Enhancing Robustness of Control Barrier Function: A Reciprocal Resistance-based Approach

TL;DR

This paper introduces a reciprocal resistance-based control barrier function (RRCBF) that improves robustness for disturbed nonlinear systems without needing explicit disturbance bounds, validated through simulations.

Contribution

The paper develops a novel RRCBF framework that enhances safety and robustness against disturbances without prior disturbance bound knowledge, including high-order and observer-based variants.

Findings

RRCBF ensures forward invariance under disturbances.

The disturbance observer-based RRCBF improves safety and control performance.

Simulations demonstrate effectiveness in linear and adaptive cruise control systems.

Abstract

In this note, a new reciprocal resistance-based control barrier function (RRCBF) is developed to enhance the robustness of control barrier functions for disturbed affine nonlinear systems, without requiring explicit knowledge of disturbance bounds. By integrating a reciprocal resistance-like term into the conventional zeroing barrier function framework, we formally establish the concept of the reciprocal resistance-based barrier function (RRBF), rigorously proving the forward invariance of its associated safe set and its robustness against bounded disturbances. The RRBF inherently generates a buffer zone near the boundary of the safe set, effectively dominating the influence of uncertainties and external disturbances. This foundational concept is extended to formulate RRCBFs, including their high-order variants. To alleviate conservatism in the presence of complex, time-varying disturbances, we further introduce a disturbance observer-based RRCBF (DO-RRCBF), which exploits disturbance estimates to enhance safety guarantees and recover nominal control performance. The effectiveness of the proposed framework is validated through two simulation studies: a second-order linear system illustrating forward invariance in the phase plane, and an adaptive cruise control scenario demonstrating robustness in systems with high relative degree.