On the number of local minima to the point feature based SLAM problem

Huang, S; Wang, H; Frese, U; Dissanayake, G

On the number of local minima to the point feature based SLAM problem

Huang, S

Wang, H

Frese, U Dissanayake, G

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Publication Type:: Conference Proceeding
Citation:: Proceedings - IEEE International Conference on Robotics and Automation, 2012, pp. 2074 - 2079
Issue Date:: 2012-01-01

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Field	Value	Language
dc.contributor.author	Huang, S https://orcid.org/0000-0002-6124-4178	en_US
dc.contributor.author	Wang, H https://orcid.org/0000-0001-5448-9903	en_US
dc.contributor.author	Frese, U	en_US
dc.contributor.author	Dissanayake, G https://orcid.org/0000-0002-7992-0680	en_US
dc.date.issued	2012-01-01	en_US
dc.identifier.citation	Proceedings - IEEE International Conference on Robotics and Automation, 2012, pp. 2074 - 2079	en_US
dc.identifier.isbn	9781467314039	en_US
dc.identifier.issn	1050-4729	en_US
dc.identifier.uri	http://hdl.handle.net/10453/22386
dc.description.abstract	Map joining is an efficient strategy for solving feature based SLAM problems. This paper demonstrates that joining of two 2D local maps, formulated as a nonlinear least squares problem has at most two local minima, when the associated uncertainties can be described using spherical covariance matrices. Necessary and sufficient condition for the existence of two minima is derived and it is shown that more than one minimum exists only when the quality of the local maps used for map joining is extremely poor. The analysis explains to some extent why a number of optimization based SLAM algorithms proposed in the recent literature that rely on local search strategies are successful in converging to the globally optimal solution from poor initial conditions, particularly when covariance matrices are spherical. It also demonstrates that the map joining problem has special properties that may be exploited to reliably obtain globally optimal solutions to the SLAM problem. © 2012 IEEE.	en_US
dc.relation.ispartof	Proceedings - IEEE International Conference on Robotics and Automation	en_US
dc.relation.isbasedon	10.1109/ICRA.2012.6224876	en_US
dc.title	On the number of local minima to the point feature based SLAM problem	en_US
dc.type	Conference Proceeding
utslib.for	091303 Autonomous Vehicles	en_US
dc.location.activity	Saint Paul, Minnesota, USA	en_US
dc.location.activity	St Paul, MN
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	closed_access
pubs.publication-status	Published	en_US

Abstract:

Map joining is an efficient strategy for solving feature based SLAM problems. This paper demonstrates that joining of two 2D local maps, formulated as a nonlinear least squares problem has at most two local minima, when the associated uncertainties can be described using spherical covariance matrices. Necessary and sufficient condition for the existence of two minima is derived and it is shown that more than one minimum exists only when the quality of the local maps used for map joining is extremely poor. The analysis explains to some extent why a number of optimization based SLAM algorithms proposed in the recent literature that rely on local search strategies are successful in converging to the globally optimal solution from poor initial conditions, particularly when covariance matrices are spherical. It also demonstrates that the map joining problem has special properties that may be exploited to reliably obtain globally optimal solutions to the SLAM problem. © 2012 IEEE.

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