A stochastic process approach for multi-agent path finding with non-asymptotic performance guarantees

Abstract

Multi-agent path finding (MAPF) is a classical NP-hard problem that considers planning collision-free paths for multiple agents simultaneously. A MAPF problem is typically solved via addressing a sequence of single-agent path finding subproblems in which well-studied algorithms such as ${\text{A}}^{⁎}$ are applicable. Existing methods based on this idea, however, rely on an exhaustive search and therefore only have asymptotic performance guarantees. In this article, we provide a modeling paradigm that converts a MAPF problem into a stochastic process and adopts a confidence bound based rule for finding the optimal state transition strategy. A randomized algorithm is proposed to solve this stochastic process, which combines ideas from conflict based search and Monte Carlo tree search. We show that the proposed method is almost surely optimal while enjoying non-asymptotic performance guarantees. In particular, the proposed method can, after solving N single-agent subproblems, produce a feasible solution with suboptimality bounded by $O(1/\sqrt{N})$. The theoretical results are verified by several numerical experiments based on grid maps.