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Title: | Stratifications of the Euclidean motion group with applications to robotics |
Authors: | Alberich-Carramiñana, Maria CSIC ORCID ; González-Alonso, Víctor; Thomas, Federico CSIC ORCID ; Torras, Carme CSIC ORCID | Keywords: | Flag manifold Stratification Euclidean motion group Cell decomposition Singular locus |
Issue Date: | 2009 | Publisher: | Springer | Citation: | Geometriae Dedicata 141(1): 19-32 (2009) | 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. | Publisher version (URL): | http://dx.doi.org/10.1007/s10711-008-9341-2 | URI: | http://hdl.handle.net/10261/30501 | DOI: | 10.1007/s10711-008-9341-2 | ISSN: | 0046-5755 |
Appears in Collections: | (IRII) Artículos |
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Stratifications of the Euclidean.pdf | 449,04 kB | Adobe PDF | ![]() View/Open |
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