Comparison of two different objective functions in 2D point feature SLAM

Wang, H; Huang, S; Yang, G; Dissanayake, G

Comparison of two different objective functions in 2D point feature SLAM

Wang, H Huang, S

Yang, G Dissanayake, G

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Publication Type:: Journal Article
Citation:: Automatica, 2018, 97 pp. 172 - 181
Issue Date:: 2018-11-01

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Field	Value	Language
dc.contributor.author	Wang, H	en_US
dc.contributor.author	Huang, S https://orcid.org/0000-0002-6124-4178	en_US
dc.contributor.author	Yang, G	en_US
dc.contributor.author	Dissanayake, G https://orcid.org/0000-0002-7992-0680	en_US
dc.date.available	2020-11-02T18:03:30Z
dc.date.issued	2018-11-01	en_US
dc.identifier.citation	Automatica, 2018, 97 pp. 172 - 181	en_US
dc.identifier.issn	0005-1098	en_US
dc.identifier.uri	http://hdl.handle.net/10453/131276
dc.description.abstract	© 2018 Elsevier Ltd This paper compares two different objective functions in 2D point feature Simultaneous Localization and Mapping (SLAM). It is shown that the objective function can have a significant impact on the convergence of the iterative optimization techniques used in SLAM. When Frobenius norm is adopted for the error term of the orientation part of odometry, the SLAM problem has much better convergence properties, as compared with that using the angle difference as the error term. For one-step case, we have proved that there is one and only one minimum to the SLAM problem, and strong duality always holds. For two-step case, strong duality always holds except when three very special conditions hold simultaneously (which happens with probability zero), thus the global optimal solution to primal SLAM problem can be obtained by solving the corresponding Lagrangian dual problem in most cases. Further, for arbitrary m-step cases, we also show using examples that much better convergence results can be obtained. Simulation examples are given to demonstrate the different convergence properties using two different objective functions.	en_US
dc.relation.ispartof	Automatica	en_US
dc.relation.isbasedon	10.1016/j.automatica.2018.08.009	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	Comparison of two different objective functions in 2D point feature SLAM	en_US
dc.type	Journal Article
utslib.citation.volume	97	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0913 Mechanical Engineering	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	08 Information and Computing Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CAS - Centre for Autonomous Systems
utslib.copyright.status	open_access	*
pubs.publication-status	Published	en_US
pubs.volume	97	en_US

Abstract:

© 2018 Elsevier Ltd This paper compares two different objective functions in 2D point feature Simultaneous Localization and Mapping (SLAM). It is shown that the objective function can have a significant impact on the convergence of the iterative optimization techniques used in SLAM. When Frobenius norm is adopted for the error term of the orientation part of odometry, the SLAM problem has much better convergence properties, as compared with that using the angle difference as the error term. For one-step case, we have proved that there is one and only one minimum to the SLAM problem, and strong duality always holds. For two-step case, strong duality always holds except when three very special conditions hold simultaneously (which happens with probability zero), thus the global optimal solution to primal SLAM problem can be obtained by solving the corresponding Lagrangian dual problem in most cases. Further, for arbitrary m-step cases, we also show using examples that much better convergence results can be obtained. Simulation examples are given to demonstrate the different convergence properties using two different objective functions.

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http://hdl.handle.net/10453/131276