Publication
Stratifications of the Euclidean motion group with applications to robotics
Journal Article (2009)
Journal
Geometriae Dedicata
Pages
19-32
Volume
141
Number
1
Doc link
http://dx.doi.org/10.1007/s10711-008-9341-2
File
Authors
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Alberich Carramiñana, Maria
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González, Víctor
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Thomas, Federico
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Torras Genís, Carme
Projects associated
Abstract
In this paper we derive stratifications of the Euclidean motion group, which provide a complete description of the singular locus in the configuration space of a family of parallel manipulators, and we study the adjacency between the strata. We prove that classically known cell decompositions of the flag manifold restricted to the open subset parameterizing the affine real flags are still stratifications, and we introduce a refinement of the classical Ehresmann-Bruhat order that characterizes the adjacency between all the different strata. Then we show how, via a four-fold covering morphism, the stratifications of the Euclidean motion group are induced.
Categories
robot kinematics.
Author keywords
flag manifold, stratification, Euclidean motion group, cell decomposition, singular locus, parallel manipulators
Scientific reference
M. Alberich-Carramiñana, V. González-Alonso, F. Thomas and C. Torras. Stratifications of the Euclidean motion group with applications to robotics. Geometriae Dedicata, 141(1): 19-32, 2009.
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