High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908274985533440 |
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| author | Xu, Jianye Alrifaee, Bassam |
| author_facet | Xu, Jianye Alrifaee, Bassam |
| contents | We examine the complexity of the standard High-Order Control Barrier Function (HOCBF) approach and propose a truncated Taylor-based approach that reduces design parameters. First, we derive the explicit inequality condition for the HOCBF approach and show that the corresponding equality condition sets a lower bound on the barrier function value that regulates its decay rate. Next, we present our Truncated Taylor CBF (TTCBF), which uses a truncated Taylor series to approximate the discrete-time CBF condition. While the standard HOCBF approach requires multiple class K functions, leading to more design parameters as the constraint's relative degree increases, our TTCBF approach requires only one. We support our theoretical findings in numerical collision-avoidance experiments and show that our approach ensures safety while reducing design complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation Xu, Jianye Alrifaee, Bassam Systems and Control Robotics We examine the complexity of the standard High-Order Control Barrier Function (HOCBF) approach and propose a truncated Taylor-based approach that reduces design parameters. First, we derive the explicit inequality condition for the HOCBF approach and show that the corresponding equality condition sets a lower bound on the barrier function value that regulates its decay rate. Next, we present our Truncated Taylor CBF (TTCBF), which uses a truncated Taylor series to approximate the discrete-time CBF condition. While the standard HOCBF approach requires multiple class K functions, leading to more design parameters as the constraint's relative degree increases, our TTCBF approach requires only one. We support our theoretical findings in numerical collision-avoidance experiments and show that our approach ensures safety while reducing design complexity. |
| title | High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2503.15014 |