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arXiv · 2509.10716

Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints

Pio Ong·Haejoon Lee·Tamas G. Molnar·Dimitra Panagou·Aaron D. Ames
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Abstract

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.

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Pio Ong, Haejoon Lee, Tamas G. Molnar, Dimitra Panagou, Aaron D. Ames. 2025-09-12. Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints. https://doi.org/10.1109/lcsys.2025.3640191

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