# Robust Control Barrier Functions with Uncertainty Estimation

arXiv: https://arxiv.org/abs/2304.08538 · HTML: https://mlsanity.com/paper/2304.08538/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2023.

## Built on by (most cited first, 3 of 3)

- [Contextual Safety Reasoning and Grounding for Open-World Robots](https://mlsanity.com/paper/2602.19983/) (2026)
- [Distributionally Safe Reinforcement Learning under Model Uncertainty: A Single-Level Approach by Differentiable Convex Programming](https://mlsanity.com/paper/2310.02459/) (2023)
- [Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Control](https://mlsanity.com/paper/2603.10392/) (2026)

## Abstract (arXiv)

This paper proposes a safety controller for control-affine nonlinear systems with unmodelled dynamics and disturbances to improve closed-loop robustness. Uncertainty estimation-based control barrier functions (CBFs) are utilized to ensure robust safety in the presence of model uncertainties, which may depend on control input and states. We present a new uncertainty/disturbance estimator with theoretical upper bounds on estimation error and estimated outputs, which are used to ensure robust safety by formulating a convex optimization problem using a high-order CBF. The possibly unsafe nominal feedback controller is augmented with the proposed estimator in two frameworks (1) an uncertainty compensator and (2) a robustifying reformulation of CBF constraint with respect to the estimator outputs. The former scheme ensures safety with performance improvement by adaptively rejecting the matched uncertainty. The second method uses uncertainty estimation to robustify higher-order CBFs for safety-critical control. The proposed methods are demonstrated in simulations of an uncertain adaptive cruise control problem and a multirotor obstacle avoidance situation.