Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911138425339904 |
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| author | Cohen, Max H. Lavretsky, Eugene Ames, Aaron D. |
| author_facet | Cohen, Max H. Lavretsky, Eugene Ames, Aaron D. |
| contents | Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems Cohen, Max H. Lavretsky, Eugene Ames, Aaron D. Systems and Control Robotics Optimization and Control Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework. |
| title | Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems |
| topic | Systems and Control Robotics Optimization and Control |
| url | https://arxiv.org/abs/2509.04220 |