Circulation-embedded Control Barrier Function for safe navigation: A solution to avoid undesired equilibria and dysfunctional circulation

The Control Barrier Function (CBF) is widely adopted in safety-critical applications such as safe navigation in an unknown environment. CBF quadratic program (CBF-QP) is a conventional CBF framework that acts as a safety filter. However, CBF-QP is prone to deadlocks, especially in dynamic and multi-agent environments, although it also occurs with convex obstacles. Specifically, CBF-QP suffers from several challenges, including undesired equilibria, accompanying slowdown behavior around these points, dysfunctional circulation, and becoming trapped in the obstacle. In this paper, we propose a practical solution to address these issues. First, we introduce the foundational principles and parameters for the proposed circulation-embedded CBF algorithm, which incorporates an effective circulation linear inequality constraint into CBF-QP. Moreover, input bounds constraints are incorporated to ensure that the rectified input is readily applicable and optimal. Then, we study the feasibility, continuity, equilibrium points, and convergence of the proposed circulation-embedded CBF-QP algorithm through propositions and formal proofs. Finally, the effectiveness of the proposed algorithm is demonstrated through experiments and comparisons involving unknown nonconvex obstacles and multi-robot scenarios without communication.