# Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models

arXiv: https://arxiv.org/abs/2403.09865 · HTML: https://mlsanity.com/paper/2403.09865/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2024.

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

- [CBF-LLM: Safe Control for LLM Alignment](https://mlsanity.com/paper/2408.15625/) (2024)
- [Constrained Decoding for Safe Robot Navigation Foundation Models](https://mlsanity.com/paper/2509.01728/) (2025)
- [Dynamic Tube MPC: Learning Tube Dynamics with Massively Parallel Simulation for Robust Safety in Practice](https://mlsanity.com/paper/2411.15350/) (2024)
- [A Comparative Study of Artificial Potential Fields and Reciprocal Control Barrier Function-based Safety Filters](https://mlsanity.com/paper/2403.15743/) (2024)
- [Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems](https://mlsanity.com/paper/2506.07347/) (2025)
- [Control Barrier Function for Aligning Large Language Models](https://mlsanity.com/paper/2511.03121/) (2025)
- [Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering](https://mlsanity.com/paper/2606.07193/) (2026)
- [Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate](https://mlsanity.com/paper/2610.04297/) (2026)

## Abstract (arXiv)

Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied.