A novel indirect muscle force sensing approach tailored for biomechanical multibody systems with equality and inequality constraints

Muscle forces play a crucial role in daily activities, enhancing physical efficiency, musculoskeletal health, and performance in sports, work, and rehabilitation. The direct measure of muscle forces is impractical due to anatomical and ethical constraints, leading researchers to rely on indirect methods like electromyography-based techniques. While these methods capture muscle activities, they are prone to noise and require extensive post-processing. Alternatively, biomechanical multibody models faithfully represent human movement, enabling detailed kinematic and dynamic analyses. However, they suffer the redundancy in muscle recruitment, making inverse dynamics problems underdetermined. Optimization-based approaches are often used to solve this problem, but they lean on multi-layer solutions that overlook possible model drift and measurement noise. Recent approaches employ Kalman filters to indirectly estimate the system dynamics. While effective for joint force reconstruction, their application to muscle force estimation is limited by redundancy issues. This study proposes a novel Kalman filter-based framework for constrained multibody models, leveraging non-invasive sensors to estimate system dynamics and muscle forces. The framework is benchmarked using OpenSim simulations of an upper-limb muscular-skeletal model, focusing on shoulder and elbow movements. • Knowledge about muscle forces is crucial in daily activities. • The inverse muscle recruitment reconstruction is an under-determinate problem. • The optimal muscle recruitment problem is formulated in a state–space form. • The proposed Kalman filter-based muscle force estimation exploits motion sensors. • The indirect sensing solution is applied to an upper limb biomechanical system.