0508137 20240103222512.220190909235959.9 85071604891 000483030700001 10.1142/S0218127419300246 29 s. P cav_un_epca*02567760218-127429World Scientific Publishing Hybrid system Walking robot Lateral dynamics Chaos cav_un_auth*0101074 Čelikovský Sergej UTIA-B Teorie řízení Department of Control Theory TŘ TR Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0215855 Lynnyk Volodymyr UTIA-B Teorie řízení Department of Control Theory TŘ TR Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2019/TR/celikovsky-0508137.pdf https://www.worldscientific.com/doi/10.1142/S0218127419300246 cav_un_auth*0347203 GA17-04682S GA ČR CZ 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. WOS BC 20000 20200 20204 2020 2 4 A hod sml 4ah 4as 20231122144230.0 RVO:67985556 http://hdl.handle.net/11104/0299379 1 1 Department of Control Theory UTIA-B 10100 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS S Copyright Transfer Form 20181204 Copyright Transfer Form 1930024 3+4 Article Computer Science Artificial Intelligence A MATHEMATICS.INTERDISCIPLINARYAPPLICATIONS|MULTIDISCIPLINARYSCIENCES 2.084 0.402 8.3 0.00712 0.442 7115 120 0.715 36.65 2.63 2000 Q1 2.080 249 Q2 26.689 66.7 Q3 Q4 0.68 Q1 75 2019 Soubory v repozitáři: celikovsky-0508137.pdf, celikovsky-0508137-copyright.pdf 85071604891 SCOPUS PUBMED 000483030700001 WOS cav_un_epca*0256776 International Journal of Bifurcation and Chaos 0218-1274 1793-6551 Roč. 29 č. 9 2019 World Scientific Publishing