Stability-Guaranteed Variable Impedance Control of Robots Based on Approximate Dynamic Inversion

Variable impedance control has been considered as one of the most important compliant control approaches for its abilities in improving compliance, safety, and efficiency in robot-environment interaction. However, existing variable impedance controllers have deficits in stability guarantee. This article proposes a stability-guaranteed variable impedance control approach for robots with modeling uncertainties based on approximate dynamic inversion (ADI). Novel constraints on variable impedance profiles are given to guarantee the exponential stability of the desired variable impedance dynamics. An ADI-based impedance control law is designed to achieve the desired variable impedance dynamics through the convergence of a variable impedance error. Based on the extended Tikhonovs theorem, it is proven that the closed-loop control system has semiglobal practical exponential stability. The proposed impedance controller can be implemented in a PID form and is appealing for its simple structure, easy implementation, and control stability guarantee. The effectiveness of the proposed variable impedance controller is illustrated by an illustrative example taken on a five-bar parallel robot.