Generalizing robust control barrier functions from a controller design perspective

Abstract

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).While control barrier functions provide a powerful tool to endow controllers with formal safety guarantees, robust control barrier functions (RCBF) can be used to extend these guarantees for systems with model inaccuracies. This paper presents a generalized RCBF framework that unifies and extends existing notions of RCBFs for a broad class of model uncertainties. Main results are conditions for robust safety through generalized RCBFs. We apply these generalized principles for more specific design examples: a worst-case type design, an estimation-based design, and a tunable version of the latter. These examples are demonstrated to perform increasingly closer to an oracle design with ideal model information. Theoretical contributions are demonstrated on a practical example of a pendulum with unknown periodic excitation. Using numerical simulations, a comparison among design examples are carried out based on a performance metric depicting the increased likeness to the oracle design. © 2022 IEEE