1. Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints A. Häusler 1, R. Ghabcheloo 2, A. Pascoal 1, A. Aguiar 1 1 Instituto Superior Técnico, Lisbon, Portugal 2 Tampere University of Technology, Tampere, Finland

2. Introduction Efficient algorithms for multiple vehicle path planning are crucial for cooperative control systems Need to take into account vehicle dynamics, mission parameters and external influences Example: Go-To-Formation maneouvre September 8h, 20102Andreas J. Häusler - IAV 2010

3. Path Planning System September 8h, 2010Andreas J. Häusler - IAV 20103 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

4. 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 8h, 2010Andreas J. Häusler - IAV 20104 Mother Ship Current

5. 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 8h, 2010Andreas J. Häusler - IAV 20105 Mother Ship

6. Path Planning Foundations September 8h, 2010Andreas J. Häusler - IAV 20106 Initial position Final position

7. Polynomial Path Planning 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 8h, 2010Andreas J. Häusler - IAV 20107

8. Polynomial Path Planning Polynomial for each coordinate with degree determined by the number of boundary conditions Temporal speed and acceleration constraints Choice for timing law with September 8h, 2010Andreas J. Häusler - IAV 20108

9. Cost Function Considerations September 8h, 2010Andreas J. Häusler - IAV 20109

10. Cost Function Considerations 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 8h, 2010Andreas J. Häusler - IAV 201010

11. Multiple Vehicle Path Planning 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 8h, 2010Andreas J. Häusler - IAV 201011

12. Multiple Vehicle Path Planning 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 8h, 2010Andreas J. Häusler - IAV 201012

13. Spatial Deconfliction September 8h, 2010Andreas J. Häusler - IAV 201013 Initial positions Final positions (target formation)

14. Temporal Deconfliction September 8h, 2010Andreas J. Häusler - IAV 201014 Initial positions Final positions (target formation)

15. Deconfliction Spatial deconfliction: subject to For temporal deconfliction, the constraint changes to Simultaneous arrival at time September 8h, 2010Andreas J. Häusler - IAV 201015

16. Environmental Constraints Incorporated through barrier function Path planning with currents for more energy- efficient paths (instead of solely relying on path following controller) Path planning with communication constraints for range keeping within the group September 8h, 2010Andreas J. Häusler - IAV 201016 (Hauser, CDC 2006)

17. Path Planning System September 8h, 2010Andreas J. Häusler - IAV 201017 AMV Data AMV Data Path Generation Optimization Algorithm Init. Position & Heading Initial Velocity Final Position & Heading Final Velocity Initial Guess Dynamical Constraints Mission Specifications Environmental Constraints Path Revised Guess Nominal Paths Speed Profiles Time-Coordinated Path Following Spatial Clearance Comm. Constraint Cost Criterion Current Obstacles

18. Time-Coordinated Path Following Closed-form solution to problems of open-loop path planning and trajectory tracking Using virtual time with September 8h, 2010Andreas J. Häusler - IAV 201018 (Ghabcheloo, ACC 2009)

19. Time-Coordinated Path Following Path following control strategy Guarantees that vehicles and are deconflicted and that they follow their trajectory if A time coordination control law can be found so that the mission remains “near optimal“ in the presence of disturbances September 8h, 2010Andreas J. Häusler - IAV 201019

20. Simulation Results Algorithm makes use of currents to minimize expected energy usage Solid lines = v w, dashed lines = v des and dotted lines = v min and v max September 8h, 2010Andreas J. Häusler - IAV 201020

21. Simulation Results Algorithm makes use of currents to minimize expected energy usage Solid lines = v w, dashed lines = v des and dotted lines = v min and v max September 8h, 2010Andreas J. Häusler - IAV 201021

22. Simulation Results Communication constraints with and without spatial deconfliction Communication break distance 50m and 80m September 8h, 2010Andreas J. Häusler - IAV 201022

23. Conclusions Recent improvements of the planner include currents and communication constraints Thereby enhances usability for mission planning Barrier function approach allows for “probing” the path limits (useful for obstacle avoidance) Algorithm easily adaptable for arbitrary number of vehicles September 8h, 2010Andreas J. Häusler - IAV 201023

24. Future Work Running time increases exponentially with number of discrete points  use different optimization approach and/or different means of path description Incorporate real vehicle dynamics instead of approximation through constraints Improve communication constraint Use more sophisticated energy usage equation Allow for specification of vehicle sub-groups September 8h, 2010Andreas J. Häusler - IAV 201024

25. Thank you for your attention! September 8h, 2010Andreas J. Häusler - IAV 201025 Outlook: trajectory optimization using a projection operator approach (blue: desired path, green: time and energy optimal path according to vehicle dynamics Outlook: obstacle avoidance using the projection operator Outlook: collision avoidance using the projection operator Outlook: obstacle and collision avoidance using a projection operator optimization approach