  Multi-agent path finding (MAPF) determines an ensemble of collision-free
paths for multiple agents between their respective start and goal locations.
Among the available MAPF planners for workspaces modeled as a graph, A*-based
approaches have been widely investigated and have demonstrated their efficiency
in numerous scenarios. However, almost all of these A*-based approaches assume
that each agent executes an action concurrently in that all agents start and
stop together. This article presents a natural generalization of MAPF with
asynchronous actions where agents do not necessarily start and stop
concurrently. The main contribution of the work is a proposed approach called
Loosely Synchronized Search (LSS) that extends A*-based MAPF planners to handle
asynchronous actions. We show LSS is complete and finds an optimal solution if
one exists. We also combine LSS with other existing MAPF methods that aims to
trade-off optimality for computational efficiency. Extensive numerical results
are presented to corroborate the performance of the proposed approaches.
Finally, we also verify the applicability of our method in the Robotarium, a
remotely accessible swarm robotics research platform.
