A Variational Calculus Framework for Motion Planning

Milo s Zefran1 and Vijay Kumar2 1California Institute of Technology, Email: [email protected] 2GRASP Laboratory, University of Pennsylvania, Email: [email protected] Abstract In this paper, we argue that it is advantageous to formulate motion planning as a variational problem. In this way, a uni ed framework for addressing redundancy, constraints, and optimality is obtained. An e cient numerical method is proposed for solving the motion planning problem in the variational form. The approach is illustrated on the problem of motion planning for systems that change dynamic equations at discrete time instants as they move. A technique is described for computing a motion plan when the sequence of dynamic equations describing the motion is known. Finally, a motion plan for a simple grasping task, a typical representative of this class of systems, is computed.