Fast Computation of the C-Space of Convex 2D Algebraic Objects

Abstract

Collision-free paths for a robot are commonly obtained in con figuration space. The major problem with this approach is the computation of the boundary of the configuration space ob stacles. While many results have been reported for polygonal environments, the general case of arbitrary object shape has received little attention in the literature so far. This article presents a new method for tackling this problem in the case of objects for which the boundaries consist of segments of pa rameterized algebraic curves. A fast numerical algorithm that computes the boundaries of the C-space obstacles in param eterized form is developed. The major result is that initially subdividing the segments guarantees the convergence and lim its the computational costs of the applied interval-subdivision Newton method. This makes it possible to compute the exact C-space for this more general class of objects. Finally, two examples with convex objects solved by our implementation are given.