TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917215987564544 |
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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 |