Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: rise of the Neimark-Sacker bifurcation

DOI10.1016/j.chaos.2018.03.026zbMath1391.70062OpenAlexW2794479101WikidataQ130111816 ScholiaQ130111816MaRDI QIDQ721743

Safya Belghith, Hassène Gritli

Publication date: 20 July 2018

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2018.03.026

zbMATH Keywords

Neimark-Sacker bifurcationcompass-gait biped modelcontrolled hybrid Poincaré mapOGY-based state-feedback controltwo-parameter bifurcation diagram

Mathematics Subject Classification ID

Feedback control (93B52) Control of mechanical systems (70Q05) Dynamical systems in control (37N35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30)

Related Items (8)

Design of an explicit expression of the Poincaré map for the passive dynamic walking of the compass-gait biped model ⋮ 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 ⋮ Chaotic behaviour and bifurcation in real dynamics of two-parameter family of functions including logarithmic map ⋮ A new method for finding the proper initial conditions in passive locomotion of bipedal robotic systems ⋮ Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator ⋮ Neimark-Sacker bifurcation and controlling chaos in a three-species food chain model through the OGY method ⋮ A further analysis of the passive compass-gait bipedal robot and its period-doubling route to chaos

Cites Work

• A passive-biped model with multiple routes to chaos
• Chaos control in passive walking dynamics of a compass-gait model
• OGY-based control of chaos in semi-passive dynamic walking of a torso-driven biped robot
• Common formation mechanism of basin of attraction for bipedal walking models by saddle hyperbolicity and hybrid dynamics
• Simple chaotic flows with a line equilibrium
• Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map
• Walking dynamics of the passive compass-gait model under OGY-based control: emergence of bifurcations and chaos
• Displayed phenomena in the semi-passive torso-driven biped model under OGY-based control method: birth of a torus bifurcation
• A gallery of chaotic systems with an infinite number of equilibrium points
• Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: analysis of local bifurcations via the hybrid Poincaré map
• Intelligent analysis of chaos roughness in regularity of walk for a two legged robot
• New bifurcations in the simplest passive walking model
• Gait Generation and Stabilization for Nearly Passive Dynamic Walking Using Auto-distributed Impulses
• Identification, Stability and Stabilization of Limit Cycles in a Compass-Gait Biped Model via a Hybrid Poincaré Map
• Orthonormal Expansion $\ell_{1}$-Minimization Algorithms for Compressed Sensing
• Bifurcation and chaos in the simple passive dynamic walking model with upper body
• Transverse Linearization for Impulsive Mechanical Systems With One Passive Link
• Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

This page was built for publication: Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: rise of the Neimark-Sacker bifurcation