Guaranteeing Safety via Active-Set Invariance Filters for Multi-Agent Space Systems with Coupled Dynamics

As space operations increase both in number and complexity, there exists a growing need for mission automation with provable safety guarantees. In this paper, we provide a formulation of the vehicle routing problem with safety guarantees for a multi-spacecraft inspection mission, where multiple "deputy" spacecraft inspect a passive "chief" spacecraft. We ensure safety through a pair of optimization-based filters: the explicit and the implicit active set-invariance filter. For each filter, we derive conditions that guarantee each deputy simultaneously satisfies constraints regarding chief collision avoidance, other deputy collision avoidance, a maximum relative distance from the chief, sun avoidance, and a distance-based maximum relative velocity. Numerical simulations demonstrate the computational efficiency of both filters, indicating the practicality of incorporating either one in real-world applications.