Periodic motion planning for virtually constrained Euler--Lagrange systems

DOI10.1016/j.sysconle.2006.06.007zbMath1117.93052OpenAlexW2045992114MaRDI QIDQ875140

N. E. Zubov

Publication date: 11 April 2007

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2006.06.007

zbMATH Keywords

periodic solutionsvirtual holonomic constraintsLyapunov Lemmamotion planning under-actuated Euler-Lagrange systems

Mathematics Subject Classification ID

Feedback control (93B52) Nonlinear systems in control theory (93C10) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Control/observation systems governed by ordinary differential equations (93C15)

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Cites Work

• Unnamed Item
• Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem
• Asymptotically stable walking for biped robots: analysis via systems with impulse effects
• Hybrid zero dynamics of planar biped walkers
• Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach
• Nonlinear control of the reaction wheel pendulum
• Partial stabilization of underactuated Euler-Lagrange systems via a class of feedback transformations

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