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Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior
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SYSNO ASEP 0508137 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior Author(s) Čelikovský, Sergej (UTIA-B) RID, ORCID
Lynnyk, Volodymyr (UTIA-B) RID, ORCIDNumber of authors 2 Article number 1930024 Source Title International Journal of Bifurcation and Chaos. - : World Scientific Publishing - ISSN 0218-1274
Roč. 29, č. 9 (2019)Number of pages 29 s. Publication form Print - P Language eng - English Country SG - Singapore Keywords Hybrid system ; Walking robot ; Lateral dynamics ; Chaos Subject RIV BC - Control Systems Theory OECD category Robotics and automatic control R&D Projects GA17-04682S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UTIA-B - RVO:67985556 UT WOS 000483030700001 EID SCOPUS 85071604891 DOI 10.1142/S0218127419300246 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2020 Electronic address https://www.worldscientific.com/doi/10.1142/S0218127419300246
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