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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 Al,…, Am, 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 &Ogr;(n log2n), where n is the total number of corners of the Al's.

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