A near-quadratic algorithm for planning the motion of a polygon in a polygonal environment

Abstract

We consider the problem of planning the motion of an arbitrary k-sided polygonal robot B, free to translate and rotate in a polygonal environment V bounded by n edges. We present an algorithm that constructs a single component of the free configuration space of B in time O((kn)2+ε), for any ε > 0. This algorithm, combined with some standard techniques in motion planning, yields a solution to the underlying motion-planning problem, within the same running time.