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Robust multi-objective optimization of parallel manipulators

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Abstract

This paper presents a novel robust optimal design for parallel manipulators to optimize the performance indices subject to the unavoidable effect of the uncertainties. The robust optimization proposed in the present contribution consists of a multi-objective optimization problem that aims at maximizing the performance index and robustness criterion simultaneously. The design variables should be adjusted to minimize the effects of the uncertainties and maximize the performance index. The single-objective optimization problem is also carried out to evaluate the optimal design obtained by using the proposed robust optimization approach. Numerical results illustrate the benefits of the proposed robust optimization applied to the optimal kinematic design of a parallel Cartesian manipulator with clearances and the optimal dynamic design of a Stewart–Gough platform.

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Acknowledgements

The authors are thankful for the financial support provided by CNPq (Process 427204/2018-6), and CAPES.

Funding

This study was funded by National Council for Scientific and Technological Development - Brazil (grant number 427204/2018-6).

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Authors and Affiliations

  1. Federal University of Technology - Paraná, Cornélio Procópio, PR, 86300-00, Brazil

    Fabian A. Lara-Molina

  2. CNRS, CentraleSuplec, Laboratoire des Signaux et Systèmes, Universit Paris-Saclay, 91 192, Gif sur Yvette cedex, France

    Didier Dumur

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  1. Fabian A. Lara-Molina
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Correspondence to Fabian A. Lara-Molina.

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Appendix: Monte Carlo simulation

Appendix: Monte Carlo simulation

The Monte Carlo simulation (MCS) to evaluate the robustness criteria of \(\gamma =\varvec{\Gamma }\left( {\mathbf {t}},\varvec{\lambda }, {\mathbf {u}} \right) \) consists of three main steps: i) sampling of the uncertain parameters of the uncertain parameters \({\mathbf {u}}\) (see Eq. (1)) to obtain a set of \(n_s\) random inputs; ii) the output of the system \(\gamma \) is computed for each random input. iii) a statical analysis is carried out to find the mean and standard deviation of the output. The algorithm of MCS is presented in Fig. 12. It is worth to mention that the pose of the end-effector \({\mathbf {t}}\) and the design variables \(\varvec{\lambda }\) are considered as constants in this procedure.

Fig. 12
figure 12

Monte Carlo simulation to compute the robustness criterion

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where the operators \(\overline{(.)}\) and \(\sigma {(.)}\) denotes the mean and standard deviation, respectively.

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Lara-Molina, F.A., Dumur, D. Robust multi-objective optimization of parallel manipulators. Meccanica 56, 2843–2860 (2021). https://doi.org/10.1007/s11012-021-01418-z

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