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Adding an integrator for output regulation of systems with matrix Lie-group states

Mahony, Robert; Hamel, Tarek; Marconi, Lorenzo

Description

This paper considers the problem of tracking reference trajectories for systems defined on matrix Lie Groups. Both the reference system (exosystem) and controlled system have states on the same matrix Lie group, with the exosystem having constant velocity. The measurements are associated with a group action on a homogeneous space of the state space and can be thought of as measured partial relative state information. We look for a controller depending only on the relative state errors and the...[Show more]

dc.contributor.authorMahony, Robert
dc.contributor.authorHamel, Tarek
dc.contributor.authorMarconi, Lorenzo
dc.coverage.spatialChicago, USA
dc.date.accessioned2016-06-14T23:19:07Z
dc.date.createdJuly 1-3 2015
dc.identifier.isbn9781479986859
dc.identifier.urihttp://hdl.handle.net/1885/102759
dc.description.abstractThis paper considers the problem of tracking reference trajectories for systems defined on matrix Lie Groups. Both the reference system (exosystem) and controlled system have states on the same matrix Lie group, with the exosystem having constant velocity. The measurements are associated with a group action on a homogeneous space of the state space and can be thought of as measured partial relative state information. We look for a controller depending only on the relative state errors and the local state of the controlled system, that is a control that is independent of the exogenous variables. The proposed design embeds an integral estimate of the unknown exosystem velocity as a dynamic state in the controller. The approach is motivated by a range of robotics applications posed on classical Lie-groups SO(3), SE(3), SL(3), although we develop a general result for kinematic systems on arbitrary matrix Lie-groups. In the specific case of SO(3), namely systems defined on the Lie-group of orthogonal rotations, we go further by presenting an 'error feedback' controller for systems modeled by kinematics and dynamics equations.
dc.publisherIEEE
dc.relation.ispartofseries2015 American Control Conference, ACC 2015
dc.sourceProceedings of the American Control Conference
dc.titleAdding an integrator for output regulation of systems with matrix Lie-group states
dc.typeConference paper
local.description.notesImported from ARIES
local.description.refereedYes
dc.date.issued2015
local.identifier.absfor010200 - APPLIED MATHEMATICS
local.identifier.absfor010300 - NUMERICAL AND COMPUTATIONAL MATHEMATICS
local.identifier.absfor080100 - ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING
local.identifier.ariespublicationa383154xPUB3294
local.type.statusPublished Version
local.contributor.affiliationMahony, Robert, College of Engineering and Computer Science, ANU
local.contributor.affiliationHamel, Tarek, Nice Sophia Antipolis University
local.contributor.affiliationMarconi, Lorenzo, Studiorum Universita di Bologna
local.description.embargo2037-12-31
local.bibliographicCitation.startpage4010
local.bibliographicCitation.lastpage4015
local.identifier.doi10.1109/ACC.2015.7171956
dc.date.updated2016-06-14T08:32:37Z
local.identifier.scopusID2-s2.0-84940923206
CollectionsANU Research Publications

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