Rectified Control Barrier Functions for High-Order Safety Constraints

TL;DR

This paper introduces Rectified Control Barrier Functions (ReCBFs), a new method for handling high-order safety constraints in control systems, improving upon existing high-order CBF approaches with a novel activation function.

Contribution

The paper proposes ReCBFs, a novel approach that overcomes limitations of existing high-order CBF methods by incorporating an activation function, applicable to various relative degrees.

Findings

ReCBFs effectively handle high relative degree safety constraints.

The approach outperforms existing methods like CBF backstepping.

Validated through examples including an aircraft control problem.

Abstract

This paper presents a novel approach for synthesizing control barrier functions (CBFs) from high relative degree safety constraints: Rectified CBFs (ReCBFs). We begin by discussing the limitations of existing High-Order CBF approaches and how these can be overcome by incorporating an activation function into the CBF construction. We then provide a comparative analysis of our approach with related methods, such as CBF backstepping. Our results are presented first for safety constraints with relative degree two, then for mixed-input relative degree constraints, and finally for higher relative degrees. The theoretical developments are illustrated through simple running examples and an aircraft control problem.