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

TL;DR

This paper introduces two algorithms for time-optimal any-angle path planning in dynamic environments, demonstrating their ability to find provably optimal solutions and outperform greedy methods in certain scenarios.

Contribution

The paper presents the first provably optimal algorithms for time-minimizing any-angle path planning with dynamic obstacles, including a more efficient, involved method.

Findings

The more involved algorithm can match the speed of greedy solvers in some cases.

Optimal solutions can be up to 76% better in cost than greedy solutions.

On average, the optimal solutions are less than 1% better than greedy solutions.

Abstract

Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms 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 elaborate on why this is the case and what techniques can be used to solve the problem optimally. We present two algorithms, grounded in the same idea, that can obtain provably optimal solutions to the considered problem. One of them is a naive algorithm and the other one is much more involved. We conduct a thorough empirical evaluation showing that, in certain setups, the latter algorithm might be as fast as the previously-known greedy non-optimal solver while providing solutions of better quality. In some (rare) cases, the difference in cost is up to 76%, while on average it is lower than one percent (the same cost difference is typically observed between optimal and greedy any-angle solvers in static environments).