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Efficient Factorization of the Joint-Space Inertia Matrix for Branched Kinematic Trees

Featherstone, Roy

Description

This paper describes new factorization algorithms that exploit branch-induced sparsity in the joint-space inertia matrix (JSIM) of a kinematic tree. It also presents new formulae that show how the cost of calculating and factorizing the JSIM vary with the topology of the tree. These formulae show that the cost of calculating for-ward dynamics for a branched tree can be considerably less than the cost for an unbranched tree of the same site. Branches can also reduce complexity; some examples are...[Show more]

dc.contributor.authorFeatherstone, Roy
dc.date.accessioned2015-12-13T22:52:25Z
dc.identifier.issn0278-3649
dc.identifier.urihttp://hdl.handle.net/1885/81570
dc.description.abstractThis paper describes new factorization algorithms that exploit branch-induced sparsity in the joint-space inertia matrix (JSIM) of a kinematic tree. It also presents new formulae that show how the cost of calculating and factorizing the JSIM vary with the topology of the tree. These formulae show that the cost of calculating for-ward dynamics for a branched tree can be considerably less than the cost for an unbranched tree of the same site. Branches can also reduce complexity; some examples are presented of kinematic trees for which the complexity of calculating and factorizing the JSIM are less than O(n2) and O(n3), respectively. Finally, a cost comparison is made between an O(n) algorithm and an O(n3) algorithm, the latter incorporating one of the new factorization algorithms. It is shown that the O(n3) algorithm is only 15% slower than the O(n) algorithm when applied to a 30-degrees-of-freedom humanoid, but is 2.6 times slower when applied to an equivalent unbranched chain. This is due mainly to the O(n 3) algorithm running about 2.2 times faster on the humanoid than on the chain.
dc.publisherSage Publications Inc
dc.sourceInternational Journal of Robotics Research
dc.subjectKeywords: Computational complexity; Graph theory; Matrix algebra; Topology; Trees (mathematics); Vectors; Branched kinematic chain; Inertia matrix; Robot dynamics; Sparse matrix factorization; Algorithms Branched kinematic chain; Inertia matrix; Robot dynamics; Sparse matrix factorization
dc.titleEfficient Factorization of the Joint-Space Inertia Matrix for Branched Kinematic Trees
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume24
dc.date.issued2005
local.identifier.absfor080101 - Adaptive Agents and Intelligent Robotics
local.identifier.ariespublicationMigratedxPub9847
local.type.statusPublished Version
local.contributor.affiliationFeatherstone, Roy, College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue6
local.bibliographicCitation.startpage487
local.bibliographicCitation.lastpage500
local.identifier.doi10.1177/0278364905054928
local.identifier.absseo890399 - Information Services not elsewhere classified
dc.date.updated2015-12-11T10:51:04Z
local.identifier.scopusID2-s2.0-19344371257
CollectionsANU Research Publications

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