IRI - Stratifications of the Euclidean motion group with applications to robotics

Publication

Stratifications of the Euclidean motion group with applications to robotics

Journal Article (2009)

Journal

Geometriae Dedicata

Pages

19-32

Volume

141

Number

Doc link

http://dx.doi.org/10.1007/s10711-008-9341-2

File

Download the digital copy of the doc pdf document

Authors

Projects associated

SGR ROBÒTICA: Grup de recerca consolidat - Grup de Robòtica

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.

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.