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Title: A computationally efficient musculoskeletal model of the lower limb for the control of rehabilitation robots: assumptions and validation
Authors: Farhat, Nidal 
Zamora, Pau 
Reichert, David 
Mata, Vicente 
Page, Alvaro 
Valera, Angel 
Keywords: Musculoskeletal system - Mathematical models;Robotic exoskeletons;Human mechanics - Mathematical models;Musculoskeletal system - Models;Musculoskeletal model;Knee - Mechanical properties;Knee - Movements - Simulation methods;Knee - Movements - Mathematical models
Issue Date: 2022
Publisher: Applied Sciences (Switzerland)
Abstract: We present and validate a computationally efficient lower limb musculoskeletal model for the control of a rehabilitation robot. It is a parametric model that allows the customization of joint kinematics, and it is able to operate in real time. Methods: Since the rehabilitation exercises corresponds to low-speed movements, a quasi-static model can be assumed, and then muscle force coefficients are position dependent. This enables their calculation in an offline stage. In addition, the concept of a single functional degree of freedom is used to minimize drastically the workspace of the stored coefficients. Finally, we have developed a force calculation process based on Lagrange multipliers that provides a closed-form solution; in this way, the problem of dynamic indeterminacy is solved without the need to use an iterative process. Results: The model has been validated by comparing muscle forces estimated by the model with the corresponding electromyography (EMG) values using squat exercise, in which the Spearman’s correlation coefficient is higher than 0.93. Its computational time is lower than 2.5 ms in a conventional computer using MATLAB. Conclusions: This procedure presents a good agreement with the experimental values of the forces, and it can be integrated into real time control systems.
DOI: 10.3390/app12052654
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