Dynamic controllers for column synchronization of rotation matrices : A QR-factorization approach
(2018) In Automatica 93. p.20-25- Abstract
In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d−1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of... (More)
In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d−1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the k columns from the remaining d−k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies.
(Less)
- author
- Thunberg, Johan LU ; Markdahl, Johan and Gonçalves, Jorge
- publishing date
- 2018-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Attitude synchronization, Consensus algorithms, Multi-agent systems, Network topologies, Sensor networks
- in
- Automatica
- volume
- 93
- pages
- 6 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85044449704
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2018.03.023
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2018 Elsevier Ltd
- id
- 119db7d6-b479-4685-aef2-7df7a524356b
- date added to LUP
- 2024-09-05 12:29:53
- date last changed
- 2025-04-04 15:26:02
@article{119db7d6-b479-4685-aef2-7df7a524356b,
abstract = {{<p>In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control design. When one specific column is considered, the problem is equivalent to synchronization on the (d−1)-dimensional unit sphere and when all the columns are considered, the problem is equivalent to synchronization on SO(d). We design dynamic control laws for these synchronization problems. The control laws are based on the introduction of auxiliary variables in combination with a QR-factorization approach. The benefit of this QR-factorization approach is that we can decouple the dynamics for the k columns from the remaining d−k ones. Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies.</p>}},
author = {{Thunberg, Johan and Markdahl, Johan and Gonçalves, Jorge}},
issn = {{0005-1098}},
keywords = {{Attitude synchronization; Consensus algorithms; Multi-agent systems; Network topologies; Sensor networks}},
language = {{eng}},
pages = {{20--25}},
publisher = {{Elsevier}},
series = {{Automatica}},
title = {{Dynamic controllers for column synchronization of rotation matrices : A QR-factorization approach}},
url = {{http://dx.doi.org/10.1016/j.automatica.2018.03.023}},
doi = {{10.1016/j.automatica.2018.03.023}},
volume = {{93}},
year = {{2018}},
}