کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
752365 | 895418 | 2006 | 8 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Periodic motion planning for virtually constrained Euler–Lagrange systems Periodic motion planning for virtually constrained Euler–Lagrange systems](/preview/png/752365.png)
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)(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.
Journal: Systems & Control Letters - Volume 55, Issue 11, November 2006, Pages 900–907