Multiagent Systems With CBF-Based Controllers: Collision Avoidance and Liveness From Instability

Assuring system stability is typically a major control design objective. In this brief, we present a system where instability provides a crucial benefit. We consider multiagent collision avoidance using control barrier functions (CBFs) and study trade-offs between safety and liveness - the ability to reach a destination without large detours or gridlocks. We consider Centralized, full information policy as the benchmark, two standard decentralized policies with only the local (host) control available, and the predictor-corrector for collision avoidance (PCCA) in which each agent optimizes for everyone using incomplete information, and corrects for discrepancies. One contribution of this brief is proving feasibility for the centralized and PCCA policies. Monte Carlo simulations show that decentralized, host-only control policies lack liveness while the PCCA policy performs as well as the Centralized avoiding gridlocks. We explain the observed results by considering two agents negotiating passing order through an intersection. We show that the structure and stability of the resulting equilibria correlates with the observed propensity to gridlock - the policies with unstable equilibria avoid gridlock while those with stable ones do not.