Robust Control Barrier Functions with Uncertainty Estimation

TL;DR

This paper introduces a novel approach combining uncertainty estimation with control barrier functions to enhance safety and robustness in nonlinear control systems with unmodelled dynamics and disturbances.

Contribution

It develops a new uncertainty estimator with theoretical bounds and integrates it into CBF-based safety control, improving robustness against model uncertainties.

Findings

Enhanced safety in simulations of adaptive cruise control.

Improved robustness in multirotor obstacle avoidance.

Effective uncertainty rejection and safety guarantees.

Abstract

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.