On the stability and accuracy of high stiffness rendering in non-backdrivable actuators through series elasticity

Abstract

This paper addresses the problem of accuracy and coupled stability of stiffness-controlled series elastic actuators, where the motor is modeled as a non-backdrivable velocity source, and the desired value of virtual stiffness is above the physical stiffness of the compliant element. We first demonstrate that, in the mentioned conditions, no linear outer-loop force control action can be applied on the velocity-sourced motor to passify the system. Relaxing the constraint of passivity, we exhaustively search the control design space defined by parametric force and stiffness controllers, expressed in a general lead-lag form, and define a lead-type stiffness compensator that results in acceptable conditions for both coupled stability and accuracy. We also address the effect of a non-ideality in the velocity control loop, such as limited-bandwidth velocity control, and derive relationships between the value of the inner velocity loop time constant and parameters of the stiffness compensator that provide the best performance in terms of both stability and accuracy of haptic display.We show that the parameters of a simple outer-loop stiffness compensator can be optimized to result in a stable and accurate display of virtual environments with stiffness values in a large range, that also comprises values of virtual stiffness higher than the physical stiffness of the compliant element. A requirement for coupled stability is that the actuator is designed such that the minimum value of inertia connected to the compliant actuator load is higher than a control-defined threshold. Finally, we extensively analyze how the minimum value of interaction mass for coupled stability can be minimized through modulation of the stiffness compensator zeros and poles, considering realistic limitations in the velocity control bandwidth of non-backdrivable motors. Our analysis, validated through both numerical simulations and experiments, opens the possibility for alternative approaches to the design of compliant actuators, whereby rendering of high stiffness is possible if the load mass is always higher than a determined threshold.