Compatibility checking of multiple control barrier functions for input constrained systems

TL;DR

This paper introduces an algorithmic method to verify the compatibility of multiple control barrier functions in constrained control systems, ensuring safe and robust controller design.

Contribution

It proposes a grid sampling and refinement algorithm with theoretical guarantees for checking CBF compatibility in perturbed systems.

Findings

Algorithm effectively verifies CBF compatibility.

Provides theoretical guarantees for robustness.

Applicable to systems with input and state constraints.

Abstract

State and input constraints are ubiquitous in control system design. One recently developed tool to deal with these constraints is control barrier functions (CBF) which transform state constraints into conditions in the input space. CBF-based controller design thus incorporates both the CBF conditions and input constraints in a quadratic program. However, the CBF-based controller is well-defined only if the CBF conditions are compatible. In the case of perturbed systems, robust compatibility is of relevance. In this work, we propose an algorithmic solution to verify or falsify the (robust) compatibility of given CBFs a priori. Leveraging the Lipschitz properties of the CBF conditions, a grid sampling and refinement method with theoretical analysis and guarantees is proposed.