplicity and low

computational requirements (1 sec), this approach can be implemented on fixed-

wing aircraft for real-time path planning. However, the method discussed may

produce an optimal geometrical path that cannot be flown due to constraints on the

flight path angle and stall speed of a real UAV. In such a case, the authors suggest

using their numerical approach to solve for a set of parametric equations. This idea

is unattractive however, as the computation time takes a minimum of 8 hours with

less accuracy. Nonetheless, the concept of using vector equations to solve for an

optimal path is simple and intuitive, and can be applied to this research.

30


Figure 2.9: Examples of clothoid curves or Cornu spirals.

Figure 2.10: Smooth trajectory formed by a symmetrical clothoid arc used to transitionbetween arcs and lines in a Dubins path (Source: Liu et al., 2007)

To address the problem of abrupt curvature discontinuities and direction rever-

sals in Dubins curves, some researchers have used clothoid arcs, or Cornu spirals as

they are otherwise known (Bernoulli, 1967) to smooth the transition between the

Dubins arcs and lines. A clothoid has the characteristic that its curvature increases

linearly with the distance along the spiral, and its curve rate is proportional to its

total length. Some examples of clothoids are shown in Figure 2.9. In practice, how-

ever, since the clothoid does not have a closed-formed solution, symmetrical clothoid

curves described by a triangular curvature and parametric approximations are used.

Figure 2.10 shows such a formulation, where the clothoid arc is circumscribed by

∠ABC and the bisector BG.

Scheuer and Fraichard (1997) propose a suboptimal planning solution for car-like

vehicles that combines line segments, circular arcs of maximum curvature, and/or

clothoid arcs. The paths contain at most eight pieces and are known as Simple

Continuous Curvature (SCC) paths, with the clothoids approximated by parametric

equations using Fresnel integrals (“Fresnel Integrals”, 1972). Scheuer et al. have also

superimposed on the path a motion polygon that traces the surface area swept by the

wheels as they rotate to follow the prescribed path. This gives in effect a collision-free

31


metric for the robot path, which is then used to refine the course roadmap generated

by a global PRM planner. The application of the motion polygon is interesting in

that it almost resembles the wing area of an aircraft, implying that the SCC path

generated can be feasibly applied to fixed-wing UAVs.

A trajectory planner using symmetrical clothoid curves is also presented by

C. Liu and Hong (2007), where the clothoids are used to guide a wheeled robot

in a smooth turn as it negotiates the junction of two lines. The planner uses the

turn angle, constant turn acceleration and linear velocity to calculate the location

of the clothoids, such that the robot will have a continuous change in direction of

motion and angular speed. To avoid colliding with objects, a buffer zone is created

around the path, effectively creating a 2-D corridor through which the vehicle moves.

Figure 2.11: Flyable paths and their curvature profiles (Source: Shanmugavel et al., 2009)

In their work for co-operative path planning of multiple UAVs, Shanmugavel

and Zbikowski (2009) define the concept of a flyable path, where clothoid arcs with

ramp curvature profiles are overlaid onto a 2-D Dubins path. The flyable path is

designed using principles of linear algebra and differential geometry, and resembles

that of Scheuer and Fraichard (1997) in providing a smooth curvature transition

between the arcs and the line segment (Figure 2.11). To handle sudden obstacles in

the flight path, the UAV is assumed to fly in a safety disc with a radius less than

the sensor range but greater than the minimum turn radius, which will allow it to

have sufficient manoeuvrability to avoid collisions. The concept of path smoothing

to avoid discontinuities and sharp transitions is important to this research, as it

32


allows the aircraft to remain airborne for longer periods, which may result in better

perception of a landing site by the onboard sensors, as well as more time available

to conduct a safe landing.

A disadvantage of the above methods using clothoids is that steering is always

applied at the maximum allowable rate until the minimum turning radius is reached,

meaning that all turns are still performed as tightly as possible. Wilde (2010)

proposes a method to generate smooth, easily drivable paths using the smallest

values for curvature and sharpness needed to achieve a given heading change over

a given distance. In this formulation, the desired deflection (change of heading),

maximum curvature, and an approximation of the distance travelled is used in the

Fresnel equations to calculate a clothoidal arc requiring minimum steering. This,

in effect, creates the shape of a half-crescent. By then adjusting the size of the

crescents and pairing them, complex paths such as that for a vehicle lane change

manoeuvre can be formed (see Figure 2.12). However, a distinct disadvantage of the

path segments is that they are applicable only to paths where the goal lies ahead of

the current position, and are not general enough for use otherwise.

Figure 2.12: A lane change manoeuvre using paths of minimum curvature and sharpness(Source: Wilde, 2009)

A more recent development in the use of splines for trajectory planning is the

Pythagorean-hodograph (PH) space curve, first studied in extent by Farouki and

Sakkalis (1994). PH curves have a number of advantages over other splines com-

monly used in robotics planning, including: (1) A small integral of curvature; (2) the

curve, its length, curvature and total bending energy being known; (3) the start and

end positions and directions are usable as boundary conditions; and (5) the curve

lengths can be traded off against curvature for different applications (Bruyninckx

& Reynaerts, 1997). These features make PH curves highly attractive for use in

geometric design, motion control, animation and path planning.

Bruyninckx and Reynaerts (1997) proposed a method for motion planning using

33


car-like robots, where the PH space curve is approximated using a Bezier quintic

spline. According to the authors, the quintic spline provides an appropriate compro-

mise between smoothness and complexity. Their derivation allows the quintic PH

spline to be solved analytically for a set of given tangent directions at the bound-

aries, and selects the curve with the least bending energy (Figure 2.13). However,

given prescribed boundary curvatures, the solution requires an iterative approach

which is not guaranteed to converge. In addition, trying to satisfy the curvature

constraints can make the path impractically long.

Figure 2.13: Four quintic PH splines solving a planning problem. The most appropriatesolution is the curve with the least bending energy (solid black line). (Source: Bruyninckxand Reynaerts, 1997)

Shah and Aouf (2009a, 2009b) proposed a method using 2-D PH curves for co-

operative path planning and perception of UAVs in a dynamic environment. Similar

to the example above, their method uses quintic splines to achieve the desired pose

between the start and goal locations, with a bound on the maximum curvature. To

ensure safe separation between the UAVs, as well as to avoid a detected object, new

control points are generated to adjust the curvature of the path until it is free of

the obstacle. Although this method may appear to be efficient in replanning the

path, it nonetheless may also excessively increase the path length in order to satisfy

the curvature constraint. Due to the iterative solver used, this in turn lengthens

the computation time and can be detrimental if applied to a UAV forced landing

problem with limited time available for manoeuvres.

Finally, Neto and Campos (2009) extends the use of quintic splines to generate

PH space curves in 3-D environments. In their methodology, quaternion vectors

and an elastic bending energy function are used to resolve a PH space curve that

34


accounts for maximum curvature, maximum torsion and maximum climb/dive angles

achievable by the aircraft, while minimizing the rate of climb/descent (Figure 2.14).

Although this solution may seem feasible for a UAV forced landing, it nevertheless

relies on choosing a set of coefficient gains that would minimize the cost function,

which inevitably also lengthens the path. As noted earlier, lengthening the path

can be detrimental to an unpowered aircraft, with limited available flight time and

landing options. Thus if PH curves were to be used, suboptimal paths would have

to be chosen. These however incur additional penalties in that sharper curvatures,

torques and dive angles are used, which will increase the sink rate and present the

aircraft with even less time to manoeuvre for landing.

Figure 2.14: 3-D Pythagorean-hodograph space curve with bounded climb angle (Source:Neto and Campos, 2009)

2.1.2.3 Dealing with Wind

Once a suitable local planner has been chosen, wind effects on aircraft performance

must be accounted for. Especially in the case of a UAV forced landing, the ad-

vantages of an optimal local planner may become quickly negated by adverse winds

acting along the flightpath, resulting in the gliding aircraft being unable to reach the

selected landing site, or becoming uncontrollable and crashing prematurely. Hence,

strategies must be employed to either account for these effects in the planning pro-

cess, or whilst the aircraft is in flight using appropriate guidance or tracking tech-

niques. Section 2.1.2.3 will examine how wind is accounted for in certain planning

processes, while Section 2.2 will investigate guidance techniques which function well

in wind.

35


Rubio and Kragelund (2003) present a system where an EA-based path plan-

ner (Section 2.1.1.2) was applied to a long range UAV flight through variable wind

fields. Realistic weather information was downloaded to the planner via gridded

binary (GRIB) data bases before the actual flight. These consist of horizontal wind

velocity at seven different pressure levels, which the planner uses to construct an

initial flight path. While en route, the planner can interpolate this wind data to

obtain wind estimates at any given location and time, or use updated wind informa-

tion to refine the flight path such that fuel consumption is minimised. Since wind

information is only updated every six hours in GRIBs (See information available at

the Australian Bureau of Meteorology website (Australian Bureau of Meteorology,

2007), this approach may not be suitable for a UAV forced landing. For such a short

flight the UAV must also use instruments for measuring wind at a higher frequency,

and combine this information with an onboard database, if available to determine

the most feasible path to fly in the presence of wind.

McGee and Hedrick (2006) assume that the wind is a known constant which has

been measured previously, and that its time-varying characteristics are bounded.

They then devise a path planner that calculates the shortest time path through a

sequence of waypoints using a turning rate lower than the maximum turning rate of

the vehicle. This allows the aircraft to have additional control authority to deal with

any wind uncertainties. To find a minimum time path between two waypoints in the

presence of a constant wind, the problem is re-expressed as one without wind, where

the second position is treated as a virtual moving target (Figure 2.15a) with velocity

equal to and opposite of the wind velocity. The output of the path planner is then

a ground path that can be followed by the control algorithm (Figure 2.15b). This

algorithm in turn divides the desired trajectory into smaller polynomials trackable by

a spatial sliding surface controller (Mechlih, 1993). The work presented by McGee

and Hedrick is interesting in that wind information is absorbed into the planned

trajectory; however, the algorithm is unable to replan the path should there be

changes in the wind estimate or waypoints. The algorithm is also susceptible to

problems of local minima due to the highly nonlinear cost function used.

Other than obtaining meteorological reports from weather stations, wind can

also be estimated using sensors onboard the aircraft. Campbell (2004) devised a

method where the aircraft inertial navigation system (INS) is used together with

the onboard global positioning system (GPS) to estimate the wind velocity relative

to the aircraft, or the ground, in three dimensions. Both INS and GPS are used

to provide estimations of the acceleration of the aircraft relative to the earth, the

dynamic pressure of air on the aircraft, and the thrust vector of the aircraft relative

to the ground. These constants are then used to determine the velocity of air

relative to the aircraft in 2-D, by solving an over-constrained set of equations that

36


Figure 2.15: Path planning with sliding surface control and virtual target - (a) Formingthe virtual target, (b) Example ground path created through multiple waypoints (Source:McGee & Hedrick, 2006)

combined force equations and a velocity equation (the vertical speed of the air) via a

weighted least squares fit. The weightings could be adjusted to account for vertical

wind speeds that are present near the earth’s surface due to topographical and

thermographic variations, by increasing the influence of the velocity equation. The

weightings could also be reassigned such that the force equations have more bearing,

in cases where the opposite is true. Using Campbell’s method, it was shown that

wind velocity estimates of greater than 10 Hertz (Hz) were possible. However, one

disadvantage of this method is that the wind estimations would be subjected to

large errors incurred over time, if the GPS signals were jammed or unavailable and

the aircraft had to rely solely on the INS.

Berman and Powell (1998) present a statistical model for wind variations that

could help limit the inherent errors associated with using a dead-reckoning naviga-

tion system such as INS. A first order Markov process is used to fit the measured wind

velocities obtained via weather forecasts from the United States National Oceanic

and Atmospheric Administration, Forecast Systems Laboratory (NOAA-FSL). The

wind profile data is collected over approximately one month, and covers a variety

of positions, altitudes and times. It is observed that the root-mean-square values of

the wind velocity differences with respect to a particular travelling time increased

monotonically for only a finite-time period before assuming a steady state, which

suggests a Markov process. Through further experiments, it was shown that the

Markov model matched the actual data very well, and could therefore be used to

interpolate wind information between successive updates.

For the forced landing descent path planning research considered in this paper, it

would be advantageous to combine estimated wind data from onboard sensors with

a predictive model (where available) based on historical, location-specific wind data

37


to further increase reliability. The wind modelling system should also be able to

incorporate updated weather information via a ground-to-air communications link.

However, as stated in Section 1.1, constructing such a model based on meteorological

data is outside the scope of this research and hence, only estimated wind data

from onboard INS and GPS sensors will be used. To deal with wind gusts and

uncertainties, the control algorithm should be such that the aircraft will always

have some amount of surplus control power when following a trajectory generated

by the path planner. Finally, it should be noted that although other technologies

exists for measuring wind patterns, such as with LIDAR sensors, the use of these

technologies will not be considered in this thesis as the focus is to implement a

low-cost automated forced landing system.

2.2 Guidance Techniques

As with path planning, numerous techniques for aircraft and robot guidance exist in

the literature, and it is infeasible to provide a thorough review of all these methods

here. However, the techniques presented below are those deemed most suitable to

the UAV forced landing problem at hand, are simple to implement and are ideal for

both path following in winds or nil-wind conditions.

Niculescu (2001) presents a lateral path following controller for an Aerosonde

UAV. Here, the wind is assumed known and wind vectors are incorporated into

the guidance process by using simple, nonlinear differential equations. The cross

and along-track velocities of the aircraft in wind is then used to generate yaw rate

commands that drive the aircraft to asymptotically follow a path. Although this con-

troller has been demonstrated in simulation to perform well in winds, it is nonetheless

limited to linear paths.

Frew et al. (2004) describe a system where vision-based control is used to guide

a small, fixed-wing UAV in following a road. The aircraft roll angle and altitude are

estimated by the onboard inertial sensors and used to calculate the lateral displace-

ment of the aircraft from the road. Then, to enable autonomous road following,

two control strategies are trialled. The first aims the aircraft a specified distance

(dahead) along the road and uses the heading error as feedback to a proportional

control loop (Figure 2.16a). The second functioned as the first but derives the er-

ror signal using the geometric relationship between the desired aircraft position and

velocity (Figure 2.16b).

From flight experiments, it has been demonstrated that using the second control

system, a UAV aircraft can successfully track a straight 2.5 km stretch of road in

crosswinds of up to 5 m/s. This tracking ability can be beneficial to the UAV forced

landing research, and thus the detection and control algorithms presented here will

38

2.2. GUIDANCE TECHNIQUES

Figure 2.16: (a) Strategy 1 - Arctan nonlinear control, (b) Strategy 2 - Velocity ratio control(Source: Frew et al., 2004)

be investigated further to determine their suitability to this problem.

Rathinam, Kim, and Sengupta (2006) extend the previous work such that the

UAV can follow various straight or curved structures. During offline processing, a

cross-section profile showing the mean, variance and boundaries of the structure to

be tracked is generated from a single sample image. This profile is then matched

to the horizontal samples (scan lines) of the target image obtained online using

correlation-based template matching. Finally, a curve-fitting algorithm is applied to

the matched samples to find the equation of the centreline of the structure on the im-

age plane. To control the vehicle to follow the detected structure, the path following

algorithm developed by Frezza, Picci, and Soatto (1998) is applied. This novel algo-

rithm utilizes a connecting contour (polynomial) to join the current location of the

vehicle to a point on the curve, thereby satisfying the geometric and non-holonomic

constraints (Figure 2.17). The fact that the aircraft is modelled as a simple unicycle

without taking into account the vehicle dynamics is a limitation in this particular

research, since it implies that the control system has to correct for large gains that

39


make the aircraft overshoot the target. Wind disturbances are also not modelled.

Although for the forced landing investigation the UAV is not required to track a

curved structure over a large distance, the connecting contour control method can

perhaps be applied when the UAV has to make a curved approach to intercept the

planned path, such as in the presence of strong crosswinds.

Figure 2.17: Illustration of the curve to be tracked and the connecting contour (Source:Rathinam et al., 2006)

A more robust lateral controller utilizing vector field commands is presented by

Griffiths et al. (2006) and D. R. Nelson et al. (2007). In their work, the control

algorithm computes the desired groundspeed and course commands (based on the

cross-track error) that allow asymptotic following for both straight and circular

paths. The course commands are obtained from previously calculated vectors that

are directed toward the path to be followed and that represent the desired direction

of flight (Figure 2.18). Although flight tests have confirmed the validity of this

approach, it nonetheless relies on the assumption that both altitude and airspeed

are held constant in the longitudinal plane, and the aircraft is able to constantly

bank at minimum turn radius to achieve the required tracking accuracy. Although

this may be infeasible for a UAV forced landing, the concept of vector fields can

nonetheless be still applied.

Park et al. (2007) present a guidance logic containing an anticipatory element

for the upcoming local, desired flight path is used to guide an UAV along both linear

and circular 2-D paths. The algorithm uses the instantaneous vehicle speed, as well

as both proportional and derivative controls on the cross-track error to enable tight

path following in the presence of winds. What is interesting about this algorithm

is that it extends proportional navigation strategies as used in missile guidance

(Zarchan, 2007) such that the aircraft is always following a moving reference point,

40

2.3. MANNED AIRCRAFT FORCED LANDING PROCEDURES

Figure 2.18: Illustrating the vector field concept for linear and circular path following. Thedesired course of the UAV is specified by the direction of the vector field. (Source: D. R.Nelson et al., 2007)

and the closing speed between the reference point and the vehicle is zero with the

line-of-sight distance fixed. This results in a smooth but rapid convergence on the

path to fly, instead of asymptotically, and is desirable in a UAV forced landing

since any path deviation translates to greater altitude loss and less time airborne.

Nevertheless, the algorithm will still need to be extended to account for 3-D paths

as well as reduce it’s susceptibility to winds.

Finally, a 3-D path following algorithm capable of following both straight lines

and arcs is described by Ambrosino et al. (2009). In this approach, an imaginary

line-of-sight is focused a short distance ahead of the vehicle, and the errors in the

three-dimensional plane are then incorporated into the aircraft kinematic equations

to produce the desired heading and flight path angles. These angles are in turn

multiplied by a gain to reduce the errors proportionally to the distance from the

desired path. Although this algorithm has been shown in simulation to perform well

in winds, it is only feasible for vehicles travelling at a constant speed and constant,

shallow flight path angle. For a UAV forced landing, more aggressive manoeuvring

in both the lateral and longitudinal plane may be required at times to deal with

adverse wind conditions, which would imply using a more robust controller.

2.3 Manned Aircraft Forced Landing Procedures

Manned aircraft forced landing manoeuvres represent some of the more complex

flight manoeuvres practiced by human pilots, and incorporate both path planning

and guidance strategies, as well as visual navigation and subjective judgment. This

section provides an overview of the standardised path planning and guidance tech-

niques employed by human pilots during a forced landing. For further information,

the interested reader is directed to (CASA, 2007; Brandon, n.d.; Robson, Sciberras,

41


& Whellum, 2002).

While flying en route at an appropriate cruising altitude, pilots maintain the

habit of continually assessing the wind velocity at the cruising altitude, as well

as the best general areas for possible landing taking the wind and glide distance

into account. To determine the wind velocity, pilots consolidate information from

a variety of sources including weather station forecasts, windsocks, smoke, water

ripples, cloud shadows or even clothing fluttering in a breeze. Ideally, the pilot tries

to locate a candidate landing site that is situated downwind of the aircraft, and

applies a further set of criteria to determine the most feasible site. These criteria

include such features as the size, shape, surface type, slope, surroundings and sun

position at the landing site.

If the engine fails, the first action is to fly the aircraft towards the chosen landing

site at the best glide speed (Vbg), using INS, GPS and/or dead reckoning calculations

for navigation. Once the aircraft is close to the site, as determined intuitively using

vision-based judgments, and is at an altitude of 2500 ft or more above ground level

(AGL), the pilot conducts a spiral descent over that area at the minimum power glide

speed (Vmp). However, the pilot can constantly adjust the pitch and airspeed of the

aircraft to counter headwinds or tailwinds. The final phase of landing involves the

pilot performing a flare manoeuvre to strike the ground with the main undercarriage

first, before rolling and braking.

Since the behaviour of localised wind cannot be predicted ahead of time, a nomi-

nal lift-to-drag ratio of 9:1 is used to calculate an estimate of the aircraft glide range

in nil-wind conditions. This in turn provides a conservative descent path angle of

10 degrees, given by:

θ = tan−1(

1

9

)≈ 6.3◦ ≈ 10◦

�� 2.1

This glide range can also be considered as the radius of a circle on the Earth’s

surface which contains all attainable landing sites. Once a feasible site is located,

pilots mentally construct a series of waypoints above the chosen site which, when

traversed in succession, will bring the aircraft in a spiralling descent path to alight

on the site (Figure 2.19). To then determine the track to fly in the presence of

wind, pilots use simple trigonometric principles to calculate the heading and airspeed

required to maintain course given a known wind disturbance.

An additional waypoint, called an overshoot point (OS), can be included in the

descent plan on final approach if the aircraft is still too high to make a landing. The

overshoot point is situated in line with the decision height waypoint (see Figure 2.20)

and at an appropriate distance away such that by flying first to this waypoint, the

aircraft can lose excess altitude and be at the desired altitude for making the landing.

42

2.3. MANNED AIRCRAFT FORCED LANDING PROCEDURES

Figure 2.19: The forced landing circuit pattern (Source: Civil Aviation Safety Authority ofAustralia (CASA), 2007)

Figure 2.20 illustrates an approach pattern showing multiple choices in the selection

of a final approach and landing run. The wind is estimated to blow from the north-

west. Path A is the planned approach and landing run from the end base position.

Paths B, C and D are alternate paths which may either delay or bring forward the

turn onto final to cater for height, wind or positioning differences. Paths E and F

show how it is possible to turn onto the landing path before reaching the end base

point, if it is required to do so.

Figure 2.20: Path planning on final approach (Source: Brandon, 2007)

The piloted forced landing path planning and control methods discussed above

are both simple and effective; yet they are heavily reliant on vision and visual-

43


based cues as humans depend on these for navigation and guidance. A machine

may not need to fly the same approach pattern to perform a forced landing, but

may utilise low level information from sensors to navigate itself, as well as other

indicators (visual or otherwise) to steer itself to the landing site. However, it is

still worthwhile to consider using a circular approach pattern for a fixed-wing UAV,

since it cannot hover or descend vertically to land like a helicopter. It may also be

feasible to combine the piloted path planning techniques with some of those used in

traditional robotics path planning, such as Dubins curves.

2.4 Summary

This chapter has presented a comprehensive assessment of existing and emerging

works that are pertinent to this research, in the areas of both robotics path planning

and guidance, as well as in piloted aircraft forced landing procedures.

Four classes of global planning methods were reviewed, namely, PRM, RDT/RRT,

cell decomposition and EA. Although PRM techniques are probabilistically com-

plete, they create a tree-like graph structure that can contain many spurious turns

and so undermine aircraft stability. Conversely, while aircraft dynamics can be

encoded into RDT and RRT algorithms, inefficient paths may still result. Cell de-

composition techniques use a coarse model of the environment to form the initial

path, and then refine this path as new information becomes available. However, the

linear paths produced still need to be smoothed for aircraft flight. EA techniques

can be applied to problems with a large number of constraints. However, due to

their stochastic nature, these planners cannot guarantee a solution within a given

time frame, nor the same solution for a fixed operating environment. Hence, cell

decomposition is the global planning method most suitable to this research. For the

UAV forced landing problem, global planning will use the current aircraft position as

well as the positions corresponding to the available landing sites, which may change

as the aircraft nears the ground. Once a start and goal position has been found, a

local planner may be used to construct a feasible trajectory between the two points.

By far the most widely used local planners are those that employ a heuristic-

based search, such as the Dijkstra algorithm, A*, D* and D* Lite. However, use

of these algorithms will unnecessarily complicate this research, as an aircraft forced

landing occurs mostly in free space with insufficient justification for cell partition

and path repairs. There is also limited time for path replanning and optimization

as no engine thrust is available. Notwithstanding, trajectory generation techniques

(a class of local planners) can still be used to generate a feasible flightpath between

the nodes.

Several trajectory generation algorithms have been investigated, including po-

44

2.4. SUMMARY

tential fields, finite horizon planning and manoeuvre generation methods. Potential

field methods are simple to use but are susceptible to local minima. Finite horizon

planning techniques such as MPC are well suited to highly nonlinear systems with

many constraints, but can also place unnecessarily high demands on onboard re-

sources due to the constant replanning involved. Manoeuvre generation techniques

such as Manoeuvre Automata and Dubins curves are extremely robust and allow a

smooth trajectory to be formed in highly demanding environments. Their ease of

implementation and construction, particularly in the case of Dubins curves, makes

them very attractive for use in the forced landing problem. To deal with curvature

discontinuities in Dubins curves, clothoid paths may be used, however, these tech-

niques do not have a closed-form solution and also require steering to be applied at

the maximum allowable rate. PH space curves using quintic splines produce smooth

paths with minimal bending energy and can be applied to this research. However,

attempting to satisfy both curvature and elevation constraints can impractically

elongate the path, as well as lead to longer computation times.

Realistic wind information can be downloaded to the global or local path planner

via GRIB data bases before flight. However, since these databases are only updated

every six hours, the planner must use wind forecasts from weather stations while en

route, and incorporate this information into the planning process. Wind velocity can

be estimated using the onboard aircraft instruments when forecasts are unavailable.

Otherwise, the planner can interpolate wind data in memory for a given location and

time, using a statistical model such as a first order Markov process. One method to

track a given waypoint in winds is to consider that point as having a velocity equal to

and opposite that of the estimated wind velocity. A spatial sliding surface controller

can then be used to track a polynomial curve joining that waypoint to the current

waypoint. To deal with uncertainties, the generated path should not require using

the maximum turning rate of the vehicle, thus providing the aircraft with reserve

control authority. For the UAV forced landing problem, a combination of some or

all of the above methods is necessary to capitalise on the individual advantages, as

well as to offset the disadvantages.

Once both a global and local planner has been selected, a suitable guidance tech-

nique must be applied to steer the aircraft with minimal cross-track errors. Guidance

techniques utilising the geometric relationship between aircraft and path, as well as

a moving reference point in the feedback loop, are most suited to this research as

they provide smooth path convergence while being robust to wind disturbances.

Where the distance between the aircraft and the path to be tracked is large, a con-

necting contour can first be used to guide the aircraft to proximity before engaging

the selected guidance controller. Vector fields can also be used to generate course

commands, and have been shown to work well in practice.

45


Finally, the procedures practiced by human pilots to generate a forced landing

descent path and correct for wind can most readily be applied to this research, since

many of the same problems experienced by manned aircraft are also encountered

by UAVs. However, to create a truly robust system, traditional robotics path plan-

ning and trajectory generation techniques should be integrated with human pilot

approaches.

46

3Path Planning for a Fixed-Wing UAV

FOLLOWING an engine failure that requires an immediate landing, a path

must quickly be found that connects the current position of the UAV to a

point above the ground where it is aligned with the longest section of the selected

landing site. Ideally, the constructed path should contain the position, heading and

altitude information necessary for the aircraft to navigate to the desired site. Two

classes of planning algorithms are investigated in this research, and it is desired

to ascertain by repeated simulation the validity of each approach. However, only

the class of algorithms that can demonstrate the best performance will be imple-

mented in actual flight tests (see Chapters 5 to 7 for further details). This chapter

begins with a discussion on the design of planning algorithms that are based on

piloted forced landing procedures. Following this, an algorithm derived from Du-

bins curves is examined, and it is shown how this algorithm can also be applied

to the forced landing scenario. The algorithms are designed and simulated within

the MATLAB® Simulink programming environment, and further details concerning

this development environment is provided in Chapter 5.

3.1 Algorithms based on Piloted Forced Landing Procedures

The algorithms derived from piloted forced landing procedures use the forced land-

ing pattern outlined in (CASA, 2007) to generate the initial target waypoints. In

this configuration, a cone, having the dimensions shown in Figure 3.1A, is defined as

the airspace to which the unpowered aircraft can fly in no wind. To reduce the engi-

neering development time, a generic Aerosonde UAV model built into MATLAB®

Simulink has been used. Using this model, and assuming a GA aircraft lift-to-drag

ratio of 9:1, the glide path angle of 10 degrees is calculated by:

θ = tan−1(

1

9

)≈ 6.3◦ ≈ 10◦

�� 3.1

The glide range is then the radius of a circle on the Earths surface which contains

47

CHAPTER 3. Path Planning for a Fixed-Wing UAV

all attainable landing sites (Figure 3.1C). With the wind taken into account, the

cone is inverted as shown in Figure 3.1B, and the waypoints for the flight planner

are selected such that they lie within the cone, implying that they can be attained

by the unpowered aircraft. By navigating to these waypoints in succession, the UAV

is then able to land on a selected site.

Figure 3.1: Determination of glide range and waypoints for a forced landing

Two path planning strategies incorporating the piloted forced landing procedure

described above were developed. The first attempts to guide the aircraft along a

predetermined circuit to the landing site as shown in Figure 3.1B. The waypoints

for the circuit were chosen such that they lie within a fixed glide range, and the

UAV then attempts to track towards the waypoints using the great-circle navigation

method, while correcting for the wind to remain on course. The second strategy

attempts to follow the standard landing circuit, however wind information is also

48

3.1. ALGORITHMS BASED ON PILOTED FORCED LANDINGPROCEDURES

continually assessed to determine its effect on the glide range, and the target way-

points are then adjusted accordingly to maximise the aircrafts ability to reach the

aim point. As before, the great-circle navigation and wind correction methods are

used while flying en route. Both path planning strategies assume that the UAV is

trimmed for a best glide speed of 19 m/s, corresponding to a lift-to-drag ratio of 9:1

and a positive pitch attitude of approximately 3 degrees for landing. For an arbitrar-

ily chosen landing site, in this case the Brisbane International Airport main runway,

the waypoint coordinates for a standard right-hand circuit (RHC) pattern are given

in Table 3.1, and their relation to the landing site is depicted in Figure 3.2. In this

figure, several possible flight paths using a combination of these waypoints are also

shown, as indicated by the red, green and blue curves. A similar set of waypoint

coordinates for a left-hand circuit pattern can also be generated. The following two

sections present in detail the functions of Algorithm 1 and Algorithm 2.

Figure 3.2: Standard RHC forced landing pattern

3.1.1 Algorithm 1

In this algorithm, a lift-to-drag ratio of 7:1 is chosen in favour of the GA ratio of

9:1 to cater for any unforeseen strong winds, with a maximum headwind of 30 m/s.

Should the aircraft ever encounter such a headwind, it will be blown off course.

However, changing winds may present an opportunity for the UAV to steer itself

back on course. Of course, if the altitude of the UAV is insufficient to perform such

49


Waypoint Φ (rads) λ (rads) Alt (ft)

High Key (HK) 0.4782 2.6725 2500Low Key (LK) 0.4783 2.6722 1700End Base (EB) 0.4786 2.6721 1200

Decision Height (DH) 0.4786 2.6723 670Overshoot (OS) 0.4787 2.6724 400Aimpoint (AP) 0.4784 2.6725 13

Table 3.1: Standard RHC Waypoint Coordinates

a manoeuvre, or a sudden, strong headwind is encountered near the ground, the

UAV will be unable to land at the designated landing site. This is an unavoidable

limitation as a constant glide speed has been assumed.

The new ratio of 7:1 is used in calculating the first threshold slant range distance

from the UAV to the aim point. Using the theorem of Pythagoras, the slant range

distance, SR is given by:

SR =√Alt2 + 7.Alt2

�� 3.2

Where Alt is the initial altitude of the aircraft at the start of a forced landing.

From the calculated SR value, seven other threshold values are created. These

values in turn define a set of four threshold boundaries for the slant range, with

each boundary corresponding to a subset of the set of waypoints similar to those

listed in Table 3.1. The boundaries are: SR; SR to SR-1600′; SR-1600′ to SR-2300′;

SR-2300′ to SR-3000′. These values were chosen based on simulations with the

Aerosonde UAV model, and represent a good approximation of which waypoints a

small to medium-sized UAV can reach, if its initial altitude produces a slant range

distance that lies within these boundaries. The actual slant range from the UAV

to the aim point is then calculated from the great-circle trigonometric equations,

using the initial UAV position and the position of the aim point (see Section 4.1.1).

If this slant range value lies within a particular threshold boundary, then the UAV

will navigate along the flight path described by the set of waypoints corresponding

to that boundary. However, the UAV is not constrained to fly successively to each

waypoint but can, depending on its current altitude above the ground, further define

its flight path using all or several of these waypoints. For instance, once the UAV

is at the end base point, if it is too low to continue to the overshoot waypoint, as

determined by whether the current UAV altitude is within certain threshold limits,

it will head for the aim point. In addition, while en route between the decision

height and overshoot waypoints, the UAV can also lose excess altitude by navigating

back and forth between these points, meaning that the UAV should be at the right

50


altitude for final approach to the landing site. If the first overshoot waypoint is not

enough to lose the required amount of altitude, a second overshoot waypoint can be

included in the flight path (compare this with Table 3.1, in which only one overshoot

waypoint has been considered). This implies that a number of different flight paths

can be generated from the one initial set of waypoints. In addition, the standard

GA forced landing pattern, describing the distances between waypoints as shown in

Figure 3.2 has been slightly reduced for this algorithm, giving the layout presented

in Figure 3.3. This layout was chosen to improve the chances of the UAV being able

to reach the aim point.

Figure 3.3: Modified RHC forced landing pattern

A further measure is built into the path planning algorithm such that if the

UAV is initially much higher (>800 ft) than the high key point, it will execute a

circling descent to lose excess altitude. For this algorithm, only landings without the

aid of flaperons have been considered. Thus, while tracking towards the aim point,

should wind changes near the ground cause the UAV to have more lift such that it

will overshoot the aim point, it is commanded to head for the far threshold of the

landing site which is 400 m away from the aim point. Once at this waypoint, if the

UAV is still in the air, it is commanded to navigate back and forth between the aim

point and the landing site threshold point until it is on the ground. The UAV can

also perform both a right and left-hand circuit pattern. The path planning strategy

described above is summarized in Figure 3.4.

51


Figure 3.4: State transition diagram for Algorithm 1

3.1.2 Algorithm 2

The second path planning algorithm can be discussed by way of example. Consider

the aircraft located at Point A in Figure 3.5, en route to Point D. For argument,

assume that a headwind is blowing with velocity Vw against the direction of travel.

At time t0 seconds, the aircraft is at altitude h0, and it is desired to know whether the

aircraft can glide to Point D. That is, at time tn seconds, will the aircraft altitude be

greater than or equal to hn? The gradient corresponding to the nominal lift-to-drag

ratio of 9:1 is shown as the dashed, red line (Figure 3.5). This gradient is used to

initialise the path planning algorithm. As the UAV moves through the air however,

it will experience longitudinal phugoid motion (solid, blue line) that varies its glide

slope, meaning that the nominal gradient is no longer valid for calculations. For

simplicity, assume that this oscillatory motion can be linearized for small time epochs

(≤ 10 seconds), as shown by the dashed, green line. Additionally, the period of 10

seconds has been chosen as Algorithm 2 was initially designed using the Aerosonde

52


UAV model, and with the aircraft flying at a Vbg of 19 m/s, this amount of time

allowed for adequate replanning to reach several different waypoints while preventing

the aircraft from turning too often and becoming unstable. Now, in the first epoch,

the gradient from A to B is given by:

m = ∆y/∆x =h0 − h1

Vg(t1 − t0)�� 3.3

Where Vg is the ground speed of the aircraft, calculated as the sum of the True

Airspeed (TAS) and the component of the wind velocity in the direction of travel:

Vg = TAS + Vw�� 3.4

If it is further assumed that the gradient is calculated every 10 seconds, using

data collected from the previous 10 seconds, then the altitude after the next 10

seconds can be predicted using the equation of a straight line, expressed in general

form as:

y = mx+ c�� 3.5a

Alttn+10 =htn−10 − htn

Vg(tn − (tn−10))Vg(tn+10) +Alttn−10

�� 3.5b

Here, n is an integer of the form 0, 1, 2...n, and Vg(tn+10) gives the quantity ∆x

in Figure 3.5.

Figure 3.5: Altitude prediction for Algorithm 2

Should the predicted altitude at each tn+10 seconds still exceed that of the tar-

geted waypoint, the UAV will continue to track towards this waypoint, otherwise, it

will search for a new waypoint. However, once within a certain threshold distance

(200 m) of the target waypoint, the UAV will start searching for another waypoint.

This is so that it will not become trapped in a local minima. If the target waypoint

53


is the final waypoint and the UAV is so low over the ground that it cannot reach

the other waypoints, then it will simply circle around this waypoint until it lands.

By continually predicting the UAV altitude as a function of changes in the wind

velocity, a flight path can be described such that it will always contain waypoints

that the UAV can navigate to. Using the experience obtained from testing the first

algorithm, the waypoints for this algorithm are selected from the standard waypoint

locations for a right-hand circuit pattern (see Table 3.1 and Figure 3.2), as it is now

known that the UAV can navigate to these waypoints and still be able to land on

the landing site. A state diagram summarizing this algorithm is depicted in Fig-

ure 3.6. Note that to reduce complexity, waypoints corresponding to a left-hand

circuit pattern were not used.

Figure 3.6: State transition diagram for Algorithm 2

3.2 3-D Dubins Curves

Although the algorithms described in Sections 3.1.1 and 3.1.2 are designed to max-

imize the chances of the aircraft reaching the desired landing site, their complexity

(particularly Algorithm 1) and the fact that they both use fixed distances between

54

3.2. 3-D DUBINS CURVES

waypoints, as well as rely on a fixed airspeed may result in their undoing, although

this will need to be proven through say, simulation. For instance, in the case of Algo-

rithm 1, having the aircraft flying back and forth between two waypoints may result

in the aircraft losing too much altitude before the final turn for the aimpoint. In ad-

dition, in the case of Algorithm 2, instability may result from the aircraft constantly

turning while seeking for a point below the projected glide slope. Hence, in the case

of a forced landing where no engine thrust and limited manoeuvrability is available,

it may be more advantages to employ a reusable algorithm which, given the starting

and goal locations, uses simple geometric shapes to form a path that also accounts

for the aircraft dynamics. From the literature, it has been found that such a path

can best be described by trajectories derived from Dubins curves (Section 2), and

although the 3-D Dubins path planning algorithm developed in this research may

appear to resemble in part that described by Ambrosino et al. (2006) for powered

aircraft, the basic idea presented there has been greatly extended to develop a novel

approach for the gliding descent of a fixed-wing aircraft. For this new series of algo-

rithms also, a model of a Boomerang 60-size UAV has been adopted as it represents

the aircraft to be used for flight tests (refer back to Section 1.2). Note however, the

algorithms disclosed here are not restricted to any specific aircraft type, but can be

applied to both manned and unmanned fixed-wing aircraft of any size and type.

3.2.1 The 2-D Dubins Path

Initially, a 2-D Dubins path is constructed having the form:

{LαRβLγ , RαLβRγ , LαSdLγ , LαSdRγ , RαSdLγ , RαSdRγ}�� 3.6

in which L and R correspond to left and right turns at a bank angle that does

not exceed the maximum bank angle of the aircraft, S corresponds to flying in a

straight line that is tangential to the arcs of turns, and α, γ ∈ [0, 2π) , β ∈ (π, 2π),

and d ≥ 0. Note that the LαRβLγ and RαLβRγ type paths are merely a special

case of the other four types of paths, where S → 0.

The above-mentioned six plausible path constructs have been proven by Dubins

(1957) to be the optimal (shortest distance) paths when the start and goal locations

are dissimilar, and the arcs are constructed using the minimum turn radius. In the

case of a UAV forced landing however, flying at the minimum turn radius will result

in a greater sink rate, and since no engine thrust is available, this action could also

result in instability if prolonged. Hence, in this research, the bank angles have been

chosen such that they produce shallow glide paths, and the initial and final bank

angles are allowed to vary to increase the number of plausible paths. This gentle

turning action also provides the ideal environment for an onboard camera to detect

55


feasible landing sites below the aircraft. Secondly, to deal with the known curvature

discontinuities and direction reversals inherent in Dubins curves (see Section 2), it

should be noted that after forming the path, the planner actually supplies the 3-D

waypoints that form the Dubins arcs and lines to lower-level guidance algorithms.

The separation between these points is such that by utilising the geometric rela-

tionship between the aircraft and path, it is possible for a spatial sliding surface

controller to steer the aircraft smoothly onto the path (see Section 4.2). In reality,

this produces the same effect as using clothoid or PH space curves to smooth the

Dubins path.

The radii of the arcs are calculated using the equation:

R0,f =VTAS

2

g tan(φ0,f )

�� 3.7

where R0,f are the initial and final radii of the arcs of circumference, VTAS

is the true airspeed of the aircraft, g is the gravitational acceleration constant

(9.80665m/s2), and φ0,f are the initial and final bank angles respectively.

To simplify the path planning process, VTAS has been taken to be the best glide

speed, Vbg of the aircraft, which gives the greatest straight line flight distance in

still air from the potential energy of height. Although the path has been designed

with only one airspeed, the actual airspeeds flown when navigating the path are

determined by the specific guidance algorithms employed (Section 4.2). These algo-

rithms use the geometric relationship between the aircraft and path, as well as the

ambient wind conditions, to produce a range of airspeeds for the aircraft to converge

smoothly onto the path. In so doing, any instability that may result in flight when

switching from following arcs to lines and vice versa is also negated.

As shown in Figure 3.7, Vbg can be estimated by first fitting a curve (black)

through the descent rates at various airspeeds (red diamonds), obtained through

simulation. The best glide speed is then found by drawing the blue line from the

origin tangent to the curve, giving Vbg as 18.63 m/s and a nominal lift-to-drag ratio

(L/D) of 24.5. Although this value may seem too optimistic, remember that it was

acquired using simulated sensor data under ideal conditions, with no wind and no

sensor errors.

Later, a series of tests were performed using the Boomerang-60 UAV to calculate

the actual L/D. The aircraft was flown with the throttle set to idle (for safety)

and at different airspeeds to simulate gliding flight, and the corresponding descent

rates were recorded. Table 3.2 lists the average sink rate recorded for each airspeed

selected. The speed polar is then generated by fitting a smooth curve to the data

(Figure 3.8). From the speed polar, Vbg is estimated to be approximately 19.7 m/s,

giving an L/D of 8.81 when the aircraft path angle is −6.5◦.

56


Figure 3.7: Speed polar diagram for a Boomerang-60 UAV using simulated data, showinghow the best glide speed Vbg is obtained.

No. TAS (m/s) Sink Rate (m/s)

1 17.5003 -2.2852 21.5001 -3.22143 23.9483 -4.21834 26.1043 -5.495 26.7189 -6.866 29.1772 -8.59757 31.3232 -9.45

Table 3.2: Sink rates at different airspeeds for the Boomerang-60 UAV

Once the radii are determined, the optimal 2-D path is obtained with a geomet-

rical construction adapted from (Ambrosino et al., 2006). First, two circles with

radii R0 are drawn containing the starting point P0 and a vector pointing along

the aircrafts initial heading ψ0 (Figure 3.9a). The circumferences of the circles are

denoted by Σ0A and Σ0B. Next, the same process is repeated at the goal point Pf

with the final aircraft heading ψf , and circumferences ΣfA and ΣfB. Following this,

tangent lines are constructed that join the circumferences of these circles, such as

depicted in Figure 3.9b for Σ0A and ΣfA. Considering Figure 3.9b, it can readily be

seen that there are four paths connecting P0 to Pf , where a path is formed by the

union of an arc on the circumference Σ0A, a segment K on one of the four tangent

lines, and finally an arc on the circumference ΣfA. However, only one of these paths,

ΓAA is compatible with the initial and final headings of the UAV (Figure 3.9b and

3.9c), and further details regarding the test for path compatibility is discussed in

Section 3.2.1.1, which is novel to this research. In a similar way, three other paths

ΓAB, ΓBA and ΓBB can be obtained – the optimal path is the shortest between ΓAA,

ΓAB, ΓBA and ΓBB and depicted as a thick, solid line in Figure 3.9c.

57


Figure 3.8: Speed polar diagram for a Boomerang-60 UAV using flight data, showing howthe best glide speed Vbg is estimated from a smooth curve fitted to the data.

Following the construction of Γxy, and given the distance dtgt from the initial

point of failure to the approach point, the path angle can then be obtained as

γxy = tan−1(zarcf − zarc0

dtgt

).

�� 3.8

This allows the UAV to descend from an altitude of zarc0 to zarcf . Here, zarc0

and zarcf are the altitudes corresponding to the xy-positions where the initial and

final arcs of circumference unite with the segment.

Now, to ensure stability, the flight path angle γ must satisfy the constraint:

γmin ≤ γ ≤ γmax. However, if the difference in altitude between the start and

end positions should result in the maximum allowable path angle being exceeded,

one of the other suboptimal paths can be selected to lose the approximate amount

of altitude required. Other options include enlarging R0 and/or Rf , as well as

commanding the aircraft along a helical trajectory (similar to a spring) to lose excess

altitude, before joining the path at the start of the first arc (see Section 3.2.2.1).

These features of the path planner are specific to this research.

3.2.1.1 Determining Path Traversability

To test for path traversability, the algorithm uses a novel approach that considers

five parameters to determine which path the aircraft should follow from the initial

arc to the final arc. These parameters are:

1. The geometric relationship between the coordinates of the initial circle and

58


Figure 3.9: (a)Step 1 of generating the 2-D path. (b)Step 2 of generating the 2-D path. (c)Step 3 of generating the 2-D path. Four plausible paths are obtained; the optimal path ispath no.1

59


the initial aircraft position;

2. The initial heading at the commencement of a forced landing;

3. The geometric relationship between the initial and final aircraft positions;

4. The geometric relationship between the coordinates of the final circle and the

final aircraft position; and

5. The final heading at the approach point.

Consider the example shown in Figure 3.10. Here, the UAV is initially located

at Point A and desires to arrive at Point F. There are four tangential paths between

circles A and C, but since cenxiA > xaci ; cenyiA < yaci ; the initial heading, ψi has

an easterly vector component; and cenxiA < cenxfC ; only two paths, namely ΓABD

and ΓACE are traversable by the aircraft from Circle A. These paths are classified

as the top tangents and flags are then set in the algorithm to register the paths.

Although it is also possible to bank the aircraft along Circle B before flying along

a tangential path to Circle C, the algorithm compares the arc lengths between the

tangential lines to circles and the initial aircraft position, and weighs the decision in

favour of the path with the lesser arc length.

Figure 3.10: Diagram showing how path traversability is determined from the geometricconstruction of the 2-D Dubins curve, and the initial and final positions of the UAV

The algorithm then considers the final aircraft position at Point F. Since at this

point cenxfC = xacf1 ; cenyfC < yacf1 ; the final heading, ψf has an easterly vector

component and cenxfC > cenxiA ; the only feasible paths to arrive at this position

are ΓABDF and ΓAC′E′F . However, by cross-checking the flags set for flying from

Circle A to Circle C, the algorithm is able to deduce that only ΓABDF is feasible in

60


this case.

Although it is also possible to navigate along Circle D before joining the final

position at F, the algorithm once again prioritises the path with the minimal length

and determines that ΓABDF is the optimal path. However, if the final position and

heading should be that shown by the aircraft symbol at G, and applying the same

reasonings, the optimal path would be ΓAHIG (for simplicity the other construction

lines are not shown). In effect, the algorithm is projecting the aircraft heading vector

along each of the plausible paths and checking whether this vector will coincide with

the final heading vector at the final position. Algorithm 3.1 outlines the points just

described in determining traversability for a 2-D Dubins path.

Algorithm 3.1: Determining Path Traversability

input : ψi,f , xaci,f , yaci,f , cenxiA−D , cenyiA−D , cenxfA−D ,cenyfA−Doutput: Indices to feasible 2-D Dubins paths

1 begin2 determine north, east vector components of ψi,f ;3 let SgnX −→ Sign of x-compt ;4 let SgnY −→ Sign of y-compt ;5 calculate tangents between each of circles A-D ;6 calculate lengths of straight segment ;7 foreach SgnX = −1, SgnX = 1, SgnY = −1, SgnY = 1 do8 foreach cenyi >= yaci, cenyi < yaci do9 foreach xacf >= xaci, xacf < xaci do

10 select relevant tangents and set corresponding flag;11 calculate initial arc lengths;

12 forall the cenyf >= yacf , cenyf < yacf do

13 forall the xacf >= xaci, xacf < xaci do

14 select relevant tangents and set corresponding flag;15 calculate final arc lengths;

16 Compare flags set for initial and final arcs;17 if flags match then18 find corresponding arc leni,f and line len;19 concatenate to form path;20 order paths from shortest to longest;

21 else22 no feasible path exists;23 perform error handling;

24 return table of path indices;

25 end

61


3.2.2 The 3-D Dubins Path

A novel approach has also been used in forming the 3-D path, which is greatly

different to that employed by Ambrosino et al. (2006). First, note that a gliding

aircraft that is rolled into a steady, coordinated turn at a constant bank angle φ and

flies at a constant descent angle γ will trace a helical path on an imaginary cylinder

with radius R. Thus, the 3-D path can be formed by a straight line at a constant

path angle that joins two arc sections. The relationship between φ and γ for an arc

section is given by

cotγφ0,f =VTASVS

cosφ0,f ,�� 3.9

where VS is the descent rate of the gliding aircraft, and VTAS/VS approximates

L/D. To form the path, Vbg is selected as VTAS .

Now, the altitude lost through one complete turn of the helix can be obtained

by

Sφ0,f = 2πR0,f tan γφ0,φf ,�� 3.10

implying that the altitude lost while traversing the sections of helix corresponding

to an arc of circumference can be calculated as

S0,f =1

2π

‖Σ0,f‖R0,f

Sφ0,f ,�� 3.11

Giving the altitude where the arc sections join the 3-D line as

zarc0 = z0 − S0,�� 3.12a

zarcf = zf + Sf ,�� 3.12b

where z0 is the altitude at the start of a forced landing, and zf is the desired

altitude to achieve at the final approach point. Given the terminal points on the

arcs Parc0 = [xarc0 yarc0 zarc0 ] and Parcf =[xarcf yarcf zarcf

], it is then a straight-

forward process to obtain Γline.

Once the predicted altitude losses for the different path sections are known, the

actual path can be described by parametric equations for the curves as well as the

line segment. Firstly, the number of full turns of a helix is calculated as

%0,f =

⌊z0,fSφ0,f

⌋,

�� 3.13

from which the parameter t for the arcs with length ‖Σ0,f‖ can be expressed as

62


t0,f = [%0,f2π + ‖Σ0,f‖ : −4 t0,f : %0,f2π] .�� 3.14

The vector function for a circular helix is then expressed as

r(t0,f ) = R0,f cos t0,f i +R0,f sin t0,f j + (ct0,f + d)k,�� 3.15

with

c = Sφ0,f /2π,�� 3.16

d =z0,fSφ0,f

%0,fSφ0,f ,�� 3.17

which is required to elevate the helix section from the ground altitude to z0 or

zarcf .

The relationship between the different elements of the 3-D path Γ, where Γ =

Γarc0 ∪ Γline ∪ Γarcf is illustrated in Figure 3.11.

Figure 3.11: Relationship between elements of the generated 3-D flight path. The generatedpath is Γarc0 ∪ Γline ∪ Γarcf .

Through simulation, it has also been observed that the Boomerand UAV will only

tolerate a negative pitch angle, θ, between 0 and -14 degrees. Hence, as an added

precaution in choosing γ, we have included the following dynamic constraints:

63


γ =

θmin if tan−1(zarcf−zarc0‖K‖

)≤ θmin,

θmax if tan−1(zarcf−zarc0‖K‖

)≥ θmax,

tan−1(zarcf−zarc0‖K‖

)otherwise,

�� 3.18

where

‖K‖ =√

(xarcf − xarc0)2 + (yarcf − yarc0)2.�� 3.19

Allowing the flight path angle to vary increases the number of manoeuvres avail-

able to the aircraft; however, to allow the aircraft additional control authority to

follow the path in the presence of uncertainty, θmin is limited to -10 degrees. Fi-

nally, the 3D path is formed by letting Γ = Γarc0 ∪ Γline ∪ Γarcf , and Γ is sampled

to generate a list of waypoints for the path following algorithm.

3.2.2.1 Dealing with Excess Altitude

If the path angle of the line segment, γline is less than θmin, such as when the

UAV is initially very high above the ground, a novel technique is used to lose the

excess altitude and, simultaneously, construct a path within the aircraft dynamic

constraints. Firstly, the Dubins path is formed by taking θmin as the line path angle,

and then incorporating additional helix spirals to account for the excess altitude.

In fact, this is similar to a manned aircraft forced landing procedure, where the

pilot would circle the aircraft above the intended site/s to lose extra altitude, before

following a final descent pattern to the selected site. Now, the number of full turns

of a helix that would fit inside this extra altitude, zex is given by

%ex =

⌊zexSφ0

⌋,

�� 3.20

with any remaining altitude to lose, zrem typically being absorbed by the altitude

lost while traversing another section of the initial arc added onto the helix coil, that

is,

S0 =θarc02π

Sφ0 .�� 3.21

This addition is necessary such that the UAV will be at the correct heading

when it joins the Dubins path at the end of the spiral. Hence, the total amount of

additional helical spirals required is

64


%extot = %ex + S0.�� 3.22

From Eqn. 3.14 and the above, the parameter tex to construct the 3-D spirals

can then be expressed as

tex = [%02π + ‖Σ0‖ : 4tex : %02π + ‖Σ0‖+ %ex2π] ,�� 3.23

and, as before, the vector function for the extra helices can be written as

r(tex) = R0 cos texi +R0 sin texj + (ctex + d)k,�� 3.24

with c as in Eqn. 3.16 and d equal to (zex/Sφ0 − %ex)Sφ0 .

However, should zrem < S0, zex < S0 or, the remainder, if any, after S0 is

subtracted from zrem be less than S0, %ex is simply added to the Dubins path, and a

connecting contour used to join the current aircraft position to the start of the helix.

In order to simplify the path, the connection is always made with an arc length of

Σ/4, where Σ is the circumference of a circle with radius R0. This gives

tjoin =

[%02π + ‖Σ0‖+ %ex2π : 4tjoin : %02π + ‖Σ0‖+ %ex2π + π/2]

if zrem < S0,

[%02π + ‖Σ0‖ : 4tjoin : %02π + ‖Σ0‖+ π/2]

if zex < S0,

�� 3.25

and the altitude where the contour initiates as

zjoin = zarc0st + Sφ0/4,�� 3.26

where zarc0st is the altitude at the start of the first Dubins arc. Then, the altitude

loss through one full turn of the helix spiral from which the connecting contour is

extracted, Sφjoin , is simply four times the size of zjoin, and the path angle of the

contour can be approximated as

γjoin = tan−1(zjoin2πR0

).

�� 3.27

Using Eqn. 3.25 and the definition of Sφjoin , the parametric equations for the

contour are expressed as

r(tjoin) = R0 cos tjoini +R0 sin tjoinj + Sφjointjoink,�� 3.28

65


Once the extra helix spirals and associated connecting contours are formed, a

final check is made on the initial and final altitudes of these sections, as well as the

Dubins path beneath them to ensure that the constructed path begins and ends

at the desired initial and final altitudes z0 and zf . Any discrepancies in altitude

is corrected by using either additional connecting contours, or decreasing the slope

of the line segment such that the entire path lies between z0 and zf . Figure 3.12

illustrates the concepts described above for a forced landing flightpath example.

From this figure, it can be seen that due to the high initial altitude, extra helix

spirals (Ψex) with a path angle of γarc0 (magenta line) are required to be formed.

These spirals are formed in such a way that the aircraft will still be at the correct

heading once it joins the Dubins path (blue line). However, in this scenario, the

altitude remaining, zrem requires a further connecting contour, Ψjoin (red line) with

a path angle of γjoin to be formed. This is because Ψex cannot fully absorb the

extra altitude zex, since it terminates at the position shown by the grey curve. This

contour begins at an altitude of zarc0st , and intersects Ψex at zarc0st + zjoin with an

arc length equal to a quarter of the circumference of the circle described by Ψex.

The unused portion of Ψex, shown by the grey curve, is simply omitted from the

final path.

Figure 3.12: Forced landing flight path example showing the use of extra helix spirals, Γex

and a connecting contour Γjoin to form a feasible path.

66


Figure 3.13: Derivation of an additional waypoint to track to improve path following per-formance in strong headwinds

3.2.2.2 Additional Waypoint for Post-Approach Point Gliding

It is also found during simulated testing that in strong headwind conditions, and

where the final arc extends for more than one-fifth of the circumference of the circle

from which it is derived (think of an S-shaped path), the UAV is not able to arrive at

the approach point within acceptable miss distances. Hence, a novel approach has

been employed in which an additional waypoint is included in the CSC style paths

such that the UAV will continue its descent in a straight line, once it is within a set

distance from the approach point and is at the correct attitude, instead of using the

approach point as the final waypoint. This new waypoint is calculated as follows.

Considering Figure 3.13 by way of example, the final waypoint coordinates in the

2-D plane are

x′f = xf − |df sinψf − π| ,y′f = yf − |df cosψf − π| ,

�� 3.29

where ψf is the desired final heading as shown, and the distance df is calculated

from the triangular relationship between the altitude above mean sea level (MSL)

at the approach point, hf , and the desired flighpath angle γpf , at this point.

Thus

d =hf

tan γpf,

�� 3.30

67


giving the final waypoint as (x′f y

′f hAGL).

3.2.2.3 Replanning

A new descent path may need to be constructed should the path planner receive

information of a more feasible landing site from the decision maker, or when adverse

winds prevent the aircraft from reaching the first selected site. The path replanning

method utilised is specific to this research, where the unflown portion of the path is

simply discarded and a new path formed from the current aircraft position to the

new approach point, using the methods described above. This new path may also

be attached to the breaking point where the unflown portion is removed from the

old path. Figure 3.14 illustrates an example of replanning, where the original path

(blue line) is calculated to take the UAV from an altitude of z0 at Point A to an

altitude of zf at Point B, and at the initial and final headings indicated by the blue

arrows. However, while en route to Point B, a decision (simulated to come from

the MDMS) is made to take the aircraft to a second landing site. Thus, a new path

is formed that joins the original path at Point C to the aimpoint at D, and at the

initial and final headings indicated by the red arrows. The unused portion of path

from C to B is then simply discarded.

Figure 3.14: Forced landing flight path example showing path replanning. Path 2 is thenew path that connects to the breaking point at Point C, where the unflown portion of theoriginal path (CB) is removed from Path 1.

68

3.3. SUMMARY

The method for replanning described above is deemed to be most suitable to a

time-critical scenario such as a UAV forced landing, in which the aircraft also pos-

sesses limited manoeuvring capabilities. Once the aircraft is below a predetermined

altitude zbound, the planner ignores any new site locations and the UAV simply fol-

lows the last updated path. This additional constraint is included for safety as well

as to increase the chances of the UAV actually being able to reach a predetermined

site. The value for zbound is calculated as

zbound = S0 + Sθmax + Sf ,�� 3.31

where S0 and Sf denote the changes in altitude associated with the initial and

final sections of helix, and Sθmax is the altitude change for the line segment at the

maximum allowable path angle (c.f. Section 3.2.2). Although this angle in theory

is zero degrees, in actual practice θmax is taken as θbg, that is, the path angle

corresponding to the best glide speed, Vbg.

3.3 Summary

This chapter has disclosed the design of two different classes of forced landing descent

planning algorithms. The first, based on piloted forced landing procedures, allows

the aircraft to navigate to the desired landing site by following an adjusted landing

pattern. Two different algorithms in this class were discussed, and it has been

shown that the second is more flexible in that it does not rely on pre-stored paths,

but rather makes use of available wind information to predict the glide slope and

thus adjust the path accordingly. However, because both algorithms function by

adjusting the path to suit a constant glide speed, this could present a problem in

changing winds, as well as lead to instability if the path is continuously adjusted, as

in the case of Algorithm 2.

The second class of algorithms, which extends the concepts of 2-D Dubins curves

to three dimensions, allows for the construction of an overall smoother path that

incorporates the aircraft dynamics. These algorithms are collectively named the 3-D

Dubins Curves, and differs from the work of Ambrosino et al. (2006) in the following

respects:

• The selection of the airspeed and bank angles to form the path;

• The test for path traversability;

• The use of suboptimal (longer) paths, enlarging the initial and final radii and

using helix spirals to lose altitude;

• The specific methods used to extend the path from 2-D to 3-D;

• The use of connecting contours to reduce altitude offsets;

69


• The use of an additional waypoint to stabilise the UAV once it has passed the

approach point; and,

• The inclusion of a replanning capacity in the algorithm design.

Further, as will be shown in Section 4.2, this planning algorithm allows the

guidance controller to adjust the airspeed of the aircraft to effectively deal with

winds as well as to reduce any path deviation incurred.

70

4Guidance and Control for a Fixed-Wing UAV

IN designing the guidance and control algorithms, a path following, rather than

a traditional trajectory tracking approach has been taken, where the objective is

to be on the path rather than at a certain point at a particular time. This removes

the time-dependency of the problem and allows the design of simpler controllers.

For the sake of convenience, the terms “path following” and “tracking” are used

interchangeably in this thesis, however, the reader should be aware of their intended

meaning as described above.

First, guidance and control techniques adapted from manned aircraft procedures

will be discussed. These algorithms are tested using the Aerosonde UAV model, for

the same reasons as that given in the previous chapter, but are also applicable to

other aircraft types. Following this, two new 3-D nonlinear guidance and control

algorithms will be presented. These algorithms draw partly from a family of guidance

algorithms that employ a look-ahead distance and moving waypoint, as discussed

in Section 2. Both algorithms share the same lateral control strategy, but employ

different techniques for control of the aircraft in the longitudinal plane. Since these

algorithms are designed to function independently of human input, they are deemed

to be more accurate than techniques adapted from manned aircraft navigational

procedures as they dispense with many of the assumptions and approximations

associated with the latter. These algorithms are tested with the Boomerang UAV

model and are also independent of aircraft type.

4.1 Great-Circle Navigation, Guidance and Control

Following the formation of a descent flight path using elements of piloted forced

landing procedures, as described in Sections 3.1.1 and 3.1.2, the associated naviga-

tional algorithm calculates the range and bearing to each successive waypoint, and

uses the wind correction algorithm as well as the waypoint following algorithm to

generate correction commands while en route. The flight controller then functions

71

CHAPTER 4. Guidance and Control for a Fixed-Wing UAV

to provide lateral and longitudinal stability as the aircraft is following the prescribed

path.

4.1.1 Waypoint Navigation

Although flat-earth approximations are sufficient to describe the distances covered

in a typical UAV forced landing, with a range error of 6.67 x 104 m at a range of

D = 1.85 x 106 m, an azimuth BT = 45◦ and a latitude of Φ =45◦ (Kayton &

Fried, 1997), these approximations were not used as a basic navigational algorithm

using the great-circle navigation method (Kayton & Fried, 1997) had already been

designed by Bruggemann, Greer, and Walker (2005) of ARCAA, and it was decided

to expand on their algorithm to reduce the engineering development time. Using

this method, the great-circle track, which is the shortest distance between two points

located on a sphere surrounding the earth, as well as the bearing between the two

points can be calculated. Hence, a flight path consisting of a sequence of waypoints

is traversed by flying a series of direct, curved paths to each successive point. From

spherical trigonometry, the range D and bearing BT to the target are given by

(Kayton & Fried, 1997):

D = RGcos−1(sin(Φ)sin(Φt) + cos(Φ)cos(Φt)cos(λ− λt)),

�� 4.1a

BT = sin−1

(cos(Φt)

sin( DRG

)sin(λ− λt)

),

�� 4.1b

where RG is the Gaussian radius of curvature at the current aircraft position,

given by

RG =√RM ×Rp.

�� 4.2

RM and RP are the meridian and prime radii at the current aircraft location.

The current aircraft latitude and longitude as measured by the onboard GPS are

given by Φ and λ and the target latitude and longitude are given by Φt and λt.

This implies that the calculated range to the target is actually the “distance-to-go”

to the target, since the aircraft position is constantly changing. This characteristic

of Eq. 4.1a is particularly important when designing a tracking algorithm that will

constantly adjust for the aircraft position (see Section 3.7). The UAV heading

command is calculated using the following equation

ψCmd = ψT − θWc −BT + kθTE ,�� 4.3

where ψT is the aircraft’s true heading, θWc is the wind correction angle, BT is

72

4.1. GREAT-CIRCLE NAVIGATION, GUIDANCE AND CONTROL

the true bearing to the target waypoint and θTE is the angle of track error, multiplied

by a constant, k. The value of k is determined empirically, such that the cross-track

error is minimised. Both waypoint navigation and path planning (see Section 3.1)

are handled by a flight planner in the simulation environment discussed in Chapter 5.

4.1.2 Wind Correction

While en route between waypoints, it is also necessary to correct for wind to remain

on course. To achieve this, principles of the wind triangle (Robson et al., 2002) are

used to calculate the wind correction angle, which is then compared with the current

aircraft heading and passed as an input to the flight planner. The wind triangle is an

analytical tool, commonly applied by GA pilots to compute the desired track to fly

in the presence of winds. From Figure 4.1, suppose that the intended path to track

is from Points A to C, and the UAV has a constant airspeed of 37 kts. However,

there is a wind blowing from the south-east with a velocity of 340◦/9.7kts, which

will cause the UAV to drift to the left if left uncorrected.

Figure 4.1: Wind triangle

The drift angle can be calculated using the law of sines as

a

sin(θWc)=

b

sin(B)⇒ θWc = sin−1

(9.7sin(100)

37

)≈ 14.96◦.

�� 4.4

This implies that the wind correction angle supplied to the flight planner must

be 15◦ in the opposite direction, such that the “track made good” will converge on

the required track to target. This is achieved by the aircraft flying first towards

Point B, located north-east at a heading of 045◦ true from Point A, before being

blown back on course by the wind. To simplify calculations, the effect of sideslips

73


due to wind has not been considered, as it is assumed that all turns made by the

aircraft are coordinated, and that the flight controller is able to effectively negate

any such sideslips.

4.1.3 Waypoint Tracking

Another function of a flight planner is to provide tracking for the required flight

path. Suppose that the flight path of the UAV as it is flying from waypoints A to B

is given by the solid, black line in Figure 4.2, and the required track to fly is given

by the dashed, red line. At point B’ the aircraft is en route to waypoint B and has

a cross track error of XTE m. The tracking algorithm calculates the angle of track

error, θTE and multiplies it by a constant, k. The value of k is chosen such that

the commanded heading, ψCmd will cause the UAV flight path to converge on the

required track to fly, meaning that XTE will be minimised. The cross-track error is

given by

XTE = DTRsin(θTE)�� 4.5

where DTR is the track distance and the distance-to-go to the next waypoint.

Figure 4.2: Flight path tracking

Note here that longitudinal tracking has not been implemented — instead, it is

assumed that the aircraft flying at a constant airspeed (Vbg) is able to follow the path

that has been designed for this airspeed, and that the path can change to account

for any adverse wind effects (see Sections 3.1.1 and 3.1.2).

4.1.4 Flight Control

Flight control for the aircraft is achieved using a combination of proportional-integral

(PI) and proportional-integral-derivative (PID) controllers. Firstly, the calculated

desired heading to waypoint (see Section 4.1.1) is converted to roll and yaw values

using a combination of limiters and PI gains, the idea being to intuitively model the

flight yoke and rudder pedal movements applied by pilots as they try to steer the

aircraft towards a given heading with zero sideslip. This is known as a coordinated

74

4.1. GREAT-CIRCLE NAVIGATION, GUIDANCE AND CONTROL

turn and is especially important when winds are present. A conceptual diagram of

the simple lateral controller described above is shown in Figure 4.3.

Figure 4.3: Simple lateral controller for the Aerosonde UAV

Longitudinal control is achieved by feeding the desired airspeed into a PID con-

troller that controls the elevator servos. For the simulations, the aircraft is con-

strained to glide with an airspeed of 19 m/s, which is the airspeed to achieve for

the longest glide distance, and the path is planned in a way such that by judiciously

following a sequence of waypoints in the path, the aircraft can lose the required

amount of altitude. The longitudinal controller is depicted in Figure 4.4.

Figure 4.4: Simple longitudinal controller for the Aerosonde UAV

Once the lateral and longitudinal controllers have been designed, they are tuned

using a combination of trial-and-error and the Ziegler-Nichols tuning method out-

lined in (R. C. Nelson, 1998) to achieve the desired closed loop response. Figure 4.5

shows the lateral controller performance for a typical forced landing descent using

the planning algorithms described in Section 3.1, while Figure 4.6 shows the airspeed

controller response for the same path flown. From the first diagram, it is evident

that the aircraft actual roll angle, φ tracks the commanded roll, φcmd well, with

very small sideslips (β ≤ 5◦). It can also be seen that as the roll angle is changing,

the aircraft yaw angle, ψ (commanded by the rudder) also changes synchronously to

provide a coordinated response. In addition, the second diagram shows that the air-

speed controller is able to maintain the desired glide speed of 19 m/s with minimal

deviations throughout the descent.

75


Figure 4.5: Lateral controller response for the Aerosonde UAV, showing good tracking ofthe commanded roll angle, φcmd. The yaw angle, ψ changes synchronously with the rollangle, φ to provide a coordinated response with a minimal side slip, β. Both the aileronsand rudder are working synchronously to provide a coordinated turn.

Although the controllers presented above are simple and enable the aircraft to

follow the path, a better design utilising more conventional methods is detailed in

Section 4.2.5, and, together with improved lateral and longitudinal guidance algo-

rithms, may provide for a more robust controller with better performance. Note

however that in both cases, no attempt has been made to model the complex PID

controllers in the autopilot hardware installed on the aircraft, as the simulated con-

trollers are deemed adequate to provide a good understanding of how the path

planning and guidance algorithms (the main contributions of this research) will per-

form.

4.2 3-D Nonlinear Guidance and Control

The 3-D nonlinear guidance algorithms are designed to control the aircraft in both

the lateral and longitudinal planes of motion. These algorithms are employed by the

Boomerang aircraft model, in particular the wind correction, path planning, guid-

ance and flight control modules depicted in Figure 5.6, and are also the algorithms

implemented for flight tests.

The lateral guidance approach is based on the work presented by Park et al.

(2007). However, this algorithm has been enhanced to include wind information

in the guidance logic, rather than merely treating wind as an adaptive element for

the control system. This addition has demonstrated robust, linear path following in

strong winds. Secondly, by making a simple assumption in formulating the circular

path following equation, the guidance logic has been simplified without sacrificing

76

4.2. 3-D NONLINEAR GUIDANCE AND CONTROL

Figure 4.6: Airspeed controller for the Aerosonde UAV, showing the desired Vbg of 19 m/sis able to be maintained throughout the forced landing descent.

performance. In addition, a longitudinal guidance and control element has been

implemented that caters for the dynamics of powerless flight. Two novel approaches

have been trialled in this regard, and it is revealed that the second approach out-

performs the first due to its robustness. Finally, following well-established aircraft

control design procedures (R. C. Nelson, 1998), the design has been separated into

two modes: an inner control loop that provides aircraft dynamic stability, and an

outer guidance loop that generates the required acceleration and position commands

to follow a path. The following sections will discuss the new lateral guidance algo-

rithm used, named the Enhanced Nonlinear Guidance (ENG) algorithm, as well

as the two, new longitudinal guidance algorithms, named the Flight Path Following

Guidance (FPFG) and Modified Proportional Navigation (MPN) algorithms respec-

tively. In addition, the inner loop controls will also be disclosed in more detail.

4.2.1 The Enhanced Nonlinear Guidance (ENG) Algorithm

For lateral guidance, a reference point Pref is selected on the desired trajectory and

used to generate an acceleration command. As shown in Figure 4.7, Pref is located

a distance L1 ahead of the vehicle and, at each point in time, a circular path (dotted

line) can be defined by the position of L1, the vehicle position, and tangential to V ,

the aircraft velocity vector.

The acceleration required to follow the instantaneous circular segment, for any

radius R, is then given by

ascmd =V 2

R= 2

V 2

L1sinη.

�� 4.6

Thus, the guidance law will tend to rotate the aircraft so that its velocity direc-

77


Figure 4.7: Diagram showing the lateral guidance law

tion will always approach the desired path at an angle that is proportional to the

relative distance between vehicle and path.

4.2.1.1 Line Following

For following a straight line, the vehicle kinematics can be modelled as shown in

Figure 4.8. Now, consider the UAV in a straight glide with velocity, V, at an

arbitrary position relative to the path between waypoints P1 and P3, and at a heading

ψ (Figure 4.8a). The expected/average wind velocity, W is also shown. Given

the aircraft and wind velocities and positions in the {north, east} reference frame,

and the angular measurements defined in Figure 4.8b, the position and velocity

components in the {xtrack, ytrack} reference frame can be obtained by:

Vtrack = TψV,�� 4.7a

Wtrack = TψW,�� 4.7b

with the rotation matrix equal to

Tψ =

[cos(ψ12 − π/2) − sin(ψ12 − π/2)

sin(ψ12 − π/2) cos(ψ12 − π/2)

].

�� 4.8

The cross-track velocity can then be written as

ytrack = Vytrack +Wytrack = −V sin(ψ(t)− ψ12)−W sin(ψw − ψ12),�� 4.9

78


Figure 4.8: Vehicle kinematics for straight line following, showing (a) the relationship be-tween the aircraft velocity V and the expected/average wind velocity W , and (b) the rela-tionship between the aircraft bearing ψ(t), the path bearing ψ12 , the wind bearing ψw , andthe angle η. In addition, the relationship between the cross-track error d, the hypotenused1 and the look-ahead distance L1 is also shown.

and assuming η is small,

sin η ≈ η1 + η2,�� 4.10

and

η1 ≈d

L1, η2 ≈

d

V,

�� 4.11

where ytrack has been relabeled as d, and d is the cross-track error. This error is

obtained by letting

d1 = nac − tan(γ)eac,�� 4.12

where nac and eac are the current aircraft north and east coordinates, and

d = d1 cos γ.�� 4.13

Finally, combining Eqs. 4.6 to 4.11, the acceleration is given by

ascmd = 2V

L1

(d+

V

L1d

).

�� 4.14

Here, the LOS distance L1 is treated as a gain, with smaller values enabling

tighter path following and sharper bank angles. However, too small a value for L1

79


would result in too high a control gain and instability. Thus, the value of L1 is

chosen based on the observed closed loop response of the bank angle.

4.2.1.2 Arc Following

For following an arc of circumference, the vehicle kinematics can be modelled as

shown in Figure 4.9.

Figure 4.9: Vehicle kinematics for circular path following

Here, the angles η1 and η2 are assumed to be small, but η3 is not necessarily

small. This gives

η1 ≈ 0, η2 ≈ 0, |η3| � 0.�� 4.15

As shown by Park et al. (2007), using Eqs. 4.6 and 4.15, sin η3 can be estimated

as

sin η3 ≈L1

2R,

�� 4.16

and c defined as

c ≡ cosn3 ≈

√1−

(L1

2R

)2

.�� 4.17

Then, using small angle assumptions for η1 and η2, the commanded acceleration

can be approximated as

ascmd =2V 2

L1sin {η1 + η2 + η3} ,

�� 4.18

80


ascmd =2V 2

L1{sin(η1 + η2) cos η3 + cos(η1 + η2) sin η3} ,

�� 4.19

ascmd ≈2V 2

L1{η1 cos η3 + η2 cos η3 + sin η3} ,

�� 4.20

with

η1 ≈d

L1cos η3, d = V sin η2 ≈ η2.

�� 4.21

Next, applying Eqs. 4.16 and 4.17, Eq. 4.20 becomes

2V 2

L1sin η =

2V 2c2

L12 d+

2V c

L1d+

V 2

R.

�� 4.22

Now, assuming that a good yaw damper can be designed to damp the aircraft

Dutch roll motion and reduce the sideslip to zero (see Section 4.2.5), the second

term on the R.H.S of Eq. 4.22 can then be neglected to obtain

ascmd =2V 2

L1sin η =

2V 2c2

L12 d+

V 2

R.

�� 4.23

This simplifies the equation and yet, as the simulation results will show, does not

sacrifice the performance of the algorithm (see Section 7.1.2). Notice also that here

additional terms have not been included in the equation for wind effects, as has been

done with the case of following a straight line. The reason is that in this case the

vehicle ground speed (as a surrogate for inertial velocity) is used for V in Eq. 4.20

at each instant in generating the acceleration command. Since the groundspeed is a

function of the airspeed and wind speed, the guidance logic accounts for the inertial

velocity changes due to wind and adapts to the situation accordingly.

Once the lateral acceleration is found, it must be converted into a desired roll an-

gle command such that the aircraft can follow the prescribed path. This conversion

is described in the following section.

4.2.1.3 Calculating Roll Angle from Acceleration

To convert the acceleration to a desired roll angle and simplify calculations, it has

been assumed in this research that the aircraft maintains sufficient lift to balance

weight (see Figure 4.10), even though banked at an angle φ. This gives

L cosφ = W = mg, L sinφ = mas,�� 4.24

and

81


φd = tan−1(asg

).

�� 4.25

Figure 4.10: Vehicle kinematics showing how roll angle is derived from acceleration

In reality, a gliding aircraft will never overcome gravity, but will descend with a

vertical velocity h; this is an inherent limitation in the forced landing problem.

4.2.1.4 Determining the Correct Turning Direction

In Sections 4.2.1 to 4.2.1.2, new techniques developed in this research to enhance

Park’s lateral guidance algorithm were described. This section and all subsequent

sections up to Section 4.2.5 present original work developed in this research for

aircraft guidance.

Firstly, once an expression for the roll angle as a function of the acceleration

is obtained, a novel method is developed that inspects the Euclidean geometry of

the aircraft in relation to the path in order to supply the correct turning directions.

Considering the example shown in Figure 4.11, in following an arc of circumfer-

ence, suppose the UAV is located at Point A. Then, if the arc to track has centre

coordinates (cenxi1 , cenyi1 ), with cenxi1 > xac and cenyi1 = yac, and the aircraft

heading ψac is in the range 0 ≤ ψac ≤ π/2, then the commanded bank angle must

be tan−1(as/g), indicating a right hand turn.

If the aircraft were pointed in the opposite direction however, then the bank

command must be − tan−1(as/g), corresponding to a left hand turn. The same

deduction can be applied to the UAV at Point B to obtain a right turn command,

with cenyi1 now below the aircraft, and a left turn command, should cenyi1 > yac.

At Point C, π/2 ≤ ψ ≤ π, and since cenxi2 < xac and cenyi2 > yac, the commanded

bank must be a right hand turn. Although not shown, a similar analysis to that

described above can also be applied to the case of the aircraft following a line, with

care given to which direction the line is pointing. Algorithm 4.1 outlines the process

82


Figure 4.11: Geometric relationship between aircraft and path

to follow in order for the guidance system to supply the correct turning direction

for a specific Dubins path.

4.2.2 The Flight Path Following Guidance (FPFG) Algorithm

In this algorithm, the desired and actual aircraft flight path angles are converted

into their equivalent pitch angles and passed through a PID loop to reduce the

angular difference, this signal is then used to control the elevators for longitudinal

path following. The pitch angle θ is simply the sum of the flight path angle γ and

the aircraft AOA, denoted as α, giving

θ = γ + α,�� 4.26

where γ is composed of γφ0,f , the path angles corresponding to the sections of

helices in the 3-D path, and γline, the path angle of the line segment (see Section 3.2).

To cater for the effects of wind while gliding, the well-known MacCready theory

(discussed by Brandon (n.d.)) is used to determine the optimal speed-to-fly. This

optimal speed is obtained from a speed polar diagram (Figure 4.12), which shows

the relationship between the rate of sink and airspeed while gliding. To counter a

headwind, the glide speed must be increased above Vbg, this increases the ground

speed and allows the aircraft to penetrate further through the air. By the same

token, the glide speed must be reduced below Vbg when flying downwind or the

aircraft will tend to overshoot the target waypoint. In a tailwind, the starting point

on the horizontal axis (airspeed) is shifted left by a distance equal to the magnitude

of the wind speed, and a line is drawn from this point tangential to the curve to

obtain the desired glide speed. For a headwind the starting point is shifted to the

83


Algorithm 4.1: Determining the Correct Turning Direction

input : ψi,f , xaci,f , yaci,f , cenxi,f , cenyi,foutput: The correct aircraft turning direction

1 begin

2 determine aircraft heading vectors, ψaci,f ;

3 for initial arc do4 if cenyi > yaci or cenyi < yaci then

5 if cenxi > xaci and ψaci points in direction of cenx,yi then6 bank in same direction;7 else8 bank in opposite direction;

9 if cenxi < xaci and ψaci points in direction of cenx,yi then10 bank in same direction;11 else12 bank in opposite direction;

13 if cenxi = xaci then14 check goal location (xacf ) and bank either left or right;

15 else

16 check direction of ψaci and goal location (xacf );

17 bank either left or right;

18 Repeat procedure for final arc;19 return corrected roll command;

20 end

right, for sinking air it is shifted upwards on the vertical axis, and for rising air it is

shifted downwards. Using the speed polar, one can also determine the speed-to-fly

in different combinations of vertical and horizontal winds when both exist. Finally,

to convert the speed-to-fly into the desired path angle, one simply takes the inverse

tangent of the slope corresponding to the tangent line.

Although this method performs well, it nonetheless requires tuning multiple sets

of aircraft type-specific PID gain schedules to cater for a range of possible wind

conditions, and hence is not robust enough for real applications. In light of this, a

search for an alternative was commenced and the result is disclosed below. The new

vertical guidance algorithm is named the Modified Proportional Navigaion (MPN)

algorithm and is robust yet easy to implement in any aircraft type.

4.2.3 The Modified Proportional Navigation (MPN) Algorithm

Similar to the control logic for lateral guidance, the Modified Proportional Naviga-

tion (MPN) method makes use of a reference point Pref located a distance L1 ahead

84


Figure 4.12: Using the speed polar diagram to determine the required speed-to-fly whilegliding in winds (Source: Brandon, 2007)

of the vehicle on the vertical path to generate an acceleration command as (Fig-

ure 4.13). This acceleration then rotates the aircraft such that its velocity direction

intercepts the desired path at an angle that is proportional to the relative distance

between vehicle and path. Since the vertical cross-section of a path of arbitrary

construct will appear as a line in the y − z plane (Figure 4.13), the same guidance

algorithm can be used to track both curved and straight path segments.

Figure 4.13: Cross-sectional view of vehicle kinematics for vertical path tracking

From Figure 4.13 and 4.14, it can be seen that the angle δ between the reference

and ground speed vector Vg can be calculated as:

δ = tan−1

(Vd√

V 2e + V 2

n

),

�� 4.27

85


Figure 4.14: Components of vehicle kinematics for vertical path tracking

where Ve, Vn and Vd are the vector components of Vg in the local North-East-

Down (NED) reference frame.

The vertical cross-track error d can then be obtained by first expressing the

hypotenuse d1 as a function of the aircraft position vector components eac, nac, uac

in the local East-North-Up (ENU) frame and the path angle to track γtrack, giving

d1 = uac − tan(γtrack)x′ac + zintercept,

�� 4.28

where

x′ac =√e2ac + n2ac.

�� 4.29

The local ENU frame is chosen in this case as it is more intuitive and allows for

easier plotting of the aircraft flight path, and the intercept of the z-axis is approxi-

mated from triangulation as

86


zint =

ru02 − tan(γarc0)√

(re02 − re01 )2 + (rn02− rn01

)2

for the first arc,

z2 − tan(γline)√

(x2 − x1)2 + (y2 − y1)2

for the line,

ruf2 − tan(γarcf )√

(ref2 − ref1 )2 + (rnf2 − rnf1 )2

for the second arc,

�� 4.30

where the subscripts arc0 and arcf denote respectively the initial and final arcs

of the Dubins path, and re, rn and ru are the cartesian coordinates of the arcs.

For following full turns of a helix spiral however, x′ac and zintercept are calculated

differently. First, the spirals are divided into semicircles, where the arc length of one

semicircle is equal to half the length of the circumference. Then, if the aircraft is

traversing the region of arc, x′ac, in which the arc angle θarg is in the range 0 ≤ θ ≤ π,

then

x′ac = θargR0,�� 4.31a

zint = z0,�� 4.31b

where z0 is the altitude where the engine failure occurred. Otherwise, if the

aircraft is traversing the region of arc where θarg is in the range π ≤ θarg ≤ 2π,

x′ac = (2π − θarg)R0,�� 4.32a

zint = z0 − Sφ0,f ,�� 4.32b

where Sφ0,f is the altitude lost by the gliding aircraft through one full turn of a

helix spiral.

Next, the vertical cross-track error d is calculated by

d = d1 cos γtrack,�� 4.33

and the vertical cross-track velocity is expressed as a function of both the aircaft

velocity V and the estimated/average wind velocity Vw as

dtrack = −V sin ((ε+ α)− ψ12)− Vw sin (ψw − ψ12) ,�� 4.34

where ε is the difference between the aircraft pitch angle θ and the angle δ of

87


Eqn. 4.27 (see also Figure 4.13), α is the aircraft angle of attack (AOA), ψ12 is the

path angle measured from the vertical axis, and ψw is the angle of the wind vector

as shown in Figure 4.13. Note that when implementing the algorithm in software,

the ground speed Vg is used for V since it provides for greater control power when

following a path in the presence of wind.

Following the same reasoning as used in Eqns. 4.10 and 4.11, the angle between

the acceleration perpendicular to the line-of-sight (LOS), a⊥L1, and the nonlinear

acceleration as is calculated as

η =d

L1+d

V,

�� 4.35

and substituting Eqn. 4.35 into Eqn. 4.6 gives the nonlinear acceleration as

as = 2V

L1

(d+

V

L1d

).

�� 4.36

Next, the nonlinear acceleration is transformed to the acceleration perpendicular

to the LOS (renamed as nc) by using the angular relationship between them, giving

a⊥L1 = nc = as cos(η).�� 4.37

This transformation has been deemed necessary as it has been found, after ex-

tensive simulated experiments, that using the LOS acceleration in this way provides

for better performance than merely using the nonlinear acceleration. The use of the

LOS acceleration, as well as the LOS angle (discussed later) are concepts borrowed

from proportional navigation missile guidance (Zarchan, 2007). However, the MPN

algorithm differs from proportional navigation in that a moving reference point is

used, and the closing speed between the vehicle and reference point is always zero

(with L1 fixed).

Once the acceleration is obtained, it must be further transposed into its compo-

nent velocities in the y−z plane, and from there, a relationship found that correlates

velocity to pitch angle, since the latter is used to control the aircraft longitudinal

motion directly.

From Figure 4.13, and taking positive reference as towards north and east, it

can be seen that the component velocities are given by

VA1 = −∫nc sin θLOS + VA10

,�� 4.38a

VA2 = −∫nc cos θLOS − VA20

,�� 4.38b

88


where the LOS angle is calculated as

θLOS = sin−1(d

L1

)+ γtrack,

�� 4.39

and the initial conditions are obtained by assuming that once the engine fails,

the aircraft will still be sinking with gravity. Since this effect is encapsulated within

the aircraft ground speed components, the initial conditions can be expressed as

VA10=√V 2e + V 2

n ,�� 4.40a

VA20= Vd.

�� 4.40b

Finally, the resultant airspeed is easily obtained as

Vcmd =√V 2A1 + V 2

A2.�� 4.41

This airspeed is then transferred to a look-up table to obtain the corresponding

pitch control angle, with linear interpolation being used to obtain interval values,

and the initial and final entries taken as the upper and lower boundaries. The look-

up table for the Boomerang size-60 UAV is derived from simulation and is presented

below:

Airspeed (m/s) Pitch (degs)

16.89 -220.86 -624.45 -10

28 -14

Table 4.1: Look-up table relating commanded airspeed to desired pitch angle for BoomerangUAV

Once this relationship has been determined, the guidance system can be tuned

by adjusting L1 in accordance with the desired closed loop response of the pitch

angle.

4.2.4 Ensuring Smooth Transition between Waypoints

Following the formation of a path from the point of engine failure to the approach

point for landing, and the calculation of the required acceleration, roll and pitch

to follow the path, a method to determine whether the UAV has actually passed

the waypoints in the path is still required. In this regard, a waypoint is considered

captured if the UAV arrives within a 50 m (165 ft) radius of it. Although this

89


method functions well in general, there are times, such as when a strong headwind

is encountered, when the UAV cannot come within the circular zone centred on

the waypoint. To prevent the aircraft from spiralling around a waypoint in this

situation, a counter is started when a new waypoint is uploaded into the guidance

system. If the preset interval has expired before the aircraft arrives at the new

waypoint, the next waypoint is immediately loaded into the system and the former

waypoint discarded. This practice is continued until the final waypoint is reached.

Figure 4.15: Diagram showing the relative position between the aircraft and the start ofthe second arc in the Dubins path. The relative position is used for more accurate pathfollowing.

As an added measure to prevent the aircraft from turning too soon when en-

countering a strong headwind, an inspection of the relative position between the

aircraft and the start of the second arc (corresponding to the end of the line seg-

ment) in the Dubins path is also performed. Considering Figure 4.15, if the line

is in the first quadrant and pointing east at an angle, θ between 0◦ and 45◦, the

algorithm checks for the following condition to determine whether a line should still

be followed: xac < xarcf and∣∣xarcf ∣∣ > ∣∣yarcf ∣∣ and xarcf > 0. If however, the angle

is between 45◦ and 90◦, the following condition is compared against: yac < yarcfand

∣∣yarcf ∣∣ > ∣∣xarcf ∣∣ and yarcf > 0. A similar deduction can also be applied to line

segments residing in each of the four quadrants and pointing in any direction.

4.2.5 Control for Flight Stability

This section will discuss the low-level controllers for both the FPFG and MPN al-

gorithms, which have been developed based on well-established aerospace control

designs discussed in the literature (Etkin, 1972; Etkin & Reid, 1996; R. C. Nelson,

90


1998). Both algorithms share the same lateral controller, but employ different lon-

gitudinal controllers, and are necessary to support the operation of the guidance

algorithms developed in this research. The lateral controller is presented first.

4.2.5.1 Lateral Control

Initially, a full, lateral dynamics model of the aircraft defined in Appendix A is

constructed using modern control design techniques (R. C. Nelson, 1998; Etkin

& Reid, 1996) and state-space tools in MATLAB®. This model is then used to

determine the system transfer functions, as well as to analyse the roll performance

of the aircraft. The model is linearised for flight at Vbg = 19 m/s and at an initial

altitude of 1000 ft, and both roll and roll rate feedback are utilised for improved

damping of the short period responses. The root locus of the aileron-to-roll-angle

transfer function is given in Figure 4.16 and shows a very well-damped response.

Figure 4.16: Root locus plot of the Boomerang lateral control autopilot using just theailerons. The pole locations indicate a very well-damped response.

Next, a yaw damper is added to oppose any yaw rate build up during the aircraft

dutch roll mode, a type of aircraft motion consisting of out-of-phase “tail-wagging”

and rocking from side to side which can be excited by any use of aileron or rudder.

However, such a yaw damper will also oppose a constant yaw value that exists

during a coordinated steady-state turn, thus requiring larger than necessary rudder

control gains to overcome the actions of the damper. To address this problem, the

feedback signal is differentiated (approximately) so that it disappears during steady-

state conditions. This approximate differentiation is accomplished using a simple

first-order high-pass filter, called a “washout filter”.

Using a time constant τwo = 3.5 s, determined empirically through simulation,

91


the “washout filter” transfer function can be modelled as

Gwo(s) =τwos

τwos+ 1,

�� 4.42

and a plot of the filter transfer function is shown in Figure 4.17.

Figure 4.17: Transfer function of the washout filter for the Boomerang-60 UAV showing themagnitude response

Figure 4.18: Root locus plot of the Boomerang lateral control autopilot using both theailerons and rudder. The pole and zero locations indicate a very well-damped response.

The roll and yaw controllers are then combined, and the system is excited with

a constant bank command of 15 deg (0.26 rad). Figure 4.18 shows the root locus

of the system, and suggests once again a very well-damped response (all poles are

attracted to corresponding zeros and are in the left-half plane).

The damping ratio and natural frequency of the system are chosen to be ζ =

92


Figure 4.19: Aileron controller response of the Boomerang-60 UAV to a 15 deg roll command

Figure 4.20: Rudder controller response of the Boomerang-60 UAV to a 15 deg roll command,showing negligible sideslips

93


Figure 4.21: Simulated lateral controller for the Boomerang UAV, showing a two-stagecontrol process for the roll angle, and a yaw damper to correct for any undesirable aircraftyawing motion. The same controller is employed by both the FPFG and MPN algorithms.

0.706 and ωn = 41.4rad/s, corresponding to a set of accepted desired flying quali-

ties (R. C. Nelson, 1998) of manned aircraft (as well as unmanned aircraft for the

purposes of this research). The system response is plotted in Figure 4.19, and shows

that the roll angle response has a fast rise time but quickly settles to a steady state

value with no overshoot, while the roll rate rapidly subsides to zero. In addition,

from Figure 4.20, it can be seen that although the yaw rate response exhibits some

slight jittering at the start (perhaps due to the pair of complex poles in Figure 4.18),

it nonetheless quickly converges to a steady state value, and any sideslip incurred is

also negligible.

Based on the observed response of the lateral controllers, the computed gains are

then used to initialise the PID/PD controllers in the actual Simulink Boomerang

model. Following well-established aerospace design procedures (R. C. Nelson, 1998;

Etkin & Reid, 1996), the commanded roll angle is compared with the actual roll of

the aircraft in an outer loop. The error signal is then fed into a PID controller to

regulate the roll rate in an inner loop and to improve stability (see Figure 4.21). In

order to simplify the construction of the model, both the inner and outer loops have

been constrained to run at the same frequency. Control of the rudder is achieved

using a single PD controller, also running at the same frequency as the aileron

controllers.

It is inevitable that adjustments and/or additions would need to be made to

the initialisation gains due to model coupling and nonlinearities, and thus the final

94


gains are calculated using an adjusted Zeigler-Nichols tuning method (R. C. Nelson,

1998) and through repeated simulations, and are tuned from the inner to outer loop

controls. Figure 4.22 shows that during a simulated forced landing with several

manoeuvres, the actual roll, φ tracks the commanded roll, φcmd very well, and with

negligible sideslips.

Figure 4.22: Good tracking of commanded roll during a simulated forced landing, withnegligible sideslips

4.2.5.2 Longitudinal Control

Design of the longitudinal controllers begins in a similar way to that of the lat-

eral controller. However, to simplify calculations, an approximate model of the

short-period longitudinal dynamics of the aircraft (see Appendix A) is implemented

in MATLAB® and used to determine the closed-loop system performance. This

approximate model has been found to be adequate in designing the simulated lon-

gitudinal flight controllers for this research. Figure 4.23 shows the root locus of the

controller, and indicates a stable, well-damped response.

The elevator-to-pitch angle response for an input pitch command of -6 degrees

is shown in Figure 4.24. From this figure, it can be seen that the pitch angle

rapidly settles to a steady-state value with no overshoot, while the initial dip of the

pitch-rate response is quickly corrected for and the pitch-rate reduces to zero in the

steady-state.

From the observed closed-loop response, gains are then chosen to initialise the

PID controllers in the Simulink model. As before, the process is essentially one

of trial-and-error using an adjusted Zeigler-Nichols method (R. C. Nelson, 1998).

Observing Figures 4.25 and 4.26, it can be seen that although the pitch and pitch-rate

95


Figure 4.23: Root locus plot of the Boomerang longitudinal control autopilot using elevatorsto control pitch. The pole and zero locations indicate a very well-damped response.

Figure 4.24: Elevator controller response of the Boomerang-60 UAV to a -6 deg pitch com-mand.

96


PID controllers form the basic control structure for the FPFG and MPN algorithms,

the actual method to derive the reference signal is different.

Figure 4.25: Longitudinal controller for the FPFG algorithm - the reference signal is selectedfrom either θde or θdewind

and passed to a lower-level pitch-to-elevator controller.

Firstly, for the FPFG algorithm (Figure 4.25), a desired pitch angle, θde is calcu-

lated from the desired path angle, γde and angle-of-attack, α. When wind is present,

this desired pitch angle is then compared with a pitch angle, θdewind derived from the

speed polar diagram (Figure 4.12) before being multiplied by a gain, kp and used as

input to the lower-level pitch controller. However, this method is really only useful

when the aircraft is following a linear path, since the speed polar was designed for

straight gliding flight. Hence, a switching signal, scont is used to select when the

pitch angle corresponding to the path angle of an arc, θarci,f should be applied. This

switching method has been observed through simulation to function well in winds.

For the MPN algorithm, the commanded LOS acceleration, ascmd is first inte-

grated to obtain the velocity before being passed into a velocity-to-pitch lookup ta-

ble. The initial conditions supplied to the controller are those defined in Eqns. 4.40a

and 4.40b, and the resultant reference pitch angle, θref is then passed to the lower-

level pitch controller (Figure 4.26).

Figure 4.26: Longitudinal controller for the MPN algorithm - the reference signal is chosenfrom a velocity-to-pitch angle lookup table before being passed to a lower-level pitch-to-elevator controller.

Figure 4.27 shows that during a simulated forced landing with constant manoeu-

97


Figure 4.27: Good tracking of commanded pitch during a simulated forced landing withconstant manoeuvring

vring, the actual aircraft pitch, θ follows the commanded pitch, θcmd very well. This

response is characteristic of the result obtained when using either the FPFG or MPN

algorithm.

4.3 Summary

This chapter has investigated two guidance and control strategies to be tested in

this research. The first is derived from manned aircraft navigational procedures,

and is comprised of waypoint navigation using the great-circle navigation method,

with wind correction and waypoint tracking also incorporated into the guidance

procedure. Although this strategy is simple to implement, it nevertheless could

pose problems with accuracy due to its assumptions regarding sideslips and the

fact that no dedicated longitudinal path following strategy has been employed. In

addition, using merely an intuitive method to control the roll and yaw, as well as

a fixed airspeed to control the altitude may be insufficient to correct for cross-track

errors, particularly in strong or changing winds.

The 3-D nonlinear designs have attempted to address these problems, and in

so doing help provide for a more accurate and robust guidance and control sys-

tem. In the case of the ENG algorithm, wind information has been included in

the guidance logic, and a yaw damper with a washout filter has also been used to

deal with sideslips. These are the main differences between the ENG and Park’s

original algorithm. As will be seen in the results, these modifications have reduced

the complexity of the algorithm for following circular paths, yet without sacrificing

98

4.3. SUMMARY

performance. In addition, these modifications have also resulted in improved path

following in winds, by allowing the airspeed to vary as a function of the required

rolling action for path tracking. Further, the design of the ENG algorithm has

also led to the development of a new method for determining the correct turning

direction.

In the case of the FPFG algorithm, a novel method of using the path angle

and the MacCready theory has allowed the creation of a very accurate vertical path

following algorithm (see the results under Section 7.1.2.1), which also uses varying

airspeeds to deal with winds and cross-track errors. However, the main disadvantage

of this algorithm is that it relies on tuning multiple gain schedules to account for a

variety of wind scenarios, and so is not conducive to flight operations.

A better alternative exists in the form of the MPN algorithm, which draws on

the basic principles underlying the ENG and proportional navigation algorithms, as

well as its own specific methods in the actual algorithm construct, to form a robust

vertical guidance algorithm that controls the airspeed by virtue of the pitch angle.

This algorithm is also easily adaptable to any aircraft type.

As part of the nonlinear design, a new method for ensuring smooth transitions

between waypoints has also been presented, which ensures that the aircraft is still

able to follow the path to completion in strong winds, as well as remain stabilised

throughout the process.

Finally, the lateral and longitudinal control modes are decoupled, meaning that

more control authority is allocated to each plane of motion. From an intuitive view-

point, it can be seen that the nonlinear design may well outperform that based on

manned aircraft procedures, however, this will need to be verified first in simulation,

and later through flight trials.

99

5The Forced Landing Simulation Environment

IN order to reduce the costs and risks associated with performing real experiments

in the developmental stages, as well as to enable a faster turnaround time in

verifying the software design, two different, albeit similar simulation environments

were developed in the MATLAB® Simulink programming environment prior to

actual flight tests. In particular, the AeroSim blockset, a third-party developed

add-on software, was used to rapidly construct nonlinear 6 degree-of-freedom (6

DOF) aircraft models. The equations of motion that dictate the performance of

the aircraft were implemented in body-axes and the model parameters, such as the

initial position and bearing were read from a user-configurable MATLAB® data

file (mat-file). The models also output the aircraft state information, such as the

aircraft velocities and angular velocities in three axes, which could then be used

as feedback to control the aircraft. The AeroSim software is also used to transfer

aircraft performance data to the open-sourced FlightGear flight simulator for real-

time visualization.

5.1 Aerosonde UAV Model

For the initial simulation experiments, a basic model of an unpowered Aerosonde

UAV (available in AeroSim) is modified and expanded to include subsystems for

flight controls, path planning, GPS waypoint navigation, wind generation, wind

correction and interfacing to FlightGear. By running MATLAB® and FlightGear

concurrently, the user is able to visualize the UAV flying in a manner as dictated by

the Simulink model (Figure 5.1). Noise and sensor errors have not introduced in this

model to reduce complexity, and a simplified diagram of the Simulink model is shown

in Figure 5.2. A detailed diagram of this model is reproduced in Appendix B.1.

In this simulation, the operating environment for the UAV is defined as a (3000

m x 3000 m x 3900 ft) volume of air space. The UAV can assume any initial bearing

and position (latitude, longitude and altitude) that lie within this area. The initial

101

CHAPTER 5. The Forced Landing Simulation Environment

Figure 5.1: Screen capture of a simulated forced landing in FlightGear, showing the plannedpath (orange), the incident wind vector and the desired landing site. The generic Cessnaskin with an actual model of an Aerosonde aircraft is used. The model is constructed usingthe classic coefficient build-up method (Nelson, 1998) and is available inside the MATLAB®

AeroSim blockset.

altitude of the UAV above ground level (AGL) is constrained between 1000 ft to

3900 ft, with the lower bound being the minimum altitude that an aircraft can

assume while flying en route over populated areas, as defined by the Civil Aviation

Safety Authority in Australia (CASA). The boundaries of the earths surface are

given by four coordinates that lie between 27◦23.4′S to 27◦25.8′S and 153◦6′E to

153◦7.8′E, with an altitude of 13 ft above mean sea level (MSL). These boundaries

define an area of approximately (3000 m x 3000 m) around the location of Brisbane

International Airport, given by the landing site aim point coordinates as 27◦24.6′S,

153◦7.2′E. The landing site is also assumed to be a (100 m x 600 m) rectangle. A

diagram illustrating the world model used in the simulation is given in Figure 5.3.

The wind model (Figure 5.2) randomly generates the input wind velocity com-

ponents in the navigation frame: WN , WE and WD, giving the profiles shown in

Figure 5.4. These wind components are subsequently used by the Aerosonde model

(Figure 5.2) to calculate the effects of the resultant wind velocities incident on the

aircraft, including wind shear and turbulence. Wind gusts have not been modelled

in this simulation, instead, the input wind is assumed to blow with a constant mag-

nitude and direction for 60 seconds, before changing magnitude and direction for

the next 60 seconds. Whilst this does not necessarily represent the wind conditions

found in an actual descent, it does present a challenging wind shift scenario for the

simulation. The values of the WN , WE and WD components are limited between ±7,

±4 and ±1 m/s respectively, with the coordinate system defined such that positive

is towards north and east. These values are chosen based on the actual wind rose

measurements for Brisbane, Australia, and correspond to a maximum wind speed

102

5.1. AEROSONDE UAV MODEL

Figure 5.2: Simplified Simulink model of Aerosonde UAV

Figure 5.3: Model of simulation world

of approximately 30 m/s. A wind rose is a diagram that summarises the occurrence

of winds at a location, showing their strength, direction and frequency. The wind

rose used in the simulation represented wind measurements taken at 9 a.m. daily,

from 1950 to 2000. More information on wind roses can be found on the Australian

Government Bureau of Meteorology website: www.bom.gov.au.

The wind correction, flight planner and flight controls blocks comprise the guid-

ance and control strategies of this model. These modules accept stimuli from the

aforementioned subsystems and respond by providing the aircraft with the required

roll and pitch commands so that it can follow a path to land within the designated

area. In particular, these modules utilize a modified version of the piloted forced

103

www.bom.gov.au


Figure 5.4: Wind components (WN : Blue, WE : Green, WD: Red). These components wereused to compute the resultant wind vector incident on the UAV.

landing procedure (refer back to Sections 3.1 and 4.1) and help to establish a baseline

from which further improvements to the forced landing path planning and guidance

algorithms can be effected.

5.2 Boomerang UAV model

Once enough experienced had been gained in using the Aerosonde model, a more

accurate model that resembled the platform to be used for flight testing was con-

structed. Similar to its predecessor, the Boomerang model is constructed using

the classic coefficient build-up method (R. C. Nelson, 1998), which was developed

as part of an undergraduate project at the Queensland University of Technology

(QUT). However, the major differences are that this model also includes noise and

sensor errors, as well as the modelling of wind gusts, turbulence and wind shears.

Taking the worst case scenario, the true airspeed, VTAS is assumed to have a

maximum error of 3 m/s, and the GPS velocity a maximum error of 1 m/s in mag-

nitude (groundspeed), and a maximum error of 1◦ in bearing. The magnetic compass

measurement was also assumed to have a maximum error of 3◦ in bearing. These

error values are consistent with instrument errors observed on small aircraft (Kayton

& Fried, 1997), and give rise to a maximum error of 1 m/s in the estimated north

and east wind component values which can be modelled as a Gaussian distribution

(Etkin, 1972).

Now, since the wind vector can be calculated as

Vw = Vg −VTAS ,�� 5.1

and including the errors in the equation

[Vwx(±1)

Vwy(±1)

]=

[Vgx(±.25)

Vgy(±.25)

]−

[Vax(±.75)

Vay(±.75)

]=

[Vgx − Vax(±1)

Vgy − Vay(±1

],

�� 5.2

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5.2. BOOMERANG UAV MODEL

where Vgx,y , Vax,y , and Vwx,y correspond to the velocity vectors of the ground-

speed, true airspeed and windspeed respectively. Then, the wind bearing can be

obtained as

∠Vw = tan−1

[Vgy − Vay(±1)

Vgx − Vax(±1

].

�� 5.3

With these stated errors, a wind bearing error of up to 42◦ has been observed in

simulations.

To model wind gusts and turbulence, the wind model is first set up as described

in Section 5.1, however, the duration of the wind changes has been reduced to 20

seconds to provide an even more challenging wind shift scenario. The input wind

velocities are then passed through a von Karman turbulence model in Simulink,

giving gust profiles as shown in Figure 5.5. In addition, as the aircraft navigates a

descent path through the air, it is subject to variations of wind speed and direction

(from the wind model) with changing altitude as well as horizontal distance. Hence,

both vertical and horizontal wind shears are also experienced by the aircraft during

a simulated forced landing.

Figure 5.5: An example of simulated wind turbulence experienced by the aircraft during aforced landing, with gusting applied in the longitudinal, lateral and vertical directions.

Finally, the Boomerang UAV model also includes subsystems for path planning,

aircraft guidance as well as flight control. These algorithms use the 3-D Dubins

curves and the nonlinear guidance laws to achieve better path formation and track-

ing in the presence of winds (see Sections 3.2 and 4.2). A simplified diagram of

the Simulink model is shown in Figure 5.6, and the complete model is depicted in

Appendix B.2.

105


Figure 5.6: Simplified Simulink model of Boomerang UAV

5.3 Summary

The design of two different, albeit similar forced landing simulation environments

have been presented in this Chapter. The inbuilt MATLAB® Aerosonde model

enables a rapid initial assessment of the path planning, guidance and control designs

that have been added to the model, as well as provides a baseline from which to

further improve the design. The Boomerang model builds upon the lessons learnt

from the first design to also include sensor errors and wind turbulence, which more

closely resemble a real forced landing scenario. Simulation results from both models

are included in Chapter 7.

106

6Flight Experiment Setup

FOLLOWING the design and simulated flight testing of the path planning and

guidance algorithms in MATLAB®, the algorithms are converted into the

ANSI C programming language such that they can be run on dedicated hardware

onboard the aircraft. This chapter describes the equipment used as well as any

modifications to existing hardware or software, and details the operations of the

flight experiments performed in this research.

6.1 Overview of the Unmanned Aircraft System

The testbed used is the Boomerang 60 model aircraft from Phoenix Models, with a

wingspan of 2.1 m and measuring 1.5 m from nose to tail. This model is powered

by an O.S. 90 FX engine driving a 15” x 8” propeller, and has been modified by

ARCAA engineer Richard Glassock from a high to low-wing configuration for added

manoeuvrability. In addition, the wingspan has been increased from 1.45 m to 1.9 m

to support a total take-off mass of 8 kg, including all onboard avionics and a full tank

of fuel. Figure 6.1 presents a schematic diagram of the unmanned aircraft system,

including onboard avionics as well as the ground control station and personnel.

The heart of the onboard electronics is comprised of an off-the-shelf MicroPilot

MP2128g autopilot and an external PC/104 central processing unit (CPU), used as

the flight computer. These items are located in the centre of the diagram. The

autopilot is a standalone unit and includes a pressure altimeter, 3-axis rate gyro-

scopes and accelerometers, an airspeed sensor and a GPS unit. It is also able to

receive navigation and control commands from the flight computer via an RS232

serial communications link, and inputs from an electronic compass through an in-

sulation displacement connection (IDC). The autopilot is connected to the elevator,

aileron, rudder and throttle servos via an external servo control board, and trans-

mits telemetry data via a radio frequency (RF) modem (RF Modem 1) to the Mobile

Operations Centre (MOC). The MOC contains the ground station computers and

107

CHAPTER 6. Flight Experiment Setup

Figure 6.1: Boomerang-60 avionics architecture

associated communications equipment in a 4x4 trailer truck. Ground Station Com-

puter 1 (GS Computer 1) receives telemetry data from the aircraft via RF modem 2,

while Ground Station Computer 2 (GS Computer 2) is used to send telecommands

to the external PC/104 CPU via RF modems 3 and 4. A pilot on the ground can also

command the aircraft during takeoff, landing and emergencies via an RC transceiver

setup. As the TGGS lacks the path planning and guidance algorithms to navigate

the aircraft from the approach point to the aimpoint, and the CSSS and MDMS are

still to be integrated with the TGGS, the services of the pilot and ground operators

are required.

6.2 Hardware Description

The following paragraphs describe in further detail each piece of equipment installed

as part of the onboard avionics system, as well as the MOC. In addition, a description

of how the equipment is mounted on the aircraft is also given.

Autopilot

The MicroPilot MP2128g autopilot is one of the smallest autopilots on the market

today, measuring 10x4x1.5 cm and weighing only 26 g, it contains a full avionics suite

108

6.2. HARDWARE DESCRIPTION

including GPS, 3-axis gyroscopes and accelerometers, a pressure altimeter, pressure

airspeed sensor and an electronic compass. This autopilot uses PID gain schedul-

ing for control stability, as well as a rudder-aileron feed forward gain for improved

turning performance. In addition, the MP2128g caters for user-definable waypoints,

holding patterns and error handlers (such as loss of GPS, low battery, etc). The

autopilot also supports both computer-in-control (CIC) and pilot-in-control (PIC)

modes, and comes with the HORIZONmp ground control software, which allows an

operator to receive telemetry data as well as send telecommands to the aircraft. An

additional plug-in capacity allows code written by the user to run alongside the au-

topilot and HORIZONmp code, and even to modify certain settings of the autopilot.

Other important information to note are:

1. The GPS unit uses a U-Blox 4 Hz receiver and a SANAV MK-76 right-hand-

circularly-polarized antenna with a gain of 28 dB. Assuming standard vertical

and horizontal dilution of precision and user estimated ranging error, the 1

sigma 3-D positional error of the GPS unit is 17 m (Parkinson & Spilker,

1996).

2. The electronic compass readings have an error of approximately ±10 degrees

for any known heading, and up to ±15 degrees when the UAV is rolled left or

right 30 degrees. Although these values may seem large, they were obtained

through calibration in the field with the aircraft (and compass) swung by

hand, and there is also no guarantee that a manual compass used for com-

paring the MicroPilot compass module is accurate to the same amount in all

directions.

3. Aircraft state data for control is updated at 30 Hz, and telemetry is logged

at 5 Hz.

Flight Computer

The flight computer consists of a LiPPERT Cool LiteRunner 2 PC/104 embedded

CPU hosting an AMD Geode™ LX800 processor running at 333 MHz and with 256

Mb of RAM. The Cool LiteRunner uses passive cooling and provides for analog VGA

output, RS232/RS485/RS422 serial data communications, Ethernet, PS/2 keyboard

and mouse connections, as well as conventional PCI and IDE expansion slots. An

Advantech PCM-3910 DC to DC power supply board is used to regulate power to the

PC/104 embedded computer. This board has a 10-24 V input range, and provides

5 V at 10 A, 12 V at 2 A, -5 V at 400 mA and -12 V at 400 mA. An additional

8 GB Transcend 2.5” IDE Solid State Drive (SSD) is used to host the Debian 5.2

operating system, as well as the path planning and guidance software. The flight

computer module also has a custom-built interface plate that houses three RS232

109


connectors, an Ethernet port, a USB port and a DC power supply connector. The

interface plate allows a monitor, keyboard and mouse to be plugged into PC/104

computer for ground testing and verification.

Servo Control Microcomputer

The servo control microcomputer is connected to the MicroPilot servo breakout

board and generates a pulse width modulated (PWM) signal to control the servo

motors. A typical PWM signal for an RC servo motor has a period of 20 ms and a

pulse width between 0.7 and 1.5 ms, and the servo deflection angle is determined by

this pulse width. In the CIC mode, the servo control computer receives the PWM

signals from the MicroPilot autopilot via an RS232 serial link, while in the PIC

mode, a PWM signal is sent from an RC transmitter to the RC receiver, which then

transmits the signal to the servo control computer. A Maxim Integrated Industry

MAX222CPE microcomputer was used to control the servo motors, and to ensure

a smooth transition between the PWM signals received from the autopilot and the

RC receiver. The associated code was written in C by ARCAA engineer Scott

McNamara.

Servo Motors

Four Hitec HS-425BB Deluxe Standard servomotors are used to control the ailerons,

elevators, rudder and engine throttle. These servos are very reliable and provide a

torque of 5.5 to 6.8 kg when subjected to voltages between 4.8 to 6.0 V, and at

speeds of 0.21 to 0.16 seconds.

RC Receiver and Transmitter

A Spektrum DX7 7-Channel, 2.4 GHz spread spectrum RC system is used to fly the

aircraft in PIC mode. The DX7 transmitter is capable of storing memory for up

to twenty different models, and was chosen due to its robustness to noise. The 2.4

GHz spread spectrum system uses the Spektrum AR7000 receiver with dual-linked

satellite antennas, and supports an operational range of up to 2 km.

Radio Modems

Four MicroHard 900 MHz wireless radio modems (operating in licensed band) are

used to communicate between the aircraft and ground operators. These industrial

grade radio modems provide 19.2 kbps throughput of data and support Point-to-

Point communications. Two of the radio modems are assigned to communications

between the MicroPilot autopilot and the HORIZONmp ground station software,

which is hosted inside an embedded industrial computer inside the MOC. Two

110


other radio modems service the data link between the flight computer and another

ruggedised computer inside the MOC. This second data link allows a ground oper-

ator to interact with the flight computer and to remotely monitor the progress of

the planning and guidance software. Three of the four radio modems use 3 dB, 900

MHz whip antennas and support a range of up to 8 km, while the fourth (attached

to the flight computer) uses a fin-shaped mobile radio antenna, also rated at 3 dB.

The choice for the fourth antenna was made based solely on where the antenna was

to be located on the aircraft, as a whip antenna was deemed unsuitable.

Power Subsystem

Table 6.1 shows the power budget for the main power consuming electronics onboard

the aircraft. It was found after some analysis that a 12V-4000 mAh Li-Po battery

pack can be used to power the autopilot (including the GPS receiver and antenna,

all gyroscopes and all sensors) as well as one radio modem, while a second 12V-

4000 mAh Li-Po pack is used to power the flight computer and its associated radio

modem. A separate 6-cell, 6V-2500 mAh Ni-Mh battery is used for the servos. With

this setup, approximately 20 minutes of running time can be safely guaranteed.

Component Quantity Voltage (V) Power (W)

MicroPilot autopilot 1 6.5 0.91Flight computer 1 5 6Radio modem 2 3.3 1RC receiver 1 4.5 1

Total 9.91

Table 6.1: Power budget for avionics (The power consumptions are under typical operatingconditions)

Equipment Assembly

To reduce the effects of engine vibration and to protect against an aircraft crash,

the following techniques are used to install the avionics components inside the air-

craft. First, the autopilot and a radio modem is mounted inside a rapid-prototyped

acrylonitrile butadiene styrene (ABS) plastic case. This case is then wrapped in a

piece of foam sheet and inserted into the fuselage. The autopilot is attached to the

airspeed sensor located on the left wing by a flexible piece of plastic tubing. Next,

the flight computer cards and memory drive are mounted on top of each other to

form a square block, which is then screwed onto an aluminium plate before being

wrapped in foam and inserted behind the autopilot box. The computer interface

plate is left attached to the stack, but is also covered with foam and mounted on top

of the stack. Following this, the servo breakout board and servo control microcom-

111


puter are soldered onto a PCB, wrapped in foam and several layers of electrical tape

then inserted into the fuselage. Rudder shock absorbers are also placed between the

engine and the fuselage bulkhead to further reduce the effects of vibration. Figure

6.2 depicts the mounting positions of the avionics inside the fuselage. Not shown

are the positions of the batteries, which are secured inside the nose cone to place the

centre of gravity at a reasonable location. In addition, the location of the electronic

compass is also unseen; this component is mounted inside the left wing.

Figure 6.2: Clockwise from top: The MicroPilot autopilot box; the flight computer stackand interface plate; location of avionics inside the fuselage.

Due to the limited space inside the fuselage, several of the avionics components

are required to be mounted outside the aircraft. These components include the

second radio modem connected to the flight computer and its antenna, the autopilot

radio modem antenna, as well as the satellite antennas of the RC receiver and the

GPS antenna. Both the radio modem and GPS antennas are first attached to

separate backing plates in contact with the internal ground plane, before being

secured to the aircraft frame. The antennas are also located far apart from each

other to reduce the effects of electromagnetic interference. Figure 6.3 shows the

locations of the avionics outside the fuselage.

112


Figure 6.3: Location of avionics outside the Boomerang UAV

Mobile Operations Centre

The ARCAA Mobile Operations Centre (MOC) is a modified Isuzu F-Series truck

capable of carrying all field equipment including the UAV, as well as up to five

ground operators. An expandable, air-conditioned trailer located behind the cabin

provides seating for crew members during flight operations, as well as a planning

table, computers and communications equipment. The HORIZONmp software is

hosted inside an Advantech ARK-3420 embedded industrial computer located inside

the trailer. This computer has an Intel® Core™ 2 Duo 1.6 GHz processor, 4 Gb of

RAM, and runs the Windows XP Professional operating system. A second computer

(Pioneer DreamBook Tough B30 with Intel® Core™ 2 Duo 1.6 GHz processor, 2 Gb

of RAM and running the Ubuntu operating system) is used to established a point-

to-point link with the radio modem of the flight computer once the aircraft is in

the air; this allows an operator to start the path planning and guidance software

when the aircraft is at the correct altitude, as well as to monitor the status of

the software. A Honda EU65is 6.5kVA petrol generator provides over 12 hours of

continuous operation for all ground equipment while in the field.

113


6.3 Software Description

In addition to the basic aircraft and mission control functions provided by the

HORIZONmp software, MicroPilot also accepts extensions to this program from

third party software that can access autopilot state data for enhanced control. The

XTENDERmp software development kit (SDK) provides a flexible set of functions

that allow the developer to easily design software that interacts with the autopilot,

and full details of the MicroPilot application programming interface (API) is con-

tained in the XTENDERmp manual (MicroPilot xTendermp Programmer’s Guide,

2008). The key points to note from the API are that

• The MP2128g autopilot is based on a microcontroller that stores state infor-

mation in memory referred to as ‘fields’.

• The API provides a method for setting ‘fields’ and a method for reading ‘fields’,

however, not all fields can be set.

In addition, the automated forced landing software architecture has been devel-

oped with the following premises:

• The path planning algorithm utilizing the 3-D Dubins curves is a simple,

sequential function, that is, for a given input a given output is produced.

This algorithm accepts as inputs the current and desired aircraft positions

and attitudes (roll, pitch, yaw), and outputs the desired descent flight path as

a series of ENU coordinates.

• The ENG and MPN guidance algorithms are also simple, sequential functions.

They accept as inputs the aircraft state information, including both positional

and attitudinal information, as well as positional information pertaining to the

desired flightpath, and output the desired pitch and roll angles for the aircraft

to follow the prescribed path.

The forced landing software is then integrated with the MicroPilot autopilot

using the following procedure.

1. The MicroPilot API method for reading ‘fields’ is used to obtain autopilot

state data for input to the ENG and MPN guidance algorithms. These el-

ements include the GPS positions and instantaneous aircraft roll, pitch and

yaw, the true airspeed, the wind velocity and the bearing.

2. The forced landing guidance algorithms are run with this data as input.

3. The guidance algorithms generate a desired pitch and roll command which are

then sent to the autopilot using the interface method for setting ‘fields’. Roll

and pitch angle limits of±20 degrees and−10 degrees have been enforced such

114

6.3. SOFTWARE DESCRIPTION

that the aircraft will not become unstable during manoeuvres. These values

were determined following analysis of the aircraft performance in simulation.

4. The pitch and roll error (difference between current and desired) are min-

imised by the autopilot control system, leading to updated state data.

5. Steps 1-4 are repeated at a rate of 25 Hz until the guidance algorithms have

aligned the aircraft for landing.

The MicroPilot autopilot control system uses a series of PID gain-scheduled loops

to maintain autonomous flight, and this setup is illustrated in Figure 6.4.

Figure 6.4: PID loop structure of the MicroPilot MP2128g autopilot (Source: MicroPilotAutopilot Installation & Operation, Stony Mountain, Manitoba Canada, 2008)

A flight plan (referred to by MicroPilot as a .fly file) is uploaded to the autopilot

prior to takeoff and defines which PID loops are active at any stage in flight, how-

ever, only the following two PID loops are of particular interest when preparing the

autopilot for use with the forced landing algorithms.

• Roll From Heading - This PID loop uses the error in the desired heading

(which is the output from either HDG From Crosstrack or Calculated HDG)

and the current heading to calculate the desired roll value.

• Pitch From Airspeed - This PID loop uses the error in the desired and current

airspeeds to calculate the desired pitch value.

Figure 6.5 depicts how these particular PID loops interface with the flight control

system of the aircraft.

115


Figure 6.5: Diagram showing how the Pitch From Airspeed and Roll From Heading PIDloops of the MicroPilot autopilot interface with the aircraft flight control system

Using the flight plan, it is necessary to deactivate both the Roll From HDG and

Pitch From Airspeed PID loops to prevent them from automatically calculating the

two ‘fields’ of interest, namely the desired roll and desired pitch. Instead, these

‘fields’ will be set at 25 Hz using the Micropilot® API, based on the output of the

forced landing guidance algorithms.

To disable the Roll From HDG PID loop is trivial and is explained in the

Micropilot® autopilot manual (MicroPilot Autopilot Installation & Operation, 2008).

The listing below shows the simple program required to disable this PID loop.

1 d e f i n e p a t t e r n 1 // Simple pattern

2 s e t c o n t r o l r o l l O f f , 0 // Disab le PID loop

3 wait 10 //Wait f o r 10 x 1/5 sec = 2 sec

4 repeat −1 //Keep wai t ing f o r an e x t e r n a l input

To disable the Pitch From Airspeed PID loop however, is non-trivial. When

an attempt is made to disable this loop using a similar method to that described

above, the autopilot no longer tracks the desired pitch, thus rendering pitch control

ineffectual. Hence, the Pitch From Airspeed loop is not disabled, but instead altered

such that it can translate errors between the desired and current airspeed to a desired

pitch value. This requires updating the proportional, integral and derivative control

parameters to the following values:

1. P = 1 deg/(feet/sec)

2. I = 0

3. D = 0

116

6.3. SOFTWARE DESCRIPTION

From the above it is clear that every 1 ft/sec error between the desired and

current airspeeds translates to 1 degree of pitch in a linear mapping. Then, if the

current airspeed is known, it is possible to set the desired airspeed to achieve the

desired pitch as shown below.

If the error, e(t) is given by

ev(t) = Vcur − Vde,�� 6.1

Then the desired pitch, θdes in the Pitch From Airspeed loop is described as

θdes = KP ev(t) +KI

∫ev(t)dt+KD

d

dtev(t),

�� 6.2

and setting KI and KD to 0 as stated above,

θdes = KP ev(t).�� 6.3

Figure 6.6 shows a plot of the desired pitch values, compared to the actual values,

and illustrates the validity of this approach.

Figure 6.6: Plot showing the relationship between the desired (black) and actual (blue) pitchvalues over one second. The actual pitch values were obtained using a linear mapping of theairspeed to a pitch value.

117


6.4 Procedures for Testing the Forced Landing Software in

Flight

In order to verify that the forced landing path planning and guidance algorithms

will function as intended, a specific test scenario has been designed that assesses

every aspect of the 3-D Dubins Curves planning algorithm, as well as the ability

of the ENG and MPN guidance algorithms to follow the prescribed path. The

implementation of this test scenario is described below.

The forced landing flight tests are conducted at a remote airstrip located at

Burrandowan, in the state of Queensland, Australia. For these series of flight tests,

the aimpoints of the forced landing sites are assumed to be already calculated by the

MDMS, and are located one-third of the way into the landing sites, labeled as Site A

and Site B in Figure 6.7. In addition, the preferred directions of approach for landing

are also assumed to have been precalculated and are indicated by the blue arrows at

the start of each site. From the aimpoints, the approach points can be calculated,

and these are shown by the red triangles in the figure. The approach points are the

final waypoints to which the aircraft will be guided in flight tests. Although the

airstrip located between the selected sites (demarked by a yellow push pin) is also

suitable for use as a forced landing site, it is not used in these tests. The yellow push

pin also marks the location of the reference point for translating between the Earth-

Centred-Earth-Fixed (ECEF) and ENU Cartesian coordinate systems required by

the guidance algorithms.

The flight tests are conducted in the following manner. First, a pilot flies the

UAV under radio control from takeoff to approximately 800 ft and facing the general

direction of the starting point for a forced landing. Control will then be translated

to the HORIZONmp ground station software, which will guide the aircraft the re-

mainder of the way to the starting point. Once the aircraft comes within 50 m of

that point, the ground station software will reduce the throttle setting to idle, and

a ground operator will then start the onboard flight computer containing the path

planning and guidance code using a point-to-point radio modem link.

Since the operational ceiling has been limited by CASA to 1500 ft, the aircraft

will initially conduct only one spiral to lose altitude, before heading for the approach

point at Site A, located at an altitude of 460 ft. While en route to Site A, a

simulated low altitude condition will cause the UAV to head for Site B, which in

this test assumes the role of a more feasible site. The approach point at Site B

has an altitude of 100 ft. However, due to the differences in altitude between the

starting position and the approach points, a joining contour is required to link the

spiral path to the 3-D Dubins curve. Thus, not only will this test assess the ability

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6.4. PROCEDURES FOR TESTING THE FORCED LANDING SOFTWAREIN FLIGHT

Figure 6.7: Aerial view of the Burrandowan test site. The two candidate landing sites arelabeled as Site A and Site B, and have their preferred direction of approach indicated by theblue arrows. Shown also is the reference point for translating between different coordinatesystems, the approach point and aimpoint for each site, as well as the starting waypoint forall forced landing descents (Source: Google Earth).

of the path planner to construct a feasible path that also accounts for the vehicle

dynamics, but will further test its replanning capability. In addition, the nature of

the path shapes will also challenge the ability of the guidance algorithms to follow

those paths.

The same test scenario described above will be repeated a number of times, with

any winds and/or wind changes being the only variable. After each test, the UAV

will be guided to land under RC. The flight logs will then be retrieved from the

aircraft before it is refuelled again for takeoff. At any time during flight, if the

pilot or ground operator judges that the aircraft has strayed too far from the test

location, or is otherwise at an unsafe position, control will be handed to the pilot

who will either stabilise the aircraft and attempt a go-around, or land the aircraft.

A schematic diagram illustrating the test procedure described above is depicted in

Figure 6.8.

Prior to conducting the actual flight tests, the forced landing scenario is run

inside the HORIZONmp simulator. This simulator is capable of simulating, amongst

other things, avionics and GPS failure, loss of flight control as well as winds, in

real-time, and is able to also accept user-configurable flight plans, written as a .fly

file. For simulation and for the actual flight tests, the same .fly file is used to guide

the UAV to the starting location and to be at the correct altitude and heading prior

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Figure 6.8: Schematic diagram of the procedures followed in conducting the UAV forcedlanding flight tests

to the commencement of each test.

A screenshot of the HORIZONmp simulator is included in Figure 6.9, showing the

flightpath of the aircraft overlaying a map of the test site, as well as the percentage

of throttle, the attitude and altitude at any given time via the central instrument

display. Note also the six buttons located under the Patterns tab in the left sidebar,

which function as a manual overwrite to certain phases of the automated forced

landing flight plan during simulation. Firstly, the figure8 button is used to simulate

a basic figure-of-eight pattern to test that the autopilot PID controls are functioning

correctly. Once this has been established, the Forcelanding button is used to man-

ually switch to forced landing mode at any point in flight, should it be necessary to

do so. This causes the autopilot to stop receiving radio control or commands from

previously uploaded flight plans, set the throttle to idle, and begin receiving roll

and pitch commands from the forced landing guidance algorithms. The EngineKill

button shuts down the engine, following which the Forcedlanding button should be

pushed to activate the forced landing algorithms. Finally, the Esc-South causes the

aircraft to leave the starting location and head south, from which the orbit-right or

orbit-left button can be used to turn the aircraft left or right for a second attempt

at the flight test.

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6.5. SUMMARY

Figure 6.9: Screen capture of the Horizonmp simulator program. This simulator allows anoperator on the ground to keep track of the aircraft throughout the flight, as well as issueany telecommands if required.

6.5 Summary

This chapter has presented in detail the equipment used for flight testing, the re-

quired modifications to existing hardware and software, as well as the procedures

followed in conducting the flight tests. It can be seen that a simple, yet effective test

scenario has been formulated to assess every capability of the forced landing path

planning and guidance software. It is expected that the results from these flight

tests will serve to verify the capabilities of the software developed in this research,

as well as provide critical feedback for any future enhancements to the algorithms.

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7Discussion of Results

THIS chapter presents the results from both the computer simulations and ac-

tual flight tests. Firstly, results from the MATLAB® simulation environment

discussed in Section 5 are presented. Following this, results from flight tests carried

out at the Burrandowan test site in North-Western Queensland are discussed and

analysed.

Section 7.1.1 describes the results obtained from simulating the planning and

guidance algorithms that are based on piloted forced landing approaches (see Sec-

tion 3.1). The performances of the individual planning and their associated guidance

algorithms are first described. Following this, the results obtained from Monte Carlo

testing of the algorithms are compared and analysed.

Section 7.1.2.1 discusses the results obtained from simulating the 3-D Dubins

planning and 3-D nonlinear guidance algorithms (Sections 3.2.2 and 4.2). The per-

formances of these algorithms is also compared to that discussed in Section 7.1.1.

In Section 7.1.2.2, the results obtained from forced landing simulations, with

enhancements to the aforementioned 3-D planning and guidance algorithms are de-

scribed. These enhancements include the use of a connecting contour (Section 3.2.2.1)

to form a smooth descent path, a nonlinear vertical guidance algorithm that dis-

penses with complicated gain scheduling (Section 4.2.3), and an additional waypoint

for post-approach point gliding that reduces the miss-distance (Section 3.2.2.2).

These results are then compared to that discussed in Section 7.1.2.1.

Section 7.1.2.3 describes the results obtained from simulating a path replanning

scenario, using the improved algorithms. Here, the UAV is initially on course for a

selected site, but at some point in flight changes course to intercept a second selected

site.

Finally, results from flight testing are presented in Section 7.2. The flight tests

are designed to assess all functions of the 3-D Dubins planning as well as the ENG

and MPN guidance algorithms in a controlled environment (c.f. Section 6.4).

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CHAPTER 7. Discussion of Results

7.1 Simulation Results

This section will first discuss results from simulations using the planning and guid-

ance algorithms adapted from piloted forced landing procedures. Next, simulation

results using the 3-D Dubins Curves and the ENG, FPFG and MPN nonlinear guid-

ance techniques are presented and analysed, followed by results obtained using the

third-party MicroPilot HORIZONmp Simulator.

7.1.1 Results from Algorithms based On Piloted Forced Landing

Procedures

Of particular interest to the earlier simulation experiments is how well the two

path planning algorithms that are based on piloted approaches, namely Algorithm

1 and Algorithm 2, will perform in varying wind conditions. To demonstrate this, a

comparison between simulated forced landings using each algorithm was conducted.

The UAV was initially located at (27◦24′′, 153◦7′′, 454′) and faced due East.

As can be seen from Figure 7.1, the Aerosonde UAV was able to navigate the

required track to fly (red path) using Algorithm 1, while compensating for changes

in the wind velocity. In this particular scenario, the wind direction was the same,

whereas the wind magnitudes were different every minute, as shown by the differing

lengths of the wind vectors (magenta lines). Notice also that the UAV could not

reach the aim point (AP) due to the strong head winds it encountered while en

route from the second overshoot waypoint (OS 2).

Using the same wind shifts for the second simulation, it can be seen from Fig-

ure 7.1B that Algorithm 2 produces a different flight path to that obtained with the

first. The UAV initially heads for the end base (EB) while continually assessing the

effects of the wind on its glide slope. After it has travelled a certain distance towards

the EB point, the path planner recalculates the glide slope gradient and realises that

this waypoint cannot be attained. The UAV then seeks for a new waypoint that can

be attained with its new glide slope, turning as it does so. While turning, the strong

cross winds have momentarily become head winds, thus providing the aircraft with

greater lift and a shallower glide slope. This causes the aircraft to initially head for

the EB point once again, before finally heading for the aim point (AP).

In both tests the UAV did not actually land within the designated area. However,

it was able to navigate to a distance within 500 m of the aim point. It should also

be mentioned that the apparent sharp turns in both flight paths are due to the large

sampling time of 10 seconds used for plotting.

Seeing that the performance of the different path planning algorithms cannot

be ascertained based on only one set of tests, a further 100 simulations were run

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7.1. SIMULATION RESULTS

Figure 7.1: Forced landing results for a single case, for (A)-Algorithm 1, and (B)-Algorithm2

for each algorithm, with randomised initial aircraft positions, headings and wind

velocities. From the first simulation using Algorithm 1, seven landings had a radial

miss distance of greater than 1000 m from the aim point, and these were excluded in

further analysis as they were deemed to be spurious data points. Of the remaining

93 landings, 23 landings were within the site boundaries (confirmed by additional

testing), giving a landing success rate of approximately 26%.

For the second simulation using Algorithm 2, all landings were within 1000 m of

the aim point, and 52 landings were within the site boundaries. This corresponds

to twice the landing success rate of the first algorithm. Although this result is not

exemplary, it does represent a good baseline from which to further enhance the path

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planning and control algorithms, such that the landing success rate can be improved.

Results from the Monte Carlo simulations are summarized in Figure 7.2.

Figure 7.2: Monte Carlo simulation results — Algorithm 2 produces more landings withinthe designated landing site and closer to the aim point (≤ 200m) than Algorithm 1 (≤ 400m)

By comparing the frequency distributions for both Algorithms 1 and 2 (Fig-

ure 7.2), it can be seen that in general, Algorithm 2 outperforms Algorithm 1. The

distribution for Algorithm 2 is skewed towards the 200 m miss distance from the

aim point, while that for Algorithm 1 tends towards the 400 m miss distance. The

200 m miss distance can be explained by the fact that that is the required threshold

distance for successfully capturing a waypoint, as defined in Algorithm 2 (see Sec-

tion 3.1.2), while the 400 m miss distance is surmised to come from the UAV being

commanded by Algorithm 1 to aim for the far threshold of the landing site (400 m

from the aim point), once the aim point is passed (see Section 3.1.1). This additional

condition was imposed as it was observed from simulation that using Algorithm 1,

the UAV was sometimes still slightly too high at the aim point for touchdown. Thus,

it would also seem that the choice of a final impact point has affected the landing

accuracies of Algorithm 1.

The differences in the assigned distances between the waypoints used for the

algorithms could also have contributed to the differences in their respective distri-

butions. Recall that Algorithm 1 followed a scaled implementation of the standard

forced landing circuit pattern, while Algorithm 2 retained the standard circuit pat-

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tern. The fact that Algorithm 1 did not include a capacity for adjusting the flight

path due to wind changes, as opposed to Algorithm 2, could also have resulted in

the larger miss distances associated with that algorithm, although both algorithms

could correct for changes to the aircraft heading due to wind, while en route between

two waypoints.

In both cases, the aircraft pitch attitude was kept at approximately 3 degrees

for landing and the aircraft flaperons were not used. Should the pitch attitude be

adjustable, such as when on final approach to the aim point, and flaperons be used

to change the aircraft lift-to-drag characteristics, it is postulated that more landings

can be made within the designated area. The strong winds (maximum of 30 m/s

headwind) modelled in the simulation could also have prevented a large number

of landings from occurring within the designated area, as these winds were often

greater than the UAV airspeed of 19 m/s. The fact that the wind vector varied

every minute could have also resulted in the larger miss distances.

Thus, these results showed that Algorithm 2, which incorporated a reactive ap-

proach to changing wind conditions in planning a path to the landing site, out-

performed Algorithm 1, which could only correct for wind while en route between

waypoints, but could not change the flight path due to adverse wind conditions. The

52% landing success rate of Algorithm 2 was then used as a performance benchmark

to evaluate successive path planning and control algorithms, such that the landing

success rate could be improved.

7.1.2 Results from Algorithms based on Nonlinear Planning and

Guidance Techniques

This section will first discuss simulation results obtained using the 3-D Dubins

Curves planning algorithm, as well as the ENG and FPFG path following algo-

rithms. Following this, results obtained using the enhanced version of the 3-D Du-

bins Curves, and the ENG and MPN algorithms will be presented and analysed.

These results will then be compared with those obtained using the original 3-D

Dubins Curves, ENG and FPFG algorithms. Finally, results demonstrating path

replanning using the enhanced 3-D Dubins algorithm, together with the ENG and

MPN algorithms will be discussed and analysed.

7.1.2.1 Initial Results obtained using the 3-D Dubins Curves, ENG and

FPFG Algorithms

For the latter simulation experiments utilising the 3-D Dubins planning algorithm

discussed in Section 3.2.2), the ENG and FPFG algorithms described in Sections 4.2.1

and 4.2.2, and the Boomerang UAV model, a large number of simulations were per-

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formed in which both the aircraft heading and position, as well as the ambient wind

conditions were allowed to vary. For these experiments, perfect knowledge of the

wind conditions has also been assumed, albeit with provisions for errors in the sensor

readings. A sample of the test data is included in Table 7.1. Table 7.1a shows the

initial and desired final positions used to plan a path from 1640 ft to 500 ft in calm

conditions, while Table 7.1b shows the positions for a descent from 850 ft to 500 ft

in winds, with a maximum wind speed of 9 m/s. Note that as this research is con-

cerned with gliding flight, the required airspeed at the approach point is absorbed

by the flight path angle requirement at this point.

Table 7.1: Sample test data for the path planning and guidance algorithms. Table 7.1ashows the desired initial and final aircraft positions and attitudes for a descent from 1640ft to 500 ft in nil wind conditions, while Table 7.1b presents the desired initial and finalaircraft positions and attitudes for a descent from 850 ft to 500 ft in winds.

Figure 7.3 shows that in planning a path from a high initial altitude (Table 7.1a),

the algorithm generates the required number of helix spirals to “bleed off” the excess

altitude, before joining the spirals with the arc-line-arc Dubins path (solid black

line). This satisfies flight path angle constraints and prevents excessive stress to the

UAV structure. The horizontal and vertical track errors at the approach point are

0.3 m and 1.3 m, which are well within the stated tolerance and comparable to the

results obtained for other flight path angles.

The difference in altitudes between aircraft and path at the start is due to the

planning algorithm rounding the required number of helix spirals to the nearest

complete (360◦) spiral turn, to preserve the desired initial heading. Notwithstanding

this, the aircraft is still able to converge onto the path at Point A. However, at Point

B the aircraft descends below the path and reaches a maximum vertical deviation

of 600 ft at Point C (the horizontal error here was approximately 9 m), but recovers

to intercept the approach point with the errors stated above.

The relatively poor vertical path following in the first half of the descent is

caused by the use of a fixed airspeed in constructing the path, as it is not possible to

predict beforehand the actual airspeed due to the control actions. In a descent, the

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Figure 7.3: Path planning and following for a forced landing from a high initial altitude innil wind conditions

varying airspeed results in a non-uniform loss in altitude. In addition, an aircraft

rolled into a continuous banking motion will also experience some amount of yawing

motion called sideslip, no matter how good the yaw damper may be; this in turn

increases the altitude lost. Thus, the amount of loss in altitude factored into the

path planning equations is ideal at best, and does not fully take into account the

associated loss in altitude due to varying airspeeds and other atmospheric effects.

Hence, the current solution relies on the path following algorithm being robust to

these uncertainties in guiding the aircraft to the desired approach point. A possible

alternative is to increase the path angle of the initial helices to more closely match

that of the straight segment, and/or increase the radii of the helices such that the

number of spirals is reduced. These will help reduce the amount of altitude loss due

to sideslips and a prolonged banking action.

Next, the performances of the path following algorithm in winds is shown (Ta-

ble 7.1b) and the results compared with those obtained using the original path

following algorithm in (Park et al., 2007), hereby referred to as the Unmodified

Nonlinear Guidance (UNG) algorithm. Two different wind scenarios are chosen for

illustration. Figure 7.4a shows the aircraft able to follow the desired path (solid

black line) in a 6 m/s south-south-westerly wind (green arrows), while Figure 7.4b

shows the aircraft following the prescribed path in changing winds from the north-

north-east and south-south-west. For the second case (Figure 7.4b), a degree of

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realism has been injected into the simulations, by including errors in the airspeed

and GPS velocity measurements, which in turn produce errors in the estimated wind

velocity. The error values and assumptions were discussed in Section 5.2).

Figure 7.4: Path planning and following in ambient winds, showing (a) Aircraft responsein 6 m/s wind from SSW; (b) Aircraft response in 0-9 m/s changing winds from NNE andSSW; (c) Horizontal and vertical track errors for case a; and (d) Horizontal and verticaltrack errors for case b.

In the scenario depicted in Figure 7.4b, the wind velocities have been pro-

grammed to vary in magnitude and direction every 20 seconds, with a maximum

wind speed of 9 m/s and with the vertical wind velocity kept constant at zero.

From Figure 7.5, it is seen that in the first 20 seconds there is calm, and then the

wind blows from 225◦ at approximately 6 m/s for the next 20 seconds. In the next

epoch it increases to approximately 9 m/s, before assuming a 180◦ phase change and

decreasing to approximately 3 m/s for the last 20 seconds. Although this constant

change in winds may not represent the actual conditions experienced during a forced

landing, it nonetheless presents a very challenging environment to test the robust-

ness of the guidance algorithms. Note that the green arrows in Figure 7.4 show only

the general direction of the incident wind vectors — the actual turbulence fields in

the longitudinal, lateral and vertical directions (including wind gusts and lulls) as

traversed by the aircraft are depicted in Figure 7.6.

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Figure 7.5: Input winds for the scenario in Figure 7.4b, showing changes in wind speed overtime, and the errors between the expected (cyan) and actual (magenta) north and east windcomponent values.

Figure 7.6: Wind turbulence for the scenario in Figure 7.4b, showing examples of gusts andlulls in the longitudinal, lateral and vertical directions.

As shown in the top halves of Figures 7.4c and 7.4d, the path following algorithm

of this research produced lateral errors at the approach point of 1.8 m and 5.5 m

respectively (blue lines), while that of UNG was 14.1 m and 80 m for the two different

wind conditions (red dashed lines). Although UNG did not include a longitudinal

path following component, the vertical track error has nonetheless been plotted to

show what might have transpired had that lateral guidance algorithm, coupled with

the longitudinal guidance algorithm developed in this research, been used to follow

the path.

As shown in the lower halve of Figure 7.4c and Figure 7.4d, the vertical track

errors stemming from the ENG algorithm is approximately 1.2 m and 1.5 m respec-

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tively for the two wind conditions, while that for the case of UNG coupled with

the FPFG algorithm is 1.5 m and 100 m. Thus, it can be clearly seen that the

ENG path following algorithm is robust to wind perturbations and uncertainties in

wind measurements in both the semi-real and ideal conditions. This algorithm also

outperforms the UNG algorithm, especially in conditions with varying winds, where

it would seem that the UNG algorithm cannot deal appropriately with significant

changes (≥ 180◦) in wind directions. Further, the average lateral and longitudinal

path errors incurred whilst using the ENG and FPFG algorithms (for the two differ-

ent wind scenarios) are well within 100 ft, which as mentioned earlier is commonly

accepted as the maximum allowable path deviation for general aviation aircraft.

From the simulations, it has also been observed that the path following algorithm

is able to contain the errors at the approach point, within the stated tolerances, for

wind speeds not exceeding 7 m/s. In stronger winds, these errors can exceed 20 m

horizontally, and be up to 5 m vertically, or the aircraft may lose control and crash.

A possible explanation is that the small size and weight (5.55 kg) of the model

aircraft used, as well as the limited thrust available means that it cannot achieve

the necessary control authority to overcome strong winds and gusts.

It has also been observed from simulations that the vertical track error at the

approach point is greater than 7 m in sinking air of 1 m/s. Once again, this relatively

poor performance may be due to the structural and aerodynamic factors stated

above. However, when compared to previous work as discussed in (Eng et al., 2007;

Fitzgerald et al., 2007), the performances of the current algorithms are far superior.

It is believed that this improved performance may be largely due to the fact that

the airspeed and flight path angle have been allowed to vary to counter different

wind scenarios.

7.1.2.2 Improved Results obtained using the 3-D Dubins Curves, ENG

and MPN Algorithms

Following simulated testing with the ENG and FPFG algorithms, further simula-

tions were performed using the ENG and MPN algorithms. As noted earlier in

Section 4.2.2, the disadvantage of the FPFG algorithm is that it relies on the use of

multiple PID gain schedules to cater for a range of plausible wind conditions, and

hence is not ideal for real applications. However, the simplicity and robustness of

the MPN vertical tracking algorithm makes it ideally suited to real applications, and

for any type of aircraft.

In addition, the results obtained from Section 7.1.2.1 led to certain modifications

to the path planning algorithm. Firstly, a connecting contour is now used to connect

the descent path such that no offset exists between the aircraft and the start of the

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path. Further, an additional waypoint is also used to direct the guidance algorithm

such that the aircraft continues tracking in a straight line once the final waypoint is

reached. This additional waypoint helps to reduce cross-track errors in high winds,

as well as help stabilise the aircraft for any subsequent path following actions.

Figure 7.7: Path planning and following for a forced landing from a high initial altitude innil wind conditions, with improved path planning and tracking algorithms

Figure 7.7 shows the descent from an initial high altitude, using the test data

supplied in Table 7.1a. As can be seen, the path (black line) now incorporates only

one spiral, which is joined to the arc-line-arc Dubins path via a connecting contour

AB. The slope of the Dubins path has also been adjusted such that it will not

exceed the maximum permissible path angle of the aircraft, and, having less spirals

means that the aircraft is less susceptible to instability from a prolonged banking

action.

As indicated by the blue line, the aircraft tracks the entire path very well, with

only a temporal deviation between A and C (due to the steeper descent path angle

used to track the connecting contour) before rejoining the rest of the path. The

lateral and vertical track errors at the approach point are 40 m and 7.6 m respec-

tively, with average track errors within 30 m. Where the aircraft deviates from the

path while following the connecting contour, the maximum lateral and vertical track

errors are approximately 100m and 10 m respectively. The large lateral miss dis-

tance at the approach point could be caused by the aircraft not having the required

control authority to quickly converge on the approach point, after it has recovered

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from the deviation at the connecting contour, since the amount of aileron deflection

is also limited for stability. In addition, the vertical track error at the approach

point, although greater than that resulting from the use of the FPFG algorithm, is

acceptable since it is generated from a more robust tracking algorithm that does not

require excessive tuning.

Figure 7.8: Path planning and following in ambient winds using improved planning andtracking algorithms, showing (a) Aircraft response in 0-9 m/s changing winds from NNEand SSW; and (b) Horizontal and vertical track errors for case a.

Figure 7.8 demonstrates the performances of the ENG and MPN algorithms in

changing winds, using the test data supplied in Table 7.1b, as well as the wind

turbulence and sensor errors described in Section 7.1.2.1. As shown in Figure 7.8b,

the lateral and vertical miss distances at the approach point are approximately 20

m and 12 m respectively, which, although larger than those incurred using the ENG

and FPFG algorithms, are still acceptable since they are generated from a robust

tracking algorithm. The average track errors are also within 30 m, which is the

stated maximum tolerance as discussed earlier.

7.1.2.3 Results demonstrating Path Replanning using the 3-D Dubins

Curves, ENG and MPN Algorithms

Next, a simulated path replanning scenario is presented (Figure 7.9). Here, the

aircraft is initially at an altitude of approximately 1400 ft, at a bearing of 180◦, and

is on course to intercept an approach point at 400 ft, at a bearing of 350◦ (Point

D), corresponding to a selected landing site. As the aircraft descends, circling to

lose altitude, strong crosswinds (maximum of 7 m/s) begin causing it to leave the

desired path momentarily (Point A), reaching a maximum lateral deviation of 120

m at Point B before rejoining the path at Point C. Due to the wind conditions, a

simulated decision from the MDMS requires the aircraft to change course and fly

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Figure 7.9: Path replanning and tracking in ambient winds using improved planning andtracking algorithms, showing (a) Top view of the aircraft response in 0-9 m/s changing windsfrom the NNE and SSW; and (b) An oblique view of the same.

to a more feasible site. The approach point corresponding to this site is selected,

and the path planner then plans a path to this point at an altitude of 200 ft, and

at a bearing of 220◦ (red line). The aircraft alters course to track the new Dubins

path, however, strong crosswinds once again cause it to leave the path, reaching

a second maximum lateral deviation of 100 m at Point E before resuming course

towards the new approach point. The wind profile used in this simulation is similar

to that depicted in Figures 7.5 and 7.6.

The lateral and vertical track errors at the new approach point are approximately

20 m and 50 m respectively. Although these figures are relatively large, the reader

should remember that they are primarily induced by the strong and sudden wind

changes. However, comparing Figures 7.9a and 7.9b, it can be seen that the aircraft

is still capable of maintaining steady, straight flight once it has passed the approach

point (recall the use of an additional waypoint discussed in Section 3.2.2.2). This

is important should a subsequent path planner be engaged that guides the aircraft

from the approach point to touchdown.

7.1.3 Results from Simulations using the HORIZONmp Simulator

As noted earlier in Section 6.4, the planned forced landing scenario is run inside the

HORIZONmp simulator in real-time prior to the actual flight tests. When compared

to the MATLAB® Simulink models, this simulator is considered to provide a more

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Figure 7.10: Path replanning and tracking in nil winds using the HORIZONmp Simulator,showing (a) Top view of the aircraft response, and (b) An oblique view of the same. Theseresults are comparable to those obtained using the MATLAB® Simulink models.

Figure 7.11: Aircraft control response from a simulated forced landing descent in theHORIZONmp Simulator, showing good tracking of the input commands in (a) Roll and(b) Pitch.

136

7.2. RESULTS FROM FLIGHT EXPERIMENTS

accurate representation of the functions of the autopilot, and hence of the aircraft

during flight. Figure 7.10 illustrates the UAV flightpath when following the planned

route in nil wind conditions. The aircraft starts the forced landing descent at the

position indicated and completes approximately one-and-a-half spirals before joining

the standard Dubins path. At Point B, the path is replanned and the aircraft

follows the new route to arrive at the approach point. The lateral and vertical miss

distances at the approach point are 10 m and 20 m respectively. Considering that

the GPS receiver modelled has a nominal error of 10 m, these associated errors are

very reasonable. In addition, the average track error is approximately 30 m, which

is within the specified bounds, with a maximum deviation of approximately 30 m

laterally and 200 ft vertically at Point A.

The roll and pitch performances for the flight is depicted in Figure 7.11, and

show good tracking of the input commands with desirable control responses. The

brief oscillations around the 100 second mark are due to the guidance system at-

tempting to follow the switching action while the path is being replanned, which

prompts a change in the roll and pitch responses. These responses indicate that

the implementation of a hysteresis control loop may be desirable, however, as can

be seen from Figure 7.10, the oscillations have little to no impact on the overall

stability of the aircraft.

7.2 Results from Flight Experiments

A total of nine flights were completed between 23-24 September 2010, and Fig-

ure 7.12 depicts the various activities carried out as part of the forced landing flight

test. These activities correspond with the test procedure described in Section 6.4.

Moving in a clockwise direction, the top left photograph shows the UAV in flight.

The next photograph shows the pilot, who is on standby for takeoff and landing, as

well as to handle any emergencies. Following this, the ground station operator is

shown. This operator monitors the progress of the flight and the aircraft health via

the HORIZONmp software, as well as the status of the path planning and guidance

algorithms via a second notebook computer. The ground operator is also able to

communicate with the pilot at any time via UHF radios, as well as monitor the local

airspace and communicate with any other aircraft that may enter this restricted

airspace. Finally, the Mobile Operations Centre is shown. The expandable trailer

of the MOC allows the ground operator a clear view of the aircraft and surrounds

during operations.

From the flights, two specific cases have been chosen to illustrate the perfor-

mances of the path planning and guidance software. The first case is depicted in

Figure 7.13. Here, the UAV starts initially at a point slightly away from the planned

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Figure 7.12: Flight activities. Clockwise from top: The Boomerang-60 UAV in flight; thepilot, who is on standby for takeoff and landing, as well as any emergencies; the groundoperator, who communicates with the pilot via UHF radio and constantly monitors theprogress of the flight, and finally, the MOC which houses the ground operator and associatedcomputing and communications equipment.

forced landing start point, and facing in a direction different to that intended (due

South). This is seen in Figure 7.13a, and is primarily due to the placement of the

waypoints that are used to guide the UAV to the start point. These waypoints are

chosen in the HORIZONmp program, and are later amended as shown in the next

example. The UAV then attempts to follow the descent flight path indicated by

the black line, with the incident wind vectors (calculated by the autopilot) depicted

by the green arrows. The maximum wind speed encountered was 4.6 m/s, with an

average of 2.4 m/s, which is well within the speeds tested in simulation. However,

as seen in the figure, the UAV strays too far from the intended path while circling

to lose altitude before heading for the approach point at Point C. When the air-

craft is at Point A, the ground operator detects that the aircraft has passed below

a previously agreed minimum safe altitude. He then transfers control to the pilot

138


who then brings the aircraft in to land. Due to the large miss distance between

the aircraft and the intended path, the UAV never arrives at the intended approach

point (Point D), which requires replanning to be conducted. The red line, indicating

the replanned path, has been included merely for reference.

Figure 7.13: Results from flight test example 1. (a) Top view of flight path; (b) Obliqueview of the same; (c) Roll performance; (d) Pitch performance

An oblique view of the descent is shown in Figure 7.13b, and it can be seen

that vertical tracking is quite poor. A post flight analysis revealed that the GPS

altitude was used to calculate the pitch required, and since this information was

only available at 4 Hz, this could have been one of the main causes of the large

track error observed. This error was corrected in subsequent flights by using the

barometric altitude. Considering a log of the pitch values plotted in Figure 7.13d,

it would also seem that the commanded pitch assumed the form of a hysteresis

controller. This can be explained by the lookup table used to convert from desired

airspeed to desired pitch (Table 4.1), where an airspeed of greater than 24.5 m/s

translates to a pitch angle of -10 degrees, and -14 degrees is the maximum pitch angle.

The value of -10 degrees was chosen in this experiment as the maximum permissible

pitch command to afford a measure of safety and guard the aircraft from diving

139


too steeply. However, this consideration was later shown to be too conservative, as

subsequent flights revealed that at -10 degrees the aircraft was travelling too slowly,

almost at the stall speed. It would also seem from Figure 7.13d that the autopilot

pitch controller did not have enough authority to follow the commanded pitch, or

the aircraft had a rate of pitch that prevented it from achieving tight following of

the pitch commands, even though Figure 6.6 has indicated otherwise. The fact that

the autopilot PID gains were previously tuned for an aircraft weight of 7.4 kg, as

opposed to the actual takeoff mass of 7.8 kg may also have contributed somewhat

to the vertical track error.

Considering the roll performance in Figures 7.13c, it can be seen that the actual

roll follows the commanded roll quite well, albeit with an offset; this could be simply

due to air turbulence affecting the longitudinal motion of a light aircraft. However,

when comparing the commanded roll with that obtained in simulation, it seems that

the former is much less than that required for tight path following. Since the airspeed

is used in calculating the required lateral acceleration and hence the required roll

(see Eqn. 4.6), the low airspeed attained could have contributed to this error.

The momentary large peaks in the actual roll and pitch angles towards the end

were caused by the switch from CIC to PIC mode, when the pilot resumed control of

the aircraft. Finally, the fact that the normal modes of roll and pitch control as used

in the MicroPilot were circumvented to accept inputs from the guidance software,

as described in Section 6.3 may have also contributed to the noisy signals received,

such as the spikes in the commanded pitch, as it is possible to have bypassed any

internal noise filters in the process.

The second case is depicted in Figure 7.14, and shows the UAV initially starting

at the correct location and with the correct heading. The wind velocities are indi-

cated by the green arrows, with a maximum wind speed of 3 m/s and and average

wind speed of 2.2 m/s. In this test, the barometric altitude was used instead of the

GPS altitude, as it is more accurate for low altitude flights. Secondly, the maximum

permissible pitch angle has been increased to -14 degrees, as per Table 4.1. Finally,

it was noticed from the previous flight that the airspeed was used in calculating the

roll angle, instead of the ground speed (see Eqns. 4.14 and 4.23), and this could have

resulted in the aircraft flying near the stall speed as stated previously. Hence, the

GPS speed was taken as the input in calculating the lateral acceleration in this test.

As seen in Figure 7.14b, the vertical track error does improve, yet at the cost of

the horizontal track error (Figure 7.14a). Further, when comparing Figures 7.14c

and 7.14d, it can also be seen that the roll performance is still much better than that

of the pitch, albeit with a noticeable lag in response. This lag could be attributed

to the GPS update rate of 4 Hz, and the poor performance in pitch, as well as the

noisy input signals, to the reasons discussed in the previous example.

140


Figure 7.14: Results from flight test example 2. (a) Top view of flight path; (b) Obliqueview of the same; (c) Roll performance; (d) Pitch performance

With these results, it is deemed that more testing needs to be conducted with

the autopilot to determine the relationship between a given roll and pitch and the

actual response, as they do not reflect the results obtained using the HORIZONmp

Simulator, let alone that obtained using the MATLAB® Simulink models. The

MicroPilot autopilot was sourced from a third party and has been treated as a closed

system in the tests, with only simulated responses used to judged its applicability to

the project at hand. It should also be noted that the autopilot PID gains were tuned

for the UAV in flight following the recommended settings from the manufacturers,

using waypoints that are spaced tens or even hundreds of meters apart. With these

waypoints, generally a larger track error is tolerated, which is detrimental to the

flight path required to be flown in this research, with waypoints spaced mostly

within a meter distance of each other.

After further consideration of the nature of the vertical guidance (MPN) algo-

rithm (Section 4.2.3) and the MicroPilot PID loop structure shown in Figure 6.4, it

is decided that future testing will be conducted using a two-pronged approach. The

first strategy will use the Pitch From Altitude control loop to determine whether

141


it is possible to control the aircraft pitch using a modification of Eqn. 4.28, and

the second strategy will use the Pitch From Airspeed control loop and Eqn.4.41 to

control the aircraft pitch. The reason that the Fixed pitch control loop will not be

used is that preliminary testing has indicated that it functions in an unpredictable

manner to input pitch commands, and so is unreliable. Future tests will also seek

to use an electronic compass calibrated to a greater degree of accuracy than that

stated in Section 6.2, as this can also affect the accuracy of the lateral path following

algorithm.

7.3 Summary

This chapter has presented detailed results from both the simulated and actual

forced landing flight experiments. From the MATLAB® simulations, it is clear

that the 3-D Dubins planning and nonlinear guidance algorithms perform much

better than those based on piloted forced landing approaches, with path tracking

accuracies that emulate those of manned, powered aircraft. In particular, the ENG

and MPN algorithms are robust and function very well in strong, changing winds,

even in wind speeds up to one-third of the aircraft airspeed. When coupled with

the enhanced 3-D Dubins path planning algorithm, they allow a UAV to navigate

to the desired landing site/s using a reconfigurable flight path that accounts for

the aircraft dynamics. The planning software can also be easily integrated with

any subsequent planning algorithms that take the UAV from the approach point to

touchdown. Simulated testing using third-party MicroPilot software have also served

to further verify the performances of the planning and guidance algorithms, with

results comparable to those obtained in MATLAB® Simulink. However, during

flight trials, an incongruence between the simulated and actual test results was

observed, although the latter results were still reasonable. This incongruence has

been attributed largely to a lack of knowledge concerning the internal functions

of the autopilot hardware, which has been treated as a closed system in the tests

described. In light of this, it is recommended that any further testing should first

seek to determine the true relationship between the commanded and actual roll and

pitch values using the autopilot, before trialling the suggested, new pitch control

strategies, as this control mode performed quite poorly in the flight tests.

142

8Conclusions

IN order to overcome the key impediments to widespread adoption of UAVs for

civil applications, they must be granted access to the NAS. Before this can

transpire, however, certain safety prerequisites must be satisfied. In particular, as

stipulated by the FAA, CASA, and other regulatory bodies, UAVs must be able to

demonstrate an ELOS to that of manned aircraft. This is especially significant in

the case of an engine failure, which would require an immediate emergency land-

ing. Further, the ability to execute a successful forced landing remains the primary

indicator for safety in the manned aviation industry, and therefore also applies to

the unmanned aircraft sector. In what is believed to be a world-first, ARCAA

researchers are developing an automated system that allows a UAV experiencing

engine failure to execute an unsupervised forced landing, and with minimal, if any,

collateral damage.

In this light, this thesis has presented in detail the design, implementation and

testing of a novel Trajectory Generation and Guidance System, which incorporates

both the aircraft dynamics and wind information into the planning and control

processes. The TGGS is intended to function alongside the CSSS and MDMS in the

Flight Guardian automated UAV forced landing system, and contains a number of

novel contributions.

Firstly, in the area of path planning, two different classes of planning algorithms

were considered. The first was based on the descent flight pattern flown by pilots

during a forced landing, and included two algorithms, namely Algorithm 1 and

Algorithm 2. Although both algorithms were suitable for the UAV forced landing

problem, they relied on a constant glide speed, and an adjustment of the desired

path-to-track based on that glide speed. As shown in simulated tests, this presented

problems in changing winds, as well as led to possible instability in the case of

Algorithm 2.

In contrast, the second class of planning algorithms used simple geometric shapes

to plan the path as well as account for limitations in the aircraft dynamics. This is

143

CHAPTER 8. Conclusions

known as the 3-D Dubins Curves, and builds upon the 2-D techniques presented by

Dubins (1957) and Ambrosino et al. (2009, 2006) for powered aircraft to cater for the

dynamics of powerless flight in three dimensions. Not only is this planning method

able to provide a smooth, connected path between any starting and goal location,

and for any aircraft attitude, it is also versatile enough that a new path can quickly

be constructed should the original path be deemed unsuitable. This replanning

capability is most advantageous when the aircraft encounters strong winds that it

cannot overcome, or a better landing site is selected by the MDMS. In addition,

the path formed by the 3-D Dubins Curves can be safely negotiated by an aircraft

flying at changing airspeeds, and also aligns the vehicle for a stable, wings-level

descent once it has passed the approach point. This is a necessary prerequisite for

any subsequent planning action that guides the aircraft from the approach point to

touchdown.

Secondly, in the area of guidance, two classes of algorithms were again consid-

ered. The initial class used the great-circle navigation method for guidance, and

incorporated wind correction and waypoint tracking methods commonly employed

by human pilots. Although this strategy is simple to implement, it nonetheless

exhibited problems with accuracy in path tracking due to assumptions regarding

sideslips, and the fact that it did not employ a dedicated longitudinal path following

strategy. In addition, the intuitive method utilized to control the roll and yaw, as

well as a fixed airspeed to control the altitude may have been inadequate to cor-

rect for cross-track errors in strong or changing winds. Hence, as observed in the

simulated results, when this class of algorithms was combined with the planning

algorithms based on piloted forced landing approaches, the cross-track errors at the

approach point averaged approximately 200 m in winds. This is much greater than

that specified in Section 1.1, that is, no greater than 10 m (approximately 30 ft) in

both the horizontal and vertical directions.

The second class of algorithms attempted to address these problems by employ-

ing a different guidance strategy, in which the airspeed was allowed to vary and the

lateral and vertical guidance modes were decoupled. One lateral and two different

vertical guidance strategies were trialled. The ENG algorithm enhanced the work

done by Park et al. (2007) by including wind information in the guidance logic, and

a yaw damper to deal with sideslips. The algorithm then made use of accelerative

forces, derived from the geometric relationship between the aircraft and the desired

path, to generate the roll angles for lateral control. The commanded roll angles

in turn rotated the aircraft in such a way that it rapidly converged on the path-

to-track, with a new method utilising the geometric relationship between aircraft

and path used to determine the direction to roll. The FPFG algorithm utilized the

MacCready theory to determine the optimal speed to fly in winds, which was sub-

144

sequently converted to a desired pitch angle for longitudinal path following. As has

been alluded to repeatedly, the main disadvantage of this method is that it relied on

a complex array of PID gain schedules to deal with possible wind shift scenarios, and

so is not suitable for real applications. Finally, the MPN algorithm built on the idea

presented in the ENG algorithm, and that of proportional navigation theory, along

with its own specific methods in the algorithm formulation, to derive a new vertical

guidance algorithm. This algorithm incorporated the path angles and wind informa-

tion into the guidance process, and is robust enough for flight testing using any type

of aircraft. For all three algorithms, a novel method employing the geometric and

time relationship between the aircraft and path was used to ensure that the aircraft

could safely follow the path to completion, even in strong winds. As demonstrated

in simulations using MATLAB®, the cross-track errors at the approach point, when

using the 3-D Dubins Curves together with the ENG, FPFG and MPN algorithms,

averaged between 10 to 20 m in winds, which is a tenfold improvement over the

class of planning algorithms derived from human piloted approaches. In addition,

the simulated results demonstrate the ability of the gliding aircraft to follow the

prescribed path in winds, with average path deviation errors that are ≤ 30, which

is comparable to or even better than that of manned, powered aircraft.

Results from simulations using the MicroPilot HORIZONmp simulator have also

further verified the performances of the ENG and MPN algorithms, with results

comparable to those obtained using MATLAB® Simulink. However, the simulator

was not fully indicative of the actual performance of the autopilot, as subsequent

flight tests have shown. In particular, the pitch control exhibited fairly poor perfor-

mance when attempting to follow a commanded pitch attitude, and it would seem

from the results that this is due to the normal control mode for pitch being circum-

vented in favour of control processes more applicable to this research. The flight test

results also indicated that the pitch performance affected that of the roll, where not

enough roll attitude could be commanded to track the path due to the low airspeed

attained. Other factors were attributed to human error, however these were quickly

identified and addressed. In any case, the flight test results are inconclusive and

it is desirable to perform further testing with the autopilot to determine the true

relationship between a commanded aircraft attitude and the actual values obtained,

before implementing new pitch control strategies that align more closely with the

intended usage of the autopilot. These control strategies have been identified as

using either the change in altitude or the airspeed itself to control the pitch, rather

than calculating the pitch directly, and it is expected that these refinements would

improve the overall path following performance of the aircraft.

To summarize, the contributions of this research to the existing body of knowl-

edge were:

145

CHAPTER 8. Conclusions

• Algorithms 1 and 2, two algorithms that utilize piloted forced landing tech-

niques to plan a path from the point of failure to the landing site;

• The 3-D Dubins Curves path planner that caters for the dynamics of powerless

flight using simple geometric shapes;

• The ENG lateral guidance algorithm that accounts for wind and sideslips in

the guidance logic;

• The FPFG vertical guidance algorithm that seeks to optimize the airspeed for

gliding flight in winds, rising or sinking air;

• The MPN algorithm that calculates the required pitch to fly, is easily adapt-

able to any aircraft type, and more robust than the FPFG algorithm, and

finally;

• A novel method for ensuring smooth transition between waypoints in the

generated path.

From these contributions, the 3-D Dubins Curves, as well as the ENG and MPN

algorithms represent the key achievements. These achievements satisfy the two

research questions posed in Section 1.1, which concerned automating the path plan-

ning and guidance strategies for a UAV experiencing engine failure, such that the

unpowered aircraft can steer itself to a selected safe landing site with acceptable

cross-track errors in winds. In so doing, these achievements have provided a signif-

icant contribution to the field of UAV forced landing research, as well as supplied

a methodological framework model for future research in this area. To reiterate,

automating the forced landing capability for UAVs will greatly enhance their au-

tonomy and safety, which in turn helps facilitate their integration into the NAS.

Finally, it should be noted that the planning and guidance techniques developed in

this research are applicable not only to fixed-wing UAVs, but also to piloted aircraft

as a flight-assist system, and to helicopters for various tracking and point-to-point

flying tasks, where the objective is to navigate a smooth trajectory to the target.

Appendix C provides further details where the techniques developed in this research

have been applied to autonomous helicopters.

8.1 Future Work

Although the research presented in this thesis will significantly enhance the safety of

UAVs, and hence facilitate their integration into the NAS, it is believed that further

work could be done to help make this a reality.

Firstly, as alluded to earlier, additional testing needs to be conducted with the

MicroPilot autopilot to ascertain its ability to follow the roll and pitch commands,

and to trial the alternative methods proposed in Section 7.2 to improve the vertical

146

8.1. FUTURE WORK

path following performance. If these additional tests prove the autopilot inadequate

to carry out the assigned tasks, than a new autopilot system will need to be sought.

Secondly, another possible avenue for future research could be to include ob-

stacles in the descent flight planning scenario, which would serve to determine the

effect of any related replanning on the obtained performance. Being able to deal

with obstacles in the flightpath is a characteristic which will greatly enhance the

effectiveness of the 3-D Dubins Curves technique described in this thesis.

Thirdly, recall that this research does not take into account the events that

transpire once the aircraft has passed the approach point, where the aircraft could

be presented with obstacles such as trees, buildings, animals and other man-made

objects in its flightpath. To navigate these objects safely, a different planning algo-

rithm must be employed. It is assumed that by first overflying the selected landing

area, a nadir-pointing camera and/or laser scanner could be used to create a 3-D

model of that area which will then be stored in the on-board computer memory.

When the UAV turns to commence landing, a forward-looking camera can be used

to detect obstacles in front of the aircraft. Although this camera may not be able to

detect hidden or occluded obstacles due to its position, these positions could have

been detected during the overflight, and thus the UAV can then use this a priori

information to better plan a final, collision-free landing trajectory, which would also

include a flare manoeuvre preceding touchdown. Such a planning algorithm should

also account for the structural and dynamic limitations of the aircraft, and could

therefore utilize elements of the 3-D Dubins curves described in this thesis.

Finally, at the earliest stage, the TGGS developed in this research should be

integrated with the CSSS and MDMS to form the complete Flight Guardian UAV

forced landing system. This system should then be verified first in simulation and

then in flight.

147

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156

AState-Space Model of Boomerang UAV

A.1 Lateral Model

The following flight parameters were used when designing the lateral controller for

the Boomerang UAV.

Basic aircraft and atmospheric properties

TAS : U0 = 19 m/s;

Initial pitch : θ0 = 0;

Gravitational acceleration : g = 9.80665;

Aircraft mass : m = 5.555 kg;

Wing surface area : S = 0.598745 m2;

Wingspan : b = 1.81 m;

Mean wing chord : c = 0.33077 m;

Sea-level air density : ρ = 1.225 kg/m3;

Sea-level air pressure : Q = 0.5ρU02 kg.m-1.s-2;

Side force coefficient

Sideslip derivative : Cyβ = -0.18003;

Roll control derivative : Cyδa = 0;

Yaw control derivative : Cyδr = 0.094752;

Roll moment coefficient : Clβ = 0.00016255;

Yaw moment coefficient : Cnβ = 0.08028;

Roll rate derivative : Cyp = 0;

Yaw rate derivative : Cyr = 0.161225;

Roll moment coefficient

Roll rate derivative : Clp = -2.73435;

Yaw rate derivative : Clr = 1.1114;

Yaw moment coefficient

157

CHAPTER A. State-Space Model of Boomerang UAV

Roll control derivative : Cnδa = -0.022417;

Yaw control derivative : Cnδa = -0.0339;

Roll rate derivative : Clδa = -0.124873;

Yaw rate derivative : Clδr = 0.010209;

Gross moments of inertia

Ixx = 1.273 kg.m2;

Iyy = 1.348 kg.m2;

Izz = 0.528 kg.m2;

Ixz = 0.035 kg.m2;

From the above, the lateral directional derivatives can be obtained from (R. C. Nel-

son, 1998) and (Etkin & Reid, 1996) as

Yv = QSCyβ/m;

Yp = QSbCyp/(2mU0);

Yr = QSbCyr/(2mU0);

Lv = QSbClβ/Ixx;

Lp = QSb2Clp/(2IxxU0);

Lr = QSb2Clr/(2IxxU0);

Nv = QSbCnβ/Izz;

Np = QSb2Cnp/(2IzzU0);

Nr = QSb2Cnr/(2IzzU0);

Yδa = QSCyδa ;

Yδr = QSCyδr ;

Lδa = QSbClδa ;

Lδr = QSbClδr ;

Nδa = QSbCnδa ;

Nδr = QSbCnδr ;

and the derivatives of inertia are given by

I ′xx = (IxxIzz − I2xz)/Izz;I ′zz = (IxxIzz − I2xz)/Ixx;

I ′xz = Ixz/(IxxIzz − I2xz).

Now, the full lateral dynamics model of the Boomerang UAV can be expressed

in the basic aircraft matrix equation

x = Ax + Bc,�� A.1

158

A.1. LATERAL MODEL

in which x = [v p r φ]T and c = [δa δr]T , and

Alat =

Yv/m Yp/m (Yr/m− U0) g cos(θ0)

Lv/I′xx + I ′xzNv Lp/I

′xx + I ′xzNp Lr/I

′xx + I ′xzNr 0

I ′xzLv +Nv/I′zz I ′xzLp +Np/I

′zz I ′xzLr +Nr/I

′zz 0

0 1 tan(θ0) 0

=

−0.7724 0 −18.9671 9.8067

1.9247 −19.9149 7.7565 0

69.1314 −23.8689 −2.5966 0

0 1 0 0

,�� A.2

Blat =

1/m 0 0

0 1/I ′xx I ′xz

0 I ′xz 1/I ′zz

0 0 0

· Yδa Yδr

Lδa Lδr

Nδa Nδr

=

0 2.2582

−23.8289 1.5015

−11.7532 −15.2855

0 0

.�� A.3

The rudder servo transfer function can be approximated for small RC aircraft as

Hr =40

s+ 40,

�� A.4

and taking the control gain as Kr = -0.025, the rudder to yaw rate transfer

function is

−611.4s3 − 7838s2 + 1.097× 105s+ 5.226× 104

s5 + 63.28s4 + 2497s3 + 8.802× 104s2 + 1.011× 106s− 2.123× 105.

�� A.5

The roll angle to aileron input transfer function is given by

Gδaφ =φ(s)

δa(s)=

Lδas(Ixxps− Lp)

,�� A.6

and the aileron servo transfer function can be approximated as

Ha =1

0.025s+ 1.

�� A.7

From a plot of the root locus, it is desired to place a pole at s = −1/γ, where

γ = 2/3, giving the transfer function of the roll controller as

159


PDr = 0.6667s+ 1.�� A.8

This gives the forward path transfer function −PDr ∗Ha ∗Gδaφ as

Gforward =19.95s+ 29.92

0.03177s3 + 1.884s2 + 24.52s,

�� A.9

and, from observing the root locus of this transfer function, the roll controller

gain of Kφ = −10 is chosen.

Now, assuming a flap effectiveness parameter of 0.025 for both the ailerons and

rudder, and a time constant of τ = 3.5 sec for the washout filter, the closed-loop

system transfer function Gfeedback can be shown to be a 8th-order system.

4701s5 + 5.914× 104s4 − 5.297× 106s3 + 7.187× 105s2 + 2.556× 108s+ 7.284× 107

s8 + 103.6s7 + 1.143× 104s6 + 5.014× 105s5 + 1.531× 107s4 + 3.887× 108s3

+ 5.951×108s2 +1.39×108s.�� A.10

A.2 Longitudinal Model

In designing the longitudinal controller for the Boomerang UAV, the same basic

aircraft and atmospheric properties as for the lateral controller was used, however,

the following additional flight parameters were also included.

Aerodynamic coefficients

Lift force alpha derivative : CLα = 4.406;

Zero-lift drag : CD0 = 0.0075;

Pitch moment alpha derivative : Cmα = -3.31504;

Pitch moment alpha-dot derivative : Cmα = -20.4799;

Pitch rate derivative : Cmq = -41.4885;

Pitch control derivative : Cmδe = -0.79182;

Pitch control (elevator) derivative : CLδe = 0.3022;

Pitch control derivative in the z (downward) direction : CZδe = −CLδe ;

From the above, the longitudinal dimensional derivatives (R. C. Nelson, 1998)

can be obtained:

Zw = −(CLα + Cδ0)QS/(mU0);

Zδe = (CZδeQS)/m;

160

A.2. LONGITUDINAL MODEL

Mw = (CmaQSc)/(U0Iyy);

Mw = (Cmαc)/2U0)(QSc/U0Iyy);

Mq = (CmqcQSc)/(2U0Iyy);

Mδe = (CmδeQSc)/Iyy;

Now, expressing the short period approximate model in the basic matrix equation

xsp = Aspxsp +Bspδe,�� A.11

where δe is the elevator input, and

xsp =

[w

q

] �� A.12

Asp =

[Zw/m U0

Iyy−1(Mw + ZwMw/m) Iyy

−1(Mq + U0 ∗Mw)

]

=

[−0.9966 19

−3.9794 −12.9991

],

�� A.13

Bsp =

[Zδe/m

Iyy−1(Mδe +MwZδe/m)/Iyy

]=

[−1.2965

−18.7890

].

�� A.14

Adding that θ = q, such that sθ = q and taking the output as θ and the input

as δe, the following transfer function is obtained

Gθδe (s) =θ(s)

δe(s)=

1

s

q(s)

δe(s)

= [0 1](sI −Asp)−1Bsp

=−18.79s− 13.57

s3 + 14s2 + 88.56s.

�� A.15

Assuming the elevator servo transfer function to be the same as that of Equa-

tion A.4, the inner loop transfer function for the pitch controller can be shown to

be

Ginner =Gθδe (s)H(s)krg

1 +Gθδe (s)H(s)krg=

161


751.6s4 + 4.056× 104s3 + 4.859× 105s2 + 2.644× 106s− 1.023× 105

s6 + 108s5 + 3462s4 + 3.657× 104s3 + 3.173× 105s2 + 1.951× 106s+ 1.265× 107,�� A.16

where H(s) corresponds to the servo transfer function, and the inner loop control

gain Krg = −1.

However, the root locus for this closed loop system is unstable, therefore, a lag

compensator (integrator) is added in the outer loop to cause the locus to be pulled

back into the Left-Half-Plane. With the outer loop gain Ka set to 1, the feedback

transfer function of the system Gfeedback is

751.6s10+1.217×105s9+7.468×106s8+2.23×108s7+3.689×109s6+4.125×1010s5

+ 3.392×1011s4 + 2.296× 1012s3 + 1.127× 1013s2 + 3.325× 1013s− 1.295× 1012

s12 + 216s11 + 1.934× 104s10 + 9.426× 105s9 + 2.798× 107s8 + 5.486× 108s7

7.67×109s6 + 8.07× 1010s5 + 6.701× 1011s4 + 4.46× 1012s3 + 2.311× 1013s2

+ 8.261×1013s+1.588×1014.�� A.17

162

BMATLAB® Simulink Models

B.1 The Aerosonde UAV Model

Figure B.1: Simulink diagram of the Aerosonde UAV model

163

CHAPTER B. MATLAB® Simulink Models

B.2 The Boomerang UAV Model

Yaw

Yaw

Wind Profile

WindVel

Wind Correction

Current Hdg

VTAS

Vn

Ve

Vd

g

InputWinds

Flag

dGlideAngle

WindSpeed

WindDirection

True

1

Throttle

0

Switch 1

Stop Sim

when A /C

on gnd

STOP

Roll Angle

Roll

Reset

0

R2D

R2D

Pitch Angle

Pitch

Mixture

13

Longitudinal Control

Pitch

Pitch Rate

alpha

dPath

dPathWind

Flag

Control

g

nc

LOS_arg

Ve

Vn

Vd

NL_accln

e_flag

e_flag _future

h_miss

Elevator 1

Longitude

Lon

Latitude

Lat

Lateral Control

Roll

Roll Rate

Yaw Rate

Roll Cmd

Aileron

Rudder

Ignition

0

Hd Err

Guidance Law

ECEF

Vn

Ve

Vd

g

Bearing

Vw

phi_w

pitch

VTAS

AOA

dRoll

dPathAngle

Control

LOS_arg

ascmd _LOS

ascmd _NL

e_flag

e_flag _future

h_miss

Flap

0

False

0

ECEF Coords

ECEF

Demux

Demux

Demux

Demux

Demux

Demux

Boomerang UAV

Controls

Winds

RST

States

Sensors

VelW

Mach

Ang Acc

Euler

AeroCoeff

PropCoeff

EngCoeff

Mass

ECEF

MSL

AGL

REarth

AConGnd

Gravity

Attitude Determination

Pitch

Yaw

ACVec

Altitude

Alt

Airspeed

Airspeed

Aircraft Velocities

AircraftVel

Figure B.2: Simulink diagram of the Boomerang UAV model

164

CPath Planning for Target Tracking Using an

Autonomous Helicopter

C.1 Background

During the course of the Ph.D. candidature, the student was also awarded an Inter-

national Research Staff Exchange Scheme (IRSES) scientific research grant by the

Australian Academy of Science. The grant was used to help support approximately

three months of overseas research work with the Computer Vision Group (CVG)

at UPM in Madrid, Spain, under the direction of Professor Pascual Campoy. This

was carried out as part of the International Cooperative Program for Unmanned

Aerial Systems (ICPUAS) venture between QUT, UPM and Cranfield University in

England. Some of the primary objectives of this project are to:

1. Develop UAS frameworks for integration into civilian airspace under a regu-

lated context;

2. Advance the state-of-the-art in computer vision, control and trajectory plan-

ning for UAS through research;

3. Develop operational and safety procedures for UAS flight requirements such

that they can be implemented by regulatory bodies in their development of

UAS regulation policies; and

4. Generate business models for an effective technology transfer of UAS and

UAS technologies to society.

Such a program will also develop new channels for information exchange and for

providing high quality research to society. It will enable access to the diversified

skill sets and facilities of each partner organization, the exchange of simulated and

real flight test data between these organizations, as well as experiments to be per-

formed under different operational conditions and environments which will be highly

beneficial in validating the different research objectives.

165

CHAPTER C. Path Planning for Target Tracking Using an AutonomousHelicopter

910 mm

1190 mm

Figure C.1: Helipad target used for obtaining the image homographies. (Source: CVGImage Repository)

As part of its goal to help integrate computer vision technologies into indus-

trial applications, CVG is investigating the use of multiple-image homographies to

estimate the 3-D pose of planar objects (Mondragon, Campoy, Martınez, & Olivares-

Mendez, 2010), such as the landing pad depicted in Figure C.1, with respect to an

autonomous helicopter. The problem of extracting image features for landing tasks

is not new, having being studied as early as the mid 1990s, with notable examples

including the work presented by Ma, Kosecka, and Sastry (1999), Shakernia, Ma,

Koo, and Sastry (1999), Saripalli, Montgomery, and Sukhatme (2003), Saripalli and

Sukhatme (2007) and Saripalli (2009). However, outside the military, the specific

task of landing a helicopter on a moving target has only been studied by a handful of

researchers, with recent examples discussed in (Saripalli & Sukhatme, 2007; Saripalli,

2009), where image extraction using Hu’s Moments of Inertia (Hu, 1962) is combined

with the well-known Variational Hamiltonian and Euler-Lagrange equations to form

a reconfigurable 3-D flightpath. However, their method of feature extraction and

path formulation is different to the image processing techniques undertaken by CVG,

as well as the path planning techniques and method of implementation discussed in

this appendix.

In particular, the platform used for this research is a Rotomotion electric un-

manned helicopter equipped with an Xscale-based flight computer, on-board sensors

such as GPS, IMU and magnetometers, as well as a pan-tilt camera system. This

UAV also carries a VIA mini-ITX 1.5 GHz on-board computer with 2 Gb Of RAM

and Firewire camera support for image processing (Figure C.2). The computers

run the Linux operating system in a multi-client wireless 802.11g ad-hoc network

using Transmission Control and User Datagram Protocols (TCP/UDP), and allow

embedded applications to run on board the helicopter as it interacts with external

166

C.1. BACKGROUND

Figure C.2: Rotomotion electric helicopter UAV used for pose estimation flight experiments.The helicopter is carrying an Xscale-based flight computer, a pan-tilt camera system and aVIA mini-ITX 1.5 GHz on-board computer.

processes. The visual control system and additional external processes are also inte-

grated with the flight control through this layer using TCP/UDP messages. The ob-

jective is to then use the landing pad position estimates in a dynamic look-and-move

visual control system (Hutchinson, Hager, & Corke, 1996), such that the helicopter

can track and manoeuvre to a hovering position above that target. This can also

be considered a precursor to landing should it be necessary to do so, and is highly

advantages for applications such as traffic surveillance, police pursuit, security or

payload delivery.

Figure C.3: UAV on-board visual control system employing a dynamic look-and-move ar-chitecture. (Source: CVG Image Repository)

As shown in Figure C.3, the control architecture employed for tracking is es-

sentially position-based visual servoing (PBVS), where the error between the cur-

rent and the desired pose of the camera-UAV system is calculated and used by the

167


zc

xc

yc

Helipad coordinate system

π

O'

x

y

z

O

North

East Down

Camera coordinate system

U.A.V. coordinate system

Helipad

Figure C.4: Relationship between the helipad, camera and UAV coordinate systems (Source:CVG Image Repository)

low-level PID controllers on board the aircraft to generate the control signals for

positioning the UAV. A reference point in coordinates relative to the helipad is then

defined, and for landing this reference point is (0, 0, 0). Now, since the estimated

position of the helipad relative to the on-board camera coordinate system is known,

this reference point can be transformed to the helicopter body frame coordinates

and also used to generate the desired NED and heading commands. The relation-

ship between the different coordinate systems used for pose estimation is shown in

Figure C.4. However, a major disadvantage of using only a PID-based control sys-

tem for both path planning (positioning) and tracking (command following) tasks is

that it can become quite difficult to correct for noisy measurements, and may even

lead to instability if large gains are applied to correct for the errors. In addition,

such a control system is also unsuitable if the UAV is initially further away, or if the

target is moving (such as for landing on ships).

C.2 Path Planning for Target Tracking

A better solution to the PBVS problem described above is to provide the UAV

with a more robust and decoupled path planning and control system. Since the

168

C.3. RESULTS

on-board flight computer is already capable of tracking waypoint coordinates with

good accuracy using commercial software, it was decided to concentrate solely on

improving the planning system. To this end, it was decided that since the 3-D

Dubins Curves described in Section 3.2 showed promising results for fixed-wing

aircraft (Section 7.1), they could be modified to suit helicopters flying paths similar

to that of fixed-wing aircraft, such as when tracking moving ground targets. The

modifications are summarized below.

1. Firstly, the minimum turn radius is set to null (since a helicopter is capable

of turning on its own axis), however, for pursuit of a moving target, a bank

angle φ of up to 45◦ is allowed;

2. Secondly, the minimum and maximum allowable value on the path angle of

the straight segment, γline is now specified as being between 0◦ and −90◦,

and the helicopter is constrained to fly at a nominal speed VTAS of 5 cm/s

to provide a stable platform for the vision algorithms to run;

3. Thirdly, the circular manoeuvres to lose excess altitude described in Sec-

tion 3.2.2.1 have been removed from this planning algorithm as they were

suitable only for fixed-wing aircraft;

4. Next, the additional waypoint described in Section 3.2.2.2 has also been re-

moved; the helicopter will simply hover above the final waypoint once it has

been reached;

5. Finally, during replanning of the path, the helicopter will continue to receive

new target positions as they become available, and is not constrained to reject

additional information by a minimum altitude zbound. This is because since

the helicopter is engaged in powered flight, γline can, if necessary, be zero,

meaning that 2-D flight paths are possible.

To demonstrate the performance of the new planning algorithm, a number of

flight scenarios were conducted using Heli3D, the Rotomotion helicopter simulation

environment. This simulator also includes a ground station user interface for flight

monitoring and video output of the helicopter flightpath, and allows the source code

being tested to be uploaded to the real aircraft through a mere redirection of the

Internet Protocol (IP) address. The results obtained from simulation are described

below.

C.3 Results

Three representative cases have been chosen to illustrate the performance of the

path planning algorithm. Section C.3.1 details a simple planning scenario in which

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the helicopter is required to track a stationary target. This scenario is then extended

in Section C.3.2 to include replanning for a new target during flight, while en route

to the first target. Finally, in Section C.3.3, the helicopter is tasked to track a

stationary target that begins moving during the flight.

All three examples share the same arbitrarily chosen initial conditions summa-

rized in Table C.1, where the xyz positions are simulated ENU coordinates of what

the image processing algorithm will provide to the path planner.

Position x(m) y(m) z(m) φ(deg) θ(deg) ψ(deg)

Init. 0 0 20 45 0 280Final 32.21 1.27 1 45 0 150

Table C.1: Initial conditions for autonomous helicopter path planning

Wind effects have not been considered in these simulations, as the Heli3D simu-

lator does not have provision for these events. However, CVG is currently developing

an enhanced version of the simulator which will allow wind effects to be modelled,

and it is expected that testing using this program will render a more accurate repre-

sentation of the helicopter performance. Notwithstanding, the Heli3D simulator is

adequate for the time being to demonstrate the performances of the path planner,

as well as the built-in control system for the target tracking tasks.

Figure C.5: Desired and actual helicopter flightpath while tracking a stationary target

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C.3. RESULTS

C.3.1 Simple Path Following

In the first tests, the helicopter is required to construct a path to track a target

located at the final ENU position given in Table C.1. Figure C.5 shows that the

helicopter first ascends from a stationary position to Point A (the start of the path),

before descending to the target indicated as shown. Once over the target, the he-

licopter enters into hover mode and maintains an elevation of 1 m over the final

position; this is a function of the internal flight control system. As can also be seen,

the control system provides very good path following with negligible cross-track

errors.

Figure C.6: Desired and actual helicopter flightpath while tracking a shifting target, showing(a) Top view of the aircraft response, and (b) An oblique view of the same.

C.3.2 Replanning with Shifting Target

Once a simple target tracking capacity has been established, the helicopter is tasked

to track a target that shifts its position during flight. This shift may be the result of

a newly acquired target (either captured by the onboard camera or transmitted from

a ground station) being given more importance during a pursuit mission. As shown

in Figure C.6, the helicopter initially ascends to Point A at the start of the first

path, before heading for the target located at Point D, with the coordinates given

in Table C.1. At Point B, the helicopter is commanded to track a new target, and

begins replanning the path for intercept. Due to the small time delay between when

the new instructions were received and the actual realization of those instructions,

a small overshoot is incurred (Point C). However, it can be seen that the helicopter

quickly recovers to intercept the new target, located at (10.11, -2.38, 15) m. Once

again, very good path following is demonstrated.

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Figure C.7: Desired and actual helicopter flightpath while tracking a moving target, showing(a) Top view of the aircraft response, and (b) An oblique view of the same.

C.3.3 Replanning with Moving Target

Following successful completion of the previous mission, a final tracking task is

assigned the helicopter. The target this time is initially located as in the preceding

examples, but now moves linearly (red line) while the helicopter is in the air to a

new location as shown. The xyz coordinates of the final target position are (48.73,

2.21, 1) m. As depicted in Figure C.7, the helicopter first plans a path to the

original target location and follows it, reaching the start of the path at Point A and

converging on the path at Point B. Around this time, the helicopter also begins to

receive updated positions of the moving target, and replans to intercept the new

target positions. The nature of the reconfigured paths (not shown) initially takes

the helicopter to Point C, but as seen in the figure, this divergence does not affect

the tracking performance of the helicopter, which is still able to converge on the

final target position.

C.3.4 Further Work

The results indicate that the modified 3-D Dubins Curves algorithm discussed can

be suitably applied to the helicopter target tracking problem. Currently, work is

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C.3. RESULTS

underway to combine the image processing software with the path planner to form

an integrated target tracking system. This system will first be tested in simulation,

then later verified in actual flight tests.

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path planning, guidance and control for a uav forced landing

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