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

arXiv: https://arxiv.org/abs/2601.15196 · HTML: https://mlsanity.com/paper/2601.15196/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2026.

## Built on by (most cited first, 1 of 1)

- [Beyond Safety Filtering: Control Barrier Function-Informed Reinforcement Learning for Connected and Automated Vehicles](https://mlsanity.com/paper/2605.16894/) (2026)

## Abstract (arXiv)

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.