On the similarities between Control Barrier Functions (CBFs) and Behavior Control Lyapunov Functions (BCLFs)

TL;DR

This paper explores the theoretical connections between Control Barrier Functions and Behavior Control Lyapunov Functions, revealing their equivalence under certain conditions and their shared property of invariant set stability.

Contribution

It demonstrates the formal similarities between CBFs and BCLFs, showing their equivalence in control set descriptions when specific restrictions are applied.

Findings

CBFs and BCLFs describe control sets that render a set invariant.

Under certain restrictions, the control sets of CBFs and BCLFs are equivalent.

Both approaches ensure the invariant set is asymptotically stable.

Abstract

Control Barrier Functions (CBFs) is an important tool used to address situations with multiple concurrent control objectives, such as safety and goal convergence. In this paper we investigate the similarities between CBFs and so-called Behavior Control Lyapunov Functions (BCLFs) that have been proposed to address the same type of problems in the aeronautics domain. The key results of both CBFs and BCLFs is the description of the set of controls that render a given set invariant. We compare the corresponding theorems, and show that if we restrict the general class K function in CBFs to be the general linear function of BCLFs, and restrict the number of objectives as well as the number of priority levels to be just one in BCLFs, the results in terms of admissible control sets are equivalent. Furthermore, both papers show that the invariant set is made asymptotically stable.