Complex Stiffness Model of Physical HumanRobot Interaction: Implications for Control of Performance Augmentation Exoskeletons Human joint dynamic stiffness plays an important role in the stability of performance augmentation exoskeletons. In this paper, we consider a new frequency domain model of the human joint dynamics which features a complex value stiffness. This complex stiffness consists of a real stiffness and a hysteretic damping. We use it to explain the dynamic behaviors of the human connected to the exoskeleton, in particular the observed nonzero low frequency phase shift and the near constant damping ratio of the resonance as stiffness and inertia vary. We validate this concept with an elbowjoint exoskeleton testbed (attached to a subject) by experimentally varying joint stiffness behavior, exoskeleton inertia, and the strength augmentation gain. We compare three different models of elbowjoint dynamic stiffness: a model with real stiffness, viscous damping and inertia; a model with complex stiffness and inertia; and a model combining the previous two models. Our results show that the hysteretic damping term improves modeling accuracy (via a statistical Ftest). Moreover, this term contributes more to model accuracy than the viscous damping term. In addition, we experimentally observe a linear relationship between the hysteretic damping and the real part of the stiffness which allows us to simplify the complex stiffness model down to a 1parameter system. Ultimately, we design a fractional order controller to demonstrate how human hysteretic damping behavior can be exploited to improve strength amplification performance while maintaining stability.

Assistive method that controls joint stiffness and antagonized angle based on human joint stiffness characteristics and its application to an exoskeleton In this paper, we propose an assistance method that controls joint stiffness and the antagonized angle using variable elastic elements. The proposed system changes the stiffness and angle so that they correspond to the phase of movement and performs movement assistance in cooperation with the wearer. To achieve structural variability in the configuration of stiffness and the antagonized angle, we propose a joint structure in which the artificial muscle and tension spring are antagonistically arranged. While performing a movement, motion analysis was conducted to investigate the change in joint stiffness and antagonized angle. We confirmed that the proposed joint and human joint have the same tendency while in motion.