Analysis of human ambulation as a chaotic time-series: with nonlinear dynamics tools

Document Type

Article

Publication Date

1-25-2026

Abstract

The aim of the present study is to investigate the complexity and stability of human ambulation and the implications on robotic prostheses control systems. Fourteen healthy individuals participate in two experiments, the first group run at three different speeds. The second group ascended and descended stairs of a five-level building block at a self-selected speed. All participants completed the experiment with seven inertial measurement units wrapped around the lower body segments and waist. The data were analyzed to determine the fractal dimension, spectral entropy, and the Lyapunov exponent (LyE). Two methods were used to calculate the long-term LyE, first LyE calculated using the full size of data sets. And the embedding dimensions were calculated using Average Mutual Information (AMI) and the False Nearest Neighbor (FNN) algorithm was used to find the time delay. Besides, a second approach was developed to find long-term LyE where the time delay was based on the average period of the gait cycle using adaptive event-based window. The average values of spectral entropy are 0.538 and 0.575 for stairs ambulation and running, respectively. The degree of uncertainty and complexity increases with the ambulation speed. The short term LyEs for tibia orientation have the minimum range of variation when it comes to stairs ascent and descent. Using two-way analysis of variance we demonstrated the effect of the ambulation speed and type of ambulation on spectral entropy. Moreover, it was shown that the fractal dimension only changed significantly with ambulation speed.

Keywords

Human ambulation, Lyapunov exponent, Fractal dimension, Entropy, Inertial measurement units

Publication Title

Computer Methods in Biomechanics and Biomedical Engineering

ISSN

1025-5842

DOI

10.1080/10255842.2024.2399023

Volume

29

Issue

2

First Page

462

Last Page

474

Publisher

Taylor & Francis

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