Using Circulation to Mitigate Spurious Equilibria in Control Barrier Function -- Extended Version

TL;DR

This paper introduces circulation inequalities into Control Barrier Functions to prevent spurious equilibria, thereby improving the reliability of safety-critical controllers in reaching goals effectively.

Contribution

The paper proposes a novel method of adding circulation constraints to CBFs, providing a theoretical framework and simulation validation for avoiding undesirable equilibria.

Findings

Circulation inequalities effectively prevent spurious equilibria.

The approach enhances controller reliability in safety-critical tasks.

Simulation results confirm improved goal-reaching performance.

Abstract

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.