Stability Criterion for Variable Impedance Model Using a Variable-Augmented Matrix

• 1、 School of Automation, Guangdong University of Technology, Guangzhou, Guangdong, 510006

Abstract：Variable impedance control is often applied to robotic tasks involving contact for adapting a robot’s behavior to changes in its environment. However, allowing arbitrary fluctuations in impedance parameters may jeopardize the stability of the system. This study focuses on analyzing the stability of an impedance system with variable stiffness. To address this concern, we propose a state-independent stability criterion, utilizing an innovative Lyapunov function. The introduction of a variable-augmented matrix in the estimation of the Lyapunov function’s derivative contributes to a stability criterion that exhibits reduced conservatism compared to existing methodologies. The proposed criterion is subsequently evaluated through both numerical examples and experiments conducted on the Franka Emika Panda Robot. The results demonstrate the criterion’s advantages in terms of reduced conservatism.

Keywords： Manipulator dynamics, variable impedance control, stability criterion.