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

Juanjuan Zhang, Steven H. Collins

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.