Validation of the Estimated Torques of an Open-chain Kinematic Model of the Human Body

Abstract

The standing human body is frequently modeled as an inverted double pendulum restricted to a single plane. In order to capture the coordination efforts and interplay between spatial dimensions, the model has to capture motion and joint torques in all spatial dimensions. Our two-segment model covers two degrees of freedom (ML and AP revolutions) at the ankle and the hip level and utilizes the Denavit-Hartenberg convention. This work aimed to validate the model's torque estimation on a diverse group of participants (11 women, 22–56 years, 11 men, 22–61 years). The inverse dynamic calculations provide estimated joint torques for a motion capture recorded trial, while standing on a force platform enables the indirect measurement of ankle torques. A 60-second-long visually guided balancing task was recorded and repeated three times. The estimated and the indirectly measured torques were compared, and offset and variance type errors ( normalized RMSE and R2 ) were analyzed. The R2-values were excellent (R2 > 0.90) 64 out of the 66 cases (97%) for AP torques and 58 out of the 66 cases (88%) for ML torques. Normalized RMSE values were dominantly under the 0.35 value with some outliers. RMSE showed no evident connection with age, body height, body mass, or BMI. An open-chain kinematic model with two segments, following the Denavit-Hartenberg convention, is well suited to estimate the control torque traces of the human body during standing balancing and needs only three tracked positions.