Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T06:59:48.416Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-organizing approach for learning the forward kinematic multiple solutions of parallel manipulators

Published online by Cambridge University Press:  14 November 2011

Samy F. M. Assal
Samy F. M. Assal*
Affiliation:
Department of Production Engineering and Mechanical Design, Faculty of Engineering, Tanta University, Tanta, Egypt
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Contrary to the inverse kinematics, the forward kinematics of parallel manipulators involves solving highly non-linear equations and provides more than one feasible end-effector pose, which are called the assembly modes, for a given set of link lengths or joint angles. Out of the multiple feasible solutions, only one solution can be achieved from a certain initial configuration. Therefore, in this paper, the Kohonen's self-organizing map (SOM) is proposed to learn and classify the multiple solution branches of the forward kinematics and then provide a unique real-time solution among the assembly modes. Each solution of the multiple feasible ones is coded using IF-THEN rules based on the values of the passive joint variables. Due to not only the classification but also the associative memory learning abilities of the SOM, the passive joint variables vector, the end-effector pose vector, and this class code are associated with the active joint variables vector constituting the input vector to the SOM in the offline learning phase. In the online testing phase, only the active joint variables vector and the class code are fed to the SOM to obtain the unique end-effector pose vector. The Jacobian matrix calculated at the SOM output layer is used for further fine tuning this output to obtain an accurate end-effector pose vector. Simulations are conducted for 3-RPR and 3-RRR planar parallel manipulators to evaluate the performance of the proposed method. The results proved high accuracy of the desired unique solution in real-time.

Keywords

Parallel manipulatorsForward kinematicsMultiple solution branchesKohonen's self-organizing mapNeural networks
Type
Articles
Information
Robotica , Volume 30 , Issue 6 , October 2012 , pp. 951 - 961
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.Griffis, M., “A forward displacement analysis of a class of Stewart platforms,” J. Robot. Syst. 6 (6), 703–720 (1989).CrossRefGoogle Scholar
2.Husty, M. L., “An algorithm for solving the direct kinematics of general Stewart–Gough platforms,” Mech. Mach. Theory 31 (4), 365–380 (1996).CrossRefGoogle Scholar
3.Raghavan, M., “The Stewart platform of general geometry has 40 configurations,” ASME J. Mech. Des. 115, 277–282 (1993).CrossRefGoogle Scholar
4.Merlet, J.-P., “Direct kinematics of parallel manipulator,” IEEE Trans. Robot. Autom. 9, 842–846 (1993).CrossRefGoogle Scholar
5.Wang, Y., “A direct numerical solution to forward kinematics of general Stewart–Gough platforms,” Robotica 25 (1), 121–128 (2007).CrossRefGoogle Scholar
6.Merlet, J.-P., “Closed-Form Resolution of the Direct Kinematics of Parallel Manipulators Using Extra Sensors,” Proceedings of the IEEE International Conference on Robotics and Automation, Atlanta, USA (May 2–6, 1993) pp. 200–204.Google Scholar
7.Bonev, I. A., Ryu, J., Kim, S.-G. and Lee, S.-K., “A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors,” IEEE Trans. Robot. Autom. 17 (2), 148–156 (2001).CrossRefGoogle Scholar
8.Geng, Z. and Haynes, L. S., “Neural network solution for the forward kinematics problem of a Stewart platform,” Robot. Comput. Integr. Manuf. 9 (6), 485–495 (1992).Google Scholar
9.Boudreau, R., Levesque, G. and Darenfed, S., “Parallel manipulator kinematics learning using holographic neural network models,” Robot. Comput. Integr. Manuf. 14, 37–44 (1998).CrossRefGoogle Scholar
10.Sadjadian, H. and Taghirad, H. D., “Comparison of different methods for computing the forward kinematics of a redundant parallel manipulator,” J. Intell. Robot. Syst. 44, 225–246 (2005).CrossRefGoogle Scholar
11.Sadjadian, H., Taghirad, H. D. and Fatehi, A., “Neural networks approaches for computing the forward kinematics of a redundant parallel manipulator,” Int. J. Comput. Intell. 2 (1), 40–47 (2005).Google Scholar
12.Parikh, P. J. and Lam, S. S. Y., “A hybrid strategy to solve the forward kinematics problem in parallel manipulators,” IEEE Trans. Robot. 21 (1), 18–25 (2005).CrossRefGoogle Scholar
13.Yee, C. S. and Lim, K.-B., “Forward kinematics solution of Stewart platform using neural networks,” Neurocomputing 16 (4), 333–349 (1997).CrossRefGoogle Scholar
14.Parikh, P. J. and Lam, S. S. Y., “Solving the forward kinematics problem in parallel manipulators using an iterative artificial neural network strategy,” Int. J. Adv. Manuf. Technol. 40, 595–606 (2009).CrossRefGoogle Scholar
15.Jamwal, P. K., Xie, S. Q., Tsoi, Y. H. and Aw, K. C., “Forward kinematics modeling of a parallel ankle rehabilitation robot using modified fuzzy inference,” Mech. Mach. Theory 45, 1537–1554 (2010).CrossRefGoogle Scholar
16.Assal, S. F. M., “Intelligent System for the Forward Kinematics of Planar Parallel Manipulators,” Proceedings of the International Conference on Modeling, Simulation and Control, Cairo, Egypt (Nov. 2–4, 2010) pp. 164–168.Google Scholar
17.Walter, J. A. and Schulten, K. J., “Implementation of self-organizing networks for visuo-motor control of an industrial robot,” IEEE Trans. Neural Netw. 4 (1), 86–95 (1993).CrossRefGoogle ScholarPubMed
18.Araujo, A. F. R. and Barreto, G. A., “Context in temporal sequence processing: A self-organizing approach and its application to robotic,” IEEE Trans. Neural Netw. 13 (1)45–57 (2002).CrossRefGoogle Scholar
19.Bishop, C. M., Neural Networks for Pattern Recognition (Oxford University Press, Oxford, 1995) pp. 207–208.CrossRefGoogle Scholar
20.Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley & Sons, New York, 1999).Google Scholar
21.Merlet, J.-P., Parallel Robots (Kluwer Academic, Dordrecht, The Netherlands, 2006).Google Scholar
22.Rolland, L., “Synthesis on Forward Kinematics Problem algebraic modeling for the planar parallel manipulator, Part 2: Displacement-based equation systems,” Adv. Robot. 20 (9), 1035–1065 (2006).CrossRefGoogle Scholar
23.Jordan, M. I., “Computational Aspects of Motor Control and Motor Learning,” In: Handbook of Perception and Action: Motor Skills (Heuer, H. and Keele, S. W., eds.) (Academic Press, New York, 1996) vol. 2, pp. 71–120.Google Scholar
24.Haykin, S., Neural Networks: A Comprehensive Foundation (Macmillan, New York, 1994).Google Scholar
25.Merlet, J.-P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33 (1), 7–20 (1998).CrossRefGoogle Scholar
26.Kiviluoto, K., “Topology Preservation in Self-Organizing Maps,” Proceedings of the IEEE International Conference on Neural Networks, Washington, DC, USA (Jun. 3–6, 1996) vol. 1, pp. 294–299.Google Scholar
27.Uriarte, E. A. and Martin, F. D., “Topology preservation in SOM,” Int. J. Appl. Math. Comput. Sci. 1 (1), 19–22 (2005).Google Scholar
28.Hasan, A. T., Ismail, N., Hamouda, A. M. S., Aris, I., Marhaban, M. H. and Al-Assadi, H. M. A. A., “Artificial neural network-based kinematics Jacobian solution for serial manipulator passing through singular configurations,” Adv. Eng. Softw. 41, 359–367 (2010).CrossRefGoogle Scholar
29.Cherif, A. R., “Toward autonomic computing: Adaptive neural network for trajectory planning,” Int. J. Cogn. Inform. Neural Intell. 1 (2), 16–23 (2007).CrossRefGoogle Scholar