Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911328230178816 |
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| author | Ong, Pio Lee, Haejoon Molnar, Tamas G. Panagou, Dimitra Ames, Aaron D. |
| author_facet | Ong, Pio Lee, Haejoon Molnar, Tamas G. Panagou, Dimitra Ames, Aaron D. |
| contents | This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints Ong, Pio Lee, Haejoon Molnar, Tamas G. Panagou, Dimitra Ames, Aaron D. Systems and Control Optimization and Control This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system. |
| title | Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2509.10716 |