Existence and stability of limit cycles in the model of a planar passive biped walking down a slope

DOI10.1098/rspa.2019.0450zbMath1472.34062arXiv1904.00517OpenAlexW2999965710WikidataQ89819526 ScholiaQ89819526MaRDI QIDQ5160845

O. Yu. Makarenkov

Publication date: 29 October 2021

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.00517

zbMATH Keywords

limit cycleswitched systemapplied mathematicspassive planar bipedperturbation theory for maps

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Discontinuous ordinary differential equations (34A36) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Stability problems in rigid body dynamics (70E50)

Related Items (6)

Erratum to: ``Design of an explicit expression of the Poincaré map for the passive dynamic walking of the compass-gait biped model ⋮ Self-excited periodic motion in underactuated mechanical systems using two-fuzzy inference system ⋮ Walking dynamics of a semi-passive compass-like robot with impulse thrust ⋮ Stabilization of the passive walking dynamics of the compass-gait biped robot by developing the analytical expression of the controlled Poincaré map ⋮ A new Poincaré map for investigating the complex walking behavior of the compass-gait biped robot ⋮ Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

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