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A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group.pdf
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README.md Updated the README Apr 1, 2018
SE-Sync - A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group.pdf

README.md

SE-Sync

SE-Sync is a certifiably correct algorithm for performing synchronization over the special Euclidean group: estimate the values of a set of unknown poses (positions and orientations in Euclidean space) given noisy measurements of a subset of their pairwise relative transforms. This problem frequently arises in the context of 2D and 3D geometric estimation; for example, the foundational problems of pose-graph SLAM (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing) all require synchronization over the special Euclidean group. SE-Sync improves upon prior methods by exploiting a novel (convex) semidefinite relaxation of the special Euclidean synchronization problem to directly search for globally optimal solutions, and is capable of producing a computational certificate of correctness (global optimality) in the (typical) case that a global minimizer is found.

A detailed description of the algorithm and its implementation can be found in our technical report.

Getting Started

MATLAB

To use the MATLAB implementation of SE-Sync, simply place the 'MATLAB' folder in any convenient (permanent) location, and then run the script MATLAB/import_SE_Sync.m. Congrats! SE-Sync is now ready to go :-). For a minimal working example, see MATLAB/examples/main.m

C++

The C++ implementation of SE-Sync can be built and exported as a CMake project. For a minimal working example, see C++/examples/main, which provides a simple command-line utility for processing .g2o files.

References

We are making this software freely available in the hope that it will be useful to others. If you use SE-Sync in your own work, please cite our papers:

@inproceedings{Rosen2016Certifiably,
title = {A Certifiably Correct Algorithm for Synchronization over the Special {Euclidean} Group},
author = {Rosen, D.M. and Carlone, L. and Bandeira, A.S. and Leonard, J.J.},
booktitle = {Intl. Workshop on the Algorithmic Foundations of Robotics (WAFR)},
month = dec,
year = {2016},
address = {San Francisco, CA},
}

@techreport{Rosen2016SESync,
title = {{SE-Sync}: A Certifiably Correct Algorithm for Synchronization over the Special {Euclidean} Group},
author = {Rosen, D.M. and Carlone, L. and Bandeira, A.S. and Leonard, J.J.},
institution = {Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology},
address = {Cambridge, MA},
number = {MIT-CSAIL-TR-2017-002},
year = {2017},
month = feb,
}

and the following paper of Absil et al., which describes the Riemannian trust-region (RTR) method that SE-Sync employs:

@article{Absil2007Trust,
title = {Trust-Region Methods on {Riemannian} Manifolds},
author = {Absil, P.-A. and Baker, C.G. and Gallivan, K.A.},
journal = {Found.\ Comput.\ Math.},
volume = {7},
number = {3},
pages = {303--330},
year = {2007},
month = jul,
}

If you use the MATLAB implementation of SE-Sync, please also cite the following reference for the Manopt toolbox, which provides the MATLAB implementation of RTR that the SE-Sync toolbox employs:

@article{Boumal2014Manopt,
  title={{Manopt}, a {MATLAB} Toolbox for Optimization on Manifolds.},
  author={Boumal, N. and Mishra, B. and Absil, P.-A. and Sepulchre, R.},
  journal={Journal of Machine Learning Research},
  volume={15},
  number={1},
  pages={1455--1459},
  year={2014}
}

Copyright and License

The C++ and MATLAB implementations of SE-Sync contained herein are copyright (C) 2016 - 2018 by David M. Rosen, and are distributed under the terms of the GNU Lesser General Public License (LGPL) version 3 (or later). Please see the LICENSE for more information.

Contact: drosen2000@gmail.com