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arXiv · 2601.15196

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

Jianye Xu·Bassam Alrifaee
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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.

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Jianye Xu, Bassam Alrifaee. 2026-01-21. TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints. https://arxiv.org/abs/2601.15196

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