Expected constant-factor optimal multi-robot path planning in well-connected environments

Abstract

Fast algorithms for optimal multi-robot path planning are sought after in both research and real-world applications. Known methods, however, generally do not simultaneously guarantee good solution optimality and fast run time for difficult instances. In this work, we develop a low-polynomial running time algorithm, called SplitAndGroup, that solves the multi-robot path planning problem on grids and grid-like environments, and produces constant factor time- and distance-optimal solutions, in expectation. In particular, SplitAndGroup computes solutions with sub-linear makespan. SplitAndGroup is capable of handling cases when the density of robot is extremely high - in a graph-theoretic setting, the algorithm supports cases where all vertices of the underlying graph are occupied by robots. SplitAndGroup attains its desirable properties through a careful combination of divide-and-conquer technique and network flow based methods for routing the robots.