1. Collaborative Robotics and Wireless Sensor Networks in Area-Coverage related Problems John Stergiopoulos Dept. Elect. & Comp. Eng. Univ. of Patras, Greece stergiopoulos@ece.upatras.gr Anthony Tzes Dept. of Elect. & Comp. Eng. Univ. of Patras, Greece tzes@ece.upatras.gr Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

2. Presentation Layout Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

3. Part I Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

4. Part I: Problem Setup (1) Coordinate the motion of the nodes in order to achieve optimum sensing coverage of a region Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

5. Part I: Problem Setup (2) Mobile-network characteristics  Homogeneous mobile nodes  Uniform symmetric limited sensing patterns  Discrete-time spatial evolution  Bounded control inputs  Communication capabilities Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

6. Part I: Problem Setup (3) Optimization cost : No analytic expression exists for the cost function Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

7. Part II Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

8. Part II: Optimization Techniques (1) Offline global optimization Ω, n, r Optimal network configuration Path planning needed for achieving optimal positioning Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

9. Part II: Optimization Techniques (2)  Computationally intensive (even for small n )  Non-adaptive  change in the region of interest (Ω)  network alteration ( n, r )  Exhaustive search (…)  “Genetic algorithms”-based strategies … however … re-perform optimization (!) Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

10. Part II: Optimization Techniques (3) Online optimization strategies  Each node self-organizes its action so that its motion contributes to netwok coverage  Decision taken is based on local information  No path planning needed; the nodes will self-position themselves accordingly through time Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

11. Part II: Optimization Techniques (4)  Gradient-based techniques  Huge/infinite number of local extrema  Convergence to locally-optimum positions  Adaptive by nature  Applicable in real-time scenarios Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

12. Part III Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

13. Part III: Voronoi Diagrams (1) Why use Voronoi tessellation? Local information – decentralized approach Each node tries to optimize its “local” area-coverage contribution through its motion Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

14. Part III: Voronoi Diagrams (2) Optimize “local” coverage contribution Motion of one node at a time is required Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

15. Part IV Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

16. Part IV: Generalized Coverage Algorithm (1) Main concept  One node moves at each time-step to ensure network’s area-coverage monotonicity, while avoiding oscillatory phenomena  Direction at which a node should move inside its Voronoi cell is defined according to “coverage-increase” criteria  Unless its motion contributes to coverage, the node does not move Stability of the network’s motion is guaranteed Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

17. Part IV: Generalized Coverage Algorithm (2) Communication issues Each node has a communication range such that local information from Delaunay neighbors at step k and k+1 is obtained Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

18. Part IV: Generalized Coverage Algorithm (3) Compute own Voronoi cell (local information – Delaunay neighbors) Compute current “local” area-coverage Define the direction at which to move Predict area-coverage at step k+1, if motion is performed at this direction Move only if coverage is to be increased Node i is to move at step k How is the selection of the node-to-move performed? Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

19. Part IV: Generalized Coverage Algorithm (4) Centralized approach step k step k-1  Need for global supervision  Communication issues arise Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

20. Part IV: Generalized Coverage Algorithm (5) Decentralized approach … or cyclic self-selection (based on the node’s ID) Randomizers on each node’s processor (same seed) Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC Motion of a node inside its Voronoi cell guarantees collision avoidance

21. Part V Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

22. Part V: Coordination Schemes (1)  At each step, a node performs an optimization to define the direction to move towards  Optimal direction is the one that leads to maximum area-coverage contribution at the next step, considering its Delaunay neighbors  ε -maneuvers are performed, so that the Voronoi cell does not alter significantly Steepest-descent scheme Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

23. Part V: Coordination Schemes (2)  CVT-based coordination strategies lead to optimization of some “symmetry” criterion CVT-based schemes  If a node moves towards the centroid of its R-limited Voronoi cell, it tends to maximize the symmetry of the unexploited regions arounds itself Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

24. Part V: Coordination Schemes (3) Since the unexploited regions of a node act as repulses, when the latter is moving towards, the algorithm is coverage-oriented A node moves towards iff its coverage contribution will increase One-step-ahead prediction ensures area-coverage monotonicity Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

25. Part VI Problem Setup Optimization Techniques Voronoi Diagrams Generalized Coverage Algorithm Coordination Schemes Simulation Studies Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

26. Part VI: Simulation Studies (1) Steepest-descent scheme Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

27. Part VI: Simulation Studies (2) Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

28. Part VI: Simulation Studies (3) CVT-based scheme Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

29. Part VI: Simulation Studies (4) Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

30. Part VI: Simulation Studies (5) In both cases, the pecentage area-coverage is a monotonically increasing function of time In the “deepest-descent” case, maximum coverage is obtained faster than in the CVT-based scenario (rational, considering the nature of the algorithm) The network tends to keep itself more cohesive via the CVT-based scheme (“move towards ”), while μicro-maneuvers are performed by the nodes when the network’s state is near-to-optimal Workshop - Autonomous Unmanned Vehicles: Collaborative Planning, Obstacle Avoidance, and Control, 2009 MSC

31. Thank you For more information please refer to: stergiopoulos@ece.upatras.gr tzes@ece.upatras.gr