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Motion Planning Solutions: From Robotics to Graphic Animation

Explore the basic problem of connecting points via paths, from robotics to animation, addressing geometric complexity and dimensions. Learn about hierarchical collision checking, PRM, probabilistic completeness, and single-query strategies. Discover examples of sampling strategies, performance evaluations, and multiple goals like tumor irradiation and map building. Delve into applications in manufacturing, humanoid robots, space robotics, and autonomous helicopters. Witness scenarios with robots, radiosurgery, and complex algorithms.

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Motion Planning Solutions: From Robotics to Graphic Animation

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  1. Motion Planning CS121 – Winter 2003 Motion Planning

  2. Basic Problem Are two given points connected by a path? Motion Planning

  3. From Robotics … Motion Planning

  4. … to Graphic Animation … Motion Planning

  5. … to Biology Motion Planning

  6. … to Biology Motion Planning

  7. How Do You Get There? ? Motion Planning

  8. Configuration Space Approximate the free space by random sampling • Problems: • Geometric complexity • Number of dimensions of space • How to discretize the free space? Motion Planning

  9. q q q q q q 2 1 3 0 n 4 Parts DOF L 19 68 H 51 118 Digital Character Q(t) Motion Planning

  10. Configuration Space Approximate the free space by random sampling • Problems: • Geometric complexity • Number of dimensions of space • How to discretize the free space? Motion Planning

  11. Hierarchical Collision Checking Motion Planning

  12. Example in 3D Motion Planning

  13. Hierarchical Collision Checking Motion Planning

  14. Hierarchical Collision Checking Motion Planning

  15. Performance Evaluation • Collision checking takes between 0.0001 and .002 seconds for 2 objects of 500,000 triangles each on a 1-GHz Pentium III • Collision checking is faster when objects collide or are far apart, and gets slower when they get closer without colliding • Overall collision checking time grows roughly as the log of the number of triangles Motion Planning

  16. local path milestone mg mb Probabilistic Roadmap (PRM) free space Motion Planning

  17. Why It Works Motion Planning

  18. Easy Narrow Passage Issue Difficult Motion Planning

  19. Probabilistic Completeness Under the generally satisfied assumption that the free space is expansive, the probability that a PRM finds a path when one exists goes to 1 exponentially in the number of milestones (~ running time). Motion Planning

  20. Multi-Query Sampling Strategies Motion Planning

  21. Multi-Query Sampling Strategies • Multi-stage strategies • Obstacle-sensitive strategies • Narrow-passage strategies Motion Planning

  22. mg mb Single-Query Sampling Strategies Motion Planning

  23. mg mb Single-Query Sampling Strategies • Diffusion strategies • Adaptive-step strategies • Lazy collision checking Motion Planning

  24. Examples Nrobot = 3,000; Nobst = 50,000 Tav = 0.17 s Nrobot = 5,000; Nobst = 83,000 Tav = 4.42 s Motion Planning

  25. Design for Manufacturing/Servicing General Motors General Motors General Electric [Hsu, 2000] Motion Planning

  26. Modular Reconfigurable Robots Casal and Yim, 1999 Xerox, Parc Motion Planning

  27. Motion Planning

  28. Humanoid Robot [Kuffner and Inoue, 2000] (U. Tokyo) Motion Planning Stability constraints

  29. Space Robotics robot obstacles air thrusters gas tank air bearing [Kindel, 2000] Motion Planning Dynamic constraints

  30. mg mb Single-Query Sampling Strategies Motion Planning

  31. Total duration : 40 sec Motion Planning

  32. Autonomous Helicopter [Feron, 2000] (AA Dept., MIT) Motion Planning

  33. Other goals The goal may not be to attain a given position, but to achieve a certain condition, e.g.: - Irradiate a tumor - Build a map of an environment - Sweep an environment to find a target Motion Planning

  34. Radiosurgery: Irradiate a Tumor Motion Planning

  35. Mobile Robots: Map Building Motion Planning

  36. Next-Best View Motion Planning

  37. Example Motion Planning

  38. 0 : the target does not hide beyond the edge 1 : the target may hide beyond the edge Information State Example of an information state = (1,1,0) Motion Planning

  39. Critical Curve Motion Planning

  40. More Complex Example Motion Planning

  41. Example with Two Robots (Greedy algorithm) Motion Planning

  42. Surgical Planning Motion Planning

  43. Half-Dome, NW Face, Summer of 2010 … Motion Planning Tim Bretl

  44. Motion Planning

  45. Rock-Climbing Robot Motion Planning

  46. Motion Planning

  47. Motion Planning

  48. Motion Planning

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