Distributed Control Lyapunov and Control Barrier Certificates for Reactive Formation

In this article, we study reactive formation control for multi-robot systems, where robots maintain safety while achieving formation objectives. In complex environments, preserving formation shape often conflicts with safety requirements. Therefore, we allow temporary formation deviations to avoid hazards (e.g., obstacles) and automatic recovery afterward. To address this, we propose a distributed CLF-CBF-based quadratic program (QP) controller, where formation goals are encoded as distributed CLF conditions and safety constraints as CBF conditions. Sufficient distributed CLF and CBF conditions are derived to guarantee controller feasibility, and the effectiveness of the proposed method is validated through simulation studies.