An efficient approach fo determining shortest paths among 2-D and 3-D weighted regions

In this paper, we propose novel cell decomposition techniques, based on new framed-subspace data structures, to determine Euclidean shortest paths in 2-D and 3-D environments consisting of weighted regions (called the weighted region problem). For the general weighted region problem, the environment is partitioned into a set of regions, each of which is associated with a certain weight factor. Solutions to this problem are used in the area of robotic path planning to represent navigation over different environmental terrains. A path through a weighted region incurs a cost that is determined by the geometric distance of the path in that region and by the region's weight factor. Our approach represents a significant improvement in efficiency and accuracy over traditional cell decomposition path planning approaches on this problem.