Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry
| Autor: | Damien Chablat, Rémi Prébet, Mohab Safey El Din, Durgesh H. Salunkhe, Philippe Wenger |
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| Přispěvatelé: | Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ), Robotique Et Vivant (LS2N - équipe ReV), Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Polynomial Systems (PolSys), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Grant FA8665-20-1-7029 of the EOARD-AFOSR, ANR-19-CE48-0015,ECARP,Algorithmes efficaces et exacts pour la planification de trajectoire en robotique(2019), ANR-18-CE33-0011,SESAME,Singularités Et Stabilité des AsservisseMEnts référencés capteurs(2018), ANR-19-CE40-0018,DeRerumNatura,Décider l'irrationalité et la transcendance(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), European Project: ECARP, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Nantes Université - École Centrale de Nantes (Nantes Univ - ECN), Robotique Et Vivant (ReV), Nantes Université (Nantes Univ)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), European Project: 813211,H2020,POEMA(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Computer Science - Symbolic Computation
FOS: Computer and information sciences robotics [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] I.1.4 critical points cuspidality computational real algebraic geometry Symbolic Computation (cs.SC) I.1.2 symbolic computation Computer Science::Robotics Computer Science - Robotics Mathematics - Algebraic Geometry 68W30 14Q30 ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO] [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] Robotics (cs.RO) Algebraic Geometry (math.AG) |
| Zdroj: | ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation ISSAC 2022-47th International Symposium on Symbolic and Algebraic Computation ISSAC 2022-47th International Symposium on Symbolic and Algebraic Computation, Jul 2022, Lille, France. ⟨10.1145/3476446.3535477⟩ 47th International Symposium on Symbolic and Algebraic Computation 2022 International Symposium on Symbolic and Algebraic Computation 2022 International Symposium on Symbolic and Algebraic Computation, Jul 2022, Lille, France. ⟨10.1145/3476446.3535477⟩ |
| Popis: | Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom robots can be a challenging problem. Many robots can be modeled as a polynomial map together with a real algebraic set so that the notion of cuspidality can be extended to these data. In this paper we design an algorithm that, on input a polynomial map in $n$ indeterminates, and $s$ polynomials in the same indeterminates describing a real algebraic set of dimension $d$, decides the cuspidality of the restriction of the map to the real algebraic set under consideration. Moreover, if $D$ and $\tau$ are, respectively the maximum degree and the bound on the bit size of the coefficients of the input polynomials, this algorithm runs in time log-linear in $\tau$ and polynomial in $((s+d)D)^{O(n^2)}$. It relies on many high-level algorithms in computer algebra which use advanced methods on real algebraic sets and critical loci of polynomial maps. As far as we know, this is the first algorithm that tackles the cuspidality problem from a general point of view. Comment: 10 pages, 4 figures, published in the Proceedings of ISSAC2022 |
| Databáze: | OpenAIRE |
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