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The forward kinematics of the 6-6 parallel manipulator using an evolutionary algorithm based on generalized generation gap with parent-centric crossover

Published online by Cambridge University Press:  19 June 2014

Luc Rolland  and
Rohitash Chandra
Luc Rolland*
Affiliation:
Memorial University, Faculty of Engineering, St-John's, Canada
Rohitash Chandra
Affiliation:
School of Computing, Information and Mathematical Sciences, University of the South Pacific, Fiji
*
*Corresponding author. Email: [email protected], [email protected]
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Summary

In this paper, a fast and efficient evolutional algorithm, called the G3-PCX has been implemented to solve the forward kinematics problem (FKP) of the general parallel manipulators being modeled by the 6-6 hexapod, constituted by a fixed and mobile platforms being non planar and non-symmetrical. The two platforms are connected by six linear actuators, each of which is located between one ball joint and one universal joint. Forward kinematics are formulated using Inverse Kinematics applying one position based equation system which is converted into an objective function by expressing the sum of squared error on kinematics chain lengths and mobile platform distances. In less than one second, the 16 unique real solutions are computed with improved accuracy when compared to previous methods.

Keywords

Parallel robotForward kinematicsPosition based modelGenetic algorithmsG3-PCX
Type
Articles
Information
Robotica , Volume 34 , Issue 1 , January 2016 , pp. 1 - 22
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Boudreau, R. and Turkkan, N., “Solving the forward kinematics of parallel manipulators with a genetic algorithm,” J. Robotic Systems 13 (2), 111–125 (1996).3.0.CO;2-W>CrossRefGoogle Scholar
2.Capi, G. and Doya, K., “Evolution of recurrent neural controllers using an extended parallel genetic algorithm,” Robot. Auton. Syst. 52 (2–3), 148–159 (2005).CrossRefGoogle Scholar
3.Chandra, R. and Rolland, L., “Hybrid meta-heuristics for the forward kinematics of 3-rpr planar parallel manipulator,” Appl. Math. Comput. (2011).Google Scholar
4.Chandra, R. and Rolland, L., “Hybrid meta-heuristics for the forward kinematics of 3-RPR planar parallel manipulator,” Appl. Math. Comput. 217 (22):8997–9008, 2011.Google Scholar
5.Dietmaier, P., “The stewart-gough platform of general geometry can have 40 real postures,” Adv. Robot Kinematics 1, 7–16 (1998).CrossRefGoogle Scholar
6.Parrish, R., Dieudonné, E. and Bardusch, R., An actuator extension transormation for a motion simulator and an inverse transformation applying newton-raphson's method. Technical Report D-7067 (NASA, Washington, 1972).Google Scholar
7.Omran, A., et al. “Genetic algorithm based optimal control for a 6-dof non redundant stewart manipulator,” Int. J. Mech. Syst. Sci. Eng. 2 (2), 73–79 (2008).Google Scholar
8.Garcia-Martinez, C., et al. “Global and local real-coded genetic algorithms based on parent-centric crossover operators,” Eur. J. Oper. Res. 185 (3), 1088–1113 (2008).CrossRefGoogle Scholar
9.Schaffer, J. D., et al. “A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization,” Proceedings of the Third International Conference on Genetic Algorithms, San Francisco, CA, USA (Morgan Kaufmann Publishers Inc., 1989) pp. 51–60.Google Scholar
10.Lozano, M., et al.Real-coded memetic algorithms with crossover hill-climbing. Evolutionary Computation 12 (3), 273–302 (2004).CrossRefGoogle ScholarPubMed
11.Sheng, et al. “Forward Kinematics of the Stewart Platform Using Hybrid Immune Genetic Algorithm,” Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation (Jun. 2006) pp. 2330–2335.CrossRefGoogle Scholar
12.Jason, T., et al. “Harnessing Mutational Diversity at Multiple Levels for Improving Optimization Accuracy in g3-pcx,” Proceedings of the IEEE Congress on Evolutionary Computation, IEEE (2007) pp. 4502–4507.Google Scholar
13.Gough, V. E. and Whitehall, S. G., “Universal Tyre Test Machine,” Proceedings of 9th International Technical Congress FISITA, Mai (1962), pp. 117–135.Google Scholar
14.Hansen, N. and Ostermeier, A., “Completely derandomized self-adaptation in evolution strategies,” Evol. Comput. 9 (2), 159–195 (2001).CrossRefGoogle ScholarPubMed
15.Holland, J. H., Adaptation in Natural and Artificial Systems (MIT Press, Cambridge, MA, USA, 1992).CrossRefGoogle Scholar
16.Husty, M., “An algorithm for solving the direct kinematic of stewart-gough-type platforms,” J. Mech. Mach. Theory 31 (4), 365–379 (1996).CrossRefGoogle Scholar
17.Anand, A., Deb, K. and Joshi, D., “A computationally efficient evolutionary algorithm for real-parameter optimization,” Evol. Comput. 10 (4), 371–395 (2002).Google Scholar
18.Lazard, D., “On the representation of rigid-body motions and its application to generalized platform manipulators,” Comput. Kinematics 1, 175–181 (1993).CrossRefGoogle Scholar
19.Lazard, D., “On the representation of rigid-body motions and its application to generalized platform manipulators,” J. Comput. Kinematics 1 (1), 175–182 (1993).CrossRefGoogle Scholar
20.MacCallion, H. and Pham, D. T., “The Analysis of a Six Dof Workstation for Mechanized Assembly,” Proceedings of the 5th World Congress on Theory of Machines and Mechanisms (1979) pp. 611–616. Montréal.Google Scholar
21.Merlet, J. P.. Les Robots parallèles, 2nd ed. (Robotique. Hermès, Paris, traité des nouvelles technologies edition, 1997).Google Scholar
22.Merlet, J. P., “Solving the forward kinematics of a gough-type parallel manipulator with interval analysis,” Int. J. Robot. Res. 23 (3), 221–235 (Mar. 2004).CrossRefGoogle Scholar
23.Mitchell, M., An Introduction to Genetic Algorithms.Google Scholar
24.Mourrain, B., “The 40 Generic Positions of a Parallel Robot,” Proceedings of the ISSAC'93 (1993) pp. 173–182.Google Scholar
25.Darenfed, S., Boudreau, R. and Turkkan, N., “étude comparative de trois nouvelles approches pour la résolution du problème géométrique direct des manipulateurs parallèles,” J. Mech. Mach. Theory 33 (5), 463–477 (1998).Google Scholar
26.Raghavan, M., “The stewart platform of general geometry has 40 configurations,” J. Mech. Design, Trans ASME 115 (2), 277–282 (1993).CrossRefGoogle Scholar
27.Raghavan, M. and Roth, B., “Solving polynomial systems for the kinematic analysis and synthesis of mechanisms and robot manipulators,” Trans. ASME 117, 71–79 (June 1995).CrossRefGoogle Scholar
28.Rolland, L., “Certified solving of the forward kinematics problem with an exact method for the general parallel manipulator,” Adv. Robot. 19 (9), 995–1025 (2005).CrossRefGoogle Scholar
29.Rolland, L., “Certified Solving and Synthesis on Modeling of the Kinematics Problems of Gough-Type Parallel Manipulators with an Exact Algebraic Method,” In: Parallel Manipulators, Towards New Applications (I-Tech Education and Publishing, 2008).Google Scholar
30.Rolland, L. and Chandra, R., “Forward Kinematics of the 6-6 General Parallel Manipulator Using Real Coded Genetic Algorithms,” Proceedings of the IEEE/ASME Conference on Advanced Intelligent Mechatronics (AIM 2009), page In Press (2009).CrossRefGoogle Scholar
31.Rolland, L. and Chandra, R., The Application of an Efficient Evolutionary Algorithm in Solving the Forward Kinematics of 6-6 General Parallel Manipulator., volume 524 of CISM International Centre for Mechanical Sciences, (Springer, Berlin, 2010) pp. 117–124. ROMANSY 18 - Robot Design, Dynamics and Control.Google Scholar
32.Ronga, F. and Vust, T., “Stewart Platforms Without Computer?,” Proceedings of the International Conference on Real, Analytic and Algebraic Geometry (1992) pp. 197–212.Google Scholar
33.Selig, J. M., Introductory Robotics (Prentice-Hall, Hemel Hemstead, 1992) pp. 157.Google Scholar
34.Stewart, D., “A platform with 6 degrees of freedom,” Proceedings of the Institution of Mechanical Engineers 180, 371–386 (1965).CrossRefGoogle Scholar
35.Altazurra, O., Petuya, V., Alonso, A. and Hernandez, A., “Resolution of the Direct Position Problem of the Parallel Kinematic Platforms Using the Geometric-Iterative Method,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona (2005) pp. 3255–3260.Google Scholar
36.Wampler, C. W., “Forward displacement analysis of general six-in-parallel sps (stewart) platform manipulators using soma coordinates,” Mech. Mach. Theory 31 (3), 331–337 (1996).CrossRefGoogle Scholar
37.Wright, A. H., “Genetic Algorithms for Real Parameter Optimization,” In: Foundations of Genetic Algorithms (Morgan Kaufmann, 1991) pp. 205–218.Google Scholar
38.Hao, M., Wang, X. and Cheng, Y., “On the use of differential evolution for forward kinematics of parallel manipulators,” Appl. Math. Comput. 205 (2), 760–769 (2008).Google Scholar