Enhanced Euler–Lagrange Formulation for Analyzing Human Gait With Moving Base Reference

Journal of Mechanisms and Robotics, vol. 17

Abstract

Abstract Euler–Lagrange's formulation is known for its systematic and simplified approach to 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 joints or the hip joints are regarded as base reference frames during the stance and swing phases 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.

Authors 4

1. Sekar Anup Chander

   Central Scientific Instruments Organisation · Council of Scientific and Industrial Research · Academy of Scientific and Innovative Research

   Affiliation as printed

   Academy of Scientific and Innovative Research (AcSIR) , Ghaziabad, Uttar Pradesh 201002 ,

   Manufacturing Science and Instrumentation Division , CSIR-Central Scientific Instruments Organisation, Sector-30C, Chandigarh 160030 , ;

   Academy of Scientific and Innovative Research (AcSIR) , Ghaziabad, Uttar Pradesh 201002 , India

   Manufacturing Science and Instrumentation Division , CSIR-Central Scientific Instruments Organisation, Sector-30C, Chandigarh 160030 , India ;

2. Ashutosh Mukherjee Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Aachen, North Rhine-Westphalia 52056 ,

   RWTH Aachen University , Aachen, North Rhine-Westphalia 52056 , Germany

3. Vhatkar Dattatraya Shivling

   Central Scientific Instruments Organisation · Council of Scientific and Industrial Research · Academy of Scientific and Innovative Research

   Affiliation as printed

   Academy of Scientific and Innovative Research (AcSIR) , Ghaziabad, Uttar Pradesh 201002 ,

   Intelligent Machines and Communication Systems Division , CSIR-Central Scientific Instruments Organisation, Sector-30C, Chandigarh 160030 , ;

   Academy of Scientific and Innovative Research (AcSIR) , Ghaziabad, Uttar Pradesh 201002 , India

   Intelligent Machines and Communication Systems Division , CSIR-Central Scientific Instruments Organisation, Sector-30C, Chandigarh 160030 , India ;

4. Ashish Singla

   Thapar Institute of Engineering & Technology

   Affiliation as printed

   Thapar Institute of Engineering and Technology Department of Mechanical Engineering, , Patiala, Punjab 147004 ,

   Thapar Institute of Engineering and Technology Department of Mechanical Engineering, , Patiala, Punjab 147004 , India