Safety-Critical Adaptive Impedance Control via Nonsmooth Control Barrier Functions under State and Input Constraints

2026-05-27

AI Summary

This work addresses the challenge of simultaneously ensuring safety and compliance in human–robot interaction under dynamic uncertainties, external forces, and actuator saturation. To this end, an online adaptive impedance control framework is proposed, featuring a novel position–velocity composite nonsmooth control barrier function that unifies the handling of relative-degree-one safety constraints. Real-time compliant interaction is achieved through a quadratic programming-based safety filter. Unknown dynamics are compensated online using an interval type-2 fuzzy system, while a soft-constraint mechanism with exact penalty recovery mitigates torque saturation effects. Theoretical analysis establishes forward invariance of the safe set and uniform ultimate boundedness of tracking errors. Experimental validation on a 7-degree-of-freedom robotic manipulator demonstrates robust and safe impedance control performance under significant model uncertainty and external disturbances.

Abstract

Safe physical interaction is critical for deploying robotic manipulators in human-robot interaction and contact-rich tasks, where uncertainty, external forces, and actuator limitations can compromise both performance and safety. We propose an online adaptive impedance control framework that enforces joint-state safety while achieving compliant interaction under uncertain dynamics. The approach combines a quadratic-program-based safety filter with a novel composed position-velocity non-smooth control barrier function (NCBF), enabling joint position and velocity constraints to be enforced through a unified relative-degree-one barrier. Unknown dynamics are compensated online using an interval type-2 fuzzy logic system, while actuator torque limits are handled through soft constraints with exact penalty recovery of feasible solutions. A disturbance-observer-enhanced safety mechanism improves robustness against modelling errors and external interaction forces. Using composite Lyapunov analysis, we prove forward invariance of the safe set and the uniform ultimately boundedness of the impedance-tracking error. Simulations on a 7-DOF manipulator with severe parametric uncertainty and external interaction wrenches demonstrate safe constraint satisfaction and robust impedance tracking.

Problem

• safety-critical control
• impedance control
• state constraints
• input constraints
• uncertain dynamics

Innovation

• Nonsmooth Control Barrier Functions
• Adaptive Impedance Control
• Interval Type-2 Fuzzy Logic
• Safety-Critical Control
• Disturbance Observer