Planning Shortest Paths among 2D and 3D Weighted Regions Using Framed-Subspaces

Abstract

The standard shortest path planning problem determines a collision- free path of shortest distance between two distinct locations in an environment scattered with obstacles. This problem, in fact, corre sponds to a special case of the weighted region problem, in which the environment is partitioned into a set of regions, with some regions (obstacles) having an associated weight of oo and other regions (free space) having a weight of 1. For the general weighted region problem, the environment consists of regions, each of which is as sociated with a certain weight factor. A path through the weighted region incurs a cost that is determined by the geometric distance of the path in that region times that region's weight factor. The weighted region problem can be used to model path planning for autonomous vehicles over different environmental terrains. This paper studies the problem of computing a shortest path between two distinct locations through a 2D or 3D environment consisting of weighted regions. The authors propose a novel cell decomposi tion approach based on new framed-subspace data structures: the weighted framed-quadtree and the weighted framed-octree.