Estimation of Tri-Axial Walking Ground Reaction Forces of Left and Right Foot from Total Forces in Real-Life Environments

Abstract

Continuous monitoring of natural human gait in real-life environments is essential in many applications including disease monitoring, rehabilitation, and professional sports. Wearable inertial measurement units are successfully used to measure body kinematics in real-life environments and to estimate total walking ground reaction forces using equations of motion. However, for inverse dynamics and clinical gait analysis, the of each foot is required separately. Using an experimental dataset of 1243 tri-axial separate-foot time histories measured by the authors across eight years, this study proposes the ‘Twin Polynomial Method’ (TPM) to estimate the tri-axial left and right foot signals from the total signals. For each gait cycle, TPM fits polynomials of degree five, eight, and nine to the known single-support part of the left and right foot vertical, anterior-posterior, and medial-lateral signals, respectively, to extrapolate the unknown double-support parts of the corresponding signals. Validation of the proposed method both with force plate measurements (gold standard) in the laboratory, and in real-life environment showed a peak-to-peak normalized root mean square error of less than 2.5%, 6.5% and 7.5% for the estimated signals in the vertical, anterior-posterior and medial-lateral directions, respectively. These values show considerable improvement compared with the currently available decomposition methods in the literature.