Invariant manifolds in human joint angle analysis during walking gait

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

The complex dynamics of human gait is yet to be completely understood. Researchers have quantified stability of walking gait using Floquet multipliers as well as Lyapunov exponents. In this article, we utilize the techniques and tools from dynamical system theory and invariant manifolds to map the gait data onto a time invariant representation of a dynamical system. As an example, the complex behavior of the joint angle during walking was studied using a conformal mapping approach that transformed the time periodic system into a time invariant linear system. Time-delay embedding was used to reconstruct the dynamics of the original gait system with time series kinematic data. This minimal realization of the system was used to construct a Single Degree of Freedom (SDOF) oscillator. The time evolution of the linear oscillatory system was mapped back using the conformal mapping derived using Lyapunov-Floquet Theory. This algorithm was verified for walking gait kinematics data for two healthy human subjects. A comparison was drawn between the phase space behavior of the original time periodic system and the remapped time invariant system. The two systems showed good correlation. The algorithm resulted in a well correlated phase space representation.

Original languageEnglish (US)
Title of host publication16th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791883914
DOIs
StatePublished - 2020
EventASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020 - Virtual, Online
Duration: Aug 17 2020Aug 19 2020

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume2

Conference

ConferenceASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2020
CityVirtual, Online
Period8/17/208/19/20

Keywords

  • Biomechanics
  • Computational dynamics of bio-mechanical and biological systems
  • Dynamics

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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