TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints

TL;DR

This paper introduces TTCBF, a novel control barrier function that efficiently enforces high-order safety constraints with fewer tuning parameters, demonstrated through numerical experiments on complex systems.

Contribution

The paper proposes TTCBF, a generalized CBF for high-order constraints requiring only one class K function, and an adaptive variant for online gain optimization.

Findings

Validated on a relative-degree-six spring-mass system.

Effective in cluttered corridor navigation scenarios.

Requires fewer control design parameters than existing methods.

Abstract

Control Barrier Functions (CBFs) enforce safety by rendering a prescribed safe set forward invariant. However, standard CBFs are limited to safety constraints with relative degree one, while High-Order CBF (HOCBF) methods address higher relative degree at the cost of introducing a chain of auxiliary functions and multiple class K functions whose tuning scales with the relative degree. In this paper, we introduce a Truncated Taylor Control Barrier Function (TTCBF), which generalizes standard discrete-time CBFs to consider high-order safety constraints and requires only one class K function, independent of the relative degree. We also propose an adaptive variant, adaptive TTCBF (aTTCBF), that optimizes an online gain on the class K function to improve adaptability, while requiring fewer control design parameters than existing adaptive HOCBF variants. Numerical experiments in a relative-degree-six spring-mass system and a cluttered corridor navigation validate the above theoretical findings.