The Cost of Executability: Temporal Margins for Continuous-Time Multi-Agent Path Finding under Closed-Loop Control

Abstract

Multi-agent path finding (MAPF) solvers are evaluated on the schedules they produce, not on how well those schedules can be executed. Specifically, continuous-time optimal solvers can achieve even lower cost than their discrete counterparts by scheduling agents with near-zero temporal/spatial separation, and by exploiting graphs with higher connectedness; however, such schedules may prove hard to execute under a realistic controller. We integrate AOC-CBS, an anytime-optimal continuous-time MAPF solver, into a fleet coordination framework in which each agent tracks its timed path using model predictive control, and we evaluate the resulting system on congested MovingAI benchmark instances with 21 to 40 agents. Without intervention, only a fraction of the instances complete execution. We then apply T-robustness by adding a time-margin, i.e., a minimum temporal gap between agents at shared locations, as well as spatial inflation of the agent footprint. Increasing either margin raises execution success, for a relatively small increase in the schedule's sum-of-costs; it also improves how closely agents adhere to the schedule: when tracking each agent's position throughout execution and comparing it against the position it should occupy according to the schedule, the mean discrepancy falls significantly as the margin increases. In general, the two margins have different effects; temporal margin decreases deviation, giving the controller room to stay on schedule. Spatial margin affects deviation less and instead increases the clearance between agents, so that the same deviation no longer leads to a blocking stall. They are nonetheless substitutes rather than complements: spatial inflation is almost free in schedule cost, but its effect on execution success is small and does not compound with a temporal margin already in place.