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CS 326 A: Motion Planning

CS 326 A: Motion Planning. http://robotics.stanford.edu/~latombe/cs326/2002 Nonholonomic Robots. d y /dx = tan q. d x /dt = v cos q d y /dt = v sin q. d q / d t = ( v / L ) tan f. | f | < F. Example: Car-Like Robot.

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CS 326 A: Motion Planning

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  1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2002 Nonholonomic Robots

  2. dy/dx = tan q dx/dt = v cos q dy/dt = v sin q dq/dt = (v/L) tan f |f| <F Example: Car-Like Robot A robot is nonholonomic if its motion isconstrained by a non-integrable equationof the form f(q,q’) = 0 f L q f y x Lower-bounded turning radius Configuration space is 3-dimensional: (x, y,q) But control space is 2-dimensional: (v, f)

  3. q (x,y,q) y x q Tangent Space/Velocity Space

  4. dy/dx = tan q dx/dt = v cos q dy/dt = v sin q dq/dt = (v/L) tan f |f| <F [X,Y]dt2 X (d t) Lie Bracket X = (v cos q, v sin q, 0) Y = (v cos q, v sin q, (v/L) tan f) -X -Y A nonholonomic robot is controllable iff the vector space of its velocities andthe Lie brackets of these velocities has the same dimensionality as the C-space Y A Lie bracket [X,Y] is a kindof “maneuver”

  5. Holonomic path Nonholonomic path Path Transform

  6. Nonholonomic Path Planning Approaches • Two-phase planning: (Laumond’s paper) • Compute collision-free path ignoring nonholonomic constraints • Transform this path into a nonholonomic one • Direct planning: (Barraquand-Latombe’s paper) • Build a tree of milestones until one is close enough to the goal (deterministic or randomized)

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