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

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Hauptverfasser: Xu, Jianye, Alrifaee, Bassam
Format: Preprint
Veröffentlicht: 2026
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author Xu, Jianye
Alrifaee, Bassam
author_facet Xu, Jianye
Alrifaee, Bassam
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_15196
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints
Xu, Jianye
Alrifaee, Bassam
Systems and Control
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.
title TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints
topic Systems and Control
url https://arxiv.org/abs/2601.15196