  Control Barrier Functions and Quadratic Programming are increasingly used for
designing controllers that consider critical safety constraints. However, like
Artificial Potential Fields, they can suffer from the stable spurious
equilibrium point problem, which can result in the controller failing to reach
the goal. To address this issue, we propose introducing circulation
inequalities as a constraint. These inequalities force the system to explicitly
circulate the obstacle region in configuration space, thus avoiding undesirable
equilibria. We conduct a theoretical analysis of the proposed framework and
demonstrate its efficacy through simulation studies. By mitigating spurious
equilibria, our approach enhances the reliability of CBF-based controllers,
making them more suitable for real-world applications.
