Generalized Unfoldings for Shortest Paths in Euclidean 3-Space

The problem of determining shortest paths in the presence of polyhedral obstacles between two points in Euclidean 3-space stems from the general problem of obtaining optimal coliision free paths in robot systems. For the special case when paths are constrained to the surfaces of 3-dimensional objects, simple planar unfoldings are used to obtain the shortest path. For the general case wben paths are tiot constrained to lie on any surface; we show the existence of generalized unfoldings wherein the shortest patb in 3-space again becomes a straight line. These unfoldings consist of multiple rotations about the edges of the polyhedral obstacles. t Department of Mathematics, Purdue University, West Lafayette, IN 47907 Generalized Unfoldings for Shortest Paths in Euclidean 3-Spacc