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Analytical solutions to feedback systems on the special orthogonal group SO(n)

Markdahl, Johan ; Thunberg, Johan LU ; Hoppe, Jens and Xiaoming hu (2013) 52nd IEEE Conference on Decision and Control, CDC 2013 p.5246-5251
Abstract
This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of... (More)
This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples.
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author
; ; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
52nd IEEE Conference on Decision and Control
pages
5246 - 5251
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
52nd IEEE Conference on Decision and Control, CDC 2013
conference location
Florence, Italy
conference dates
2013-12-10 - 2013-12-13
external identifiers
  • scopus:84902337762
ISBN
978-1-4673-5717-3
978-1-4673-5714-2
DOI
10.1109/CDC.2013.6760714
language
English
LU publication?
no
id
677eb965-689a-47c5-b054-c5a669b6baee
date added to LUP
2024-09-05 14:39:54
date last changed
2024-10-07 16:10:02
@inproceedings{677eb965-689a-47c5-b054-c5a669b6baee,
  abstract     = {{This paper provides analytical solutions to the closed-loop kinematics of two almost globally exponentially stabilizing attitude control laws on the special orthogonal group SO(n). By studying the general case we give a uniform treatment to the cases of SO(2) and SO(3), which are the most interesting dimensions for application purposes. Working directly with rotation matrices in the case of SO(3) allows us to avoid certain complications which may arise when using local and global many-to-one parameterizations. The analytical solutions provide insight into the transient behaviour of the system and are of theoretical value since they can be used to prove almost global attractiveness of the identity matrix. The practical usefulness of analytical solutions in problems of continuous time actuation subject to piece-wise unavailable or discrete time sensing are illustrated by numerical examples.<br/>}},
  author       = {{Markdahl, Johan and Thunberg, Johan and Hoppe, Jens and Xiaoming hu}},
  booktitle    = {{52nd IEEE Conference on Decision and Control}},
  isbn         = {{978-1-4673-5717-3}},
  language     = {{eng}},
  pages        = {{5246--5251}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Analytical solutions to feedback systems on the special orthogonal group SO(n)}},
  url          = {{http://dx.doi.org/10.1109/CDC.2013.6760714}},
  doi          = {{10.1109/CDC.2013.6760714}},
  year         = {{2013}},
}