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Genetic Algorithm Coupled with the Krawczyk Method for Multi-Objective Design Parameters Optimization of the 3-UPU Manipulator

Published online by Cambridge University Press:  27 August 2019

Safa El Hraiech ,
Ahmed H. Chebbi Open the ORCID record for Ahmed H. Chebbi [Opens in a new window] ,
Zouhaier Affi  and
Lotfi Romdhane
Safa El Hraiech
Affiliation:
LGM, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia E-mails: safa_el_hraiech@hotmail.fr, zouhaier.affi@gmail.com
Ahmed H. Chebbi*
Affiliation:
LGM, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia E-mails: safa_el_hraiech@hotmail.fr, zouhaier.affi@gmail.com
Zouhaier Affi
Affiliation:
LGM, National Engineering School of Monastir, University of Monastir, Monastir, Tunisia E-mails: safa_el_hraiech@hotmail.fr, zouhaier.affi@gmail.com
Lotfi Romdhane
Affiliation:
Department of Mechanical Engineering, American University of Sharjah, Sharjah, UAE E-mail: lotfi.romdhane@gmail.com
*
*Corresponding author. E-mail: ahmed.h.chebbi@gmail.com
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Summary

In this paper, a multi-objective design optimization of the 3-UPU translational parallel manipulator is presented. Based on a new algorithm, which combines the genetic algorithms and the Krawczyk operator, the robot position error is minimized and the robot design parameters tolerances are maximized, simultaneously. The results show that the designer can maintain the manipulator accuracy by using a specific size of the base, and can restrict its tolerance even by enlarging the actuators’ tolerance intervals. This algorithm is also used to determine the maximum design parameters tolerances for an allowable robot position error. The proposed algorithm can be extended to optimize other types of robots.

Keywords

Interval analysisKrawczyk operatorGenetic algorithmUncertaintiesOptimizationTolerances

Information

Type
Articles
Information
Robotica , Volume 38 , Issue 6 , June 2020 , pp. 1138 - 1154
Copyright
© Cambridge University Press 2019

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References

Tsai, M. J. and Lai, T. H., “Accuracy analysis of a multi-loop linkage with joint clearances,” Mech. Mach. Theory, 1141–1157 (2008).CrossRefGoogle Scholar
Kong, L., Chen, G., Zhang, Z. and Wang, H., “Kinematic calibration and investigation of the influence of universal joint errors on accuracy improvement for a 3-DOF parallel manipulator,” Robot. Cim-Int. Manuf., 388–397 (2018).CrossRefGoogle Scholar
Schade, G. R., “Probabilistic models in computer automated slider-crank function generator design,” ASME J. Mech. Des. 103(4), 835–841 (1981).Google Scholar
Lee, S. J., Gilmore, B. J. and Ogot, M. M., “Dimensional tolerance allocation of stochastic dynamic mechanical systems through performance and sensitivity analysis,” ASME J. Mech. Des. 115(3), 392–402 (1993).CrossRefGoogle Scholar
Wang, N., Guo, S., Fang, Y. and Li, X., “Error sensibility analysis of 3-UPU parallel manipulator based on probability distribution,” Second International Conference on Mechanic Automation and Control Engineering, Inner Mongolia, China (2011).Google Scholar
Rao, S. S. and Bhatti, P. K., “Probabilistic approach to manipulator kinematics and dynamics,” Reliab. Eng. Syst. Safe. 72(1), 47–58 (2001).CrossRefGoogle Scholar
Merlet, J. P., “Interval analysis for certified numerical solution of problems in robotics,” Int. J. Appl. Math. Comput. Sci. 19(3), 399–412 (2009).CrossRefGoogle Scholar
Pickard, J., Carretero, J. A. and Merlet, J. P., “Accounting for tolerances in the design parameters of the 3-RRR,” Advances in Robot Kinematics, Grasse, France (2016).Google Scholar
Rao, R. S. and Agrawal, S. K., “Inverse kinematic solution of robot manipulators using interval analysis,” ASME J. Mech. Des. 120(1), 147–150 (1988).CrossRefGoogle Scholar
Rao, S. S. and Berke, L., “Analysis of Uncertain Structural Systems Using Interval Analysis,” AIAA J. 35(4), 727–735 (1997).CrossRefGoogle Scholar
Wu, W. and Rao, S. S., “Interval approach for the modeling of tolerances and clearances in mechanism analysis,” ASME J. Mech. Des. 126(4), 581–592 (2004).CrossRefGoogle Scholar
Jaulin, L., Kieffer, M., Didrit, O. and Walter, E., “Applied interval analysis with examples in parameter and state estimation, robust control and robotics,” (Springer-Verlag, 2001) ISBN: 1852332190.Google Scholar
Tannous, M., Caro, S. and Goldsztejn, A., “Sensitivity analysis of parallel manipulators using an interval linearization method,” Mech. Mach. Theory 71, 93–114.CrossRefGoogle Scholar
Goldzstejn, A., “Sensitivity Analysis Using a Fixed Point Interval Iteration,” HAL report number: hal-00339377 (2008).Google Scholar
Badreddine, E. L., Houidi, A., Affi, Z. and Romdhane, L., “Application of multi-objective genetic algorithms to the mechatronic design of a four bar system with continuous and discrete variables,” Mech. Mach. Theory 61, 68–83 (2013).Google Scholar
Chaudhury, A. N. and Ghosal, A., “Optimum design of multi-degree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method,” Mech. Mach. Theory 118, 115–138 (2017).CrossRefGoogle Scholar
Lou, Y., Liu, G. and Li, Z., “Randomized optimal design of parallel manipulators,” IEEE Trans. Automat. Sci. Eng. 5(2), 223–233 (2008).Google Scholar
Boudreau, R. and Gosselin, C. M., “The synthesis of planar parallel manipulators with a genetic algorithm,” ASME J. Mech. Des. 121(4), 533–537 (1999).CrossRefGoogle Scholar
Laribi, M. A., Mlika, A., Romdhane, L. and Zeghloul, S., “A combined genetic algorithm-fuzzy logic method (GA-FL) in mechanisms synthesis,” Mech. Mach. Theory 39(7), 717–735 (2004).CrossRefGoogle Scholar
Bilel, N., Mohamed, N., Affi, Z. and Romdhane, L., “An improved imperialist competitive algorithm for multi-objective optimization,” Eng. Optimiz. 48(11), 1823–1844 (2016).CrossRefGoogle Scholar
Mohamed, N., Bilel, N., Affi, Z. and Romdhane, L., “Multi-objective robust design optimization of the mechanism in a sewing machine,” Mech. Ind. 18(6), 729–739 (2017).Google Scholar
Varedi, S. M., Daniali, H. M. and Ganji, D. D., “Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method,” Nonlinear Anal. Real World Appl. 10(3), 1767–1774 (2009).CrossRefGoogle Scholar
Chebbi, A. H., Affi, Z. and Romdhane, L., “Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot,” Mech. Mach. Theory 44(9), 1768–1783 (2009).CrossRefGoogle Scholar
Tsai, L.-W. and Joshi, S., “Kinematic and optimization of a spatial 3-UPU parallel manipulator,” ASME J. Mech. Des. 122(4), 439–446 (1999).CrossRefGoogle Scholar
Ji, P. and Wu, H., “Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator,” Robot. Autonom. Syst. 42(2), 117–123 (2003).CrossRefGoogle Scholar
Rump, S. M., “INTLAB – INTerval LABoratory,” In:Developments in Reliable Computing (Csendes, T., ed.) (Kluwer Academic Publishers, Dordrecht, 1999) pp. 77–104.CrossRefGoogle Scholar
Chebbi, A. H., Chouaibi, Y., Affi, Z. and Romdhane, L., “Sensitivity analysis and prediction of the orientation error of a three translational parallel manipulator,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 232, 140–161 (2018).CrossRefGoogle Scholar
El Hraiech, S., Chebbi, A. H., Affi, Z. and Romdhane, L., “Error estimation and sensitivity analysis of the 3-UPU translational parallel robot due to design parameter uncertainties,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. DOI: 10.1177/0954406218793673.CrossRefGoogle Scholar
McCall, J., “Genetic algorithms for modelling and optimisation,” J. Computat. Appl. Math. 184(1), 205–222 (2005).CrossRefGoogle Scholar
Man, K. F., Tang, K. and Kwong, S., “Genetic algorithms: Concepts and applications,” IEEE Trans. Ind. Electron. 43(5), 519–534 (1996).CrossRefGoogle Scholar