Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F19%3A00508137" target="_blank" >RIV/67985556:_____/19:00508137 - isvavai.cz</a>

Result on the web

<a href="https://www.worldscientific.com/doi/10.1142/S0218127419300246" target="_blank" >https://www.worldscientific.com/doi/10.1142/S0218127419300246</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218127419300246" target="_blank" >10.1142/S0218127419300246</a>

Result language

angličtina

Original language name

Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

Original language description

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this article. The chaotic behavior, when being externally harmonically perturbed, is demonstrated. Two rather exceptional features are analyzed. Firstly, the unperturbed undamped hybrid inverted pendulum behaves inside a certain stability region periodically and its respective frequencies range from zero (close to the boundary of that stability region) to infinity (close to its double support equilibrium). Secondly, the constant lateral forcing less than a certain threshold does not affect the periodic behavior of the hybrid inverted pendulum and preserves its equilibrium at the origin. The latter is due to the hybrid nature of the equilibrium at the origin, which exists only in the Filippov sense. It is actually a trivial example of the so-called pseudo-equilibrium [Kuznetsov et al., 2003]. Nevertheless, such an observation holds only for constant external forcing and even arbitrary small time-varying external forcing may destabilize the origin. As a matter of fact, one can observe many, possibly even infinitely many, distinct chaotic attractors for a single system when the forcing amplitude does not exceed the mentioned threshold. Moreover, some general properties of the hybrid inverted pendulum are characterized through its topological equivalence to the classical pendulum. Extensive numerical experiments demonstrate the chaotic behavior of the harmonically perturbed hybrid inverted pendulum.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

20204 - Robotics and automatic control

Project

<a href="/en/project/GA17-04682S" target="_blank" >GA17-04682S: Control of walking robots using collocated virtual holonomic constraints</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

International Journal of Bifurcation and Chaos

ISSN

0218-1274

e-ISSN

—

Volume of the periodical

29

Issue of the periodical within the volume

9

Country of publishing house

SG - SINGAPORE

Number of pages

29

Pages from-to

1930024

UT code for WoS article

000483030700001

EID of the result in the Scopus database

2-s2.0-85071604891