An efficient algorithm for planning collision-free translational motion of a convex polygonal object in 2-dimensional space amidst polygonal obstacles

Abstract

We state and prove a theorem about the number of points of local nonconvexity in the union of m Minkowski sums of planar convex sets, and then apply it to planning a collision-free translational motion of a convex polygon B amidst several (convex) polygonal obstacles Ax following a basic approach suggested by Lozano- Perez and Wesley. Assuming that the number of corners of B is fixed, the algorithm developed here runs in time 0(n log™), where n is the total number of corners of the A's.