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Thor I. Fossen Professor of Guidance, Navigation and Control

Centre for Autonomous Marine Operations and Systems (AMOS)

Department of Engineering Cybernetics Norwegian University of Science and Technology (NTNU)

NO-7491 Trondheim, Norway

Lecture Notes: TTK 4190 Guidance and Control of Vehicles

Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)

WIKI page: http://www.fossen.biz/TTK4190

Home page: http://www.fossen.biz/

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Textbook Fossen, T. I. (2011) Handbook of Marine Cra/ Hydrodynamics and Mo4on Control. John Wiley & Sons Ltd.


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Useful References

Fossen, T. I. (1994). Guidance and Control of Ocean Vehicles, John Wiley & Sons Ltd. ISBN 0-471-94113-1

xb

yb

zb

u ( )surge

r ( )yaw

v ( )sway

( )heavew

( )rollp

( )pitchq

SNAME (1950). Nomenclature for TreaEng the MoEon of a Submerged Body Through a Fluid. The Society of Naval Architects and Marine Engineers, Technical and Research Bulle4n No. 1-5, April 1950, pp. 1-15.


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Goals for the Course: 1. MathemaEcal modeling

of vehicles. This includes: KinemaEcs KineEcs EquaEons of moEon

for marine craO and aircraO

Wind, wave and ocean current models

Hydrodynamics: maneuvering and seakeeping theory

Copyright Bjarne Stenberg/NTNU


2. Design of guidance, navigaEon and moEon control systems for a large number of applicaEons

3. Simulate the moEons of marine craO and aircraO in the Eme-domain using hydrodynamic/aerodynamic models

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TTK 4190 Guidance and Control (T. I. Fossen)

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TTK 4190 Guidance and Control (T. I. Fossen) Lecture Notes 2005

Pipe-laying vessel

Geological survey

Heavy lift operations

Position mooring

Pipe and cable laying

Marine Craft in Operation

ROV operations Vibration control of marine risers

Cable-laying vessel

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Marine Craft in Operation

Copyright Bjarne Stenberg/NTNU Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)

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Italian supply ship Vesuvio refueling two ships at sea.

Courtesy: Hepburn Eng. Inc.

Path Following and Trajectory Tracking

Underactuated container ship in transit. Fully actuated supply ship cruising at low speed.


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Formation Control/Underway Replenishment


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Interdisciplinary: Rocket Launch / DP system / THCS

SMMarine Segment

Courtesy: SeaLaunch

http://www.sea-launch.com

Courtesy: SeaLaunch LLC


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Trim & Heel Correction System (THCS)

Process and Marine Control


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NTNU Infrastructure


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Optimisation of hull resistance with and without waves

Identification of hydrodynamic parameters by:

Planar Motion Mechanism (PMM) tests

Vertical Motion Mechanism (VMM) tests

Towing Tests of Ships and Floating Structures

Model testing in Peerlesspool in London


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Marine Cybernetics Laboratory (MCLab)

MCLab Dimensions:

The soOware is developed by using rapid prototyping techniques and automaEc code generaEon under Matlab/Simulink and RT-Lab.

The target PC onboard the model scale vessels runs the QNX real-Eme operaEng system, while experimental results are presented in real-Eme on a host PC using Labview.

L ! B ! D " 40 m! 6.5 m! 1. 5 m

Cybership II


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NTNU Research Groups: Department of Marine Technology Department of Biology incl. UNIS and CalPoly Department for Archaeology and Religious Studies Department of Engineering CyberneEcs Centre for Autonomous Marine OperaEons and Systems (AMOS)

Scientific Focus Areas: Development of technology for guidance, navigaEon and control of underwater vehicles (ROVs and AUVs)

Environmental monitoring and mapping at sea surface, water column, and sea bed

OperaEons under ice in the arcEc Study of any object of interest (bio-geo-chemical objects) InspecEon/surveillance for environmental agencies, oil industry, ecotoxicology

Deepwater archaeology Deepwater ecology research Complex deepwater underwater operaEons including inspecEon and intervenEon

Deepwater mineral extracEon

ROV Minerva

AUV REMUS 100 at Svalbard

Applied Underwater Robotics Laboratory AUR-Lab

RV Gunnerus

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NTNU Research Vessel Gunnerus 31 meters long Top speed 13 knots

http://www.ntnu.edu/marine/gunnerus

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UAV Factory Penguin B w/ Piccolo SL

28 m/s cruise speed

Gasoline, 8 hr

endurance

MTOW 21 kg

2-5 kg payload

capacity

Large payload bay

80W generator

Avionics system

integration made with Maritime Robotics based on Cloudcap technology

Telemetry on 2.4 GHz radio, GPRS (and VHF)

Catapult launch

Custom payload

system integration with avionics interface

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Skywalker X8 w/Ardupilot 18 m/s cruise speed

Catapult launch

Belly or net landing

Electric, 1hr

endurance

Large payload bay

>1 kg payload

capacity

Inexpensive

Flexible avionics and

payload system integration with ArduPilot open source autopilot and mission planning SW

Currently telemetry on 433 MHz or 5.8 GHz radio for VLOS

Can be set up for BLOS with GPRS and VHF radio links

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3DRobotics hexa-copter w/Ardupilot

Electric, 5-10 min

endurance

1 kg payload capacity

Inexpensive

Flexible system

integration with Ardupilot open source autopilot and mission planning SW

Telemetry on 433 MHz og 5.8 GHz radio


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Microdrone Quad-copter

Turn-key solution

Various camera, video

and radio systems

Electric, 45 min

endurance

2-3 kg payload

capacity

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Marine craD: ships, high-speed craO, semi-submersibles, oaEng rigs, submarines, remotely operated and autonomous underwater vehicles, torpedoes and other propelled/powered structures for instance a oaEng air eld. Vehicles that do not travel on land (ocean and ight vehicles) are usually called craO. Vessel: "hollow structure made to oat upon the water for purposes of transportaEon and navigaEon; especially, one that is larger than a rowboat ". The words vessel, ship and boat are oOen used interchangeably. In Encyclopedia Britannica, a ship and a boat are disEnguished by their size through the following deniEon: Ship: "any large oaEng vessel capable of crossing open waters, as opposed to a boat, which is generally a smaller craO. The term formerly was applied to sailing vessels having three or more masts; in modern Emes it usually denotes a vessel of more than 500 tons of displacement. Submarine: "any naval vessel that is capable of propelling itself beneath the water as well as on the water's surface. This is a unique capability among warships, and submarines are quite dierent in design and appearance from surface ships Underwater Vehicle: "small vehicle that is capable of propelling itself beneath the water surface as well as on the water's surface. This includes unmanned underwater vehicles (UUV), remotely operated vehicles (ROV) and autonomous underwater vehicles (AUV).

Marine Craft Ref. Encyclopedia Britannica


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Marine vessels are also classied according to their maximum operaEng speed. For this purpose it is common to use the Froude number

Marine Craft

Fn ! UgL

The pressure carrying the vessel can be divided into hydrostaEc and hydrodynamic pressure. The corresponding forces are:

Buoyancy force due to the hydrostaEc pressures (proporEonal to the displacement of the ship) Hydrodynamic force due to the hydrodynamic pressure (approximately proporEonal to the square of the speed)

Then we can classify the vessels according to (FalEnsen 2005):

Displacement vessels (Fn1.0-1.2): The hydrodynamic force mainly carries the weight.

U: ship speed L: overall (submerged length of the ship) G: acceleraEon of gravity

In this course, only displacement vessels are covered


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Degrees-of-Freedom (DOF)

xb

yb

zb

surge

yaw

sway

heave

roll

pitch

In maneuvering, a marine craO experiences moEon in 6 DOF. The moEon in the horizontal plane is referred to as surge (longitudinal moEon, usually superimposed on the steady propulsive moEon) and sway (sideways moEon). Heading, or yaw (rotaEon about the verEcal axis) describes the course of the vessel. The remaining three DOFs are roll (rotaEon about the longitudinal axis), pitch (rotaEon about the transverse axis), and heave (verEcal moEon). Roll is probably the most troublesome DOF, since it produces the highest acceleraEons and, hence, is the principal villain in seasickness. Similarly, pitching and heaving feel uncomfortable to humans. When designing ship autopilots, yaw is the primary mode for feedback control. StaEonkeeping of a marine craO implies stabilizaEon of the surge, sway and yaw modes.


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When designing feedback control systems for marine vessels, reduced order models are oOen used since most vehicles do not have actuaEon in all DOF. This is usually done by decoupling the moEons of the vessel according to: 1-DOF models can be used to design forward speed controllers (surge), heading autopilots (yaw) and roll damping systems (roll). 3-DOF models are usually: Horizontal plane models (surge, sway and yaw) for ships, semi-submersibles and underwater vehicles that are used in dynamic posiEoning systems, trajectory-tracking control systems and path-following systems. For slender bodies like submarines, it is also common to assume that the moEons can be decoupled into longitudinal and lateral moEons. Longitudinal models (surge, heave and pitch) for forward speed, diving and pitch control. Lateral model (sway, roll and yaw) for turning and heading control. 4-DOF models (surge, sway, roll and yaw) are usually formed by adding the roll equaEon to the 3 DOF horizontal plane model. These models are used in maneuvering situaEons where it is important to include the rolling moEon usually with the purpose of reducing roll by acEve control of ns, rudders or stabilizing liquid tanks. 6-DOF models (surge, sway, heave, roll, pitch and yaw) are fully coupled equaEons of moEon used for simulaEon and predicEon of coupled vessel moEons. These models can also be used in advanced control systems for underwater vehicles which can be actuated in all DOF.

Degrees of Freedom (DOF)


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Classification of Models Simulation Model: This model is the most accurate descripEon of a system, for instance a 6-DOF high-delity model for simulaEon of coupled moEons in the Eme domain. It includes the marine craO dynamics, propulsion system, measurement system and the environmental forces due to wind, waves and ocean currents. The model should be able to reconstruct the Eme responses of the real system and it should also be possible to trigger failure modes so you can simulate accidents and erroneous signals etc. SimulaEon models where the uid memory eects are included (frequency-dependent models) typically consist of 50-200 ODEs while a frequency-independent model can be represented in 6 DOF with 12 ODEs for generalized posiEon and velocity. In addiEon you need some states to describe the environmental loads and actuators but sEll the number of states will be less than 50 for a frequency-independent vessel model


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Classification of Models Control Design Model: The controller model is a reduced-order or simplied version of the simulaEon model that is used to design the moEon control system. In its simplest form, this model is used to compute a set of constant gains for a PID controller. More sophisEcated control systems use a dynamic model to generate feedforward and feedback signals. This is referred to as model-based control. The number of ODEs used in convenEonal model-based ship control systems is usually less than 20. A PID controller typically requires two states: one for the integrator and one for the low-pass lter used to limit noise amplicaEon. Consequently, setpoint regulaEon in 6 DOF can be implemented by using 12 ODEs. However, trajectory-tracking controllers require addiEonal states for feedforward as well as ltering so higher-order control laws are not uncommon. Observer Design Model: The observer model will in general be dierent from the model used in the controller since the purpose is to capture the addiEonal dynamics associated with the sensors and navigaEon systems as well as disturbances. It is a simplied version of the simulaEon model where asenEon is given to accurate modeling of measurement noise, failure situaEons including dead-reckoning capabiliEes, ltering and moEon predicEon. For marine craO, the model-based observer oOen includes a disturbance model where the goal is to esEmate wave, wind and ocean current forces by treaEng these as colored noise. For marine craO the number of ODEs in the state esEmator will typically be 20 for a DP system while a basic heading autopilot is implemented with less than 5 states.


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The Classical Models in Naval Architecture

m!u! ! vr " wq ! xg"q2 " r2# " yg"pq ! r!# " zg"pr " q! #$ # Xm!v! ! wp " ur ! yg"r2 " p2# " zg"qr ! p! # " xg"qp " r!#$ # Ym!w! ! uq " vp ! zg"p2 " q2# " xg"rp ! q! # " yg"rq " p! #$ # ZIxp! " "Iz ! Iy#qr ! "r! " pq#Ixz " "r2 ! q2#Iyz " "pr ! q! #Ixy

" m!yg"w! ! uq " vp# ! zg"v! ! wp " ur#$ # KIyq! " "Ix ! Iz#rp ! "p! " qr#Ixy " "p2 ! r2#Izx " "qp ! r!#Iyz

" m!zg"u! ! vr " wq# ! xg"w! ! uq " vp#$ # MIzr! " "Iy ! Ix#pq ! "q! " rp#Iyz " "q2 ! p2#Ixy " "rq ! p! #Izx

" m!xg"v! ! wp " ur# ! yg"u! ! vr " wq#$ # N

The moEons of a marine craO exposed to wind, waves and ocean currents are usually modeled in 6 DOF by applying Newton's 2nd law:


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The Classical Models in Naval Architecture

The external forces and moments X,Y,Z,K,M and N acEng on a marine craO are usually modeled by using: Maneuvering Theory: The study of a ship moving at constant posiEve speed U in calm water within the framework of maneuvering theory is based on the assumpEon that the maneuvering (hydrodynamic) coecients are frequency independent (no wave excitaEon). The maneuvering model will in its simplest representaEon be linear while nonlinear representaEons can be derived using methods like cross-ow drag, quadraEc damping or Taylor-series expansions. Seakeeping Theory: The moEons of ships at zero or constant speed in waves can be analyzed using seakeeping theory where the hydrodynamic coecients and wave forces are computed as a funcEon of the wave excitaEon frequency using the hull geometry. The frequency-dependent models are usually derived within a linear framework while extensions to nonlinear theory is an important eld of research.


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Maneuvering Theory

Assumes that the ship is moving in restricted calm water. Hence, the maneuvering model is derived for a ship moving at posiEve speed U under a zero-frequency wave excitaEon assumpEon such that added mass and damping can be represented by using hydrodynamic derivaEves (constant parameters). The zero-frequency assumpEon is only valid for surge, sway and yaw since the natural period of a PD controlled ship will be in the range of 100-150 s. For 150 s this result in:

!n ! 2"T! 0.04 rad/s #

The natural frequencies in heave, roll and pitch are much higher so it is not straighworward to remove the frequency dependence in these channels.


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Maneuvering Theory It is common to formulate the ship maneuvering model as a coupled surge-sway-yaw model and thus neglect heave, roll and pitch moEons:

Hydrodynamic added mass potenEal damping due to wave radiaEon and viscous damping HydrostaEc forces (spring sEness) Wind forces Wave forces (1st- and 2nd-order) Control and propulsion forces

m!u! ! vr ! xgr2 ! ygr! " " Xm!v! # ur ! ygr2 # xgr! " " YIzr! # m!xg#v! # ur$ ! yg#u! ! vr$" " N

#

MRB!" ! CRB!!"! " #RB #

!RB ! !hyd " !hs hydrodynamic andhydrostatic forces

" !wind " !waveenvironmental forces

" !control #

!i ! !Xi,Yi,Zi,Ki,Mi,Ni"!, i ! #hyd, hs, wind, wave, control$ #


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Linearized Maneuvering Models

In the linear 6-DOF case there will be a total of 36 mass and 36 damping elements proporEonal to velocity and acceleraEon. In addiEon to this, there will be restoring forces, propulsion forces and environmental loads. If the generalized force is wrisen in component, the linear added mass and damping forces become:

where Xu,Xv , . . . ,Nr are the linear damping coefficientsand Xu! ,Xv! , . . . ,Nr! represent hydrodynamic added mass.

!hyd

X1 ! Xuu " Xvv " Xww " Xpp " Xqq " Xrr" Xu# u# " Xv# v# " Xw# w# " Xp# p# " Xq# q# " Xr#r#

!

N1 ! Nuu " Nvv " Nww " Npp " Nqq " Nrr" Nu# u# " Nv# v# " Nw# w# " Np# p# " Nq# q# " Nr#r#

#

#


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Nonlinear Maneuvering Models ApplicaEon of nonlinear theory implies that many elements must be included in addiEon to the 36 linear elements. Truncated Taylor-series expansions using odd terms (1st- and 3rd-order) which are sed to experimental data (Abkowitch 1964) or 2nd-order modulus terms (Fedyaevsky 1963)

The equaEons become relaEvely complicated due to the large number of hydrodynamic coecients on the right-hand side needed to represent the hydrodynamic forces. Taylor-series expansions are frequently used in commercial planar moEon mechanism (PMM) tests where the purpose is to derive the maneuvering coes. experimentally.

X1 ! Xu" u" # Xuu # Xuuuu3 # Xv" v" # Xvv # Xvvvv3 #!"

N1 ! Nu" u" # Nuu # Nuuuu3 # Nv" v" # Nvv # Nvvvv3 #!

#

#

X1 ! Xu" u" # Xuu # X |u|u|u|u # Xv" v" # Xvv # X |v|v |v|v #!"

N1 ! Nu" u" # Nuu # N |u|u|u|u # Nv" v" # Nvv # N |v|v |v|v #!

#

#


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Seakeeping, is the study of moEon when there is wave excitaEon and the craO keeps its course and its speed constant (which includes the case of zero speed). This introduces a dissipaEve force known as uid memory eects (Cummins 1962). The governing model is formulated in the Eme domain (Cummins equaEon):

Seakeeping Theory

!MRB ! A"!#$!" ! B total"!#!# ! "0

tK"t # !#!#"!#d! ! C! " $wind ! $wave ! "$ #


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Unified Theory: Seakeeping & Maneuvering

A unied theory for maneuvering and seakeeping is useful since it allows for Eme-domain simulaEon of a ship in a seaway. This is usually done by solving the linear seakeeping equaEons of moEon in the Eme domain (includes uid memory eects). The next step is to assume linear superposiEon such that wave forces can be added for dierent speeds U and sea states. A similar assumpEon is used to add nonlinear damping and restoring forces such that the resulEng model is a unied nonlinear model combining the most important terms from both the maneuvering and seakeeping theories. Care with respect to "double counEng" must be taken. This refers to the problem that hydrodynamic eects can be modeled twice when merging the results from two theories. For instance, since both models have linear damping, the resulEng damping matrix must be chosen such that it represents the total damping.


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- body-xed velociEes: - posiEon and Euler angles: - M, C and D denote the system inerEa, Coriolis and damping matrices - g is a vector of gravitaEonal and buoyancy forces and moments

- q is a vector of joint angels - is a vector of torque - M and C are the system inerEa and Coriolis matrices

In Fossen (1991) the robot model:

M!q"q! " C!q,q# "q $ %

was used as foundaEon to write the 6 DOF marine craO equaEons of moEon in a compact vectorial sexng. Vectorial RepresentaEon The robot model was modied to describe marine craOs in a vectorial sexng

!

! ! !u,v,w,p, q, r"T! ! !x,y, z,!, ",#"T

Fossen's Robot-Like Vectorial Model for Marine Craft

M!" ! C!!"! ! D!!"! ! g!#" ! g0 " $ ! $wind ! $wave


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It is advantageous to use the model representaEon Fossen (1991) since nonlinear system properEes like:

symmetry of matrices skew-symmetry of matrices posiEveness of matrices

can be exploited in the stability analysis. These properEes relates to passivity of the model. These properEes also represents physical properEes of the system which should be exploited

when designing nonlinear controllers and observers for marine vessels.

Model Representations for Marine Craft

M!" ! C!!"! ! D!!"! ! g!#" ! g0 " $ ! $wind ! $wave

Lecture Notes TTK 4190 Guidance and Control (T. I. Fossen)


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Documents

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london lecture notes

fossen lecture notes

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norway lecture notes