# Measurement-Robust Control Barrier Functions: Certainty in Safety with Uncertainty in State

arXiv: https://arxiv.org/abs/2104.14030 · HTML: https://mlsanity.com/paper/2104.14030/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2021.

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

- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [Contextual Safety Reasoning and Grounding for Open-World Robots](https://mlsanity.com/paper/2602.19983/) (2026)
- [Enhancing Feature Tracking Reliability for Visual Navigation using Real-Time Safety Filter](https://mlsanity.com/paper/2502.01092/) (2025)
- [Robust Verification of Controllers under State Uncertainty via Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2511.14755/) (2025)
- [Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate](https://mlsanity.com/paper/2610.04297/) (2026)

## Abstract (arXiv)

The increasing complexity of modern robotic systems and the environments they operate in necessitates the formal consideration of safety in the presence of imperfect measurements. In this paper we propose a rigorous framework for safety-critical control of systems with erroneous state estimates. We develop this framework by leveraging Control Barrier Functions (CBFs) and unifying the method of Backup Sets for synthesizing control invariant sets with robustness requirements -- the end result is the synthesis of Measurement-Robust Control Barrier Functions (MR-CBFs). This provides theoretical guarantees on safe behavior in the presence of imperfect measurements and improved robustness over standard CBF approaches. We demonstrate the efficacy of this framework both in simulation and experimentally on a Segway platform using an onboard stereo-vision camera for state estimation.