Hostname: page-component-6766d58669-nqrmd Total loading time: 0 Render date: 2026-05-24T20:53:21.959Z Has data issue: false hasContentIssue false
  • English
  • Français

Wavelet neural network-based H∞ trajectory tracking for robot manipulators using fast terminal sliding mode control

Published online by Cambridge University Press:  13 May 2016

Vikas Panwar
Vikas Panwar*
Affiliation:
School of Vocational Studies and Applied Sciences, Gautam Buddha University, Greater Noida - 201310, Uttar Pradesh, India
*
*Corresponding author. E-mail: vikasdma@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

This paper focuses on fast terminal sliding mode control (FTSMC) of robot manipulators using wavelet neural networks (WNN) with guaranteed H∞ tracking performance. The FTSMC for trajectory tracking is employed to drive the tracking error of the system to converge to an equilibrium point in finite time. The tracking error arrives at the sliding surface in finite time and then converges to zero in finite time along the sliding surface. To deal with the case of uncertain and unknown robot dynamics, a WNN is proposed to fully compensate the robot dynamics. The online tuning algorithms for the WNN parameters are derived using Lyapunov approach. To attenuate the effect of approximation errors to a prescribed level, H∞ tracking performance is proposed. It is shown that the proposed WNN is able to learn the system dynamics with guaranteed H∞ tracking performance and finite time convergence for trajectory tracking. Finally, the simulation results are performed on a 3D-Microbot manipulator to show the effectiveness of the controller.

Keywords

Robot controlTerminal sliding modeWavelet neural network approximationH∞ tracking performance

Information

Type
Articles
Information
Robotica , Volume 35 , Issue 7 , July 2017 , pp. 1488 - 1503
Copyright
Copyright © Cambridge University Press 2016 

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.)

Article purchase

Temporarily unavailable

References

1. Astrom, K. J. and Hugglund, T., “Automatic tuning of simple regulators with specifications on phase and amplitude margins,” Automatica, 20 (5), 645–651 (1984).Google Scholar
2. Luo, G. L. and Saridis, G. N., “L-Q design of PID controllers for robot arms,” IEEE J. Robotic. Autom. RA–1 (3), 152–159 (1985).CrossRefGoogle Scholar
3. Su, Y. X., Sun, D. and Duan, B. Y., “Design of an enhanced nonlinear PID controller,” Mechatronics, 15 (8), 1005–1024 (2005).Google Scholar
4. Lewis, F. L., Dawson, D. M. and Abdallah, C. T., Robot Manipulator and Control - Theory and Practice, (Marcel Dekker, New York, 2004).Google Scholar
5. Stoline, J. J. E. and Li, W., Applied Nonlinear Control, (Prentice-Hall, Englewood Cliffs, NJ, 1991).Google Scholar
6. Bailey, E. and Arapostathis, A., “Simple sliding mode control applied to robot manipulators,” Int. J. Control, 25 (4), 1197–1209 (1987).Google Scholar
7. Lanzon, A. and Richards, R. J., “Trajectory/Force Control of Robot Manipulators Using Sliding Mode and Adaptive Control,” Proceedings of the American Control Conference (San Diego, California, USA, 1999) vol. 3, pp. 1940–1944.Google Scholar
8. Su, C. Y. and Leung, T. P., “A sliding mode controller with bound estimation for robot manipulators,” IEEE Trans. Robotic. Autom., 9 (2), 208–214 (1993).CrossRefGoogle Scholar
9. Ertugrul, M., Kaynak, O. and Kerestecioglu, F., “Gain adaptation in sliding mode control of robotic manipulators,” Int. J. Syst. Sci., 31 (9), 1099–1106 (2000).Google Scholar
10. Venkataraman, S. T. and Gulati, S., “Control of nonlinear systems using terminal sliding modes,” J. Dyn. Syst. Meas. Control, 115 (3), 554–560 (1993).Google Scholar
11. Tao, C. W., Taur, J. S. and Chan, M. L., “Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties,” IEEE Trans. Syst. Man Cybern. B, 34 (1), 225–262 (2004).Google Scholar
12. Zhihong, M., Paplinski, A. P. and Wu, H. R., “A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators,” IEEE T. Automat. Control, 39 (12), 2464–2469 (1994).Google Scholar
13. Wang, L., Chai, T. and Zhai, L., “Neural-network-based terminal sliding-mode control of robotic manipulators including actuator dynamics,” IEEE Trans. Indust. Electron. 56 (9), 3296–3304 (2009).CrossRefGoogle Scholar
14. Neila, M. B. and Tarak, D., “Adaptive terminal sliding mode control for rigid robotic manipulators,” Int. J. Automat. Comput. 8 (2), 215–220 (2011).CrossRefGoogle Scholar
15. Park, K. B. and Lee, J. J., “Comments on ‘A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators’,” IEEE Trans. Automat. Control, 41 (5), 761–762 (1996).Google Scholar
16. Feng, Y., Yu, X. H. and Man, Z. H., “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, 38 (12), 2159–2167 (2002).CrossRefGoogle Scholar
17. Geng, J., Sheng, Y. and Liu, X., “Time varying nonsingular terminal sliding mode control for robot manipulators,” Trans. Inst. Meas. Control, 36 (5), 604–617 (2014).CrossRefGoogle Scholar
18. Yu, X. and Zhihong, M., “Fast terminal sliding-mode control design for nonlinear dynamical systems,” IEEE Trans. Circuits -I, 49 (2), 261–264 (2002).Google Scholar
19. Yu, S., Yu, X., Shirinzadeh, B. and Man, Z., “Continuous finite time control for robot manipulators with terminal sliding mode,” Automatica, 41, 1957–1964 (2005).CrossRefGoogle Scholar
20. Lewis, F. L., Jagannathan, S. and Yesildirek, A., Neural Network Control of Robot Manipulators and Nonlinear Systems, (Taylor and Francis, London UK, 1999).Google Scholar
21. Patre, P. M., Gainesville, F. L., Mackunis, W. and Dixon, W. E., “Asymptotic tracking for uncertain dynamic systems via a multilayer neural network Feedforward and RISE feedback control structure,” IEEE Trans. Automat. Control, 53 (9), 2180–2185 (2008).Google Scholar
22. Lee, M. J. and Choi, Y. K., “An adaptive neurocontroller using RBFN for robot manipulators,” IEEE Trans. Ind. Electron. 51 (3), 711–717 (2004).Google Scholar
23. Kumar, N., Panwar, V., Borm, J. H. and Chai, J., “Enhancing precision performance of trajectory tracking controller for robot manipulators using RBFNN and adaptive bound,” Appl. Math. Comput. 231, 320–328 (2014).Google Scholar
24. Er, M. J. and Gao, Y., “Robust adaptive control of robot manipulators using generalized fuzzy neural networks,” IEEE Trans. Ind. Electron. 50 (3), 620–628 (2003).Google Scholar
25. Wai, R. J. and Yang, Z. W., “Adaptive Fuzzy Neural Network Control of Robot Manipulator Using T-S Fuzzy Model Design,” Proceedings of the IEEE International Conference Fuzzy Systems, (Hong Kong, 2008) pp. 90–97.Google Scholar
26. Tian, L., Wang, J. and Mao, Z., “Constrained motion control of flexible robot manipulators based on recurrent neural networks,” IEEE Trans. Syst. Man Cybern. B, 34 (3), 1541–1552 (2004).Google Scholar
27. Hung, C. P., “Integral variable structure control of nonlinear system using a CMAC neural network learning approach,” IEEE Trans. Syst. Man Cybern. B, 34 (1), 702–709 (2004).Google Scholar
28. Lin, C. K., “Nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks,” IEEE Trans. Fuzzy Syst. 14 (6), 849–859 (2006).CrossRefGoogle Scholar
29. Wang, H., Zhu, S. and Liu, S., “Robust Adaptive Wavelet Network Control for Robot Manipulators,” Proceedings of the WRI Global Congress on Intelligent Systems, (Xiamen China, 2009) vol. 2, pp. 313–317.Google Scholar
30. Sun, T., Pei, H., Pan, Y., Zhou, H. and Zhang, C., “Neural network-based sliding mode adaptive control for robot manipulators,” Neurocomputing, 74 (14–15), 2377–2384 (Jul. 2011).CrossRefGoogle Scholar
31. Zhang, C., Sun, T. and Pan, Y., “Neural network observer-based finite-time formation control of mobile robots,” Math. Probl. Eng., vol. 2014, p. Article ID 267307 (Jul. 2014).Google Scholar
32. Zhang, Q. and Benveniste, A., “Wavelet networks,” IEEE Trans. Neural Netw. 3 (6), 889–898 (1992).CrossRefGoogle ScholarPubMed
33. Zhang, J., Walter, G. G., Miao, Y. and Lee, W. N. W., “Wavelet neural networks for function learning,” IEEE Trans. Signal Process. 43 (6), 1485–1497 (1995).Google Scholar
34. Li, S. T. and Chen, S. C., “Function Approximation using Wavelet Neural Networks,” Proceedings of the 14th IEEE International Conference on Tools with Artificial. Intelligence, (Washington DC, 2002) pp. 483–488.Google Scholar
35. Zainnuddin, Z. and Pauline, O., “Modified neural network in function approximation and its application in prediction of time series pollution data,” Appl. Soft Comput. 11 (8), 4866–4874 (2011).Google Scholar
36. Alexandridis, A. K. and Zapranis, A. D., “Wavelet neural networks: A practical guide,” Neural Netw. 42, 1–27 (2013).CrossRefGoogle ScholarPubMed
37. Sun, T., Pei, H., Pan, Y. and Zhang, C., “Robust wavelet network control for a class of autonomous vehicles to track environmental contour line,” Neurocomputing, 74 (17), 2886–2892 (Oct. 2011).Google Scholar
38. Zames, G., “Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses”, IEEE Trans. Automat. Control, 26, 301–320 (1981).Google Scholar
39. Doyle, J., Glover, K., Khargonekar, P. P. and Francis, B. A., “Statespace solutions to standard H2 and H∞ control problem,” IEEE Trans. Automat. Control, 34, 831–847 (1989).Google Scholar
40. Schaft, A. J. V., “A state space approach to nonlinear H∞ control,” Syst. Control Lett. 16, 1–8 (1991).CrossRefGoogle Scholar
41. Wang, W. Y., Chan, M. L., Hsu, C. C. J. and Lee, T. T., “H∞ tracking-based sliding mode control for uncertain nonlinear systems via an adaptive fuzzy-neural approach,” IEEE Trans. Syst. Man Cybern. B, 32 (4), 483–492 (2002).Google Scholar
42. Zou, Y. and Wang, Y., “Robust H∞ Intelligent Tracking Control for Robot Manipulators,” Proceedings of the 7th World Congress on Intelligent Control and Automation, (Chongqing China, 2008) pp. 4819–4824.Google Scholar
43. Hong, J. C., Shu, L. H. and Zhong, S. L., “An LMI Approach to H∞ Control for Affine Nonlinear System,” Proceedings of the International Conference on Electronics and Optoelectronics, (Liaoning, China, 2011) vol. 2, 26–29.Google Scholar
44. Pan, Y., Er, M. J., Huang, D. and Wang, Q., “Fire-rule-based direct adaptive type-2 fuzzy H∞ tracking control,” Eng. Applica. Artif. Intell. 24 (7), 1174–1185 (Oct. 2011).CrossRefGoogle Scholar
45. Pan, Y., Er, M. J., Huang, D. and Sun, T., “Practical adaptive fuzzy H∞ tracking control of uncertain nonlinear systems,” Int. J. Fuzzy Syst. 14 (4), 463–473 (Dec. 2012).Google Scholar
46. Pan, Y., Zhou, Y., Sun, T. and Er, M. J., “Composite adaptive fuzzy H∞ tracking control of uncertain nonlinear systems,” Neurocomputing, 99, 15–24 (Jan. 2013).Google Scholar
47. Hong, Y., Huang, J. and Xu, Y., “On an output finite-time stabilization problem,” IEEE Trans. Automat. Control, 46 (2), 305–309 (2001).Google Scholar
48. Horn, R. A. and Johnson, C. R., Matrix Analysis, (Cambridge University Press, New York, 2013).Google Scholar
49. Bhat, S. P. and Bernstein, D. S., “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim. 38, 751–766 (2000).Google Scholar
50. Wolovich, W. A., Robotics: Basic Analysis and Design, (Rinehart and Winston, Holt, 1987).Google Scholar