Construction of optimal-path maps for homogeneous-cost-region path-planning problems.

Abstract : Fast path-planning algorithms are needed for autonomous vehicles and tactical terrain-analysis tools. We explore a new approach using 'optimal-path maps', that give the best path to a goal point from any given start point in cross-country two-dimensional terrain for a moving agent of negligible size. Such maps allow fast point-location algorithms at run-time to categorize the start point according to the behavior of the optimal path to the goal, from which the path can be reconstructed. We study terrain modelled by piecewise- linear roads and rivers, polygonal obstacles, and by convex polygonal homogeneous-cost areas ('weighted regions'). We explore two methods for constructing optimal-path maps, one based on wavefront-propagation point-to- point path planning, and a more exact divide-and conquer algorithm that reasons about how optimal paths must behave. In the exact approach, boundaries caused by terrain features are characterized using analytical geometry and optimal-path principles, and partial optimal-path maps are merged into complete ones. Paths, Routes, Path-planning, Shortest-path maps, Optimal-path maps, Weighted region problem, Wavefront propagation.