On the similarities between Control Barrier Functions (CBFs) and Behavior Control Lyapunov Functions (BCLFs)
This work clarifies theoretical connections between two existing methods in control theory, which is incremental for researchers in robotics and aeronautics.
The paper investigates the similarities between Control Barrier Functions (CBFs) and Behavior Control Lyapunov Functions (BCLFs), both used for multiple control objectives like safety and goal convergence, and shows that under specific restrictions (e.g., linear functions and single objectives), the results in terms of admissible control sets are equivalent, with both making the invariant set asymptotically stable.
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.