1. Temporally and Spatially Deconflicted Path Planning for Multiple Marine Vehicles A. Häusler 1, R. Ghabcheloo 2, A. Pascoal 1, A. Aguiar 1 I. Kaminer 3, V. Dobrokhodov 3 1 Instituto Superior Técnico, Lisbon, Portugal 2 Tampere University of Technology, Tampere, Finland 3 Naval 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 September 18th, 20092Andreas J. Häusler - MCMC 2009

3. The Go-To-Formation Maneouvre 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) September 18th, 2009Andreas J. Häusler - MCMC 20093 Mother Ship Current

4. The Go-To-Formation Maneouvre 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 September 18th, 2009Andreas J. Häusler - MCMC 20094 Mother Ship

5. Path Planning System September 18th, 2009Andreas J. Häusler - MCMC 20095 MULTIPLE VEHICLE PATH PLANNING SYSTEM MULTIPLE VEHICLE PATH PLANNING SYSTEM Initial Positions Initial Velocities Final Positions Final Velocities Cost Criterion (e.g. weighted sum of energies, maneouvring time) Vehicle dynamical constraints Collision avoidance constraints External constraints (e.g. Obstacles) Nominal Paths and Speed Profiles Nominal Paths and Speed Profiles

6. Path Planning Foundations September 18th, 2009Andreas J. Häusler - MCMC 20096 Initial position Final position

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 September 18th, 2009Andreas J. Häusler - MCMC 20097

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 September 18th, 2009Andreas J. Häusler - MCMC 20098

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 September 18th, 2009Andreas J. Häusler - MCMC 20099

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 September 18th, 2009Andreas J. Häusler - MCMC 200910

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 September 18th, 2009Andreas J. Häusler - MCMC 200911

12. Spatial Deconfliction September 18th, 2009Andreas J. Häusler - MCMC 200912 Initial positions Final positions (target formation)

13. Temporal Deconfliction September 18th, 2009Andreas J. Häusler - MCMC 200913 Initial positions Final positions (target formation)

14. Deconfliction Spatial deconfliction: subject to For temporal deconfliction, the constraint changes to September 18th, 2009Andreas J. Häusler - MCMC 200914

15. Deconfliction Simultaneous arrival at time Time-coordinated path following using virtual time with September 18th, 2009Andreas J. Häusler - MCMC 200915 (Ghabcheloo, ACC 2009)

16. Simulation Results Spatial deconfliction in 2D for three vehicles – paths and velocity profiles September 18th, 2009Andreas J. Häusler - MCMC 200916

17. Simulation Results Temporal deconfliction in 2D for three vehicles – paths and velocity profiles September 18th, 2009Andreas J. Häusler - MCMC 200917

18. Simulation Results Spatial deconfliction in 3D for three vehicles – paths and velocity profiles September 18th, 2009Andreas J. Häusler - MCMC 200918

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 September 18th, 2009Andreas J. Häusler - MCMC 200919

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 September 18th, 2009Andreas J. Häusler - MCMC 200920

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) September 18th, 2009Andreas J. Häusler - MCMC 200921

22. Thank you for your attention! September 18th, 2009Andreas J. Häusler - MCMC 200922 Delfim (IST/ISR)Infante (IST/ISR) ASTER x (IFR) Seawolf (ATL) Arquipélago (IMAR)Delfim X (IST/ISR)