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Path finding is a well-studied problem in AI, which is often framed as graphsearch. Any-angle path finding is a technique that augments the initial graphwith additional edges to build shorter paths to the goal. Indeed, optimalalgorithms for any-angle path finding in static environments exist. However,when dynamic obstacles are present and time is the objective to be minimized,these algorithms can no longer guarantee optimality. In this work, we elaborateon why this is the case and what techniques can be used to solve the problemoptimally. We present two algorithms, grounded in the same idea, that canobtain provably optimal solutions to the considered problem. One of them is anaive algorithm and the other one is much more involved. We conduct a thoroughempirical evaluation showing that, in certain setups, the latter algorithmmight be as fast as the previously-known greedy non-optimal solver whileproviding solutions of better quality. In some (rare) cases, the difference incost is up to 76%, while on average it is lower than one percent (the same costdifference is typically observed between optimal and greedy any-angle solversin static environments).

Towards Time-Optimal Any-Angle Path Planning With Dynamic Obstacles