Analysis of Minima for Geodesic and Chordal Cost for a Minimal 2-D Pose-Graph SLAM Problem

Kong, FH; Zhao, J; Zhao, L; Huang, S

Analysis of Minima for Geodesic and Chordal Cost for a Minimal 2-D Pose-Graph SLAM Problem

Kong, FH Zhao, J Zhao, L

Huang, S

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Robotics and Automation Letters, 2020, 5, (2), pp. 323-330
Issue Date:: 2020-04-01

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Field	Value	Language
dc.contributor.author	Kong, FH
dc.contributor.author	Zhao, J
dc.contributor.author	Zhao, L https://orcid.org/0000-0003-4063-8183
dc.contributor.author	Huang, S https://orcid.org/0000-0002-6124-4178
dc.date.accessioned	2020-10-31T20:22:32Z
dc.date.available	2020-10-31T20:22:32Z
dc.date.issued	2020-04-01
dc.identifier.citation	IEEE Robotics and Automation Letters, 2020, 5, (2), pp. 323-330
dc.identifier.issn	2377-3766
dc.identifier.issn	2377-3766
dc.identifier.uri	http://hdl.handle.net/10453/143648
dc.description.abstract	© 2016 IEEE. In this letter, we show that for a minimal 2D pose-graph SLAM problem, even in the ideal case of perfect measurements and spherical covariance, using geodesic distance (in 2D, the 'wrap function') to compare angles results in multiple suboptimal local minima. We numerically estimate regions of attraction to these local minima for some examples, give evidence to show that they are of nonzero measure, and that these regions grow in size as noise is added. In contrast, under the same assumptions, we show that the chordal distance representation of angle error has a unique minimum up to periodicity. For chordal cost, we find that initial conditions failing to converge to the global minimum are far fewer, fail because of numerical issues, and do not seem to grow with noise in our examples.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation.ispartof	IEEE Robotics and Automation Letters
dc.relation.isbasedon	10.1109/LRA.2019.2958492
dc.rights	info:eu-repo/semantics/closedAccess
dc.rights	© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.subject	0913 Mechanical Engineering
dc.title	Analysis of Minima for Geodesic and Chordal Cost for a Minimal 2-D Pose-Graph SLAM Problem
dc.type	Journal Article
utslib.citation.volume	5
utslib.for	0913 Mechanical Engineering
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - CAS - Centre for Autonomous Systems
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
utslib.copyright.status	closed_access	*
dc.date.updated	2020-10-31T20:22:15Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	5
utslib.citation.issue	2

Abstract:

© 2016 IEEE. In this letter, we show that for a minimal 2D pose-graph SLAM problem, even in the ideal case of perfect measurements and spherical covariance, using geodesic distance (in 2D, the 'wrap function') to compare angles results in multiple suboptimal local minima. We numerically estimate regions of attraction to these local minima for some examples, give evidence to show that they are of nonzero measure, and that these regions grow in size as noise is added. In contrast, under the same assumptions, we show that the chordal distance representation of angle error has a unique minimum up to periodicity. For chordal cost, we find that initial conditions failing to converge to the global minimum are far fewer, fail because of numerical issues, and do not seem to grow with noise in our examples.

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http://hdl.handle.net/10453/143648