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Dynamic model and input shaping control of a flexible link parallel manipulator considering the exact boundary conditions

Published online by Cambridge University Press:  01 April 2014

Quan Zhang ,
James K. Mills ,
William L. Cleghorn ,
Jiamei Jin  and
Zhijun Sun
Quan Zhang
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
James K. Mills*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
William L. Cleghorn
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada
Jiamei Jin
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China
Zhijun Sun
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, P.R. China
*
*Corresponding author. E-mail: mills@mie.utoronto.ca
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Summary

In this paper, a rigid–flexible planar parallel manipulator (PPM) actuated by three linear ultrasonic motors for high-accuracy positioning is proposed. Based on the extended Hamilton's principle, a rigid–flexible dynamic model of the proposed PPM is developed utilizing exact boundary conditions. To derive an appropriate low-order dynamic model for the design of the controller, the assumed modes method is employed to discretize elastic motion. Then to investigate the interaction between the rigid and elastic motions, a proportional derivative feedback controller combined with a feed-forward-computed torque controller is developed to achieve motion tracking while attenuating the residual vibration. Then the controller is extended to incorporate an input shaper for the further suppression of residual vibration of flexible linkages. Computer simulations are presented as well as experimental results to verify the proposed dynamic model and controller. The input shaping method is verified to be effective in attenuating residual vibration in a highly coupled rigid–flexible PPM. The procedure employed for dynamic modeling and control analysis provides a valuable contribution into the vibration suppression of such a PPM.

Keywords

Flexible parallel manipulatorDynamic modelExact boundary conditionsPD feedbackInput shaping

Information

Type
Articles
Information
Robotica , Volume 33 , Issue 6 , July 2015 , pp. 1201 - 1230
Copyright
Copyright © Cambridge University Press 2014 

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References

1. Merlet, J.-P., Parallel Robots (Springer, New York, NY, 2006).Google Scholar
2. Zhao, C., Ultrasonic Motors (Springer-Verlag, Berlin, Germany, 2011).Google Scholar
3. Shi, Y., Li, Y., Zhao, C. and Zhang, J., “A new type butterfly-shaped transducer linear ultrasonic motor,” J. Intell. Mater. Syst. Struct. 22 (6), 567–575 (2011).Google Scholar
4. Korayem, M., Heidari, A. and Nikoobin, A., “Maximum allowable dynamic load of flexible mobile manipulators using finite element approach,” Int. J. Adv. Manuf. Technol. 36 (5–6), 606–617 (2008).Google Scholar
5. Winfrey, R. C., “Elastic link mechanism dynamics,” J. Eng. Ind. 93, 268 (1971).Google Scholar
6. Ahmad, M. A., Mohamed, Z. and Hambali, N., “Dynamic Modelling of a Two-Link Flexible Manipulator System Incorporating Payload,” Proccedings of 3rd IEEE Conference on Industrial Electronics and Applications (ICIEA 2008), Singapore (2008) pp. 96–101.Google Scholar
7. Loudini, M., Boukhetala, D. and Tadjine, M., “Comprehensive mathematical modelling of a lightweight flexible link robot manipulator,” Int. J. Modelling, Identif. Control 2 (4), 313–321 (2007).Google Scholar
8. Meirovitch, L. and Parker, R., “Fundamentals of vibrations,” Appl. Mech. Rev. 54, 100 (2001).Google Scholar
9. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Dynamic modeling and experimental validation of a 3-PRR parallel manipulator with flexible intermediate links,” J. Intell. Robot. Syst. 50 (4), 323–340 (2007).Google Scholar
10. De Luca, A. and Siciliano, B., “Closed-form dynamic model of planar multilink lightweight robots systems,” IEEE Trans. Man Cybern. 21 (4), 826–839 (1991).Google Scholar
11. Krishnamurthy, K. and Yang, L., “Dynamic modeling and simulation of two cooperating structurally flexible robotic manipulators,” Robotica 13 (4), 375–384 (1995).Google Scholar
12. Tokhi, M. O. and Azad, A. M., Flexible Robot Manipulators: Modelling, Simulation and Control (Institution of Engineering and Technology, UK, 2008).Google Scholar
13. Dwivedy, S. K. and Eberhard, P., “Dynamic analysis of flexible manipulators, a literature review,” Mech. Mach. Theory 41 (7), 749–777 (2006).Google Scholar
14. Wang, X. and Mills, J. K., “Substructuring Dynamic Modeling and Active Vibration Control of a Smart Parallel Platform,” Proccedings of 2004 ASME International Mechanical Engineering Congress, Anaheim, CA, (2004) pp. 1–8.Google Scholar
15. Yu, Y.-Q., Du, Z.-C., Yang, J.-X. and Li, Y., “An experimental study on the dynamics of a 3-RRR flexible parallel robot,” IEEE Trans. Robot. 27 (5), 992–997 (2011).Google Scholar
16. Liu, S.-Z., Yu, Y.-Q., Zhu, Z.-C., Su, L.-Y. and Liu, Q.-B., “Dynamic modeling and analysis of 3-RRS parallel manipulator with flexible links,” J. Cent. South Univ. Technol. 17 (2), 323 (2010).Google Scholar
17. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Study on the Effect of Elastic Deformations on Rigid Body Motions of a 3-PRR Flexible Parallel Manipulator,” Proceedings of the International Conference on Mechatronics and Automation, Harbin, P.R. China (2007) pp. 1805–1810.Google Scholar
18. Hu, J., Li, P. and Cui, X., “Active Vibration Control of a High-Speed Flexible Robot Using Variable Structure Control,” Fifth International Conference on Intelligent Computation Technology and Automation, Zhangjiajie, Hunan, P.R. China (2012) pp. 57–60.Google Scholar
19. Sun, T., Song, Y.-M. and Yan, K., “Kinetostatic analysis of a novel high-speed parallel manipulator with rigid–flexible coupled links,” J. Cent. South Univ. Technol. 18 (3), 593 (2011).Google Scholar
20. Shabana, A. and Wehage, R., “Variable degree-of-freedom component mode analysis of inertia variant flexible mechanical systems,” J. Mech. Transm. Autom. Des. 105, 371–378 (1983).Google Scholar
21. Matsuno, F., Ohno, T. and Orlov, Y. V., “Proportional derivative and strain (PDS) boundary feedback control of a flexible space structure with a closed-loop chain mechanism,” Automatica 38 (7), 1201–1211 (2002).Google Scholar
22. Mansour, T., Konno, A. and Uchiyama, M., “Modified PID control of a single-link flexible robot,” Adv. Robot. 22 (4), 433–449 (2008).Google Scholar
23. Ahmad, M., Ramli, M., Ismail, R. R., Hambali, N. and Zawawi, M., “The Investigations of Input Shaping with Optimal State Feedback for Vibration Control of a Flexible Joint Manipulator,” Proccedings of Conference on Innovative Technologies in Intelligent Systems and Industrial Applications, Kuala Lumper, Malaysia (2009) pp. 446–451.Google Scholar
24. Liu, Y. and Sun, D., “Stabilizing a flexible beam handled by two manipulators via PD feedback,” IEEE Trans. Autom. Control 45 (11), 2159–2164 (2000).Google Scholar
25. Su, Y., Sun, D., Ren, L. and Mills, J. K., “Integration of saturated PI synchronous control and PD feedback for control of parallel manipulators,” IEEE Trans. Robot. 22 (1), 202–207 (2006).Google Scholar
26. Kang, B., Yeung, B. and Mills, J. K., “Two-time scale controller design for a high-speed planar parallel manipulator with structural flexibility,” Robotica 20 (5), 519–528 (2002).Google Scholar
27. Singer, N. C., “Residual Vibration Reduction in Computer Controlled Machines,” Ph.D. Dissertaion, Massachusetts Institute of Technology, Cambridge, MA (1989).Google Scholar
28. Zhou, T., Goldenberg, A. A. and Zu, J. W., “Modal Force Based Input Shaper for Vibration Suppression of Flexible Payloads,” Proceedings of IEEE International Conference on Robotics and Automation, Washington DC (2002) pp. 2430–2435.Google Scholar
29. Shan, J., Sun, D. and Liu, D., “Design for robust component synthesis vibration suppression of flexible structures with on-off actuators,” IEEE Trans. Robot. Autom. 20 (3), 512–525 (2004).Google Scholar
30. Singhose, W. E. and Singer, N. C., “Effects of input shaping on two-dimensional trajectory following,” IEEE Trans. Robot. Autom. 12 (6), 881–887 (1996).Google Scholar
31. Li, B., Zhang, X., Mills, J. K., Cleghorn, W. L. and Xie, L., “Vibration Suppression of a 3-PRR Flexible Parallel Manipulator Using Input Shaping,” International Conference on Mechatronics and Automation, Changchun, Jilin, P.R. China (2009) pp. 3539–3544.Google Scholar
32. Heerah, I., Benhabib, B., Kang, B. and Mills, J. K., “Architecture selection and singularity analysis of a three-degree-of-freedom planar parallel manipulator,” J. Intell. Robot. Syst. 37 (4), 355–374 (2003).Google Scholar
33. Staicu, S., “Inverse dynamics of the 3-PRR planar parallel robot,” Robot. Auton. Syst. 57 (5), 556–563 (2009).Google Scholar
34. Zhang, Q., Mills, J. K., Cleghorn, W. L., Jin, J. and Zhao, C., “Trajectory tracking and vibration suppression of a 3-PRR parallel manipulator with flexible links,” Multibody Syst. Dyn. 1–34 (2013). doi:10.1007/s11044-013-9407-2.Google Scholar
35. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Effect of Axial Forces on Lateral Stiffness of a Flexible 3-PRR Parallel Manipulator Moving with High-Speed,” International Conference on Information and Automation, Zhangjiajie, Hunan, P.R. China (2008) pp. 1458–1463.Google Scholar
36. Zhou, T., Zu, J. W. and Goldenberg, A. A., “Vibration Controllability of Flexible Robot-Payload Systems,” Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, CA (2000) pp. 1484–1489.Google Scholar
37. Shan, J., Liu, H.-T. and Sun, D., “Modified Input Shaping for a Rotating Single-Link Flexible Manipulator,” J. Sound Vib. 285 (1), 187–207 (2005).Google Scholar
38. Zhang, X., Mills, J. K. and Cleghorn, W. L., “Multi-mode vibration control and position error analysis of parallel manipulator with multiple flexible links,” Trans. Can. Soc. Mech. Eng. 34 (2), 197–213 (2010).Google Scholar
39. Bingül, Z. and Karahan, O., “Dynamic identification of Staubli RX-60 robot using PSO and LS methods,” Expert Syst. Appl. 38 (4), 4136–4149 (2011).Google Scholar