Periodic motion planning for virtually constrained Euler-Lagrange systems
2006 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 55, no 11, 900-907 p.Article in journal (Refereed) PublishedText
The paper suggests an explicit form of a general integral of motion for some classes of dynamical systems including n-degrees of freedom Euler-Lagrange systems subject to (n - 1) virtual holonomic constraints. The knowledge of this integral allows to extend the classical results due to Lyapunov for detecting a presence of periodic solutions for a family of second order systems, and allows to solve the periodic motion planning task for underactuated Euler-Lagrange systems, when there is only one not directly actuated generalized coordinate. As an illustrative example, we have shown how to create a periodic oscillation of the pendulum for a cart-pendulum system and how then to make them orbitally exponentially stable following the machinery developed in [A. Shiriaev, J. Perram, C. Canudas-de-Wit, Constructive tool for an orbital stabilization of underactuated nonlinear systems: virtual constraint approach, IEEE Trans. Automat. Control 50 (8) (2005) 1164-1176]. The extension here also considers time-varying virtual constraints.
Place, publisher, year, edition, pages
Amsterdam: Elsevier, 2006. Vol. 55, no 11, 900-907 p.
motion planning under-actuated Euler-Lagrange systems, virtual holonomic constraints, Lyapunov lemma, periodic solutions
Robotics Control Engineering
IdentifiersURN: urn:nbn:se:umu:diva-119377DOI: 10.1016/j.sysconle.2006.06.007ISI: 000241096800005OAI: oai:DiVA.org:umu-119377DiVA: diva2:928662