Safety-critical control is a crucial aspect of modern systems, and Control Barrier Functions (CBFs) have gained popularity as the framework of choice for ensuring safety. However, implementing a CBF requires exact knowledge of the true state, a requirement that is often violated in real-world applications where only noisy or estimated state information is available. This paper introduces the notion of Robust Control Barrier Functions (R-CBF) for ensuring safety under such state uncertainty without requiring prior knowledge of the magnitude of uncertainty. We formally characterize the class of robustifying terms that ensure robust closed-loop safety and show how a robustly safe controller can be constructed. We demonstrate the effectiveness of this approach through simulations and compare it to existing methods, highlighting the additional robustness and convergence guarantees it provides.
@article{arxiv.2508.17226,
title = {Safety Under State Uncertainty: Robustifying Control Barrier Functions},
author = {Rahal Nanayakkara and Aaron D. Ames and Paulo Tabuada},
journal= {arXiv preprint arXiv:2508.17226},
year = {2025}
}