Optimal grid-free path planning across arbitrarily contoured terrain with anisotropic friction and gravity effects

The authors address anisotropic friction and gravity effects as well as ranges of impermissible-traversal headings due to overturn danger or power limitations. The method does not require imposition of a uniform grid, nor does it average effects in different directions, but reasons about a polyhedral approximation of terrain. It reduces the problem to a finite but provably optimal set of possibilities and then uses A* search to find the cost-optimal path. However, the possibilities are not physical locations but path subspaces. The method also exploits the insight that there are only four ways to optimally traverse an anisotropic homogeneous region: (1) straight across without braking, which is the standard isotropic-weighted-region traversal; (2) straight across without braking but as close as possible to a desired impermissible heading; (3) making impermissibility-avoiding switchbacks on the path across a region; and (4) straight across with braking. The authors prove specific optimality criteria for transitions on the boundaries of regions for each combination of traversal types