★TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints
arXiv preprint arXiv:2601.15196 · 2026
BibTeX
@article{xu2026ttcbf,
archiveprefix = {arXiv},
author = {Xu, Jianye and Alrifaee, Bassam},
doi = {10.48550/arXiv.2601.15196},
eprint = {2601.15196},
journal = {arXiv preprint arXiv:2601.15196},
primaryclass = {eess},
publisher = {arXiv},
title = {TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints},
year = {2026}
}About this paper
High-Order Control Barrier Functions (HOCBFs) handle safety constraints with relative degree greater than one by introducing a chain of auxiliary functions. This requires multiple class K functions, whose number and tuning burden grow with the relative degree. Because their parameters affect the conservatism and feasibility of the resulting control constraint, tuning them can complicate controller design. We introduce a Truncated Taylor Control Barrier Function (TTCBF), which extends the discrete-time CBF formulation to high-order safety constraints using a single class K function, independent of relative degree. We also propose an adaptive variant, aTTCBF, which optimizes the class K gain online. This paper updates our earlier TTCBF preprint, which remains available at its original arXiv record.
