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CS 326A: Motion Planning

CS 326A: Motion Planning. ai.stanford.edu/~latombe/cs326/2007/index.htm Motion Planning for Legged Robots. Coordination for Multiple Robots (Notes for HW#2). n robots R1, …, Rn, with configuration spaces C1, …, Cn, sharing the same workspace

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CS 326A: Motion Planning

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  1. CS 326A: Motion Planning ai.stanford.edu/~latombe/cs326/2007/index.htm Motion Planning for Legged Robots

  2. Coordination for Multiple Robots (Notes for HW#2) • n robots R1, …, Rn, with configuration spaces C1, …, Cn, sharing the same workspace • Problem: Plan coordinated motion so that each robot achieves its own goal configuration. • Centralized planning: Plan the coordinated motion in C1xC2x…xCn (but very high dimensional space) • Decoupled planning: Plan the motion of each robot ignoring the other robots; then coordinate their motions so that no two robots collide • Prioritized planning: Plan the motion of one robot ignoring the other robots; then plan the trajectory of a second robot in its configurationxtime space treating the first robot as a moving obstacle; then plan the trajectory of a third robot …

  3. Coordination Space • 2 robots R1 and R2 • 2 paths: ti : si  [0,1]  Ci (i=1,2) • 2-D coordination space • Generalize to n robots  n-D coordination space s2 1 0 1 s1

  4. Variants of Decoupled Planning • #1: Coordinate the n paths in n-D coordination space • #2:Coordinate paths of R1 and R2 in a 2-D coordination diagram ( path of “R1-R2”) , then coordinate paths of R1-R2 and R3 in 2-D coordination diagram, etc… s1

  5. Today’s Papers • Footstep planning for a humanoid robot:J. Kuffner, K. Nishiwaki, S. Kagami, M. Inaba, and H. Inoue. Footstep Planning Among Obstacles for Biped Robots. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS), 2001. • Motion planning for a climbing robot:T. Bretl. Motion Planning of Multi-Limbed Robots Subject to Equilibrium Constraints: The Free-Climbing Robot Problem. International Journal of Robotics Research, 25(4):317-342, Apr 2006.  

  6. Some New Ideas • Equilibrium constraint • Footstep planning: Where to make contact? • Stance (+ configuration space at a stance) • Multi-step planning

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