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Volume 11
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Article

Evolutionary Multiobjective Design Approach for Robust Balancing of the Shaking Force, Shaking Moment, and Torque under Uncertainties: Application to Robotic Manipulators

by
Ricardo Mejia-Rodriguez 
1,
Miguel Gabriel Villarreal-Cervantes 
1,*,
Alejandro Rodríguez-Molina 
2,
José Humberto Pérez-Cruz 
3 and
Víctor Manuel Silva-García 
1
1
Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, Mecatronic Section, Postgraduate Department, Mexico City 07700, Mexico
2
Tecnológico Nacional de México/ IT de Tlalnepantla, Research and Postgraduate Division, Tlalnepantla de Baz 54070, Mexico
3
Instituto Politécnico Nacional, ESIME Azcapotzalco, Sección de Estudios de Posgrado e Investigación, Mexico City 02250, Mexico
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(8), 1776; https://doi.org/10.3390/math11081776
Submission received: 18 February 2023 / Revised: 31 March 2023 / Accepted: 1 April 2023 / Published: 7 April 2023
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing, 3rd Edition)
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Abstract

In this paper, the environmental uncertainties are taken into account when designing a robotic manipulator to balance the shaking force, shaking moment, and torque. The proposed robust balancing design approach does not consider the probability distributions of the uncertainties and is addressed without dependence on specific trajectories. This is expressed as a nonlinear constrained multiobjective optimization problem in which the nominal performance in the time-independent terms of the shaking force balancing, the shaking moment balancing, and the torque delivery, as well as their three sensitivities to uncertainties, are simultaneously optimized to provide a set of link shapes that match link mass distributions in a single stage. The proposal is applied to a three-degree-of-freedom serial-parallel manipulator, and the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is used to solve the associated problem. Comparative results with other design approaches reveal that the selected design achieves a suitable tradeoff in balancing the shaking force balancing, the shaking moment balancing, and the torque delivery and their sensitivities, leading to a reduction in their values and variations under mass changes in the manipulator end-effector with different operating conditions (tasks).
Keywords: dynamic balancing; torque delivery; robustness; optimization; evolutionary computing dynamic balancing; torque delivery; robustness; optimization; evolutionary computing

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MDPI and ACS Style

Mejia-Rodriguez , R.; Villarreal-Cervantes , M.G.; Rodríguez-Molina , A.; Pérez-Cruz , J.H.; Silva-García , V.M. Evolutionary Multiobjective Design Approach for Robust Balancing of the Shaking Force, Shaking Moment, and Torque under Uncertainties: Application to Robotic Manipulators. Mathematics 2023, 11, 1776. https://doi.org/10.3390/math11081776

AMA Style

Mejia-Rodriguez  R, Villarreal-Cervantes  MG, Rodríguez-Molina  A, Pérez-Cruz  JH, Silva-García  VM. Evolutionary Multiobjective Design Approach for Robust Balancing of the Shaking Force, Shaking Moment, and Torque under Uncertainties: Application to Robotic Manipulators. Mathematics. 2023; 11(8):1776. https://doi.org/10.3390/math11081776

Chicago/Turabian Style

Mejia-Rodriguez , Ricardo, Miguel Gabriel Villarreal-Cervantes , Alejandro Rodríguez-Molina , José Humberto Pérez-Cruz , and Víctor Manuel Silva-García . 2023. "Evolutionary Multiobjective Design Approach for Robust Balancing of the Shaking Force, Shaking Moment, and Torque under Uncertainties: Application to Robotic Manipulators" Mathematics 11, no. 8: 1776. https://doi.org/10.3390/math11081776

APA Style

Mejia-Rodriguez , R., Villarreal-Cervantes , M. G., Rodríguez-Molina , A., Pérez-Cruz , J. H., & Silva-García , V. M. (2023). Evolutionary Multiobjective Design Approach for Robust Balancing of the Shaking Force, Shaking Moment, and Torque under Uncertainties: Application to Robotic Manipulators. Mathematics, 11(8), 1776. https://doi.org/10.3390/math11081776

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