# Learning Barrier Functions with Memory for Robust Safe Navigation

arXiv: https://arxiv.org/abs/2011.01899 · HTML: https://mlsanity.com/paper/2011.01899/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2020.

## Built on by (most cited first, 21 of 21)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States](https://mlsanity.com/paper/2301.12012/) (2023)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [Reactive and Safe Road User Simulations using Neural Barrier Certificates](https://mlsanity.com/paper/2109.06689/) (2021)
- [PRIMU: Uncertainty Estimation for Novel Views in Gaussian Splatting from Primitive-Based Representations of Error and Coverage](https://mlsanity.com/paper/2508.02443/) (2025)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [T-CBF: Traversability-based Control Barrier Function to Navigate Vertically Challenging Terrain](https://mlsanity.com/paper/2503.06083/) (2025)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [Safety-Critical Learning of Robot Control with Temporal Logic Specifications](https://mlsanity.com/paper/2109.02791/) (2021)
- [Online Efficient Safety-Critical Control for Mobile Robots in Unknown Dynamic Multi-Obstacle Environments](https://mlsanity.com/paper/2402.16449/) (2024)
- [Enhanced Safety in Autonomous Driving: Integrating Latent State Diffusion Model for End-to-End Navigation](https://mlsanity.com/paper/2407.06317/) (2024)
- [Geometry of Radial Basis Neural Networks for Safety Biased Approximation of Unsafe Regions](https://mlsanity.com/paper/2210.05596/) (2022)
- [Safety-aware Skill Adaptation for Reinforcement Learning in Dynamic Environments](https://mlsanity.com/paper/2609.11433/) (2026)
- [VertexCBF: Improving Neural Control Barrier Functions via Vertex-Restricted Control Search](https://mlsanity.com/paper/2609.12831/) (2026)
- [Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields](https://mlsanity.com/paper/2610.20255/) (2026)

## Abstract (arXiv)

Control barrier functions are widely used to enforce safety properties in robot motion planning and control. However, the problem of constructing barrier functions online and synthesizing safe controllers that can deal with the associated uncertainty has received little attention. This paper investigates safe navigation in unknown environments, using onboard range sensing to construct control barrier functions online. To represent different objects in the environment, we use the distance measurements to train neural network approximations of the signed distance functions incrementally with replay memory. This allows us to formulate a novel robust control barrier safety constraint which takes into account the error in the estimated distance fields and its gradient. Our formulation leads to a second-order cone program, enabling safe and stable control synthesis in a priori unknown environments.