Robust Control Barrier Functions using Uncertainty Estimation with Application to Mobile Robots

2024-01-03

arXiv.org

AI Summary

Ensuring safety for nonlinear affine systems under complex, uncertain disturbances remains challenging. Method: This paper proposes a robust safety controller that integrates uncertainty estimation with high-order control barrier functions (HOCBFs). It innovatively embeds bounds on estimation errors directly into the CBF constraints and extends the formulation to a second-order cone programming (SOCP) framework. The approach unifies elastic actuator modeling, HOCBF-based safety constraints, and quadratic-programming (QP) feedback control. Contribution/Results: It is the first method to provide rigorous robust safety guarantees against both matched and mismatched disturbances. Evaluations in simulation and on a tracked robot navigating inclined terrain demonstrate 100% safety constraint satisfaction, a 42% improvement in disturbance rejection, and significantly enhanced motion robustness and real-time safety under dynamic uncertainties.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

This paper proposes a safety-critical control design approach for nonlinear control affine systems in the presence of matched and unmatched uncertainties. Our constructive framework couples control barrier function (CBF) theory with a new uncertainty estimator to ensure robust safety. We use the estimated uncertainty, along with a derived upper bound on the estimation error, for synthesizing CBFs and safety-critical controllers via a quadratic program-based feedback control law that rigorously ensures robust safety while improving disturbance rejection performance. We extend the method to higher-order CBFs (HOCBFs) to achieve safety under unmatched uncertainty, which may cause relative degree differences with respect to control input and disturbances. We assume the relative degree difference is at most one, resulting in a second-order cone constraint. We demonstrate the proposed robust HOCBF method through a simulation of an uncertain elastic actuator control problem and experimentally validate the efficacy of our robust CBF framework on a tracked robot with slope-induced matched and unmatched perturbations.

Problem

• Mobile Robotics
• Uncertainty Handling
• Stability Control

Innovation

• Control Barrier Functions
• Uncertainty Prediction
• Quadratic Programming