Modeling and Loop Shaping of Single-Joint Amplification Exoskeleton with Contact Sensing and Series Elastic Actuation

Abstract

In this paper we consider a class of exoskeletons designed to amplify the strength of humans through feedback of sensed human-robot interactions and actuator forces. We define an amplification error signal based on a reference amplification rate, and design a linear feedback compensator to attenuate this error. Since the human operator is an integral part of the system, we design the compensator to be robust to both a realistic variation in human impedance and a large variation in load impedance. We demonstrate our strategy on a one-degree of freedom amplification exoskeleton connected to a human arm, following a three dimensional matrix of experimentation: slow or fast human motion; light or extreme exoskeleton load; and soft or clenched human arm impedances. We demonstrate that a slightly aggressive controller results in a borderline stable system-but only for soft human musculoeskeletal behavior and a heavy load. This class of exoskeleton systems is interesting because it can both amplify a human's interaction forces -so long as the human contacts the environment through the exoskeleton-and attenuate the operator's perception of the exoskeleton's reflected dynamics at frequencies within the bandwidth of the control.

Complex Stiffness Model of Physical Human-Robot Interaction: Implications for Control of Performance Augmentation Exoskeletons

“…Based on (8) and (10), (14) is able to explain both the nonzero phase shift at low frequencies and the near constant value of ζ h-e/α across all the experiments. This, in turn, supports the use of (14) as a 1-parameter model of S h-e/α for augmentation controller design.…”

“…With the assistance of actuator torques produced from the augmentation command, the human's interaction forces with the exoskeleton are amplified by a factor of α. This exoskeleton augmentation strategy differs from the one we applied in [14] in the directness of the augmentation feedback.…”

“…As in [14], the augmentation control we discuss here is designed to eliminate the augmentation error signal τ α = (α − 1)τ c + τ s by feeding it back to the actuator command τ d with an augmentation controller. Different from the direct augmentation feedback shown in Fig.…”

“…However, it is not clear from the literature that a linear relationship between the damping and the stiffness of a human joint can be expected in more general cases. Another way to model the damping in the linear massspring-damper model is through the empirical observation that a relatively consistent damping ratio is maintained by the human elbow across different joint stiffnesses [14]. Frequency domain identification of the ankle joint impedance [16], [21] also showed a consistent damping ratio within the range from 0.22 to 0.49.…”

Compliance Shaping for Control of Strength Amplification Exoskeletons with Elastic Cuffs

“…More accurate bounds on the human's capabilities lead to higher performance controllers which are still stable when interfacing with humans [23]. Bounded uncertain human impedance models have also been applied to design the closed loop interface dynamics of an amplification exoskeleton [24]. This paper introduces a mechanical spring between the human cuff and the exoskeleton structure in order to improve the passivity properties of the system.…”