Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T06:58:32.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiobjective optimization of parallel kinematic mechanisms by the genetic algorithms

Published online by Cambridge University Press:  30 September 2011

Ridha Kelaiaia ,
Olivier Company  and
Abdelouahab Zaatri
Ridha Kelaiaia*
Affiliation:
Department of Mechanical Engineering, Faculty of Technology, Skikda University, Algeria LIRMM UMR 5506 CNRS–UM2, 161 rue Ada, 34392 Montpellier Cedex 5, France
Olivier Company
Affiliation:
LIRMM UMR 5506 CNRS–UM2, 161 rue Ada, 34392 Montpellier Cedex 5, France
Abdelouahab Zaatri
Affiliation:
Laboratory of Advanced Technologies, University of Constantine, Algeria
*
*Corresponding author. E-mail: Ridha.kelaiaia@lirmm.fr
Get access Rights & Permissions [Opens in a new window]

Summary

It is well known that Parallel Kinematic Mechanisms (PKMs) have an intrinsic dynamic potential (very high speed and acceleration) with high precision and high stiffness. Nevertheless, the choice of optimal dimensions that provide the best performances remains a difficult task, since performances strongly depend on dimensions. On the other hand, there are many criteria of performance that must be taken into account for dimensional synthesis, and which are sometimes antagonist. This paper presents an approach of multiobjective optimization for PKMs that takes into account several criteria of performance simultaneously that have a direct impact on the dimensional synthesis of PKMs. We first present some criteria of performance such as the workspace, transmission speeds, stiffness, dexterity, precision, as well as dynamic dexterity. Secondly, we present the problem of dimensional synthesis, which will be defined as a multiobjective optimization problem. The method of genetic algorithms is used to solve this type of multiobjective optimization problem by means of NSGA-II and SPEA-II algorithms. Finally, based on a linear Delta architecture, we present an illustrative application of this methodology to a 3-axis machine tool in the context of manufacturing of automotive parts.

Keywords

Parallel robotsParallel kinematic machine toolCriteria of performanceMultiobjective optimizationGenetic algorithms NSGA-II and SPEA-II
Type
Articles
Information
Robotica , Volume 30 , Issue 5 , September 2012 , pp. 783 - 797
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.J.-P., Merlet, Parallel Robots, 2nd ed. (Springer, Heidelberg, Germany, 2006).Google Scholar
2.J.-P., Merlet, “Designing a parallel manipulator for a specific workspace,” Int. J. Robot. Res. 16 (4), 545–556 (1997).Google Scholar
3.Schönherr, J., “Evaluation and Optimum Design of Parallel Manipulators Having Defined Workspace,” In: Proceedings of the DECTC, Baltimore, Maryland (Sep. 10–13, 2000) pp. 1–9.Google Scholar
4.Gosselin, C. and Angeles, J., “The optimum kinematic design of a planar three-degree-of-freedom parallel manipulator,” ASME J. Mech. Transm. Autom. Des. 110, 35–41 (Mar. 1988).CrossRefGoogle Scholar
5.Gosselin, C. and Lavoie, E., “On the kinematic design of spherical three-degree-of-freedom parallel manipulator,” Int. J. Robot. Res. 12 (4), 394–402 (Aug. 1993).CrossRefGoogle Scholar
6.Boudreau, R. and Gosselin, C., “La synthèse d'une plate-forme de Gough-Stewart pour un espace atteignable prescrit,” Mech. Mach. Theory 36, 327–342 (2001).CrossRefGoogle Scholar
7.Majoux, F., “Analyse cinétostatique des machines parallèles à translation,” Thèse de Doctorat (Ecole centrale de Nante, France, Nov. 2004).Google Scholar
8.Zanganeh, K. E. and Angeles, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res. 16 (2), 185–197 (1997).CrossRefGoogle Scholar
9.Yoshikawa, T., Foundations of Robotics: Analysis and Control (MIT Press, Cambridge, MA, 1990).Google Scholar
10.Yoshikawa, T., “Manipulability of robotic mechanism,” Int. J. Robot. Res. 4 (2), 3–9 (1985).CrossRefGoogle Scholar
11.Gosselin, C. and Angeles, J., “Singularly analysis of closed loop kinematic chains,” ASME J. Mech. Des. 112 (3), 331–336 (1990).CrossRefGoogle Scholar
12.Gosselin, C. and Angeles, J., “A Global performance index for the kinematic optimisation of robotic manipulators,” J. Mech. Des. 113, 220–226 (Sep. 1991).CrossRefGoogle Scholar
13.Pittens, K. H. and Podhorodeski, R., “A family of platforms with optimal dexterity,” J. Robot. Syst. 10 (4), 463–479 (1993).CrossRefGoogle Scholar
14.Jinsong, W. and Xiaoqiang, T., “Analysis and dimensional design of a novel hybrid machine tool,” Int. J. Mach. Tools Manuf. 43, 647–655 (2003).Google Scholar
15.Bhattacharya, S., Htval, H. and Gosh, A., “On the optimum design of Stewart platform type parallel manipulator,” Robotica 13, 133–140 (1995).CrossRefGoogle Scholar
16.Han, C.-S., Tesar, D. and Traver, A. “The Optimum Design of a 6 DOF Fully Parallel Micromanipulator for Enhanced Robot Accuracy,” In: Proceedings of ASME Design Automation Conference, Montréal (Sep. 17–20, 1989), pp. 357–363.Google Scholar
17.Ryu, J. and Cha, J. “Volumetric error analysis and architecture optimization for accuracy of HexaSlide type parallel manipulators,” Mech. Mach. Theory, 38 (3), 227–240 (2003).CrossRefGoogle Scholar
18.Wang, J. and Masory, O., “On the Accuracy of a Stewart Platform – Part I. The Effect of Manufacturing Tolerances,” In: Proceedings of the IEEE International Conference on Robotics Automation, Atlanta, Georgia (May 1993) pp. 114–120.Google Scholar
19.Patel, A. J. and Ehmann, K. F., “Volumetric error of a Stewart platform-based machine tool,” Ann. CIRP 46, 287–290 (1997).CrossRefGoogle Scholar
20.Ma, O. and Angeles, J., “Optimal Design of Manipulator under Dynamic Isotropy Conditions,” In: Proceeding of the IEEE International Conference on Robotics and Automation, Atlanta Georgia (May 1993) pp. 470–475.Google Scholar
21.Asada, H., “A geometrical representation of manipulator dynamics and its application to arm design,” ASME J. Dyn. Sys. Meas. Control 105, 131–135, 142 (1983).CrossRefGoogle Scholar
22.Toumi, Y. and Asada, H., “The Design of Arm Linkages with Decoupled and Configuration Invariant Inertia Tensors – Part I and II,” In: Proceedings of the ASME Winter Annual Meeting, Robotics and Manufacturing Automation Symposium, Wam, Miami (Nov. 1985) pp. 145–161.Google Scholar
23.Yang, D. C. H and Tzeng, S. W., “Simplification and linearization of manipulator dynamics by the design of inertia distribution,” Int. J. Robot. Res. 5 (3), 120–128 (1986).CrossRefGoogle Scholar
24.Yoshikawa, T., “Dynamic manipulability of robot manipulators,” Int. J. Robot. Res. 2 (1), 113–124 (1985).Google Scholar
25.Stock, M. and Miller, K., “Optimal kinematic design of spatial parallel manipulator: Application to linear delta robot,” ASME J. Mech. Des. 125, 292–301 (June 2003).CrossRefGoogle Scholar
26.Zhang, D., Xu, Z., Mechefske, C. M. and Xi, F., “Design Optimization of Parallel Kinematic Toolheads with Genetic Algorithms,” 3rd Parallel Kinematic Seminar, PKS International Conference, Chemnitz, Germany (Apr. 23–25, 2002).Google Scholar
27.Klein, C. A. and Blaho, B. E., “Dexterity measures for the design and control of kinematically redundant manipulators,” Int. J. Robot. Res. 6 (2), 72–83 (1987).CrossRefGoogle Scholar
28.Kurtz, R. and Hayward, V., “Multiple-goal kinematic optimization of a parallel spherical mechanism with actuator redundancy,” IEEE Trans. Robot. Autom. 8 (5), 644–651 (1992).CrossRefGoogle Scholar
29.Ma, O. and Angeles, J., “Optimum Architecture Design of Platform Manipulator,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Nice, France (May 1991) pp. 1131–1135.Google Scholar
30.Zanganeh, K. E. and Angeles, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res. 16 (2), 185–197 (1997).CrossRefGoogle Scholar
31.Chablat, D., Wenger, P., Majoux, F. and Merlet, J.-P., “An interval analysis based study for the design and the comparison of 3-DOF parallel kinematic machines,” Int. J. Robot. Res. 23 (6), 615–624 (2004).CrossRefGoogle Scholar
32.Julius, K., Steve, S., Allington, J., Bobrow, J.-E. and Reinkensmeyer, D.-J., “Optimization of a parallel shoulder mechanism to achieve a high-force, low-mass, robotic-arm exoskeleton,” IEEE Trans. Robot. 26 (4), 710–715 (2010).Google Scholar
33.Pritschow, G., Wurst, K. -H. “Systematic design of hexapods and other parallel link systems,” Ann. CIRP 46 (1), 291–295 (1997).CrossRefGoogle Scholar
34.Company, O. and Pierrot, F., “Modelling and design issues of a 3-axis parallel machine-tools,” Mech. Mach. Theory 37, 1325–1345 (2002).CrossRefGoogle Scholar
35.Huang, T., Whitehouse, D. J. and Jinsong, W., “The local dexterity, optimal architecture and design criteria of parallel machine tools,” Ann. CIRP 47 (1) (1998).CrossRefGoogle Scholar
36.Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 2nd ed. (Springer-Verlag, Heidelberg, Germany, 2003).CrossRefGoogle Scholar
37.Koteswara, A. B., Rao, P. V. M. and Saha, K., “Workspace and Dexterity Analyses of Hexaslide Machine Tools,” Proceedings of the IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sep. 14–19, 2003).Google Scholar
38.Wang, J., Wu, C. and Liu, X.-J., “Performance evaluation of parallel manipulators: Motion/force transmissibility and its index,” Mech. Mach. Theory 45 (10), 1462–1476 (2010)CrossRefGoogle Scholar
39.Lewis, F. L., Abdallah, C. T. and Dawson, D. M., Control of Robot Manipulators (Macmillan, New York, 1993).Google Scholar
40.Codourey, A., “Dynamic modeling of parallel robots for computed-torque control implementation,” Int. J. Robot. Res. 17 (2), 1325–1336 (1998).CrossRefGoogle Scholar
41.Wu, J., Jinsong, W., Tiemin, L., Wang, L. and Guan, L., “Dynamic dexterity of a planar 2-DOF parallel manipulator in a hybrid machine tool,” Robotica 26, 93–98 (2008).CrossRefGoogle Scholar
42.Yunjiang, L., “Optimal Design of Parallel Manipulators,” Ph.D. Thesis (Hong Kong University of Science and Technology, Hong Kong, 2006).Google Scholar
43.Deb, K., Agrawal, S., Pratap, A. and Meyarivan, T., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput. 6 (2), 182–197 (2002).CrossRefGoogle Scholar
44.Zitzler, E., Laumanns, M. and Thiele, L., “Spea2: Improving the Strength Pareto Evolutionary Algorithm,” Technical Report 103 (Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland, 2001).Google Scholar