Reconstruction Of Ground Reaction Force Data Using Lyapunov Floquet Theory And Invariant Manifold Theory
Published in International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2020
Sandesh G. Bhat, Thomas G. Sugar, Sangram Redkar.
Abstract
Ground Reaction Force (GRF) is an essential gait parameter. GRF analysis provides important information regarding various aspects of gait. GRF has been traditionally measured using bulky force plates within lab environments. There exist portable force sensing units, but their accuracy is wanting. Estimation of GRF has applications in remote wearable systems for rehabilitation, to measure performance in athletes, etc. This article explores a novel method for GRF estimation using the Lyapunov-Floquet (LF) and invariant manifold theory. We assume human gait to be a periodic motion without external forcing. Using time delayed embedding, a reduced order system can be reconstructed from the vertical GRF data. LF theory can be applied to perform system identification via Floquet Transition Matrix and the Lyapunov Exponents. A Conformal Map was generated using the Lyapunov Floquet Transformation that maps the original time periodic system on a linear Single Degree of Freedom (SDoF) oscillator. The response of the oscillator system can be calculated numerically and then remapped back to the original domain to get GRF time evolution. As an example, the GRF data from an optical motion capture system for two subjects was used to construct the reduced order model and system identification. A comparison between the original system and its reduced order approximation showed good correspondenc.