Impedance Control and Performance Measure of Series Elastic Actuators

Series elastic actuators (SEAs) have become prevalent in torque-controlled robots in recent years to achieve compliant interactions with environments and humans. However, designing optimal impedance controllers and characterizing impedance performance for SEAs with time delays and filtering are still underexplored problems. This article addresses the controller design problem by devising a critically damped gain design method for a class of SEA cascaded control architectures, which is composed of outer impedance and inner torque feedback loops. We indicate that the proposed gain design criterion solves optimal controller gains by maximizing phasemargin- based stability. Meanwhile, we observe a tradeoff between impedance and torque controller gains and analyze their interdependence in terms of closed-loop stability and overall impedance performance. Via the proposed controller design criterion, we adopt frequency-domain methods to thoroughly analyze the effects of time delays, filtering, and load inertia on SEA impedance performance. A novel impedance performance metric, defined as "Z-region," is proposed to simultaneously quantify achievable impedance magnitude range (i.e., Z-width) and frequency range (i.e., Z-depth). Maximizing the Z-region enables SEA-equipped robots to achieve a wide variety of Cartesian impedance tasks without alternating the control structure. Simulations and experimental implementations are performed to validate the proposed method and performance metric.