Time-To-Reach Separation and Safety Filtering for Safe, Fair, and Efficient Multi-Agent Coordination

Abstract: Advanced Air Mobility (AAM) operations are expected to significantly increase aerial traffic in urban airspace, requiring autonomous traffic management systems to ensure collision-free operations in highly congested environments. In this paper, we propose a multi-agent coordination framework that uses minimum time-to-reach (TTR) as a unifying metric for priority assignment, temporal separation, and safety filtering. We focus on the problem of coordinating multiple aerial vehicles merging into an air corridor while maintaining safe separation between vehicles. Vehicles are assigned arrival-consistent priority based on TTR, and target TTR values are used to enforce temporal spacing that induces spatial separation. A priority-consistent safety filtering layer based on Hamilton-Jacobi reachability value functions ensures collision avoidance while minimally modifying the reference guidance. Simulation results in a highly congested corridor merging scenario show that the proposed method improves safety, fairness, and efficiency compared to time-optimal guidance and priority-agnostic safety filtering.