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

TL;DR

This paper introduces Measurement-Robust Control Barrier Functions (MR-CBFs), a framework that ensures safety in robotic systems despite imperfect state measurements, combining robustness with formal safety guarantees.

Contribution

The paper develops MR-CBFs by integrating backup set methods with CBFs, providing a novel approach for safety-critical control under measurement uncertainty.

Findings

The framework guarantees safety despite measurement errors.

MR-CBFs outperform standard CBFs in robustness.

Experimental validation on a Segway demonstrates practical effectiveness.

Abstract

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.