Robust Multi-Agent Pickup and Delivery with Delays

Multi-Agent Pickup and Delivery (MAPD) is the problem of computing collision-free paths for a group of agents such that they can safely reach delivery locations from pickup ones. These locations are provided at runtime, making MAPD a combination between classical Multi-Agent Path Finding (MAPF) and online task assignment. Current algorithms for MAPD do not consider many of the practical issues encountered in real applications: real agents often do not follow the planned paths perfectly, and may be subject to delays and failures. In this paper, we study the problem of MAPD with delays, and we present two solution approaches that provide robustness guarantees by planning paths that limit the effects of imperfect execution. In particular, we introduce two algorithms, $k-\mathbf{TP}$ and $p-\mathbf{TP}$, both based on a decentralized algorithm typically used to solve MAPD, Token Passing (TP), which offer deterministic and probabilistic guarantees, respectively. Experimentally, we compare our algorithms against a version of TP enriched with online replanning. $k-\mathbf{TP}$ and $p-\mathbf{TP}$ provide robust solutions, significantly reducing the number of replans caused by delays, with little or no increase in solution cost and running time.