Control Barrier Function Meets Interval Analysis: Safety-Critical Control with Measurement and Actuation Uncertainties

TL;DR

This paper introduces a novel framework combining control barrier functions with interval analysis to design safe feedback controllers for systems with uncertainties, ensuring safety despite measurement and actuation errors.

Contribution

It develops a new sampled-data control barrier function condition using interval Taylor models, addressing uncertainties and higher relative degrees in safety-critical control.

Findings

Successfully ensures safety in numerical simulations.

Demonstrates real-time control on a Crazyflie quadcopter.

Provides conditions for safe control with uncertainties.

Abstract

This paper presents a framework for designing provably safe feedback controllers for sampled-data control affine systems with measurement and actuation uncertainties. Based on the interval Taylor model of nonlinear functions, a sampled-data control barrier function (CBF) condition is proposed which ensures the forward invariance of a safe set for sampled-data systems. Reachable set overapproximation and Lasserre's hierarchy of polynomial optimization are used for finding the margin term in the sampled-data CBF condition. Sufficient conditions for a safe controller in the presence of measurement and actuation uncertainties are proposed, for CBFs with relative degree 1 and higher relative degree individually. The effectiveness of the proposed method is illustrated by two numerical examples and an experimental example that implements the proposed controller on the Crazyflie quadcopter in real-time.