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Bicentered Interval Newton Operator for Robot’s Workspace Approximation

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Optimization and Applications (OPTIMA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14395))

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Abstract

The paper considers the approximation of the robot workspace. The developed method, based on interval Newton operator relies on Baumann bicentered theorem. We used this method for approximation of the solution sets of undetermined non-linear equation. This problem refers to the one of the most important problems in robotics: workspace approximation, since the robot kinematic systems are set with undetermined (usually non-linear) systems. We perform experiments for the DexTar robotic system and visualize the obtained approximations. As expected the bicentered modification provides tight approximation of the workspace compared with classical Newton method.

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Acknowledgment

The research was carried out using the infrastructure of the Shared Research Facilities “High Performance Computing and Big Data” (CKP “Informatics”) of FRC CSC RAS (Moscow).

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences (FRC CSC RAS), 44/2, Vavilova street, 119333, Moscow, Russian Federation

    Artem Maminov & Mikhail Posypkin

  2. HSE University, 20 Myasnitskaya Ulitsa, 101000, Moscow, Russian Federation

    Artem Maminov & Mikhail Posypkin

Authors
  1. Artem Maminov
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  2. Mikhail Posypkin
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Corresponding author

Correspondence to Artem Maminov .

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Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  4. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Maminov, A., Posypkin, M. (2023). Bicentered Interval Newton Operator for Robot’s Workspace Approximation. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2023. Lecture Notes in Computer Science, vol 14395. Springer, Cham. https://doi.org/10.1007/978-3-031-47859-8_25

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  • DOI: https://doi.org/10.1007/978-3-031-47859-8_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-47858-1

  • Online ISBN: 978-3-031-47859-8

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