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C-obstacle Query Computation for Motion Planning

C-obstacle Query Computation for Motion Planning. COMP290-58 Project Presentation Liang-Jun Zhang 12/13/2005. Collision detection: do they intersect?. Continuous Collision detection, do they intersect?. Can it escape ?. What is the problem?. Query in Configuration.

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C-obstacle Query Computation for Motion Planning

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  1. C-obstacle Query Computation for Motion Planning COMP290-58 Project Presentation Liang-Jun Zhang 12/13/2005

  2. Collision detection: do they intersect? Continuous Collision detection, do they intersect? Can it escape ? What is the problem?

  3. Query in Configuration Is p in Free-space or C-obstacle? p Free space l Is l fully in Free-space? c C-Obstacle Is c fully in C-obstacle space? Configuration Space

  4. Why need C-obstacle query • Cell Decomposition based method • Star-shaped roadmap approach • Efficiently cull them • It is a fundamental query for Motion Planning

  5. What is the difficulty? 1. A continuous problem 2. `C-obstacle ’ query is more expensive than `Free-space’ query A A B B

  6. Focus: C-obstacle Cell Query A(qa) B

  7. The intuition of solution • PD: How much of the robot A penetrate into the obstacle B? • Motion: How much can the robot A move? • Culling CriteriaIf PD > Motionit is in C-obstacle. A(qa) B

  8. PD computation • Translational PDonly works for robots with translational DOFs B A Robot

  9. Generalized PD • Both translation and rotation are considered • Defined on traveling distance when the object moves • Convex A, B: PDG(A,B)=PDT(A,B)

  10. Algorithm-Lower bound on PDG • Convex covering • PDT over each pair • LB(PDG) = Max over all PDTs

  11. Query Criteria If PD > Motion It is in C-obstacle.

  12. Query Criteria If PD > Motion It is in C-obstacle.

  13. Upper bound of Motion • A line segement • a cell qa qb r y A(qa) x B

  14. Applied for 2D planar robot Video

  15. Performance • Culling Ratio= Culled Cells / All queried cells • Timing 0.04ms to 0.12 ms for 2D

  16. Speedup For Star-shaped method

  17. Future work • Method for C-obstacle space Query • Non-path existence • together with star-shaped test • To enhance the PRM • Difficulty • Conservative test • 6-DOF

  18. Questions?

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