# ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks

arXiv: https://arxiv.org/abs/2509.16614 · HTML: https://mlsanity.com/paper/2509.16614/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 20 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [Learning Safe, Generalizable Perception-based Hybrid Control with Certificates](https://mlsanity.com/paper/2201.00932/) (2022)
- [Learning Barrier Functions with Memory for Robust Safe Navigation](https://mlsanity.com/paper/2011.01899/) (2020)
- [Refining Control Barrier Functions through Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2204.12507/) (2022)
- [Neural Control Barrier Functions for Safe Navigation](https://mlsanity.com/paper/2407.19907/) (2024)
- [Advances in the Theory of Control Barrier Functions: Addressing Practical Challenges in Safe Control Synthesis for Autonomous and Robotic Systems](https://mlsanity.com/paper/2312.16719/) (2023)
- [Bridging Model Predictive Control and Deep Learning for Scalable Reachability Analysis](https://mlsanity.com/paper/2505.03830/) (2025)
- [Patching Approximately Safe Value Functions Leveraging Local Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2304.09850/) (2023)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments](https://mlsanity.com/paper/2508.03428/) (2025)

## Built on by (most cited first, 2 of 2)

- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)
- [VertexCBF: Improving Neural Control Barrier Functions via Vertex-Restricted Control Search](https://mlsanity.com/paper/2609.12831/) (2026)

## Abstract (arXiv)

Control barrier functions (CBFs) have been demonstrated as an effective method for safety-critical control of autonomous systems. Although CBFs are simple to deploy, their design remains challenging, motivating the development of learning-based approaches. Yet, issues such as suboptimal safe sets, applicability in partially observable environments, and lack of rigorous safety guarantees persist. In this work, we propose observation-conditioned neural CBFs based on Hamilton-Jacobi (HJ) reachability analysis, which approximately recover the maximal safe sets. We exploit certain mathematical properties of the HJ value function, ensuring that the predicted safe set never intersects with the observed failure set. Moreover, we leverage a hypernetwork-based architecture that is particularly suitable for the design of observation-conditioned safety filters. The proposed method is examined both in simulation and hardware experiments for a ground robot and a quadcopter. The results show improved success rates and generalization to out-of-domain environments compared to the baselines.