multiple marine vehile deconflicted path planning with currents and communication constraints

Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints

A. Häusler1, R. Ghabcheloo2, A. Pascoal1, A. Aguiar1

1Instituto Superior Técnico, Lisbon, Portugal2Tampere University of Technology, Tampere, Finland

Andreas J. Häusler - IAV 2010 2

Introduction

Efficient algorithms for multiple vehicle path planning are crucial for cooperative control systemsNeed to take into account vehicle dynamics, mission parameters and external influencesExample: Go-To-Formation maneouvre

September 8h, 2010


The Go-To-Formation Maneouvre

An initial formation pattern must be established before mission startDeploying the vehicles cannot be done in formation (no hovering capabilities)Vehicles can’t be driven to target positions separately (no hovering capabilities)

September 8h, 2010

Mother Ship

Cur

rent


The Go-To-Formation Maneouvre

Need to drive the vehicles to the initial formation in a concerted mannerEnsure simultaneous arrival times and equal speedsEstablish collision avoidance through maintaining a spatial clearance

September 8h, 2010

Mother Ship


Path Planning Foundations

September 8h, 2010

0 0( ), ( )p t v t

( ), ( )f fp t v t

Initial position

Final position

( ( )), ( ( )), ( ( ))i i ip t v t a t


Polynomial Path Planning

Dispense with absolute time in planning a path (Yakimenko)

Establish timing laws describing the evolution of nominal speed with Spatial and temporal constraints are thereby decoupled and captured by &Choose and as polynomialsPath shape changes with only varying

September 8h, 2010

( )t

( ) [ ( ), ( ), ( )]p x y z

( )p ( ) d dt

( ) ( )p

f

[0, ]f


Polynomial Path Planning

Polynomial for each coordinate with degree determined by the number of boundary conditionsTemporal speed and acceleration constraints

Choice for timing law with

September 8h, 2010

0( ) N k

xkkx a

0 0ff

τη τ = η + η τ ητ

2 2 2( ) ( ) ' ( ) ' ( ) ' ( ) ( ) '( )v x y z p 2( ) ''( ) ( ) '( ) '( ) ( )a p p

(0) (0)v ( ) ( )f fv t


Cost Function Considerations

September 8h, 2010

cv

totv

wvT

L

D

H C


Cost Function Considerations

A path is feasible if it can be tracked by a vehicle without exceeding , , and

It can be obtained by minimizing the energy

consumption

subject to temporal speed and acceleration constraints

September 8h, 2010

minv maxv maxa

2

0 0

1( ) ( ) ( ) ( ) ( )2

f f

w w wD wJ D T v t dt C v t A ma t v t dt

max


Multiple Vehicle Path Planning

Instead of trying to minimize the arrival time

interval, we can fix arrival times to be exactly

equal and still get different path shapes

Integrate for

September 8h, 2010

( )

(0) ( ) (0)

( ) (0)( ) (0)

ln( ( ) (0))

i

ii

i

i

i f i f i

i f ifi f i

i f i

t


Multiple Vehicle Path Planning

Then we obtain ,

from which the spatial paths are computedThe result is in turn used to compute velocity and accelerationOptimization is done using direct search

September 8h, 2010

( ) (0)

( ) ( )(0)1 ( ) (0)

( ) ( ) (0)

i i

f

i i

f f i f i

tti i fi

f i f ii f i f i

t t

t


Spatial Deconfliction

September 8h, 2010

1 0 1 0( ), ( )p t v t

2 0 2 0( ), ( )p t v t

1 1( ), ( )f fp t v t

2 2( ), ( )f fp t v t

d E

Initial positions

Final positions(target formation)


Temporal Deconfliction

September 8h, 2010

1 0 1 0( ), ( )p t v t

2 0 2 0( ), ( )p t v t

1 1( ), ( )f fp t v t

2 2( ), ( )f fp t v t

Initial positions

Final positions(target formation)


Deconfliction

Spatial deconfliction: subject to

For temporal deconfliction, the constraint changes to

Simultaneous arrival at time

September 8h, 2010

; 1, , 1

mini

n

i ii n i

w J

2 0i k j lp τ p τ E ;E >

2 0i jp t p t E ;E > 1, 0, fi, j = ,n,i j,t t

1, 0, 0,k l f fi ji, j = ,n,i j, τ ,τ τ τ

1 2

opt

, 1

arg minf

n

f i it t t i

t w J


Environmental Constraints

Incorporated through barrier function

Path planning with currents for more energy-efficient paths (instead of solely relying on path following controller)Path planning with communication constraints for range keeping within the group

September 8h, 2010

log( )

( ) 1 1 log( )1

k

z z

z k z k zk k

(Hauser, CDC 2006)


Path Planning System

September 8h, 2010

AMVData

Path Generation Optimization

Algorithm

Init. Position & Heading

Initial Velocity

Final Position & Heading

Final Velocity

Initial Guess

Dynamical Constraints

Mission Specifications

Environmental Constraints

Path

Revised Guess

Nominal Paths

Speed Profiles

Time-C

oordinated Path Following

Spatial Clearance

Comm. Constraint

Cost Criterion

Current

Obstacles


Time-Coordinated Path Following

Closed-form solution to problems of open-loop

path planning and trajectory tracking

Using virtual time with

September 8h, 2010

0,1ft t

( ) (0)

ln 1 ( ) (0) 1( ) (0)

ln ( ) (0)

i i

i i

i

i

i f i f i

i f i i ffi f i

i f i

t t

(Ghabcheloo, ACC 2009)


Time-Coordinated Path Following

Path following control strategy

Guarantees that vehicles and are deconflicted and that they follow their trajectory if

A time coordination control law can be found so that the mission remains “near optimal“ in the presence of disturbances

September 8h, 2010

( ) ( ) ( ( ))i ii ie t t p t p p

0, ( ) ( )i jt t t i j

( )i t t


Simulation Results

Algorithm makes use of currents to minimize expected energy usageSolid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax

September 8h, 2010


Simulation Results

Communication constraints with and without spatial deconflictionCommunication break distance 50m and 80m

September 8h, 2010


Conclusions

Recent improvements of the planner include currents and communication constraintsThereby enhances usability for mission planningBarrier function approach allows for “probing” the path limits (useful for obstacle avoidance)Algorithm easily adaptable for arbitrary number of vehicles

September 8h, 2010


Future Work

Running time increases exponentially with number of discrete points use different optimization approach and/or different means of path descriptionIncorporate real vehicle dynamics instead of approximation through constraintsImprove communication constraintUse more sophisticated energy usage equationAllow for specification of vehicle sub-groups

September 8h, 2010


Thank you for your attention!

September 8h, 2010

Outlook: trajectory optimization using a projection operator approach

(blue: desired path, green: time and energy optimal path according to vehicle dynamics

Outlook: obstacle avoidance using the projection operator

Outlook: collision avoidance using the projection operatorOutlook: obstacle and collision avoidanceusing a projection operator optimization

approach

multiple marine vehile deconflicted path planning with currents and communication constraints

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