Optimal Multi-Agent Path Finding for Precedence Constrained Planning Tasks

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents from their start locations to end locations. We consider an extension to this problem, Precedence Constrained Multi-Agent Path Finding (PC-MAPF), wherein agents are assigned a sequence of planning tasks that contain precedence constraints between them. PC-MAPF has various applications, for example in multi-agent pickup and delivery problems where some objects might require multiple agents to collaboratively pickup and move them in unison. Precedence constraints also arise in warehouse assembly problems where before a manufacturing task can begin, its input resources must be manufactured and delivered. We propose a novel algorithm, Precedence Constrained Conflict Based Search (PC-CBS), which finds makespan-optimal solutions for this class of problems. PC-CBS utilizes a Precedence-Constrained Task-Graph to define valid intervals for each planning task and updates them when precedence conflicts are encountered. We benchmark the performance of this algorithm over various warehouse assembly, and multi-agent pickup and delivery tasks, and use it to evaluate the sub-optimality of a recently proposed efficient baseline.