Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T16:30:10.812Z Has data issue: false hasContentIssue false
  • English
  • Français

Neuro-fuzzy adaptive control of a revolute stewart platform carrying payloads of unknown inertia

Published online by Cambridge University Press:  22 May 2014

Mojtaba Eftekhari ,
Mahdi Eftekhari  and
Hossein Karimpour
Mojtaba Eftekhari
Affiliation:
Department of Mechanical Engineering, School of Engineering, Shahid Bahonar University of Kerman, Iran
Mahdi Eftekhari
Affiliation:
Department of Computer Engineering, School of Engineering, Shahid Bahonar University of Kerman, Iran
Hossein Karimpour*
Affiliation:
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran
*
*Corresponding author. E-mail: karimpour@iaukhsh.ac.ir
Get access Rights & Permissions [Opens in a new window]

Summary

In this research, a Stewart parallel platform with rotary actuators is simulated and a prototype is tested under different operative conditions. The purpose is to make the robot robust against inertia variations considering the fact that different payloads of unknown size may be transported. Due to the complexity issued by expressing the equations of motion with independent variables, the governing equations are derived by Lagrange's method using Lagrange multipliers for imposing the kinematic constraints imposed on this parallel robot. Eliminating Lagrange multipliers by projecting the equations onto the orthogonal complement of the space of constraints, the equations of motion are transformed to a reduced form suitable for the purpose of controller design. The control approach considered here is based on a neuro-fuzzy interference method. As a first step, each revolute arm link are individually trained under different loadings and diverse maneuvers. It is purposed that once employed together, the links will have learned how to collaborate with each others for performing a common task. Training data are divided to several clusters by using a subtractive clustering algorithm. For every cluster, a fuzzy rule is derived so that the output follows the desired trajectory. In the last stage, these rules are employed by utilizing back propagation algorithms and the effectiveness of the neuro-fuzzy system becomes approved by performing multiple maneuvers and its robustness is checked under various inertia loads. The controller has ultimately been implemented on a prototype of the Stewart mechanism in order to analyze the reliability and feasibility of the method.

Keywords

Stewart platformUnknown inertia payloadNeuro-Fuzzy control
Type
Articles
Information
Robotica , Volume 33 , Issue 9 , November 2015 , pp. 2001 - 2024
Copyright
Copyright © Cambridge University Press 2014 

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. Stewart, D., “A platform with 6 degrees of freedom,” Proc. Inst. Mech. Eng. 180 (15), 371–386 (1965).Google Scholar
2. Singh, R. P. and Linkins, P. W., “Singular value decomposition for constrainted dynamical system,” J. Appl. Mech. 52, 943–948 (1985).Google Scholar
3. Zhang, D. and Gosselin, C. M., “Kinetostatic modeling of parallel mechanisms with a passive constraining leg and revolute actuators,”, Mech. Mach. Theory 37, 599–617 (2002).Google Scholar
4. Rao, N. M. and Rao, K. M., “Dimensional synthesis of a spatial 3-RPS parallel manipulator for a prescribed range of motion of spherical joints,” Mech. Mach. Theory 44, 477–486 (2009).Google Scholar
5. Huiping, S., Tingli, Y., Lv-zhong, M., “Synthesis and structure analysis of kinematic structures of 6-dof parallel robotic mechanisms,” Mech. Mach. Theory 40, 1164–1180 (2005).Google Scholar
6. Leggs, T. H., “A proposal new design for a large radio telescope,” Astron. Astrophys. Suppl. 130, 369–379 (1998).Google Scholar
7. Dasgupta, B. and Mruthyunjaya, T. S., “The Stewart platform manipulator”: A review,” Mech. Mach. Theory 35 (1), 15–40 (2000).Google Scholar
8. Yan Jin, A., Chen, I-M. and Yang, G., “Kinematic design of a family of 6-DOF partially decoupled parallel manipulators,” Mech. Mach. Theory 44, 912–922 (2009).Google Scholar
9. Wu, J., Li, T., Wang, J. and Wang, L. “Stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates,” Robot. Auton. Syst. 61 (8), 868–875 (2013).Google Scholar
10. Wu, J., Li, T., Wang, J. and Wang, L., “Performance analysis and comparison of planar 3-DOF parallel manipulators with one and two additional branches,” J. Intell. Robot. Syst. 72 (1), 73–82 (2013).Google Scholar
11. Staicu, S. and Zhang, D., “A novel dynamic modelling approach for parallel mechanisms analysis,” Robot. Comput.-Integr. Manuf. 24 (1), 167–72 (2008).Google Scholar
12. Staicu, S., “Recursive modelling in dynamics of Agile Wrist spherical parallel robot,” Robot. Comput.-Integr. Manuf. 25, 409–416 (2009).Google Scholar
13. Staticu, S., “Dynamics of the 6-6 Stewart parallel manipulator,” Robot. Comput.-Integr. Manuf. 27, 212–220 (2011).Google Scholar
14. Zhao, Y. and Gao, F., “Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work,” Robotica 27, 259–268 (2009).Google Scholar
15. Enferadi, J. and Akbarzadeh Tootoonchi, A., “Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work,” Nonlinear Dyn. 61, 419–434 (2010).Google Scholar
16. Yangmin, L. and Staicu, S., “Inverse dynamic of a 3-PRC parallel kinematic machine,” Nonlinear Dyn. 67, 1031–1041 (2012).Google Scholar
17. Abdellatif, H. and Heimann, B., “Computational efficient inverse dynamics of 6-DOF fully parallel manipulator by using the Lagrangian formalism,” Mach. Mach. Theory 44 (1), 192–207 (2009).Google Scholar
18. Yang, C., Huang, Q., Jiang, H., Peter, O. O. and Han, J., “PD control with gravity compensation for hydraulic 6-DOF parallel manipulator,” Mech. Mach. Theory 45 (4), 666–677 (2010).Google Scholar
19. Su, Y. X., Sun, D., Ren, L., Wang, X. and Mills, J. K., “Nonlinear PD Synchronized Control for Parallel Manipulators,” In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation (2005) pp. 1374–1379.Google Scholar
20. Su, Y. X., Sun, D., Ren, L., Wang, X. and Mills, J. K., “Robust nonlinear task space control for 6 DOF parallel manipulator,” Automatica 41 (9), 1591–1600 (2005).Google Scholar
21. Su, Y. X., Duan, B. Y. and Zheng, C. H., “Nonlinear PID control of a six-DOF parallel manipulator,” IEE Proc. 151 (1), 95–102 (2004).Google Scholar
22. Wu, J., Wang, J., Wang, L. and Li, T., “Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy,” Mech. Mach. Theory 44 (4), 835–849 (2009).Google Scholar
23. Stan, S., Manic, M., Maties, M. and Balan, R., “Kinematics Analysis, Design, and Control of an Isoglide3 Parallel Robot (ig3pr)”, In: Proceedings of the 34th Annual Conference of the IEEE Industrial Electronics Society (2008) pp. 1265–1275.Google Scholar
24. Shang, W. and Cong, S., “Nonlinear computed torque control for a high-speed planar parallel manipulator,” Mechatronics 19 (6) (2009) pp. 987–992.Google Scholar
25. Yang, C., Hung, Q. and Han, J., “Computed force and velocity control for spatial multi-DOF electro-hydraulic parallel manipulator,” Mechatronics 22 (6), 715–722 (2012).Google Scholar
26. Pi, Y. and Wang, X., “Trajectory tracking control of a 6 DOF parallel manipulator with uncertain load disturbances,” Control Eng. Pract. 19 (2), 185–193 (2011).Google Scholar
27. Guo, H., Liu, Y. G., Liu, G. and Li, H., “Cascade contol of a hydraulically driven 6-DOF parallel robot manipulator based on a sliding mode,” Control Eng. Pract. 16 (9), 1055–1068 (2008).Google Scholar
28. Davliakos, I. and Papadopoulos, E., “Model-based control of a 6-dof electrohydraulic Stewart–Gough platform,” Mech. Mach. Theory 43 (11), 1385–1400 (2008).Google Scholar
29. Dongsu, W. and Hongbin, G., “Adaptive sliding control of six-DOF flight simulator motion platform,” Chin. J. Aeronaut. 20 (5), 425–433 (2007).Google Scholar
30. Zhu, X., Tao, G., Yao, B. and Cao, J., “Adaptive robust posture control of a parallel manipulator driven by pneumatic muscles,” Automatica 44 (9), 2248–2257 (2008).Google Scholar
31. Honegger, M., “Adaptive Control of the Hexaglide, A 6-DOF Parallel Manipulator,” Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque (1997) pp. 543–548.Google Scholar
32. Shang, W. W., Cong, S. and Ge, Y., “Adaptive computed torque control for a parallel manipulator with redundant actuation,” Robotica 30 (3), 457–466 (2012).Google Scholar
33. Shang, W. W., Cong, S. and Ge, Y., “Coordination motion control in the task space for parallel manipulators with actuation redundancy,” IEEE Trans. Autom. Sci. Eng. 10 (3), 665–673 (2013).Google Scholar
34. Theodoridis, D. C., Boutalis, Y. S. and Christodoulou, M. A., “A new adaptive neuro-fuzzy controller for trajectory tracking of robot manipulators,” Int. J. Robot. Autom. 26 (1), 64–75 (2011).Google Scholar
35. Craig, J. J., Introduction to Robotics Mechanics and Control, 2nd ed. (Addission – Weslay Publishing Company, 1989).Google Scholar
36. Singh, R. P. and Linkins, P. W., “Singular value decomposition for constrained dynamical system,” J. Appl. Mech. 52, 943–948 (1985).Google Scholar
37. Nikravesh, P. E. and Haung, E. J., “Generalized coordinate partitioning for analysis of mechanical systems with nonholomic constraint,” J. Mech. Transm. Autom. Des. 105, 183–188 (1983).Google Scholar
38. Jang, R. J.-S., Sun, C.-T. and Mizutani, E., Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence (Prentice Hall, Inc., Upper Saddle River, NJ 1997).Google Scholar
39. Chiu, S., “Fuzzy model identification based on cluster estimation,” J. Intell. Fuzzy Syst. 2 (3), 267–278 (1994).Google Scholar
40. Xu, H. Y., Wang, G. Z. and Baird, C. B., “A fuzzy neural networks technique with fast backpropagation learning,” Int. Joint Conference on Neural Networks, IJCNN 1, 214–219 (1992).Google Scholar