Anisotropic Graph Search on Multi-Layer Terrain Maps for Mobile Robot Path Planning

Rough-terrain traversal costs are inherently direction-dependent, meaning that routes of similar geometric length may differ significantly in cost depending on their orientation relative to the terrain slope. In this paper, an A*-based planner is proposed in which the classical graph-search procedure is preserved, whereas the isotropic edge weights are substituted by a cost that varies with the direction of motion. This cost is obtained from three co-registered raster layers, namely an inflated obstacle map, an elevation map, and a terrain-multiplier map. For every admissible move, it combines the step length in 3D, the average terrain multiplier of the two cells concerned, a pitch-related component along the slope, and a roll-related component across the slope, determined from the local elevation difference. Because the cost of a move between two cells may depend on its direction, planning is performed on a directed weighted graph. Five variants of the planner were tested on six benchmark maps, and each resulting path was assessed using one common terrain-aware objective. On every map, the complete formulation attained the lowest shared cost, either alone or jointly with another variant.