A Minimax Scheduling Framework for Inertially-Constrained Multi-Agent Systems

Scheduling of physical space in multi-agent systems is crucial in widespread applications including transportation and industrial manufacturing. However, few existing works focused on improving the scheduling efficiency when agents are inertially constrained and some non-cooperative agents with unknown and uncontrollable trajectories exist. In this article, we establish a minimax framework aiming to ensure the robustness of scheduling against the uncertainty of non-cooperative agents. Specifically, we propose a function characterizing the preference of different states based on a given situation information, and formulate a trajectory planning policy by establishing a minimax optimization problem. Furthermore, the tractability of the proposed policy is ensured by developing an approximate algorithm and a truncation method, and the safety guarantee of the policy is also proved. Finally, numerical simulations suggest a 90% reduction on the empirical probability of high-cost scenarios compared with heuristic policies, validating the robustness of the proposed policy.