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.

The impact of anatomical uncertainties on the predictions of a musculoskeletal hand model – a sensitivity study

“…The kinematic inaccuracies that inevitably occur during the measurement can also impact model predictions (Myers et al 2015). In combination with the inverse dynamic, these kinematic inaccuracies can cause unrealistic joint torques approach according to Bailly et al (2021). In addition, due to the time-independent nature of the static optimization, an inverse dynamic calculation prevents the activation dynamics from being taken into account.…”

Bioptim, a Python framework for Musculoskeletal Optimal Control in Biomechanics

“…where T i with i ∈ [1,2,3,4,5] are the final times of the i th phase respectively, and T 0 = 0; ω h = −100 is the weight of the jump height term defined negative to maximize it; ω t = 0.1, ω sd = 0.1 and ω x = 1.0 are the weights of their respective objective functions;q is the generalized velocities part of the state vector x; andx is the state vector excluding the translations of the root segment. Thex * corresponds to a reference static position of the avatar with its knee slightly flexed and its arms horizontal.…”

“…III-E). For a more in-depth analysis of the real-time estimation capabilities of Bioptim, see [2]. Alongside with the 3D visualizer Bioviz that animates the solution, Bioptim proposes a series of online-generated figures, inspired by the real-time graphics from Muscod-II [24], [25], to visualize the optimized variables at each iteration of the solver.…”

“…Biomechanics researchers rely on numerical simulations of motion to gain understanding on a variety of scientific topics such as the physiological causes of movement disorders and their consequences on health [1], the estimation of non-measurable physiological quantities (e.g., muscle forces [2]) and the optimality of human movement [3]. The musculoskeletal models used in these simulations generally have a large number of degrees of freedom and they are governed by several ordinary differential equations (ODEs) which mainly describe multibody and muscle activation dynamics.…”

Optimal Estimation of the Centroidal Dynamics of Legged Robots

“…To do so, a moving horizon estimation scheme should be implemented in optimized C/C++ in order to make the convergence time fit inside the control loop. In this case, the speed/accuracy trade-off should be thoroughly investigated in order to maintain an accurate estimation while going real-time [19]. Next, the presented approach should be compared to Kalman smoothing algorithms both in terms of accuracy and performances, as they present similarities (back-propagation of measurement information), and the theoretical link between them should be investigated.…”