Open Access
ARTICLE
A Geometrical Approach to Compute Upper Limb Joint Stiffness
Davide Piovesan1, *, Roberto Bortoletto2
1 Biomedical, Industrial and Systems Engineering, Gannon University, 109 University Square, Erie, PA, 16541, USA.
2 221e Ltd., Piazza dell’Artigianato, 10, 35031 Abano Terme (PD), Italy.
* Corresponding Author: Davide Piovesan. Email: .
(This article belongs to this Special Issue: Computer Methods in Bio-mechanics and Biomedical Engineering)
Computer Modeling in Engineering & Sciences 2020, 123(1), 23-47. https://doi.org/10.32604/cmes.2020.09231
Received 24 November 2019; Accepted 29 January 2020; Issue published 01 April 2020
Abstract
Exoskeletons are designed to control the forces exerted during the physical
coupling between the human and the machine. Since the human is an active system, the
control of an exoskeleton requires coordinated action between the machine and the load
so to obtain a reciprocal adaptation. Humans in the control loop can be modeled as active
mechanical loads whose stiffness is continuously changing. The direct measurement of
human stiffness is difficult to obtain in real-time, thus posing a significant limitation to
the design of wearable robotics controllers. Electromyographic (EMG) recordings can
provide an indirect estimation of human muscle force and stiffness, but current methods
for the acquisition of the signals limit their use and efficiency. This work proposes a
hybrid method for the estimation of upper limb joint stiffness during reaching movements
that combines EMG-driven muscle models and constrained optimization. Using these two
stages process, we estimated an optimal joints’ stiffness bounded in a physiologically
sound variability range. This information is crucial when designing exoskeletons user
interfaces in which the limb stiffness is an integral part of the control loop. Point-to-point
human reaching movements were analyzed to reconstruct the joint stiffness of the upper
limb. An accurate 3D model of the arm, encompassing all bones from the hand to the
scapula and the majority of the upper limb muscles, was developed to represent the
sliding center of rotation of the joints. A well-posed parallel mechanism between the
skeleton and the configuration of the tracking markers was implemented. Thus, the
muscles’ force and joint stiffness were calculated using a generalized pseudo-inversion of
the Jacobian transformation between the muscles and Cartesian Space. The maximal and
minimal forces exertable by the muscles were set as the boundary condition for the
generalized pseudo-inverse by means of a state-of-the-art muscle model.
Keywords
Cite This Article
Piovesan, D., Bortoletto, R. (2020). A Geometrical Approach to Compute Upper Limb Joint Stiffness.
CMES-Computer Modeling in Engineering & Sciences, 123(1), 23–47.