Temporal segmentation in multi agent path finding with applications to explainability

Multi-Agent Path Finding (MAPF) is the problem of planning paths for agents to reach their targets from their start locations, such that the agents do not collide while executing the plan. In many settings, the plan (or a digest thereof) is conveyed to a supervising entity, e.g., for confirmation before execution, for a report, etc. In such cases, we wish to convey that the plan is collision-free with minimal amount of information. To this end, we propose an explanation scheme for MAPF. The scheme decomposes a plan into segments such that within each segment, the agents' paths are disjoint. We can then convey the plan whilst convincing that it is collision-free, using a small number of frames (dubbed an explanation). We can also measure the simplicity of a plan by the number of segments required for the decomposition. We study the complexity of algorithmic problems that arise by the explanation scheme and the tradeoff between the length (makespan) of a plan and its minimal decomposition. We also introduce two centralized (i.e. runs on a single CPU with full knowledge of the multi-agent system) algorithms for planning with explanations. One is based on a coupled search algorithm similar to A⁎, and the other is a decoupled method based on Conflict-Based Search (CBS). We refer to the latter as Explanation-Guided CBS (XG-CBS), which uses a low-level search for individual agents and maintains a high-level conflict tree to guide the low-level search to avoid collisions as well as increasing the number of segments. We propose four approaches to the low-level search of XG-CBS by modifying A⁎ for explanations and analyze their effects on the completeness of XG-CBS. Finally, we highlight important aspects of the proposed explanation scheme in various MAPF problems and empirically evaluate the performance of the proposed planning algorithms in a series of benchmark problems.