Constant-Sum High-Order Barrier Functions for Safety Between Parallel Boundaries
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914211446128640 |
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| author | Kim, Kwang Hak Diagne, Mamadou Krstić, Miroslav |
| author_facet | Kim, Kwang Hak Diagne, Mamadou Krstić, Miroslav |
| contents | This paper takes a step towards addressing the difficulty of constructing Control Barrier Functions (CBFs) for parallel safety boundaries. A single CBF for both boundaries has been reported to be difficult to validate for safety, and we identify why this challenge is inherent. To overcome this, the proposed method constructs separate CBFs for each boundary. We begin by presenting results for the relative degree one case and then extend these to higher relative degrees using the CBF backstepping technique, establishing conditions that guarantee safety. Finally, we showcase our method by applying it to a unicycle system, deriving a simple, verifiable condition to validate the target CBFs for direct implementation of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constant-Sum High-Order Barrier Functions for Safety Between Parallel Boundaries Kim, Kwang Hak Diagne, Mamadou Krstić, Miroslav Optimization and Control Systems and Control This paper takes a step towards addressing the difficulty of constructing Control Barrier Functions (CBFs) for parallel safety boundaries. A single CBF for both boundaries has been reported to be difficult to validate for safety, and we identify why this challenge is inherent. To overcome this, the proposed method constructs separate CBFs for each boundary. We begin by presenting results for the relative degree one case and then extend these to higher relative degrees using the CBF backstepping technique, establishing conditions that guarantee safety. Finally, we showcase our method by applying it to a unicycle system, deriving a simple, verifiable condition to validate the target CBFs for direct implementation of our results. |
| title | Constant-Sum High-Order Barrier Functions for Safety Between Parallel Boundaries |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.15932 |