Enhanced Euler-Lagrange Formulation for Analyzing Human Gait with Moving Base Reference

Euler-Lagrange's formulation is known for its systematic and simplified approach in deriving dynamics of complex systems. In order to apply the existing formulation to human gait dynamics, the base reference frame must be assumed as an inertial reference frame. Conventionally, the ankle joint or the hip joint are regarded as base reference frames during the stance and swing phase of human walking. As these joints are non-inertial in nature during actual locomotion, this assumption could result in inaccurate calculation of lower-limb joint torques and forces. Therefore, in this paper, an existing Euler-Lagrange based formulation originally developed for fixed-base robotic manipulators is considered and modified to accommodate the movement of the base reference frame with respect to an inertial frame of reference defined outside the human body. The applicability of the modified formulation is studied, implemented, and validated using three standard and publicly available gait datasets covering the phases of walking and running. The joint torques obtained using the proposed dynamic model are compared with reference torques by calculating the mean absolute error values and visually through Bland-Altman plots. The obtained joint torque values and plots indicate a close agreement with published torques, thereby validating the accuracy of the proposed dynamic model. The robust formulation implementation makes it a valuable resource for researchers in this field, offering a reliable framework for gait analysis and the design of lower-limb prosthetics or exoskeletons.