The document discusses path planning for multiple marine vehicles. It notes that marine robots are increasingly being used for complex multi-vehicle missions but face stringent limitations like dynamical constraints. Several technical approaches for path planning are covered, including describing paths geometrically and optimizing for multiple vehicles simultaneously. Simulation examples demonstrate the approach, which separates the geometric path from the time-dependent trajectory to allow flexibility. Future trends may include different mappings between paths and trajectories or switching between spatial and temporal deconfliction.

1. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Multiple Marine Vehicles:
Foundations and Future Trends
Andreas J. Häusler, António M. Pascoal and A. Pedro Aguiar
Dynamical Systems and Ocean Robotics Laboratory
Institute for Systems and Robotics
Instituto Superior Técnico
Lisbon, Portugal
{ahaeusler,antonio,pedro}@isr.ist.utl.pt
FREEsubNET Montpellier
March 27, 2009
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

2. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Path Planning for Autonomous Marine Vehicles
Widening fields of application
Robots become increasingly sophisticated
Presence of stringent limitations (dynamical constraints, energy,
external disturbances)
Multiple vehicle missions
Robust path planning methods required
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

3. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Path Planning for Autonomous Marine Vehicles
Widening fields of application
Robots become increasingly sophisticated
Presence of stringent limitations (dynamical constraints, energy,
external disturbances)
Multiple vehicle missions
Robust path planning methods required
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

4. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Path Planning for Autonomous Marine Vehicles
Widening fields of application
Robots become increasingly sophisticated
Presence of stringent limitations (dynamical constraints, energy,
external disturbances)
Multiple vehicle missions
Robust path planning methods required
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

5. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Path Planning for Autonomous Marine Vehicles
Widening fields of application
Robots become increasingly sophisticated
Presence of stringent limitations (dynamical constraints, energy,
external disturbances)
Multiple vehicle missions
Robust path planning methods required
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

6. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Path Planning for Autonomous Marine Vehicles
Widening fields of application
Robots become increasingly sophisticated
Presence of stringent limitations (dynamical constraints, energy,
external disturbances)
Multiple vehicle missions
Robust path planning methods required
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

7. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Examples & Applications
Simultaneous arrival and rendezvous problem
E.g. Go-To-Formation maneouvre and information exchange
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

8. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Examples & Applications
Simultaneous arrival and rendezvous problem
E.g. Go-To-Formation maneouvre and information exchange
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

9. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning for Autonomous Marine Vehicles
Examples & Applications
Examples & Applications
Simultaneous arrival and rendezvous problem
E.g. Go-To-Formation maneouvre and information exchange
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

10. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning in General
Path Planning for Marine Vehicles
Path Planning in General
Describing the paths
Lines-and-arcs, Splines, Dubins Paths, Pythagorean Hodographs,
Bézier Curves
Online Path Generation & Replanning
Replanning Existing Paths, Step-wise advance planning & refinement
Multiple Vehicle Approaches
Different sensor/actuator capabilities, Voronoi cells around threats,
Lyapunov-based optimal solutions
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

11. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning in General
Path Planning for Marine Vehicles
Path Planning in General
Describing the paths
Lines-and-arcs, Splines, Dubins Paths, Pythagorean Hodographs,
Bézier Curves
Online Path Generation & Replanning
Replanning Existing Paths, Step-wise advance planning & refinement
Multiple Vehicle Approaches
Different sensor/actuator capabilities, Voronoi cells around threats,
Lyapunov-based optimal solutions
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

12. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning in General
Path Planning for Marine Vehicles
Path Planning in General
Describing the paths
Lines-and-arcs, Splines, Dubins Paths, Pythagorean Hodographs,
Bézier Curves
Online Path Generation & Replanning
Replanning Existing Paths, Step-wise advance planning & refinement
Multiple Vehicle Approaches
Different sensor/actuator capabilities, Voronoi cells around threats,
Lyapunov-based optimal solutions
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

13. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning in General
Path Planning for Marine Vehicles
Path Planning for Marine Vehicles
Describing the paths
Polynomial-based with geometrical abstraction, Metrics for optimal
paths
Optimization for Multiple Vehicles
High mission performance, Energy minimization, simultaneous arrival
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

14. Motivation & Problem Statement
Technical Approaches
Conclusion
Path Planning in General
Path Planning for Marine Vehicles
Path Planning for Marine Vehicles
Describing the paths
Polynomial-based with geometrical abstraction, Metrics for optimal
paths
Optimization for Multiple Vehicles
High mission performance, Energy minimization, simultaneous arrival
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

15. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Our Approach
Spatial Deconfliction
||pi(τk ) − pj(τl)||2
≥ E2
; E > 0,
∀ i, j = 1, . . . , n; i = j and (τk , τl) ∈ [0, τfi
] × [0, τfj
],
Temporal Deconfliction
||pi(t) − pj(t)||2
≥ E2
, ∀ i, j = 1, . . . , n; i = j and t ∈ [0, tf ],
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

16. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Our Approach
Spatial Deconfliction
||pi(τk ) − pj(τl)||2
≥ E2
; E > 0,
∀ i, j = 1, . . . , n; i = j and (τk , τl) ∈ [0, τfi
] × [0, τfj
],
Temporal Deconfliction
||pi(t) − pj(t)||2
≥ E2
, ∀ i, j = 1, . . . , n; i = j and t ∈ [0, tf ],
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

17. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Simulation Examples
0 100 200 300 400 500 600 700
0
100
200
300
400
500
0.00 s
45.10 s110.09 s 196.03 s
283.67 s
363.08 s
445.35 s
537.00 s
622.88 s
684.56 s
720.00 s
0.00 s
28.90 s
91.69 s
184.60 s
265.78 s
317.29 s
392.30 s
506.57 s
621.07 s693.58 s
720.00 s
x1
x2 vmean
= 1.18 m/s, tf
= 720.00 s, lf
= 849.10 m
vmean
= 1.86 m/s, tf
= 720.00 s, lf
= 1336.10 m
0 100 200 300 400 500 600 700
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
t
v(t)
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

18. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Simulation Examples
0 100 200 300 400 500
0
50
100
150
200
250
300
350
400
450
500
0.00 s
58.73 s
117.46 s
176.19 s
234.93 s
293.66 s
352.39 s
411.12 s
469.85 s
528.58 s
575.57 s
0.00 s
58.73 s
117.46 s
176.19 s
234.93 s
293.66 s
352.39 s
411.12 s
469.85 s
528.58 s
575.57 s
x1
x2
vmean
= 1.26 m/s, tf
= 575.57 s, lf
= 728.33 m
vmean
= 1.23 m/s, tf
= 575.57 s, lf
= 707.48 m
0 100 200 300 400 500
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
t
v(t)
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

19. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Simulation Examples
0 100 200 300 400 500
0
200
400
−250
−200
−150
−100
−50
0
50
100
150
200
0.00 s
717.64 s
x1
0.00 s
719.99 s
x2
x3
vmean
= 1.07 m/s, tf
= 717.64 s, lf
= 770.28 m
vmean
= 1.06 m/s, tf
= 719.99 s, lf
= 761.56 m
0 100 200 300 400 500 600 700
1.05
1.055
1.06
1.065
1.07
1.075
1.08
1.085
t
v(t)
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

20. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Future Trends
Clean mathematical separation from geometrical path and
time-dependent trajectory
Allows for different mapping functions from path to trajectory
Allows for easily switching between spatial and temporal
deconfliction
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

21. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Future Trends
Clean mathematical separation from geometrical path and
time-dependent trajectory
Allows for different mapping functions from path to trajectory
Allows for easily switching between spatial and temporal
deconfliction
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

22. Motivation & Problem Statement
Technical Approaches
Conclusion
Our Approach
Simulation Examples
Future Trends
Future Trends
Clean mathematical separation from geometrical path and
time-dependent trajectory
Allows for different mapping functions from path to trajectory
Allows for easily switching between spatial and temporal
deconfliction
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

23. Appendix Bibliography
Selected Literature I
J.-P. Laumond, Ed.
Robot Motion Planning and Control.
Laboratoire d’Analyse et d’Architecture des Systèmes (LAAS),
1998.
S. M. LaValle.
Planning Algorithms.
Cambridge University Press, 2006.
R. Ghabcheloo, I. Kaminer, A. P. Aguiar, and A. Pascoal.
A General Framework for Multiple Vehicle Time-Coordinated Path
Following Control.
American Control Conference (to be published), 2009.
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

24. Appendix Bibliography
Selected Literature II
I. Kaminer, O. A. Yakimenko, V. Dobrokhodov, A. Pascoal,
N. Hovakimyan, C. Cao, A. Young, and V. Patel.
Coordinated Path Following for Time-Critical Missions of Multiple
UAVs via L1 Adaptive Output Feedback Controllers.
AIAA Guidance, Navigation and Control Conference and Exhibit,
Aug. 2007.
R. M. Murray.
Recent Research in Cooperative Control of Multi-Vehicle Systems.
Journal of Dynamic Systems, Measurement and Control, 2007.
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

25. Appendix Bibliography
Selected Literature III
N. E. Leonard, D. Paley, F. Lekien, R. Sepulchre, D. Fratantoni, and
R. Davis.
Collective Motion, Sensor Networks and Ocean Sampling.
Proceedings of the IEEE, Special Issue on the Emerging
Technology of Networked Control Systems, Jan. 2007.
A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles