Shortest Paths in Euclidean Space with Polyhedral Obstacles.

Abstract

This document considers the problem of finding a minimum length path between two points in Euclidean space which avoids a set (not necessarily convex) polyhedral obstacles; we let n denote the number of the obstacle edges and k denote the number of islands in the obstacle space. For two dimensions, an island is defined to be a maximal convex obstacle surface such that for any two points contained in the interior of the island, a minimal length path between these two points is strictly contained in the interior of the island; for example, a set of i disconnected convex polyhedra forms a set of i islands, however, a single non-convex polyhedron will constitute more than one island. Keywords: Mover's problem; robotics motion planning.