Real-Time and Dynamically Consistent Estimation of Muscle Forces Using a Moving Horizon EMG-Marker Tracking Algorithm—Application to Upper Limb Biomechanics

Abstract

Real-time biofeedback of muscle forces should help clinicians adapt their movement recommendations. Because these forces cannot directly be measured, researchers have developed numerical models and methods informed by electromyography (EMG) and body kinematics to estimate them. Among these methods, static optimization is the most computationally efficient and widely used. However, it suffers from limitation, namely: unrealistic joint torques computation, non-physiological muscle forces estimates and inconsistent for motions inducing co-contraction. Forward approaches, relying on numerical optimal control, address some of these issues, providing dynamically consistent estimates of muscle forces. However, they result in a high computational cost increase, apparently disqualifying them for real-time applications. However, this computational cost can be reduced by combining the implementation of a moving horizon estimation (MHE) and advanced optimization tools. Our objective was to assess the feasibility and accuracy of muscle forces estimation in real-time, using a MHE. To this end, a 4-DoFs arm actuated by 19 Hill-type muscle lines of action was modeled for simulating a set of reference motions, with corresponding EMG signals and markers positions. Excitation- and activation-driven models were tested to assess the effects of model complexity. Four levels of co-contraction, EMG noise and marker noise were simulated, to run the estimator under 64 different conditions, 30 times each. The MHE problem was implemented with three cost functions: EMG-markers tracking (high and low weight on markers) and marker-tracking with least-squared muscle excitations. For the excitation-driven model, a 7-frame MHE was selected as it allowed the estimator to run at 24 Hz (faster than biofeedback standard) while ensuring the lowest RMSE on estimates in noiseless conditions. This corresponds to a 3,500-fold speed improvement in comparison to state-of-the-art equivalent approaches. When adding experimental-like noise to the reference data, estimation error on muscle forces ranged from 1 to 30 N when tracking EMG signals and from 8 to 50 N (highly impacted by the co-contraction level) when muscle excitations were minimized. Statistical analysis was conducted to report significant effects of the problem conditions on the estimates. To conclude, the presented MHE implementation proved to be promising for real-time muscle forces estimation in experimental-like noise conditions, such as in biofeedback applications.