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Stratifications of the Euclidean motion group with applications to robotics

AuthorsAlberich-Carramiñana, Maria ; González-Alonso, Víctor; Thomas, Federico ; Torras, Carme
KeywordsFlag manifold
Euclidean motion group
Cell decomposition
Singular locus
Issue Date2009
CitationGeometriae Dedicata 141(1): 19-32 (2009)
AbstractIn 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.
Publisher version (URL)http://dx.doi.org/10.1007/s10711-008-9341-2
Appears in Collections:(IRII) Artículos
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