Motivation & Problem StatementTechnical 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 LaboratoryInstitute for Systems and Robotics

Instituto Superior TécnicoLisbon, Portugal

ahaeusler,antonio,pedro@isr.ist.utl.pt

FREEsubNET MontpellierMarch 27, 2009

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Path Planning for Autonomous Marine Vehicles

Widening fields of applicationRobots become increasingly sophisticatedPresence of stringent limitations (dynamical constraints, energy,external disturbances)Multiple vehicle missionsRobust path planning methods required

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Path Planning for Autonomous Marine Vehicles

Widening fields of applicationRobots become increasingly sophisticatedPresence of stringent limitations (dynamical constraints, energy,external disturbances)Multiple vehicle missionsRobust path planning methods required

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Path Planning for Autonomous Marine Vehicles

Widening fields of applicationRobots become increasingly sophisticatedPresence of stringent limitations (dynamical constraints, energy,external disturbances)Multiple vehicle missionsRobust path planning methods required

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Path Planning for Autonomous Marine Vehicles

Widening fields of applicationRobots become increasingly sophisticatedPresence of stringent limitations (dynamical constraints, energy,external disturbances)Multiple vehicle missionsRobust path planning methods required

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Path Planning for Autonomous Marine Vehicles

Widening fields of applicationRobots become increasingly sophisticatedPresence of stringent limitations (dynamical constraints, energy,external disturbances)Multiple vehicle missionsRobust path planning methods required

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Examples & Applications

Simultaneous arrival and rendezvous problemE.g. Go-To-Formation maneouvre and information exchange

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Examples & Applications

Simultaneous arrival and rendezvous problemE.g. Go-To-Formation maneouvre and information exchange

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning for Autonomous Marine VehiclesExamples & Applications

Examples & Applications

Simultaneous arrival and rendezvous problemE.g. Go-To-Formation maneouvre and information exchange

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning in GeneralPath Planning for Marine Vehicles

Path Planning in General

Describing the pathsLines-and-arcs, Splines, Dubins Paths, Pythagorean Hodographs,Bézier Curves

Online Path Generation & ReplanningReplanning Existing Paths, Step-wise advance planning & refinement

Multiple Vehicle ApproachesDifferent sensor/actuator capabilities, Voronoi cells around threats,Lyapunov-based optimal solutions

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning in GeneralPath Planning for Marine Vehicles

Path Planning in General

Describing the pathsLines-and-arcs, Splines, Dubins Paths, Pythagorean Hodographs,Bézier Curves

Online Path Generation & ReplanningReplanning Existing Paths, Step-wise advance planning & refinement

Multiple Vehicle ApproachesDifferent sensor/actuator capabilities, Voronoi cells around threats,Lyapunov-based optimal solutions

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning in GeneralPath Planning for Marine Vehicles

Path Planning in General

Describing the pathsLines-and-arcs, Splines, Dubins Paths, Pythagorean Hodographs,Bézier Curves

Online Path Generation & ReplanningReplanning Existing Paths, Step-wise advance planning & refinement

Multiple Vehicle ApproachesDifferent sensor/actuator capabilities, Voronoi cells around threats,Lyapunov-based optimal solutions

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning in GeneralPath Planning for Marine Vehicles

Path Planning for Marine Vehicles

Describing the pathsPolynomial-based with geometrical abstraction, Metrics for optimalpaths

Optimization for Multiple VehiclesHigh mission performance, Energy minimization, simultaneous arrival

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Path Planning in GeneralPath Planning for Marine Vehicles

Path Planning for Marine Vehicles

Describing the pathsPolynomial-based with geometrical abstraction, Metrics for optimalpaths

Optimization for Multiple VehiclesHigh mission performance, Energy minimization, simultaneous arrival

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Our Approach

Spatial Deconfliction

||pi(τk )− pj(τl)||2 ≥ E2; E > 0,∀ i , j = 1, . . . ,n; i 6= j and (τk , τl) ∈ [0, τfi ]× [0, τfj ],

Temporal Deconfliction

||pi(t) − pj(t)||2 ≥ E2,∀ i , j = 1, . . . ,n; i 6= j and t ∈ [0, tf ],

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Our Approach

Spatial Deconfliction

||pi(τk )− pj(τl)||2 ≥ E2; E > 0,∀ i , j = 1, . . . ,n; i 6= j and (τk , τl) ∈ [0, τfi ]× [0, τfj ],

Temporal Deconfliction

||pi(t) − pj(t)||2 ≥ E2,∀ i , j = 1, . . . ,n; i 6= j and t ∈ [0, tf ],

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Simulation Examples

0 100 200 300 400 500 600 700

0

100

200

300

400

500

0.00 s45.10 s110.09 s 196.03 s

283.67 s

363.08 s

445.35 s

537.00 s

622.88 s

684.56 s720.00 s

0.00 s

28.90 s

91.69 s

184.60 s

265.78 s

317.29 s392.30 s506.57 s

621.07 s693.58 s720.00 s

x1

x2

vmean

= 1.18 m/s, tf = 720.00 s, l

f = 849.10 m

vmean

= 1.86 m/s, tf = 720.00 s, l

f = 1336.10 m

0 100 200 300 400 500 600 7001.1

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

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Simulation Examples

0 100 200 300 400 5000

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

v

mean = 1.26 m/s, t

f = 575.57 s, l

f = 728.33 m

vmean

= 1.23 m/s, tf = 575.57 s, l

f = 707.48 m

0 100 200 300 400 5001.1

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

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Simulation Examples

0 100 200 300 400 5000200

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

x 3

vmean

= 1.07 m/s, tf = 717.64 s, l

f = 770.28 m

vmean

= 1.06 m/s, tf = 719.99 s, l

f = 761.56 m

0 100 200 300 400 500 600 7001.05

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

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Future Trends

Clean mathematical separation from geometrical path andtime-dependent trajectoryAllows for different mapping functions from path to trajectoryAllows for easily switching between spatial and temporaldeconfliction

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Future Trends

Clean mathematical separation from geometrical path andtime-dependent trajectoryAllows for different mapping functions from path to trajectoryAllows for easily switching between spatial and temporaldeconfliction

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

Motivation & Problem StatementTechnical Approaches

Conclusion

Our ApproachSimulation ExamplesFuture Trends

Future Trends

Clean mathematical separation from geometrical path andtime-dependent trajectoryAllows for different mapping functions from path to trajectoryAllows for easily switching between spatial and temporaldeconfliction

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

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 PathFollowing Control.American Control Conference (to be published), 2009.

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles

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 MultipleUAVs 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

Appendix Bibliography

Selected Literature III

N. E. Leonard, D. Paley, F. Lekien, R. Sepulchre, D. Fratantoni, andR. Davis.Collective Motion, Sensor Networks and Ocean Sampling.Proceedings of the IEEE, Special Issue on the EmergingTechnology of Networked Control Systems, Jan. 2007.

A. Häusler, A. Pascoal, A. Aguiar Path Planning for Multiple Marine Vehicles