Periodic motion planning for virtually constrained Euler-Lagrange systems
(2006) In Systems & Control Letters 55(11). p.900-907- Abstract
- 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... (More)
- 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. (C) 2006 Elsevier B.V. All rights reserved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/388317
- author
- Shiriaev, A ; Robertsson, Anders LU ; Perram, J and Sandberg, A
- organization
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- holonomic constraints, motion planning under-actuated Euler-Lagrange systems, virtual, Lyapunov lemma, periodic solutions
- in
- Systems & Control Letters
- volume
- 55
- issue
- 11
- pages
- 900 - 907
- publisher
- Elsevier
- external identifiers
-
- wos:000241096800005
- scopus:33748432231
- ISSN
- 0167-6911
- DOI
- 10.1016/j.sysconle.2006.06.007
- language
- English
- LU publication?
- yes
- id
- 0de211af-3588-435d-9a52-63c85bd54f7d (old id 388317)
- date added to LUP
- 2016-04-01 12:26:22
- date last changed
- 2022-03-05 23:33:01
@article{0de211af-3588-435d-9a52-63c85bd54f7d,
abstract = {{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. (C) 2006 Elsevier B.V. All rights reserved.}},
author = {{Shiriaev, A and Robertsson, Anders and Perram, J and Sandberg, A}},
issn = {{0167-6911}},
keywords = {{holonomic constraints; motion planning under-actuated Euler-Lagrange systems; virtual; Lyapunov lemma; periodic solutions}},
language = {{eng}},
number = {{11}},
pages = {{900--907}},
publisher = {{Elsevier}},
series = {{Systems & Control Letters}},
title = {{Periodic motion planning for virtually constrained Euler-Lagrange systems}},
url = {{http://dx.doi.org/10.1016/j.sysconle.2006.06.007}},
doi = {{10.1016/j.sysconle.2006.06.007}},
volume = {{55}},
year = {{2006}},
}