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Periodic motion planning for virtually constrained Euler-Lagrange systems

Shiriaev, A ; Robertsson, Anders LU ; Perram, J and Sandberg, A (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)
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author
; ; and
organization
publishing date
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
2020-12-15 03:34:08
@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},
  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},
}