Optimal Trajectories for Planar Rigid Bodies with Switching Costs

The optimal trajectory with respect to some metric may require very many switches between controls, or even infinitely many, a phenomenon called chattering; this can be problematic for existing motion planning algorithms that plan using a finite set of motion primitives. One remedy is to add some penalty for switching between controls. This paper explores the implications of this switching cost for optimal trajectories, using rigid bodies in the plane (which have been studied extensively in the cost-free-switch model) as an example system. Blatt’s Indifference Principle (BIP) is used to derive necessary conditions on optimal trajectories; Lipschitzian optimization techniques together with an A* search yield an algorithm for finding trajectories that can arbitrarily approximate the optimal trajectories.