A variational calculus framework for motion planning

We argue that it is advantageous to formulate motion planning as a variational problem. In this way, a unified framework for addressing redundancy, constraints, and optimality is obtained. An efficient 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.