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Distributed synchronization of Euclidean transformations with guaranteed convergence

Thunberg, Johan LU ; Bernard, Florian and Gonçalves, Jorge (2017) 56th IEEE Annual Conference on Decision and Control, CDC 2017 p.3757-3762
Abstract

This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph are equal to the identity. Given a set of non-synchronized transformations, the problem at hand is to find a set of synchronized transformations approximating well the non-synchronized transformations. This is formulated as a nonlinear least-squares optimization problem. We present a distributed synchronization algorithm that converges to the optimal solution to an approximation of the optimization problem. This approximation stems from a spectral relaxation of the rotational part on the one hand and from a separation between the... (More)

This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph are equal to the identity. Given a set of non-synchronized transformations, the problem at hand is to find a set of synchronized transformations approximating well the non-synchronized transformations. This is formulated as a nonlinear least-squares optimization problem. We present a distributed synchronization algorithm that converges to the optimal solution to an approximation of the optimization problem. This approximation stems from a spectral relaxation of the rotational part on the one hand and from a separation between the rotations and the translations on the other. The method can be used to distributively improve the measurements obtained in sensor networks such as networks of cameras where pairwise relative transformations are measured. The convergence of the method is verified in numerical simulations.

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Please use this url to cite or link to this publication:
author
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
pages
6 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
56th IEEE Annual Conference on Decision and Control, CDC 2017
conference location
Melbourne, Australia
conference dates
2017-12-12 - 2017-12-15
external identifiers
  • scopus:85046246639
ISBN
9781509028733
DOI
10.1109/CDC.2017.8264211
language
English
LU publication?
no
additional info
Publisher Copyright: © 2017 IEEE.
id
a220d6cc-6b42-4eeb-b5d0-5c6e2d83d569
date added to LUP
2024-09-05 12:31:48
date last changed
2025-04-04 15:24:05
@inproceedings{a220d6cc-6b42-4eeb-b5d0-5c6e2d83d569,
  abstract     = {{<p>This paper addresses synchronization of Euclidean transformations over graphs. Synchronization in this context, unlike rendezvous or consensus, means that composite transformations over loops in the graph are equal to the identity. Given a set of non-synchronized transformations, the problem at hand is to find a set of synchronized transformations approximating well the non-synchronized transformations. This is formulated as a nonlinear least-squares optimization problem. We present a distributed synchronization algorithm that converges to the optimal solution to an approximation of the optimization problem. This approximation stems from a spectral relaxation of the rotational part on the one hand and from a separation between the rotations and the translations on the other. The method can be used to distributively improve the measurements obtained in sensor networks such as networks of cameras where pairwise relative transformations are measured. The convergence of the method is verified in numerical simulations.</p>}},
  author       = {{Thunberg, Johan and Bernard, Florian and Gonçalves, Jorge}},
  booktitle    = {{2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017}},
  isbn         = {{9781509028733}},
  language     = {{eng}},
  month        = {{06}},
  pages        = {{3757--3762}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Distributed synchronization of Euclidean transformations with guaranteed convergence}},
  url          = {{http://dx.doi.org/10.1109/CDC.2017.8264211}},
  doi          = {{10.1109/CDC.2017.8264211}},
  year         = {{2017}},
}