Multiple-Input Multiple-Output Robust Control for Independent-Setup Variable Stiffness Actuator

This paper presents the development of a multiple-input multiple-output (MIMO) coupling controller for the independent-setup variable stiffness actuator (VSA). The dynamic model of the independent-setup VSA is typically considered decoupled due to the slight coupling between the joint and stiffness actuation. However, the model can be formulated in a coupled manner by taking into account the various uncertainties arising from physical stiffness variations. To describe the coupling, we present a linear parameter-varying (LPV) model. In this LPV model, the time-varying parameters are defined to capture the interaction between the two actuation components. Then, we introduce a robust MIMO coupling controller designed to ensure reliable operation. The controller is synthesized using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> mixed-sensitivity loop-shaping and LPV technique. This synthesis ensures the quadratic stability of the closed-loop system in the presence of time-varying parameters, along with effective tracking of joint and stiffness trajectories. Additionally, the generalized extended state observer is employed as a design paradigm to verify whether the proposed baseline LPV controller can be integrated with other advanced control strategies previously explored in VSA control. The effectiveness of all control schemes is experimentally validated on an updated mechanical-rotary variable impedance actuator prototype.