Path Planning for Multiple
Marine Vehicles
Andreas J. Häusler¹, Reza Ghabcheloo², Isaac Kaminer³
António M. Pascoal¹, A. Pedro Aguiar¹
¹Instituto Superior Técnico, Lisbon, Portugal
²Tampere University of Technology, Tampere, Finland
³Naval Postgraduate School, Monterey, USA
Introduction
Current
Mother Ship
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.
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
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
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Spatial Deconfliction
p1 (t f 1 ), v1 (t f 1 )
d E
Final positions
(target formation)
p2 (t f 2 ), v2 (t f 2 )
p1 (t0 ), v1 (t0 )
Vehicle 1
Initial positions
May 13th, 2009 - Oceans '09 IEEE Bremen
p2 (t0 ), v2 (t0 )
Vehicle 2
Häusler et al. - Path Planning for Multiple Marine Vehicles
Temporal Deconfliction
p1 (t f 1 ), v1 (t f 1 )
Final positions
(target formation)
Intermediate
positions
p2 (t f 2 ), v2 (t f 2 )
p1 (t0 ), v1 (t0 )
p2 (t0 ), v2 (t0 )
Vehicle 1
Initial positions
May 13th, 2009 - Oceans '09 IEEE Bremen
Vehicle 2
Häusler et al. - Path Planning for Multiple Marine Vehicles
Path Planning System
Vehicle dynamical constraints
Vehicle collision avoidance
constraints
External constraints
(e.g., obstacles)
Initial Positions
Initial Velocities
Final Positions
Final Velocities
MULTIPLE VEHICLE
PATH PLANNING
SYSTEM
Nominal
Paths and
Speed Profiles
Cost criterion
(e.g.weighted sum of
energies, maneuvering time)
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
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)
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Decoupling of Space and Time
Reduces number of opt. parameters  suitable
for real-time implementation
Single vehicle path p( )   x( ), y( ), z ( ) 
T
Parameterized by   0; f 
N
k
x
(

)

a

 xk
Polynomial for each coordinate
k 0
Degree determined by no. of boundary conditions
Original work by Yakimenko and Kaminer
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Decoupling of Space and Time
Optimization produces paths pi  τi  without time
constraints, but with timing laws τ i  t 
dτ i
Evolution of τ i with time is ηi  τ i  =
dt
Temporal speed v ( (t )) and acceleration a ( (t ))
v( )   ( ) x '2 ( )  y '2 ( )  z '2 ( )   ( ) p '( )
a( )  p ''( ) 2 ( )  p '( ) '( ) ( )
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Flexibility of Generated Paths
Path shape can be
changed by varying  f
Simple choice
η  τ  = η  0 +
 (0)  v(0)

τ
η  τ f   η  0
τf

Path geometry is “shaped”
simply by varying  f
 ( f )  v(t f )
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Multiple Vehicle Path Generation
f
Cost J   c f cD  ( ) p '( ) d
3
3
(Energy consumption)
0
Constraints vmin   ( ) p '( )  vmax
p ''( ) 2 ( )  p '( ) '( ) ( )  amax
Optimize using zero order methods
n
Spatial deconfliction:
min
i ;i 1, , n
pi  τ k   p j  τl   E ; E > 0
w J
i 1
i
i
subject to
2
i, j = 1, ,n,i  j, τ k ,τl   0,τ f   0,τ f 
j 
 i 
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Simulation Results
Spatial Deconfliction in 2D
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Simulation Results
Spatial Deconfliction in 3D
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Temporal Deconfliction
Deconfliction constraint changes to
pi  t   p j  t   E 2 ; E > 0
i, j = 1, ,n,i  j,t  0,t f 
n
opt
t
Simultaneous arrival at time f  arg min  wi J i
t f t1 ,t2 
i 1
Time-coordinated path following using virtual
time   t t f 0,1
Cooperation to adjust vehicle motions in reaction
to deviations from original plan (Ghabcheloo)
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Temporal Deconfliction
t
Common path parametrization variable   t  0,1
f
*
tt
t  tf
t 0
p1 ( 1 )
p2 ( 2 )
0
 1 (t f )
 1 (t*)
 2 (t f )
 2 (t*)
0
 3 (t f )
p3 ( 3 )
 3 (t*)
0
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
Simulation Results
Temporal Deconfliction in 2D
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
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
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
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
May 13th, 2009 - Oceans '09 IEEE Bremen
Häusler et al. - Path Planning for Multiple Marine Vehicles
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