August 2001, 21pp.
We study the sensor-based motion planning problem using the concepts of weak slope and generalised gradient from nonsmooth analysis. We give a nonsmooth analysis of the pointwise minima function Fmin(x) = mini {fi(x)} where each of the fi(x) are nonsmooth and non-convex, and in particular present a method to determine critical points of Fmin(x). We present a detailed nonsmooth analysis of the distance function of a free-floating body in SE(3) and SE(3) and use this to develop a novel algorithm for navigating in unknown environments for SE(2).