Prof. Dr. Ing. Pavel Zemčík

ILA Viorela S., POLOK Lukáš, SMRŽ Pavel, ŠOLONY Marek a ZEMČÍK Pavel. Incremental Block Cholesky Factorization for Nonlinear Least Squares in Robotics. In: In proceedings of The Robotics: Science and Systems 2013 Conference. Berlín: MIT Press, 2013, s. 1-8. ISBN 978-981-07-3937-9. Dostupné z: http://roboticsproceedings.org/rss09/p42.html
Jazyk publikace:angličtina
Název publikace:Incremental Block Cholesky Factorization for Nonlinear Least Squares in Robotics
Název (cs):Inkrementální Choleskyho faktorizace nad blokovými maticemi pro řešení metody nejmenších čtverců v robotických aplikacích
Strany:1-8
Sborník:In proceedings of The Robotics: Science and Systems 2013 Conference
Konference:Robotics: Science and Systems 2013
Místo vydání:Berlín, DE
Rok:2013
URL:http://roboticsproceedings.org/rss09/p42.html
ISBN:978-981-07-3937-9
DOI:10.15607/RSS.2013.IX.042
Vydavatel:MIT Press
Soubory: 
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Klíčová slova
SLAM, Nonlinear least squares, Cholesky Factorization, Incremental Factorization, Sparse block matrix
Anotace
Publikace navrhuje rozšíření maticových faktorizačních metod na metody s pokračováním, vhodné pro inkrementální aplikace, kde velikost řešeného systému rovnic v čase roste, ale zbytek systému se přitom nemění. Implementace dosahuje velmi dobrých výsledků, porovnatelných a až na výjimky lepších, než u implementací pracujících nad grafovými faktorizacemi. Navržená metoda je však výrazně jednodušší a je vhodná k implementaci v HW. 
Abstrakt
Efciently solving nonlinear least squares (NLS) problems is crucial for many applications in robotics. In online applications, solving the associated nolinear systems every step may become very expensive. This paper introduces online, incremental solutions, which take full advantage of the sparse-block structure of the problems in robotics. In general, the solution of the nonlinear system is approximated by incrementally solving a series of linearized problems. The most computationally demanding part is to assemble and solve the linearized system at each iteration. In our solution, this is mitigated by incrementally updating the factorized form of the linear system and changing the linearization point only if needed. The incremental updates are done using a resumed factorization only on the parts affected by the new information added to the system at every step. The sparsity of the factorized form directly affects the efciency. In order to obtain an incremental factorization with persistent reduced ll-in, a new incremental ordering scheme is proposed. Furthermore, the implementation exploits the block structure of the problems and offers efcient solutions to manipulate block matrices, including a highly efcient Cholesky factorization on sparse block matrices. In this work, we focus our efforts on testing the method on SLAM applications, but the applicability of the technique remains general. The experimental results show that our implementation outperforms the state of the art SLAM implementations on all tested datasets.
BibTeX:
@INPROCEEDINGS{
   author = {S. Viorela Ila and Luk{\'{a}}{\v{s}} Polok and
	Pavel Smr{\v{z}} and Marek {\v{S}}olony and Pavel
	Zem{\v{c}}{\'{i}}k},
   title = {Incremental Block Cholesky Factorization for
	Nonlinear Least Squares in Robotics},
   pages = {1--8},
   booktitle = {In proceedings of The Robotics: Science and Systems 2013
	Conference},
   year = 2013,
   location = {Berl{\'{i}}n, DE},
   publisher = {MIT Press},
   ISBN = {978-981-07-3937-9},
   doi = {10.15607/RSS.2013.IX.042},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php.cs?id=10348}
}

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