Distance metrics and algorithms for task space path optimization

We propose a method for generating a configuration space path that closely follows a desired task space path despite the presence of obstacles. We formalize closeness via two path metrics based on the discrete Hausdorff and Frechet distances. Armed with these metrics, we can cast our problem as a trajectory optimization problem. We also present two techniques to assist our optimizer in the case of local minima by further constraining the trajectory Finally, we leverage shape matching analysis, the Procrustes metric, to compare with respect to only their shape.