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Randomized Motion Planning: New Ideas and Applications

Randomized Motion Planning: New Ideas and Applications. Sam Hasinoff CPSC 515 April 7, 2000. animation. manufacturing. biology. Introduction. Configuration Space. One dimension per DOF Examples Planar robot – 3 DOF Rigid body – 6 DOF PUMA – 6 DOF Human character – ~80 DOF

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Randomized Motion Planning: New Ideas and Applications

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  1. Randomized Motion Planning: New Ideas and Applications Sam Hasinoff CPSC 515 April 7, 2000

  2. animation manufacturing biology Introduction

  3. Configuration Space • One dimension per DOF • Examples • Planar robot – 3 DOF • Rigid body – 6 DOF • PUMA – 6 DOF • Human character – ~80 DOF • “Curse of dimensionality”

  4. Simple Motion Planning • Complete geometric description of robot and obstacles known a priori • Only easy kinematic constraints • Essentially static • Rigid objects • P-SPACE Hard [Reif, 1979]

  5. Previous Work • Complete (<4 DOF) • Visibility graph, A* [Nilsson, 1969] • Resolution Complete (4-5 DOF) • Cell decomposition [1980’s] • Probabilistic Complete (6+ DOF) • Potential Field [Latombe, 1991] • Roadmap [Kavraki et al., 1996]

  6. Roadmap Motion Planner

  7. Basic RoadmapAlgorithm 1 PREPROCESSING: generate r milestones pick a configuration q at random from C if (CLEARANCE(q) > 0) store q as a milestone for each pair of milestones m1 and m2 with distance less than d, do CONNECT(m1,m2) invoke RESAMPLE to expand the roadmap by s-r milestones

  8. Basic Roadmap Algorithm 2 QUERY PROCESSING: for i={start,end} if some milestone m sees qi then mi=m else try g times to pick q in the neighbourhood of qi such that q sees both qi and a milestone m return if mstart and mend are in the same component

  9. CLEARANCE(q)[Quinlan, 1994] • Sphere trees for distance computation • Tile surface polygons • Heuristics build the tree and guide search • Fast for establishing approx bounds

  10. CONNECT(m1,m2)Local Planner • Straight-line segments in C • Uses CLEARANCE to determine adjacency between two configurations • Recursively breaks line segment between m1 and m2 until • Endpoints of the segment are adjacent or • One the endpoints is not in free space

  11. RESAMPLEA useful heuristic • Create additional milestones, biased towards special areas • Low milestone density • Near low-degree milestones • Near free space boundary • Works in general • Narrow passages still a problem

  12. State of the Art • Applied to complicated, many-DOF manufacturing problems • Fast enough for planar robots with moving obstacles • Non-holonomic constraints • Manipulation problems

  13. Future Research • Faster distance calculation (90% time) • hardware, KDS • Path quality • smoothness, realism, optimality • Coordinating multiple robots • Deformable objects • Getting a negative answer

  14. References • Latombe, J.C. 1999. Motion planning: A journey of robots, molecules, digital actors, and other artifacts.IJRR 18(11):1119-1128.

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