Using Framed - Subspaces to Solve the 2 - D and 3 - DWeighted Region

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, corresponds 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 1 while other regions (free space) have a weight of 1. For the general weighted region problem, the environment consists of regions each of which is associated 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 robotic motion planning over diierent environmental terrains. In this paper, we study the problem of computing a shortest path between two distinct locations through a 2-D or 3-D environment consisting of weighted regions. We propose a novel cell decomposition approached based on new framed-subspace data structures, called the weighted framed-quadtree and weighted framed-octree respectively. Our techniques represent a signiicant improvement in eeciency and accuracy over traditional path planning approaches on this problem.