Safety Under State Uncertainty: Robustifying Control Barrier Functions

TL;DR

This paper introduces Robust Control Barrier Functions (R-CBF) that ensure safety in control systems despite state estimation uncertainties, without needing prior knowledge of the uncertainty magnitude.

Contribution

The paper formally characterizes robustifying terms for R-CBFs and demonstrates how to construct controllers that maintain safety under state uncertainty.

Findings

R-CBFs provide robustness without prior uncertainty bounds

Simulations show improved safety and convergence guarantees

Compared to existing methods, R-CBFs enhance robustness in uncertain environments

Abstract

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.