Class #11: Kinodynamic Planning
________________________________________________________________________________________________________________

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