Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints

1. Multiple Marine Vehile Deconflicted Path Planning with Currents and Communication Constraints A. Häusler1, R. Ghabcheloo2, A. Pascoal1, A. Aguiar1 1Instituto Superior Técnico, Lisbon, Portugal 2Tampere 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 Andreas J. Häusler - IAV 2010

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 - IAV 2010

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 - IAV 2010

5. Path Planning Foundations Final position Initial position Andreas J. Häusler - IAV 2010

6. 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 Andreas J. Häusler - IAV 2010

7. 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 Andreas J. Häusler - IAV 2010

8. CostFunctionConsiderations Andreas J. Häusler - IAV 2010

9. 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 Andreas J. Häusler - IAV 2010

10. 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 Andreas J. Häusler - IAV 2010

11. 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 Andreas J. Häusler - IAV 2010

12. Spatial Deconfliction Final positions (target formation) Initial positions Andreas J. Häusler - IAV 2010

13. Temporal Deconfliction Final positions (target formation) Initial positions Andreas J. Häusler - IAV 2010

14. Deconfliction • Spatial deconfliction: subject to • For temporal deconfliction, the constraint changes to • Simultaneous arrival at time Andreas J. Häusler - IAV 2010

15. Environmental Constraints • Incorporated throughbarrier function • Path planningwithcurrentsformoreenergy-efficientpaths (insteadofsolelyrelying on pathfollowingcontroller) • Path planningwithcommunicationconstraintsforrangekeepingwithinthegroup (Hauser, CDC 2006) Andreas J. Häusler - IAV 2010

16. Path Planning System MissionSpecifications SpatialClearance Optimization Algorithm Comm. Constraint CostCriterion PathGeneration InitialGuess AMV Data Init. Position & Heading Path Nominal Paths InitialVelocity Time-CoordinatedPathFollowing Final Position & Heading Revised Guess SpeedProfiles Final Velocity DynamicalConstraints EnvironmentalConstraints Current Obstacles Andreas J. Häusler - IAV 2010

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

18. Time-Coordinated Path Following • Path followingcontrolstrategy • Guaranteesthatvehiclesandaredeconflictedandthattheyfollowtheirtrajectoryif • A time coordinationcontrollawcanbefound so thatthemissionremains “near optimal“ in thepresenceofdisturbances Andreas J. Häusler - IAV 2010

19. Simulation Results • Algorithm makes use of currents to minimize expected energy usage • Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax Andreas J. Häusler - IAV 2010

20. Simulation Results • Algorithm makes use of currents to minimize expected energy usage • Solid lines = vw, dashed lines = vdes and dotted lines = vmin and vmax Andreas J. Häusler - IAV 2010

21. Simulation Results • Communication constraints with and without spatial deconfliction • Communication break distance 50m and 80m Andreas J. Häusler - IAV 2010

22. 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 Andreas J. Häusler - IAV 2010

23. 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 Andreas J. Häusler - IAV 2010

24. Thank you for your attention! Outlook: trajectoryoptimizationusing a projectionoperatorapproach (blue: desiredpath, green: timeandenergyoptimalpathaccording to vehicledynamics Outlook: obstacleavoidanceusing the projectionoperator Outlook: collisionavoidanceusing the projectionoperator Outlook: obstacle and collision avoidance using a projection operatoroptimization approach Andreas J. Häusler - IAV 2010