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The Role of Symmetry in Rigidity Analysis: A Tool for Network Localisation and Formation Control

Stacey, Geoffrey; Mahony, Robert

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The classical notion of rigidity (that a formation of agents in IR2 or IR3 is rigidly constrained by inter-agent distances up to rigid-body transformations of space) is inherently dependent on the nature of Euclidean space and the nature of distance measurements. In this paper we present a generalised formulation of rigidity where agent states may lie in heterogeneous and non-Euclidean state-spaces with arbitrary differentiable measurement constraints. A key aspect of our approach is to...[Show more]

dc.contributor.authorStacey, Geoffrey
dc.contributor.authorMahony, Robert
dc.date.accessioned2021-04-16T01:33:45Z
dc.identifier.issn0018-9286
dc.identifier.urihttp://hdl.handle.net/1885/230024
dc.description.abstractThe classical notion of rigidity (that a formation of agents in IR2 or IR3 is rigidly constrained by inter-agent distances up to rigid-body transformations of space) is inherently dependent on the nature of Euclidean space and the nature of distance measurements. In this paper we present a generalised formulation of rigidity where agent states may lie in heterogeneous and non-Euclidean state-spaces with arbitrary differentiable measurement constraints. A key aspect of our approach is to recognise the crucial role that the symmetry action of rigid-body transformations plays in classical rigidity theory. We consider a general symmetry given by a Lie-group action on a heterogeneous state-space, and define global rigidity of a formation to be the case where the inter-agent measurements fully constrain the agent locations up to the invariance encoded by the group action. In this framework we develop general definitions of local rigidity and infinitesimal rigidity, and introduce a new notion of robust rigidity that we believe will be important for control applications. To motivate the development, we show how the proposed theory can be applied to generalisations of the established problems of network localisation and formation control. The provided results are directly applicable to networks of robotic vehicles involving a mixture of bearing and distance sensors, as well as cases where a collection of ground, submersible, and aerial vehicles operate in a single formation
dc.description.sponsorshipThis work was supported by the Australian Research Council through Discovery Grant DP120100316 “Integrated High-Performance Control of Aerial Robots in Dynamic Environments.”
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.rights© 2017 IEEE
dc.sourceIEEE Transactions on Automatic Control
dc.subjectFormation control
dc.subjectmulti-robot systems
dc.subjectnetwork localization
dc.subjectrigidity theory
dc.titleThe Role of Symmetry in Rigidity Analysis: A Tool for Network Localisation and Formation Control
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume63
dcterms.dateAccepted2017-08-03
dc.date.issued2017-08-31
local.identifier.absfor090602 - Control Systems, Robotics and Automation
local.identifier.ariespublicationu4351680xPUB91
local.publisher.urlhttps://ieeexplore.ieee.org/
local.type.statusPublished Version
local.contributor.affiliationStacey, Geoffrey, College of Engineering and Computer Science, ANU
local.contributor.affiliationMahony, Robert, College of Engineering and Computer Science, ANU
local.description.embargo2099-12-31
dc.relationhttp://purl.org/au-research/grants/arc/DP120100316
local.bibliographicCitation.issue5
local.bibliographicCitation.startpage1313
local.bibliographicCitation.lastpage1328
local.identifier.doi10.1109/TAC.2017.2747760
dc.date.updated2020-11-23T11:58:46Z
local.identifier.scopusID2-s2.0-85029154323
CollectionsANU Research Publications

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