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Title: Bifurcation and chaos in the simple passive dynamic walking model with upper body

Abstract

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.

Authors:
;  [1];  [2]
  1. Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China)
  2. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
Publication Date:
OSTI Identifier:
22351015
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; FLEXIBILITY; LENGTH; MAPS; MASS; TOPOLOGY; VERIFICATION

Citation Formats

Li, Qingdu, Guo, Jianli, and Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn. Bifurcation and chaos in the simple passive dynamic walking model with upper body. United States: N. p., 2014. Web. doi:10.1063/1.4890834.
Li, Qingdu, Guo, Jianli, & Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn. Bifurcation and chaos in the simple passive dynamic walking model with upper body. United States. doi:10.1063/1.4890834.
Li, Qingdu, Guo, Jianli, and Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn. Mon . "Bifurcation and chaos in the simple passive dynamic walking model with upper body". United States. doi:10.1063/1.4890834.
@article{osti_22351015,
title = {Bifurcation and chaos in the simple passive dynamic walking model with upper body},
author = {Li, Qingdu and Guo, Jianli and Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn},
abstractNote = {We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.},
doi = {10.1063/1.4890834},
journal = {Chaos (Woodbury, N. Y.)},
number = 3,
volume = 24,
place = {United States},
year = {Mon Sep 01 00:00:00 EDT 2014},
month = {Mon Sep 01 00:00:00 EDT 2014}
}
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