Biologically-Inspired Impedance Control With Hysteretic Damping

Abstract

Recent experiments have shown that human joints can maintain a constant damping ratio across a wide range of external loads. This behavior can be explained by the use of a “complex stiffness” frequency-domain model approximating the impedance of the human joint. However, for a robot to replicate this naturally beneficial human behavior would require a time-domain model of this nonlinear joint impedance. This letter demonstrates that there exists a nonlinear time-domain model (originally from the structural mechanics community) that has a frequency-domain “describing function” that matches the complex stiffness model observed in humans. We provide an extension of this nonlinear time-domain model that removes the need to implement hard-switching control input. In addition, we demonstrate that this proportional-and-hysteretic-damping controller has inertia-invariant overshoot and therefore offers an advantage over the more common proportional-derivative control approach. Implementing the proposed proportional-and-hysteretic-damping control in a single-joint test-robot, we demonstrate for the first time that the desired frequency domain behavior can be reproduced in practice.