Distributed Implementation of Control Barrier Functions for Multi-agent Systems

In this letter, we propose a distributed implementation framework for control barrier functions induced quadratic programs for multi-agent systems. The quadratic program aims at minimally modifying nominal local controllers, which relate to the underlying system tasks, while always respecting a single coupling constraint which relates to system safety. Unlike previous implementations, no approximation or pre-allocation of the coupling constraint over the agents is needed. Instead, to solve the quadratic problem exactly, an auxiliary variable is assigned to each agent and then locally updated and transmitted among agents. The proposed distributed implementation ensures that the control barrier function constraint is enforced at every time instant, and the optimal to the quadratic program control signal is achieved in finite time. The efficacy of our method is demonstrated through two numerical examples.