Some in-parallel robots, such as the 3-2-1 and the 3/2 manipulators, have attracted attention because their forward kinematics can be solved by three consecutive trilaterations. In this paper, we identify a class of these robots, which we call flagged manipulators, whose singularity loci admit a well-behaved decomposition, i.e., a stratification, derived from that of the flag manifold. Two remarkable properties must be highlighted. First, the decomposition has the same topology for all members in the class, irrespective of the metric details of each particular robot instance. Thus, we provide explicitly all the singular strata and their connectivity, which apply to all flagged manipulators without any tailoring. Second, the strata can be easily characterized geometrically, because it is possible to assign local coordinates to each stratum (in the configuration space of the manipulator) that correspond to uncoupled rotations and/or translations in the workspace. ; This work was supported by projects: 'Planificador de trayectorias para sistemas robotizados de arquitectura arbitraria' (J-00930), 'Grup de recerca consolidat - ROBÒTICA' (8007). ; The work of F. Thomas and C. Torras was supported in part by the Spanish Committee for Science and Technology (CICYT) under Project DPI2004-07358, and in part by the Catalan Research Commission through the Robotics and Control Group. The work of M. Alberich-Carramiñana was supported in part under DGYCIT BFM2002-01240 and DGYCIT BFM2003-06001, and in part by the Programa Ramón y Cajal of the Ministerio de Ciencia y Tecnología. ; Peer Reviewed
Stratifying the singularity loci of a class of parallel manipulators
2006-01-01
Article (Journal)
Electronic Resource
English
DDC: | 629 |
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