Post on 23-Feb-2016
description
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 formationAn initial formation pattern must be established before the mission startsLack of hovering capabilities vehicles cannot be deployed and brought to formation separatelyNeed to drive the vehicles to an initial formation pattern in a concerted manner.
Go-To-Formation Maneouvre
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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 1Vehicle 2Initial positions
Final positions(target formation)
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Temporal Deconfliction
Final positions(target formation)
Vehicle 1Vehicle 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
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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)
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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 =
dtτ i
( ( ))v t ( ( ))a t
2 2 2( ) ( ) ' ( ) ' ( ) ' ( ) ( ) '( )v x y z p
2( ) ''( ) ( ) '( ) '( ) ( )a p p
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Flexibility of Generated Paths
Path shape can be
changed by varying
Simple choice 0 0ff
τη τ = η + η τ ητ
f
(0) (0)v
( ) ( )f fv t
Path geometry is “shaped”simply by varying f
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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 >
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Simulation Results
Spatial Deconfliction in 2D
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Simulation Results
Spatial Deconfliction in 3D
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Temporal Deconfliction
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
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Temporal Deconfliction
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
tt
Common path parametrization variable
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
Simulation Results
Temporal Deconfliction in 2D
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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 arrivalDecoupling of space and time, resulting in great flexibility for time-coordinated path following
Häusler et al. - Path Planning for Multiple Marine VehiclesMay 13th, 2009 - Oceans '09 IEEE Bremen
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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