Constant Factor Optimal Multi-Robot Path Planning in Well-Connected Environments

Fast algorithms for optimal multi-robot path planning are sought after in many real-world applications. Known methods, however, generally do not simultaneously guarantee good solution optimality and fast run time (e.g., polynomial). 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.