Using computer algebra tools to classify serial manipulators
Autor: | Fabrice Rouillier, Solen Corvez |
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Přispěvatelé: | Solving problems through algebraic computation and efficient software (SPACES), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP), Calcul formel (CALFOR), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS) |
Jazyk: | angličtina |
Rok vydání: | 2002 |
Předmět: |
0209 industrial biotechnology
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] robots sériels 02 engineering and technology Workspace computer.software_genre 01 natural sciences Serial manipulator serial manipulators law.invention Computer Science::Robotics Gröbner basis 020901 industrial engineering & automation Singularity triangular sets law Computer Aided Design Cartesian coordinate system groebner basis ensembles triangulaires 0101 mathematics semialgebraic sets Mathematics 010102 general mathematics cylindrical algebraic decomposition Symbolic computation Cylindrical algebraic decomposition ensembles semi-algébriques bases de groebner décomposition cylindrique algébrique computer Algorithm |
Zdroj: | Fourth International Workshop on Automated Deduction in Geometry-ADG 2002 Fourth International Workshop on Automated Deduction in Geometry-ADG 2002, Sep 2002, Hagenberg, Austria. pp.31-43, ⟨10.1007/978-3-540-24616-9_3⟩ Automated Deduction in Geometry ISBN: 9783540209270 Automated Deduction in Geometry |
DOI: | 10.1007/978-3-540-24616-9_3⟩ |
Popis: | Colloque avec actes et comité de lecture. internationale.; International audience; In this paper we present a classification of 3-revolute-jointed manipulators based on the cuspidal behaviour. It was shown in a previous work [16] that this ability to change posture without meeting a singularity is equivalent to the existence of a point in the workspace, such that a polynomial of degree four depending on the parameters of the manipulator and on the cartesian coordinates of the effector has a triple root. More precisely, from a partition of the parameters’space, such that in any connected component of this partition the number of triple roots is constant, we need to compute one sample point by cell, in order to have a full description, in terms of cuspidality, of the different possible configurations. This kind of work can be divided into two parts. First of all, thanks to Groebner Bases computations, the goal is to obtain an algebraic set in the parameters’space describing the cuspidality behavior and then to compute a CAD adapted to this set. In order to simplify the problem, we use strongly the fact that a manipulator cannot be constructed with exact parameters, in other words, we are just interested in the generic solutions of our problem. This consideration leads us to work with triangular sets rather than with the global Groebner Bases and to adapt the CAD of Collins as we will just take care of the cells of maximal dimension. |
Databáze: | OpenAIRE |
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