Temporally and Spatially Deconflicted Path Planning for Multiple Marine Vehicles

1. Temporally and Spatially Deconflicted Path Planning for Multiple Marine Vehicles A. Häusler1, R. Ghabcheloo2, A. Pascoal1, A. Aguiar1 I. Kaminer3, V. Dobrokhodov3 1Instituto Superior Técnico, Lisbon, Portugal 2Tampere University of Technology, Tampere, Finland 3Naval Postgraduate School, Monterey, California

2. Introduction • Challenges in underwater environments can be overcome through the use of fleets of heterogeneous vehicles • Central to cooperative control systems are efficient algorithms for multiple vehicle path planning • Example: Go-To-Formation maneouvre Andreas J. Häusler - MCMC 2009

3. The Go-To-Formation Maneouvre Current Mother Ship • An initial formation pattern must be established before mission start • Deploying the vehicles cannot be done in formation (no hovering capabilities) • Vehicles can’t be driven to target positions separately (no hovering capabilities) Andreas J. Häusler - MCMC 2009

4. The Go-To-Formation Maneouvre Mother Ship • Need to drive the vehicles to the initial formation in a concerted manner • Ensure simultaneous arrival times and equal speeds • Establish collision avoidance through maintaining a spatial clearance Andreas J. Häusler - MCMC 2009

5. Path Planning System Vehicle dynamical constraints Collision avoidance constraints External constraints (e.g. Obstacles) MULTIPLE VEHICLE PATH PLANNING SYSTEM Initial Positions Nominal Paths and Speed Profiles Initial Velocities Final Positions Final Velocities Cost Criterion (e.g. weighted sum of energies, maneouvring time) Andreas J. Häusler - MCMC 2009

6. Path Planning Foundations Final position Initial position Andreas J. Häusler - MCMC 2009

7. Path Planning Foundations • Dispense with absolute time in planning a path (Yakimenko) • Establish timing laws describing the evolution of nominal speed with • Spatial and temporal constraints are thereby decoupled and captured by & • Choose and as polynomials • Path shape changes with only varying Andreas J. Häusler - MCMC 2009

8. Path Planning for Single Vehicles • Polynomial for each coordinate with degree determinded by number of boundary conditions • Temporal speed and acceleration constraints • Choice for timing law with Andreas J. Häusler - MCMC 2009

9. Path Planning for Single Vehicles • A path is feasible if it can be tracked by a vehicle without exceeding , , and • It can be obtained by minimizing the energy consumption , • subject to temporal speed and acceleration constraints Andreas J. Häusler - MCMC 2009

10. Optimization for Multiple Vehicles • Instead of trying to minimize the arrival time interval, we can fix arrival times to be exactly equal and still get different path shapes • Integrate for Andreas J. Häusler - MCMC 2009

11. Optimization for Multiple Vehicles • Then we obtain , from which the spatial paths are computed • The result is in turn used to compute velocity and acceleration • Optimization is done using direct search Andreas J. Häusler - MCMC 2009

12. Spatial Deconfliction Final positions (target formation) Initial positions Andreas J. Häusler - MCMC 2009

13. Temporal Deconfliction Final positions (target formation) Initial positions Andreas J. Häusler - MCMC 2009

14. Deconfliction • Spatial deconfliction: subject to • For temporal deconfliction, the constraint changes to Andreas J. Häusler - MCMC 2009

15. Deconfliction • Simultaneous arrival at time • Time-coordinated path following using virtual time with (Ghabcheloo, ACC 2009) Andreas J. Häusler - MCMC 2009

16. Simulation Results • Spatial deconfliction in 2D for three vehicles – paths and velocity profiles Andreas J. Häusler - MCMC 2009

17. Simulation Results • Temporal deconfliction in 2D for three vehicles – paths and velocity profiles Andreas J. Häusler - MCMC 2009

18. Simulation Results • Spatial deconfliction in 3D for three vehicles – paths and velocity profiles Andreas J. Häusler - MCMC 2009

19. Simulation Results • Temporal deconfliction in 2D, facing a current of 0.5 m/s coming from the east • Additional optimization criterion: final velocity to match desired value of 1.5 m/s Andreas J. Häusler - MCMC 2009

20. Conclusions • Multiple vehicle path planning techniques based on direct optimization methods • Flexibility in time-coordinated path following through decoupling of space and time • No complicated timing laws – constraints are incorporated in spatial description (e.g. initial and final heading) • Suitable for real-time mission planning thanks to fast algorithm convergence Andreas J. Häusler - MCMC 2009

21. Future Work • Show robustness of algorithm through extensive simulations • Compare our results with results from optimal control • Employ path planning on vehicle hardware (GREX, Co3-AUVs) for sea trials • Incorporate avoidance of fixed obstacles • Integrate constraints imposed by cooperative path following (e.g. communication links) Andreas J. Häusler - MCMC 2009

22. Thank you for your attention! Seawolf (ATL) Delfim (IST/ISR) Infante (IST/ISR) Arquipélago (IMAR) DelfimX(IST/ISR) ASTERx (IFR) Andreas J. Häusler - MCMC 2009