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Manipulation Planning A Geometrical Formulation

Manipulation Planning A Geometrical Formulation. Manipulation Planning. Hanoï Tower Problem. Manipulation Planning. Hanoï Tower Problem: a “pure” combinatorial problem. Finite state space. Manipulation Planning. A disk manipulating another disk. Manipulation Planning.

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Manipulation Planning A Geometrical Formulation

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  1. Manipulation Planning A Geometrical Formulation

  2. Manipulation Planning • Hanoï Tower Problem

  3. Manipulation Planning • Hanoï Tower Problem: a “pure” combinatorial problem Finite state space

  4. Manipulation Planning • A disk manipulating another disk

  5. Manipulation Planning • A disk manipulating another disk The state space is no more finite!

  6. Manipulation Space • Any solution appearsa collision-freepath in the composite space(CSRobotCSObject )Admissible • However: anypath in (CSRobotCSObject )Admissibleis not necessarily a manipulation path

  7. Manipulation Space • Any solution appearsa collision-freepath in the composite space(CSRobotCSObject )Admissible • Any solution appearsa collision-freepath in the composite space(CSRobotCSObject )Admissible • Whatis the topological structure of the manipulation space? • How to translate the continuousprobleminto a combinatorial one?

  8. A workexample

  9. A workexample

  10. Allowed configurations • Grasp • Placement • Not allowed

  11. Allowed configurations • GraspSpaceGS • Placement SpacePS • Manipulation Space • GS PS

  12. Allowedpaths • Transit paths • Transfer paths • Not allowedpaths

  13. Allowedpathsinduce foliations in GS PS • Transit paths • Transfer paths • Not allowedpaths

  14. Manipulation spacetopology GS PS GS PS

  15. Manipulation spacetopology GS PS GS PS Adjacency by transferpaths

  16. Manipulation spacetopology GS PS GS PS Adjacency by transit paths

  17. Manipulation space graph

  18. Topologicalproperty in GS PS Theorem: Whentwo foliations intersect, anypathcanbe approximated by pathsalongboth foliations.

  19. Topologicalproperty in GS PS Corollary: Paths in GSPScanbeapproximated by finitesequences of transit and transferpaths

  20. Manipulation space graph Corollary: A manipulation pathexistsiffbothstarting and goal configurations canberetracted on twoconnectednodes of the manipulation graph.

  21. Manipulation space graph Proof

  22. Manipulation space Transit Path GSPSPath Transit Path GSPSPath Transfer Path Transit Path

  23. Manipulation algorithms • Capturing the topology • of GS PS • Computeadjacency

  24. The case of finitegrasps and placements • Graph search

  25. The case of twodisks • Capturing the topology of GS PS: projection of the celldecomposition of the composite space • Adjacency by retraction • B. Dacre Wright, J.P. Laumond, R. Alami • Motion planning for a robot and a movableobjectamidst polygonal obstacles. • IEEE International Conference on Robotics and Automation, Nice,1992. • J. Schwartz, M. Sharir • On the Piano Mover III • Int. Journal on RoboticsResearch, Vol. 2 (3), 1983

  26. The general case • Capturing the topology of GS PS • Computeadjacency

  27. The general case • Capturing the topology of GS PS: • Path planning for closedchainsystems • Computeadjacency • Inverse kinematics

  28. The general case: probabilisticalgorithms • T. Siméon, J.P. Laumond, J. Cortes, A. Sahbani • Manipulation planning withprobabilisticroadmaps • Int. Journal on RoboticsResearch, Vol. 23, N° 7-8, 2004. • J. Cortès, T. Siméon, J.P. Laumond • A randomloopgenerator for planning motions of closedchainswith PRM methods • IEEE Int. Conference on Robotics and Automation, Nice, 2002.

  29. J. Cortès, T. Siméon, J.P. Laumond A randomloopgenerator for planning motions of closedchainswith PRM methods IEEE Int. Conference on Robotics and Automation, Nice, 2002.

  30. C. Esteves, G. Arechavaleta, J. Pettré, J.P. Laumond Animation planning for virtual mannequins cooperation ACM Trans. on Graphics, Vol. 25 (2), 2006.

  31. E. Yoshida, M. Poirier, J.P. Laumond, O. Kanoun, F. Lamiraux, R. Alami, K. Yokoi Pivotingbased manipulation by a humanoid robot Autonomous Robots, Vol. 28 (1), 2010.

  32. E. Yoshida, M. Poirier, J.-P. Laumond, O. Kanoun, F. Lamiraux, R. Alami, K. Yokoi Regrasp Planning for Pivoting Manipulation by a Humanoid Robot IEEE International Conference on Robotics and Automation, 2009.

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