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

0508137 - ÚTIA 2020 RIV SG eng J - Journal Article
Čelikovský, Sergej - Lynnyk, Volodymyr
Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior.
International Journal of Bifurcation and Chaos. Roč. 29, č. 9 (2019), č. článku 1930024. ISSN 0218-1274. E-ISSN 1793-6551
R&D Projects: GA ČR(CZ) GA17-04682S
Institutional support: RVO:67985556
Keywords : Hybrid system * Walking robot * Lateral dynamics * Chaos
OECD category: Robotics and automatic control
Impact factor: 2.469, year: 2019
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2019/TR/celikovsky-0508137.pdf https://www.worldscientific.com/doi/10.1142/S0218127419300246

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.
Permanent Link: http://hdl.handle.net/11104/0299379