Efficient sampling-based bottleneck pathfinding over cost maps

We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map M : R
^d
Å R, which assigns to every point in space a real value, we wish to find a path connecting two given points, which minimizes the maximal value with respect to M. We demonstrate the capabilities of our algorithm, which we call bottleneck tree (BTT), on several challenging instances of the problem involving multiple agents, where it outperforms the state-of-the-art cost-map planning technique T-RRT. In addition to its efficiency, BTT requires the tuning of only a single parameter: the number of samples. On the theoretical side, we study the asymptotic properties of our method and consider the special setting where the computed trajectories must be monotone in all coordinates. This constraint arises in cases where the problem involves the coordination of multiple agents that are restricted to forward motions along predefined paths.