Computational algebraic geometry and global analysis of regional manipulators

Teijo Arponen, Andreas Müller, Samuli Piipponen and Jukka Tuomela

Applied Mathematics and Computation, 2014, vol. 232, issue C, 820-835

Abstract: The global analysis of the singularities of regional manipulators is addressed in this paper. The problem is approached from the point of view of computational algebraic geometry. The main novelty is to compute the syzygy module of the differential of the constraint map. Composing this with the differential of the forward kinematic map and studying the associated Fitting ideals allows for a complete stratification of the configuration space according to the corank of singularities. Moreover using this idea we can also compute the boundary of the image of the forward kinematic map. Obviously this gives us also a description of the image itself, i.e. the manipulator workspace. The approach is feasible in practice because generators of syzygy modules can be computed in a similar way as Gröbner bases of ideals.

Keywords: Regional manipulators; Kinematical analysis; Algebraic geometry; Gröbner bases; Ideal decomposition (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:820-835

DOI: 10.1016/j.amc.2014.01.138

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