International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Modeling, Identification and Control of a Redundant Planar 2-DOF Parallel Manipulator

  • Zhang, Yao-Xin (Department of Automation, University of Science and Technology of China) ;
  • Cong, Shuang (Department of Automation, University of Science and Technology of China) ;
  • Shang, Wei-Wei (Department of Automation, University of Science and Technology of China) ;
  • Li, Ze-Xiang (Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology) ;
  • Jiang, Shi-Long (Googol Technology(Shenzhen) LTD)
  • Published : 2007.10.31
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Abstract

In this paper, the dynamic controller design problem of a redundant planar 2-dof parallel manipulator is studied. Using the Euler-Lagrange equation, we formulate the dynamic model of the parallel manipulator in the joint space and propose an augmented PD controller with forward dynamic compensation for the parallel manipulator. By formulating the controller in the joint space, we eliminate the complex computation of the Jacobian matrix of joint angles with end-effector coordinate. So with less computation, our controller is easier to implement, and a shorter sampling period can be achieved, which makes the controller more suitable for high-speed motion control. Furthermore, with the combination of static friction model and viscous friction model, the active joint friction of the parallel manipulator is studied and compensated in the controller. Based on the dynamic parameters of the parallel manipulator evaluated by direct measurement and identification, motion control experiments are implemented. With the experiments, the validity of the dynamic model is proved and the performance of the controller is evaluated. Experiment results show that, with forward dynamic compensation, the augmented PD controller can improve the tracking performance of the parallel manipulator over the simple PD controller.

Keywords

References

  1. F. X. Wu, W. J. Zhang, Q. Li, and P. R. Ouyang, 'Integrated design and PD control of high-speed closed-loop mechanisms,' ASME Journal of Dynamic Systems, Measurement, and Control, vol. 124, no. 4, pp. 522-528, 2002 https://doi.org/10.1115/1.1513179
  2. F. H. Ghorbel, O. Chetelat, R. Gunawardana, and R. Longchamp, 'Modeling and set point control of closed-chain mechanisms: Theory and experiment,' IEEE Trans. on Control Systems Technology, vol. 8, no. 5, pp. 801-815, 2000 https://doi.org/10.1109/87.865853
  3. F. Ghorbel and R. Gunawardana, 'A validation study of PD control of a closed-chain mechanical system,' Proc. of the 36th IEEE Conference on Decision and Control, vol. 2, pp. 1998-2004, 1997
  4. Y. K. Yiu and Z. X. Li, 'PID and adaptive robust control of a 2-dof over-actuated parallel manipulator for tracking different trajectory,' Proc. of the IEEE International Symposium on Computational Intelligence in Robotics and Automation, vol. 3, pp. 1052-1057, July 16-20, 2003
  5. P. R. Ouyang, W. J. Zhang, and F. X. Wu, 'Nonlinear PD control for trajectory tracking with consideration of the design for control methodology,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 4126-4131, May 2002
  6. Y. X. Su, D. Sun, and C. H. Zheng, 'Nonlinear trajectory tracking control of a closed-chain manipulator,' Proc. of the 5th World Congress on Intelligent Control and Automation, pp. 5012- 5016, June 15-19, 2004
  7. P. Begon, F. Pierrot, and P. Dauchez, 'Fuzzy sliding mode control of a fast robot,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 1178-1183, 1995
  8. I. F. Chung, H. H. Chang, and C. T. Lin, 'Fuzzy control of a six-degree motion platform with stability analysis,' Proc. of the IEEE International Conference on Systems, Man, and Cybernetics, vol. 1, pp. 325-330, 1999
  9. C. Pernechele, F. Bortoletto, and E. Giro, 'Neural network algorithm controlling a hexapod platform,' Proc. of the IEEE-INNSENNS International Joint Conference on Neural Networks, vol. 4, pp. 349-352, 2000
  10. Y. X. Su, D. Sun, L. Ren, and J. K. Mills, 'Integration of saturated PI synchronous control and PD feedback for control of parallel manipulators,' IEEE Trans. on Robotics, vol. 22, no. 1, pp. 202-207, 2006 https://doi.org/10.1109/TRO.2005.858852
  11. S. H. Lee, J. B. Song, W. C. Choi, and D. Hong, 'Controller design for a Stewart platform using small workspace characteristics,' Proc. of the IEEE International Conference on Intelligent Robots and Systems, vol. 4, pp. 2184-2189, 2001
  12. S. Cherdchoosilpa, S. Kuntanapreeda, and N. Chaiyaratana, 'MIMO controller design for a parallel manipulator system: A practitioner's approach,' Proc. of the IEEE International Conference on Industrial Technology, vol. 2, pp. 673-677, 2002
  13. S. H. Lee, J. B. Song, W. C. Choi, and D. Hong, 'Position control of a Stewart paltform using inverse dynamics control with approximate dynamics,' Mechatronics, vol. 13, no. 6, pp. 605-619, 2003 https://doi.org/10.1016/S0957-4158(02)00033-8
  14. L. Beji, A. Abichou and M. Pascal, 'Tracking control of a parallel robot in the task space,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 3, pp. 2309-2314, 1998
  15. G. F. Liu, Y. L. Wu, X. Z. Wu, Y. Y. Kuen, and Z. X. Li, 'Analysis and control of redundant parallel manipulators,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 3748-3754, 2001
  16. H. Cheng, Y. K. Yiu, and Z. X. Li, 'Dynamics and control of redundantly actuated parallel manipulators,' IEEE Trans. on Mechatronics, vol. 8, no. 4, pp. 483-491, 2003 https://doi.org/10.1109/TMECH.2003.820006
  17. M. W. Walker, 'Adaptive control of manipulator containing closed kinematic loops,' IEEE Trans. on Robotics and Automations, vol. 6, no. 1, pp. 10-19, 1990 https://doi.org/10.1109/70.88113
  18. M. R. Sirouspour and S. E. Salcudean, 'Nonlinear control of hydraulic robots,' IEEE Trans. on Robotics and Automation, vol. 12, no. 2, pp. 173-182, 2001
  19. G. F. Liu and Z. X. Li, 'A unified geometric approach to modeling and control of constrained mechanical systems,' IEEE Trans. on Robotics and Automation, vol. 18, no. 4, pp. 574-587, 2002 https://doi.org/10.1109/TRA.2002.802207
  20. F. Aghili, 'A unified approach for inverse and direct dynamics of constrained multibody systems based on linear projection operator: Applications to control and simulation,' IEEE Trans. on Robotics and Automation, vol. 21, no. 5, pp. 834-849, 2005 https://doi.org/10.1109/TRO.2005.851380
  21. M. A. Nahon and J. Angeles, 'Force optimization in redundantly-actuated closed kinematic chains,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 951-956, 1989
  22. J. F. O'Brien and J. T. Wen, 'Redundant actuation for improving kinematic manipulability,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 1520- 1525, 1999
  23. A. Muller, 'Internal preload control of redundantly actuated parallel manipulators-its application to backlash avoiding control,' IEEE Trans. on Robotics and Automation, vol. 21, no. 4, pp. 668-677, 2005 https://doi.org/10.1109/TRO.2004.842341
  24. A. Muller, 'Stiffness control of redundantly actuated parallel manipulators,' Proc. of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 1153-1158, 2006