Analytical solutions to feedback systems on the special orthogonal group SO(n)
(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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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/677eb965-689a-47c5-b054-c5a669b6baee
- author
- Markdahl, Johan ; Thunberg, Johan LU ; Hoppe, Jens and Xiaoming hu
- publishing date
- 2013-12
- 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}}, }