path planning for multiple marine vehicles andreas j. häusler¹, reza ghabcheloo², isaac kaminer³...

Path Planning for MultipleMarine Vehicles

Andreas J. Häusler¹, Reza Ghabcheloo², Isaac Kaminer³

António M. Pascoal¹, A. Pedro Aguiar¹

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

³Naval Postgraduate School, Monterey, USA

Mother Ship

Cur

rent

Introduction

Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen

Introduction

Multiple vehicle missions require the vehicles to be in formation

An initial formation pattern must be established before the mission starts

Lack of hovering capabilities vehicles cannot be deployed and brought to formation separately

Need to drive the vehicles to an initial formation pattern in a concerted manner.

Go-To-Formation Maneouvre


Go-To-Formation Maneouvre

Launch of multiple marine vehicles

Formation to be reached before mission starts

Simultaneous arrival time and equal speeds

Collision avoidance & deconfliction clearance


Spatial Deconfliction

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

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

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

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

Vehicle 1

Vehicle 2Initial positions

Final positions(target formation)


Temporal Deconfliction

Final positions(target formation)

Vehicle 1

Vehicle 2

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

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

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

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

Initial positions

Intermediate positions


MULTIPLE VEHICLE

PATH PLANNINGSYSTEM

Initial Positions

Initial Velocities

Final Positions

Final Velocities

Vehicle dynamical constraints

External constraints(e.g., obstacles)

Cost criterion (e.g.weighted sum of energies, maneuvering time)

Nominal Paths and Speed Profiles

Vehicle collision avoidance constraints

Path Planning System


Path Planning: an overview

Core methodology: based on the work on single vehicle

path planning using direct methods (Yakimenko)

Extension to multiple air vehicle path planning with

spatial deconfliction (Yakimenko, Kaminer, Pascoal)

Extension to multiple marine vehicle path planning with

temporal deconfliction (Aguiar, Ghabcheloo, Häusler, Kaminer,

Pascoal)


Decoupling of Space and Time

Reduces number of opt. parameters suitable

for real-time implementation

Single vehicle path

Parameterized by

Polynomial for each coordinate

Degree determined by no. of boundary conditions

Original work by Yakimenko and Kaminer

( ) ( ), ( ), ( )p x y z T

0; f

0

( )N

kxk

k

x a


Decoupling of Space and Time

Optimization produces paths without time

constraints, but with timing laws

Evolution of with time is

Temporal speed and acceleration

i ip τ

iτ t

ii i

dτη τ =

dtτi

( ( ))v t ( ( ))a t

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

2( ) ''( ) ( ) '( ) '( ) ( )a p p


Flexibility of Generated Paths

Path shape can be

changed by varying

Simple choice 0 0ff

τη τ = η + η τ η

τ

f

(0) (0)v

( ) ( )f fv t

Path geometry is “shaped”simply by varying f


Multiple Vehicle Path Generation

Cost (Energy consumption)

Constraints

Optimize using zero order methods

Spatial deconfliction: subject to

33

0

( ) '( )f

f DJ c c p d

min max( ) '( )v p v

2max''( ) ( ) '( ) '( ) ( )p p a

; 1, ,1

mini

n

i ii n

i

w J

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

2 0i k j lp τ p τ E ;E >


Simulation Results

Spatial Deconfliction in 2D


Simulation Results

Spatial Deconfliction in 3D



Deconfliction constraint changes to

Simultaneous arrival at time

Time-coordinated path following using virtual

time

Cooperation to adjust vehicle motions in reaction

to deviations from original plan (Ghabcheloo)

1 2

opt

, 1

arg minf

n

f i it t t i

t w J

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

0,1ft t



0

0

0

1( *)t

2( *)t

3( *)t

0t *t t ft t

1( )ft

2( )ft

3( )ft

1 1( )p

2 2( )p

3 3( )p

0,1f

t

t Common path parametrization

variable


Simulation Results

Temporal Deconfliction in 2D


Conclusions

Use of direct optimization methods (Yakimenko)

Efficient and fast techniques for path generation first used for UAVs (Kaminer et al.)

Extension to temporal deconfliction allows for equal times of arrival

Decoupling of space and time, resulting in great flexibility for time-coordinated path following


Future Trends

Incorporate effects of current fields

Add obstacle avoidance

Improve optimization techniques towards online

re-planning

Sea tests with multiple marine vehicles planned

for the Fall of 2009

Thank you for your attention!

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path planning for multiple marine vehicles andreas j. häusler¹, reza ghabcheloo², isaac kaminer³...

Documents

single vehicle path

ieee bremen husler

kaminer slide

formation maneouvre

pascoal slide

usa slide

initial formation pattern

temporal deconfliction