Finding Optimal-Path Maps for Path Planning Across Weighted Regions

This paper appeared in the International Journal of Robotics Research, 19, 2 (February 2000), pp. 83-95, with elaborating additions from [Rowe and Alexander, 1997]. The equations were redone for greatly improved clarity in 2008.Optimal-path maps tell robots or people the best way to reach a goal point from anywhere in a known terrain area, eliminating most of the need to plan during travel. We address the construction of optimal-path maps for twodimensional polygonal weighted-region terrain, terrain partitioned into polygonal areas such that the cost per unit distance traveled is homogeneous and isotropic within each polygon. This is useful for overland route planning across varied ground surfaces and vegetation. We propose a new algorithm that recursively partitions terrain into regions of similar optimal-path behavior, and defines corresponding "path subspaces" for these regions. This process constructs a piecewise-smooth function of terrain position whose gradient direction is everywhere the optimal-path direction, permitting quick finding of optimal paths. Our algorithm is more complicated than the current path-caching and wavefront-propagation algorithms, but gives more accurate maps requiring less space to represent. Experiments with an implementation confirm the practicality of our algorithm.This work was supported in part by the U.S. Army Combat Developments Experimentation Center under MIPR ATEC 88-86. This work was also prepared in part in conjunction with research conducted for the Naval Air Systems Command and funded by the Naval Postgraduate School.supported in part by the U.S. Army Combat Developments Experimentation Center under MIPR ATEC 88-86. This work was also prepared in part in conjunction with research conducted for the Naval Air Systems Command and funded by the Naval Postgraduate School.Approved for public release; distribution is unlimited