Estimation of the equivalent external force using a musculoskeletal model with muscle coactivation

• Published in: Medical & biological engineering & computing
• Main Authors: Zamora-Ortiz, Pau, Escarabajal, Rafael J., Pulloquinga, José L., Valera, Ángel, Valles, Marina
• Format: Journal Article
• Language: English
• Published: United States 24.05.2025
• Subjects: Lower limb; MusculoSkeletal model; Rehabilitation; Karush-Kuhn-Tucker; Multidimensional optimisation
• ISSN: 0140-0118; 1741-0444; 1741-0444
• DOI: 10.1007/s11517-025-03376-0

The present work introduces a novel method to determine the force vector that a subject must exert at the end of a limb in order to achieve the desired muscle force, taking into account muscle coactivation. The obtained force vector is referred to as the equivalent external force, as it represents the exerted force at the end-effector needed to provoke a desired muscle force. By using a musculoskeletal model of the lower limb and applying the Karush-Kuhn-Tucker conditions, a precise solution has been achieved to calculate the equivalent external force at the foot for the desired muscle force. The method has been tested with a four-degree-of-freedom robot, generating optimal activation trajectories for the vasti and confirming that the desired force level is achieved. The results validate the effectiveness of the proposed method and highlight its potential applications in both medical rehabilitation and sports training. This significant advancement in the field of biomechanics would provide a valuable tool for health and sports professionals, improving training and rehabilitation strategies.