Minimizing Worst-Case Weighted Latency for Multi-Robot Persistent Monitoring: Theory and RL-Based Solutions
arXiv:2605.09633v2 Announce Type: replace Abstract: We study multi-robot persistent monitoring on weighted graphs, where node weights encode monitoring priorities and edge weights encode travel distances. The goal is to design joint robot trajectories that minimize the worst-case weighted latency across all nodes over an infinite time horizon. The widely adopted worst-case latency objective evaluates team performance over the entire time horizon and therefore may fail to distinguish strategies with poor transient behavior but strong asymptotic performance. To address this limitation, we propose a family of tail-performance objectives that generalize the standard objective and study the resulting functional optimization problems. We establish several key theoretical properties, including the existence of optimal strategies, relationships among the proposed objectives and their corresponding optimization problems, approximation by periodic solutions to arbitrary accuracy, and reductions

