Robust Safety Critical Control Under Multiple State and Input Constraints: Volume Control Barrier Function Method

2025-03-18

AI Summary

This paper addresses safety-critical control of uncertain dynamical systems subject to multiple state and input constraints. Methodologically, it proposes a minimal-intervention safety-filtering framework comprising three key components: (1) a novel Volume-Control Barrier Function (VCBF), which quantifies the feasible volume of quadratic programming (QP) constraints to guarantee solution existence under coupled constraints; (2) a composite disturbance observer–Robust Integral of the Sign of the Error (DOB-RISE) estimator that achieves exponential convergence of uncertainty estimation, with its compensation explicitly embedded into safety constraints to reduce conservatism; and (3) a QP-based safety filter incorporating disturbance compensation. Experimental and simulation results demonstrate that the approach maintains QP feasibility, system safety, and consistent closed-loop performance under strong external disturbances and tight constraint bounds—significantly enhancing robustness of the safety boundary and minimizing unnecessary control intervention.

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

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

In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that minimizes changes to reference inputs when safety risks arise, ensuring a balance between safety and performance. A nonlinear disturbance observer (DOB) based on the robust integral of the sign of the error (RISE) is used to estimate system uncertainties, ensuring that the estimation error converges to zero exponentially. This error bound is integrated into the safety-critical controller to reduce conservativeness while ensuring safety. To further address the challenges arising from multiple CBF and input constraints, a novel Volume CBF (VCBF) is proposed by analyzing the feasible space of the quadratic programming (QP) problem. % ensuring solution feasibility by keeping the volume as a positive value. To ensure that the feasible space does not vanish under disturbances, a DOB-VCBF-based method is introduced, ensuring system safety while maintaining the feasibility of the resulting QP. Subsequently, several groups of simulation and experimental results are provided to validate the effectiveness of the proposed controller.

Problem

• Develops a safety-critical control framework for uncertain systems under constraints.
• Proposes Volume Control Barrier Function to handle multiple constraints effectively.
• Integrates nonlinear disturbance observer to ensure safety and reduce conservativeness.

Innovation

• Develops Volume Control Barrier Function (VCBF) method
• Integrates nonlinear disturbance observer with RISE
• Ensures safety and performance via QP feasibility