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Visibility based Probabilistic Motion Planning

Visibility based Probabilistic Motion Planning. T. Siméon, J.P. Laumond, C. Nissoux , Visibility based probabilistic roadmaps for motion planning Advanced Robotics Journa l, Vol. 14, N°6, 2000 J.P. Laumond, T Siméon, Notes on visibility roadmaps and path planning

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Visibility based Probabilistic Motion Planning

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  1. Visibilitybased Probabilistic Motion Planning T. Siméon, J.P. Laumond, C. Nissoux, Visibilitybasedprobabilisticroadmaps for motion planning Advanced Robotics Journal, Vol. 14, N°6, 2000 J.P. Laumond, T Siméon, Notes on visibilityroadmaps and path planning in Algorithmic and ComputationalRobotics: New Directions B. Donald, K. Lynch, D. Rus Eds, A.K. Peters, 2001

  2. Configuration Space • Any admissible motion for the 3D mechanical system appears a collision-freepath for a point in the CSpace • Translating the continuousprobleminto a combinatorial one • Capturing the topologyof CSfreewithgraphs

  3. Configuration SpaceTopology and Small Time Controllability • Anysteeringmethodaccounting for the small time controllability of the system induces the sametopology

  4. Configuration SpaceTopology and Small Time Controllability • Exemples: • linear interpolation, • Manhattan paths, • Reeds and Shepp paths, • flatnessbasedmethods Euclidean Manhattan Reeds-Shepp

  5. Manhattan like Euclidean Sametopology, differentvisibility sets Reeds-Shepp

  6. Combinatorialtopology (1) • Existence and robustness of finite coverage Euclidean Manhattan

  7. No Combinatorialtopology (1) • Existence and robustness of finite coverage Euclidean Manhattan

  8. No Combinatorialtopology (1) • Existence and robustness of finite coverage Euclidean Manhattan Euclidean Manhattan

  9. Combinatorialtopology (1) • Existence and robustness of finite coverage Euclidean Euclidean Manhattan Manhattan

  10. Combinatorialtopology (2) • Optimal coverage (related to art gallery problem) Euclidean Manhattan

  11. Combinatorialtopology (2) • Optimal coverage: finite? bounded? Euclidean and 2D polygonal obstacles: finite and bounded

  12. Combinatorialtopology (3) • Optimal coverage: finite? bounded? Euclidean: finite and unbounded

  13. Combinatorialtopology (4) • From (optimal) coverage to (visibility) roadmaps Guards + Connectors

  14. Computational challenge • No explicit knowledge of CS-obstacles • No explicit knowledge of visible (reachable) sets

  15. Computational challenge • Probabilistic method ingredients: • A collision checker • A steering method • Two type methods: • Learning CS topology by sampling • Answering single query by diffusion

  16. Computational challenge Randomsampling

  17. Computational challenge Random diffusion

  18. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures

  19. Visibilybasedsampling

  20. Visibilybasedsampling

  21. Visibilybasedsampling

  22. Visibilybasedsampling

  23. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=10)

  24. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=100)

  25. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=200)

  26. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=500)

  27. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=1000)

  28. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=10000)

  29. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failures (#try=1000000000!)

  30. Visibilybasedsampling • Algorithm: • Generate guards and connectors randomly • Stop after #try failure • Theorems: • The estimated percentage of non-covered free-space is #try-1 • Probability to find an existing path increases as an exponential function of time

  31. Visibilybasedsampling • Possible online estimation of #try coverage % 100 # guards

  32. Visibilybasedsampling • Real time demonstrations

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