System Identification around periodic orbits with application to steady state human walking

System Identification around periodic orbits with application to steady state human walking

Bibliographic Details
Main Author: Wang, Yang
Language:English
Published: The Ohio State University / OhioLINK 2013
Subjects:
Mechanical Engineering
Biomechanics
System Identification
Poincare Section
Stability
Perturbation
Human Walking
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1366331185
id ndltd-OhioLink-oai-etd.ohiolink.edu-osu1366331185
record_format oai_dc
collection NDLTD
language English
sources NDLTD
topic Mechanical Engineering
Biomechanics
System Identification
Poincare Section
Stability
Perturbation
Human Walking
spellingShingle Mechanical Engineering
Biomechanics
System Identification
Poincare Section
Stability
Perturbation
Human Walking
Wang, Yang
System Identification around periodic orbits with application to steady state human walking
author Wang, Yang
author_facet Wang, Yang
author_sort Wang, Yang
title System Identification around periodic orbits with application to steady state human walking
title_short System Identification around periodic orbits with application to steady state human walking
title_full System Identification around periodic orbits with application to steady state human walking
title_fullStr System Identification around periodic orbits with application to steady state human walking
title_full_unstemmed System Identification around periodic orbits with application to steady state human walking
title_sort system identification around periodic orbits with application to steady state human walking
publisher The Ohio State University / OhioLINK
publishDate 2013
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1366331185
work_keys_str_mv AT wangyang systemidentificationaroundperiodicorbitswithapplicationtosteadystatehumanwalking
_version_ 1719419237260328960
spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu13663311852021-08-03T05:22:27Z System Identification around periodic orbits with application to steady state human walking Wang, Yang Mechanical Engineering Biomechanics System Identification Poincare Section Stability Perturbation Human Walking To walk without falling down, human walking motions, by definition, need to be stable and humans need the ability to recover from perturbations. This thesis is about methods for analyzing human walking dynamics, as well as the application of these methods to human walking data. During steady human walking, each step is similar to every other step, but the steps are not all identical. If the deviations from periodic motion are due to random perturbations, the near-periodic steady state behavior has information about the dynamics of the underlying dynamical system near the nominal periodic orbit.In Chapter 2, we review and develop statistical techniques to construct models of the dynamics (that is, perform `system identification') near the periodic motion from noise-driven near-periodic data. Our principal construction is a sequence of Poincare sections, transverse to the periodic orbit, in the neighborhood of the periodic orbit and linearized dynamics of the state from one Poincare section to the next, resulting in a piecewise linear dynamical system around the periodic orbit.We apply these methods to synthetic data derived from the simulation of known discrete and continuous dynamical systems, both univariate and multivariate, with periodic orbits perturbed by various kinds of noise, to demonstrate effectiveness of these methods. We obtain asymptotic relations on how the accuracy of the inference procedure in simple situations depends on how many Poincare sections we use. This method of describing and inferring dynamics around periodic orbits is applied and verified by using data from a noise-driven van der Pol oscillator.In Chapter 3, the collection of human walking data is described. In the experiments, five subjects were asked to walk on a treadmill at specific speeds, both in steady state and as well as performing some time-varying movements. Marker-based motion capture data (movement of body segments) was collected for all the walking trials.In Chapter 4, we analyze the collected human walking data by investigating the ``top view dynamics"; We use a step-to-step model, which considers the foot placement and the upper body motion to represent walking, and compute this model from data using least squares method. We compute the effects of the upper body movements on the foot placements. In particular, we show how a higher-than-normal sideways speed or position of the upper body is corrected by stepping to the side more (using a bigger step width) and using a smaller step length. A higher-than-normal forward speed of the upper body is corrected by taking a slightly longer step. While these features of human walking have previously been conjectured and used in models of walking stability, we do not know of a rigorous data-based derivation of such features.We use the step-to-step model to examine the stability (return map eigenvalues) of human walking. We extend the model to predict motions of blind-folded people over long-durations -- people walking with no visual feedback provided -- showing how they may eventually deviate from a straight line.In Chapter 5, we analyze the walking data by looking at dynamics in the sagittal plane (``side-view dynamics"); Here, we use a 2D kinematic model of the body to first infer from data and then simulate the dynamics steady walking and perturbed walking. The comparison between the simulation results and experiment data is given; model-based prediction performs better at predicting transients than the null hypothesis of natural variability. With the confidence of this agreement, we predict human walking under different perturbations. We again show how humans step longer or shorter when, for example, a push forward or backward is applied on the swing or stance leg during steady walking.In future work, building on the inference of 2D dynamics of human walking here, we hope to improve the statistical methods, extend the dynamical models to 3D, and also infer controllers that map body state to muscle action. 2013-08-06 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1366331185 http://rave.ohiolink.edu/etdc/view?acc_num=osu1366331185 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

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