Class #11: Kinodynamic Planning
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The car is a good example of non-holonomic vehicle: it has only two controls, but its configuration space has dimension 3. The second drawing from the left shows the coordination of two non-holonomic robots among fixed obstacles. The two drawings on the right show a robot (gray disc) with limited acceleration negotiating its ways through moving obstacles. The rightmost drawing shows the robot’s trajectory in configuration x time space (the green cylinders are the maps of the moving obstacles).

  • Topics
    - Non-holonomic and dynamic motion constraints
    - Motion planner for car-like robot using basic maneuvers
    - Transformation of holonomic path into a non-holonomic one
    - Treatment of kinodynamic constraints in probabilistic roadmap planner 
    - Probabilistic roadmap in state x time space
  • Required Readings:
    • Basic maneuvers for a car-like robot:
      J.P. Laumond. Feasible Trajectories for
      Mobile Robots with Kinematic and Environment Constraints. Proc. Int. Conf. on Intelligent Systems, Amsterdam, pages 346-354, 1986. [Hardcopy will be given in class]
    • PRM-based kinodynamic planner:
      D. Hsu, R. Kindel, J.C. Latombe, and S. Rock. Randomized Kinodynamic Motion Planning with Moving Obstacles. Int. J. of Robotics Research, 21(3):233-255, March 2002. [ps] [pdf]
  • Other Readings:
    • A basic paper:
      B. Donald, P. Xavier, J. Canny, and J. Reif. Kinodynamic Motion Planning Journal of the ACM, 40(5):1048-1066, 1993. [pdf]
    • Planner based on deterministic sampling:
      J. Barraquand and J.C. Latombe. Nonholonomic Multibody Robots: Controllability and Motion Planning in the Presence of Obstacles. Algorithmica, 10:121-155, 1993. [Hardcopy available on demand]
    • Collection of papers on non-holonomic motion planning:
      Robot Motion Planning and Control


    • Under-actuated robots:
      K. M. Lynch, N. Shiroma, H. Arai, and K. Tanie. Collision-free trajectory planning for a 3-DOF robot with a passive joint. International Journal of Robotics Research, 19(12):1171-1184, December 2000. [pdf]  (see also http://lims.mech.nwu.edu/~lynch/papers/index.html#underactuated)
  • Powerpoint slides