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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20204 - Robotics and automatic control

Projekt

<a href="/cs/project/GA17-04682S" target="_blank" >GA17-04682S: Řízení kráčejících robotů metodou sladěných virtuálních holonomních omezení</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

International Journal of Bifurcation and Chaos

ISSN

0218-1274

e-ISSN

—

Svazek periodika

29

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

29

Strana od-do

1930024

Kód UT WoS článku

000483030700001

EID výsledku v databázi Scopus

2-s2.0-85071604891