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Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs

Khosravian Hemami, Alireza; Trumpf, Jochen; Mahony, Robert; Lageman, Christian

Description

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of Lie groups, a question for which only case studies of specific Lie groups are currently available. We show that any...[Show more]

dc.contributor.authorKhosravian Hemami, Alireza
dc.contributor.authorTrumpf, Jochen
dc.contributor.authorMahony, Robert
dc.contributor.authorLageman, Christian
dc.date.accessioned2016-06-14T23:18:42Z
dc.identifier.issn0005-1098
dc.identifier.urihttp://hdl.handle.net/1885/102583
dc.description.abstractThis paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of Lie groups, a question for which only case studies of specific Lie groups are currently available. We show that any candidate observer (with the same state space dimension as the observed system) results in non-autonomous error dynamics, except in the trivial case where the Lie-group is Abelian. This precludes the application of the standard non-linear observer design methodologies available in the literature and leads us to propose a new design methodology based on employing invariant cost functions and general gain mappings. We provide a rigorous and general stability analysis for the case where the underlying Lie group allows a faithful matrix representation. We demonstrate our theory in the example of rigid body pose estimation and show that the proposed approach unifies two competing pose observers published in prior literature.
dc.publisherPergamon-Elsevier Ltd
dc.sourceAutomatica
dc.titleObservers for invariant systems on Lie groups with biased input measurements and homogeneous outputs
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume55
dc.date.issued2015
local.identifier.absfor090602 - Control Systems, Robotics and Automation
local.identifier.ariespublicationa383154xPUB1449
local.type.statusPublished Version
local.contributor.affiliationKhosravian Hemami, Alireza, College of Engineering and Computer Science, ANU
local.contributor.affiliationTrumpf, Jochen, College of Engineering and Computer Science, ANU
local.contributor.affiliationMahony, Robert, College of Engineering and Computer Science, ANU
local.contributor.affiliationLageman, Christian, University of Wurzburg
local.description.embargo2037-12-31
local.bibliographicCitation.startpage19
local.bibliographicCitation.lastpage26
local.identifier.doi10.1016/j.automatica.2015.02.030
dc.date.updated2016-06-14T08:28:23Z
local.identifier.scopusID2-s2.0-84927920582
CollectionsANU Research Publications

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