Banach Control Barrier Functions for Large-Scale Swarm Control

This paper studies the safe control of very large multi-agent systems via a generalized framework that employs so-called Banach Control Barrier Functions (B-CBFs). Modeling a large swarm as probability distribution over a spatial domain, we show how B-CBFs can be used to appropriately capture a variety of macroscopic constraints that can integrate with large-scale swarm objectives. Leveraging this framework, we define stable and filtered gradient flows for large swarms, paying special attention to optimal transport algorithms. Further, we show how to derive agent-level, microscopical algorithms that are consistent with macroscopic counterparts in the large-scale limit. We then identify conditions for which a group of agents can compute a distributed solution that only requires local information from other agents within a communication range. Finally, we showcase the theoretical results over swarm systems in the simulations section.