# Composing Control Barrier Functions for Complex Safety Specifications

arXiv: https://arxiv.org/abs/2309.06647 · HTML: https://mlsanity.com/paper/2309.06647/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2023.

## Built on by (most cited first, 8 of 8)

- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Multi-Constraint Safe Reinforcement Learning via Closed-form Solution for Log-Sum-Exp Approximation of Control Barrier Functions](https://mlsanity.com/paper/2505.00671/) (2025)
- [Safe Vision Language Action Models via Barrier Enhanced Flow Matching](https://mlsanity.com/paper/2607.29569/) (2026)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)
- [Spatial Envelope MPC: High Performance Driving without a Reference](https://mlsanity.com/paper/2509.18506/) (2025)
- [CAffNet: Hard Constraint-Affine Neural Networks](https://mlsanity.com/paper/2605.24437/) (2026)
- [VLPSA: Vision-Language-Poisson-Safe Actions for Full-Body Safety of Learned Policies](https://mlsanity.com/paper/2609.22462/) (2026)

## Abstract (arXiv)

The increasing complexity of control systems necessitates control laws that guarantee safety w.r.t. complex combinations of constraints. In this letter, we propose a framework to describe compositional safety specifications with control barrier functions (CBFs). The specifications are formulated as Boolean compositions of state constraints, and we propose an algorithmic way to create a single continuously differentiable CBF that captures these constraints and enables safety-critical control. We describe the properties of the proposed CBF, and we demonstrate its efficacy by numerical simulations.