New Method for Motion Planning for Non-holonomic Systems using Partial Differential Equations

We present in this paper a novel approach to the long-standing problem of motion planning for non-holonomic systems. Our method is built upon a parabolic partial differential equation that arises in the study of Riemannian manifold. We show how it can be brought to bear to provide a solution to a non-holonomic motion planning problem. We illustrate the method on canonical examples, namely the unicycle, the non-holonomic integrator, and the parallel parking task for a non-holonomic car model. We also briefiy address computational issues pertinent to solving this particular partial differential equation, and point out the existence of fast algorithms and the fact that the problem is easily parallelizable.