@Article{cmes.2020.09231,
AUTHOR = {Davide Piovesan, Roberto Bortoletto},
TITLE = {A Geometrical Approach to Compute Upper Limb Joint Stiffness},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {123},
YEAR = {2020},
NUMBER = {1},
PAGES = {23--47},
URL = {http://www.techscience.com/CMES/v123n1/38483},
ISSN = {1526-1506},
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.},
DOI = {10.32604/cmes.2020.09231}
}