The Passive Series Stiffness That Optimizes Torque Tracking for a Lower-Limb Exoskeleton in Human Walking.

Juanjuan Zhang,Steven H Collins

doi:10.3389/fnbot.2017.00068

Abstract

This study uses theory and experiments to investigate the relationship between the passive stiffness of series elastic actuators and torque tracking performance in lower-limb exoskeletons during human walking. Through theoretical analysis with our simplified system model, we found that the optimal passive stiffness matches the slope of the desired torque-angle relationship. We also conjectured that a bandwidth limit resulted in a maximum rate of change in torque error that can be commanded through control input, which is fixed across desired and passive stiffness conditions. This led to hypotheses about the interactions among optimal control gains, passive stiffness and desired quasi-stiffness. Walking experiments were conducted with multiple angle-based desired torque curves. The observed lowest torque tracking errors identified for each combination of desired and passive stiffnesses were shown to be linearly proportional to the magnitude of the difference between the two stiffnesses. The proportional gains corresponding to the lowest observed errors were seen inversely proportional to passive stiffness values and to desired stiffness. These findings supported our hypotheses, and provide guidance to application-specific hardware customization as well as controller design for torque-controlled robotic legged locomotion.

Highlights

Direct control of interaction forces or torques have been used in physical human-robot interaction to reduce interface impedance, increase reactiveness of the robotic devices and improves human safety and comfort (Haddadin et al, 2008; Lasota et al, 2014)
Optimal Passive Stiffness To further ease the theoretical analysis for the prediction of passive stiffness optimum in series elastic actuators, we modeled the assisted walking with the ankle exoskeleton as an oscillator
This paper investigates the existence of an optimal passive stiffness that benefits torque tracking in lower-limb exoskeletons driven by series elastic actuator during walking

Summary

Introduction

Direct control of interaction forces or torques have been used in physical human-robot interaction to reduce interface impedance, increase reactiveness of the robotic devices and improves human safety and comfort (Haddadin et al, 2008; Lasota et al, 2014). Various efforts have been made toward accurate torque tracking of lower-limb wearable robotic devices bym means of controller design (van Dijk et al, 2013; Zanotto et al, 2013; Zhang et al, 2015, 2017) This type of systems have complicated, time-varying and uncertain dynamics due to human-robot interactions and possible transmission frictions. Inter-subject and inter-step variations of human gait introduce hardto-quantify noise and disturbances Such characteristics result in the effectiveness of a torque tracking structure made of the combination of model-free, integration-free feedback control and iterative learning (van Dijk et al, 2013; Zhang et al, 2015, 2017). This paper explores the possibility to improve torque control performance in lowerlimb exoskeletons under fixed control objectives, with limited knowledge of the complete system dynamics, by optimizing the passive stiffness of actuators

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Discussion

Conclusion