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On the Taylor series asymptotic tracking control of robots

Published online by Cambridge University Press:  12 October 2018

Seyed Mohammad Ahmadi Open the ORCID record for Seyed Mohammad Ahmadi [Opens in a new window]  and
Mohammad Mehdi Fateh
Seyed Mohammad Ahmadi*
Affiliation:
Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran. E-mail: mmfateh@shahroodut.ac.ir
Mohammad Mehdi Fateh
Affiliation:
Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran. E-mail: mmfateh@shahroodut.ac.ir
*
*Corresponding author. E-mail: s.m.ahmadi1365@gmail.com
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Summary

Achieving the asymptotic tracking control of electrically driven robot manipulators is a challenging problem due to approximation/modelling error arising from parametric and non-parametric uncertainty. Thanks to the specific property of Taylor series systems as they are universal approximators, this research outlines two robust control schemes using an adaptive Taylor series system for robot manipulators, including actuators' dynamics. First, an indirect adaptive controller is designed such as to approximate an uncertain continuous function by using a Taylor series system in the proposed control law. Second, a direct adaptive scheme is established to employ the Taylor series system as a controller. In both controllers, not only a robustifying term is constructed using the estimation of the upper bound of approximation/modelling error, but the closed-loop stability, as well as the asymptotic convergence of joint-space tracking error and its time derivative, is ensured. Due to the design of the Taylor series system in the tracking error space, our technique clearly has an advantage over fuzzy and neural network-based control methods in terms of the small number of tuning parameters and inputs. The proposed methods are simple, model free in decentralized forms, no need for uncertainty bounding functions and perfectly capable of dealing with parametric and non-parametric uncertainty and measurement noise. Finally, simulation results are introduced to confirm the efficiency of the proposed control methods.

Keywords

Taylor series systemDirect adaptive controlIndirect adaptive controlElectrically driven robot manipulatorsAsymptotic tracking controlUniversal approximatorRobustifying term
Type
Articles
Information
Robotica , Volume 37 , Issue 3 , March 2019 , pp. 405 - 427
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Ahmadi, S. M. and Fateh, M. M., “Robust control of electrically-driven robots using adaptive uncertainty estimation,” Comput. Electric. Eng. 56, 674–687 (2016).Google Scholar
2. Slotine, J. J. E., “The robust control of robot manipulators,” Int. J. Robot. Res. 4 (2), 49–64 (1985).Google Scholar
3. Spong, M. W., “On the robust control of robot manipulators,” IEEE Trans. Automat. Control 37 (11), 1782–1786 (1992).Google Scholar
4. Sage, H. G., De Mathelin, M. F. and Ostertag, E., “Robust control of robot manipulators: A survey,” Int. J. Control 72 (16), 1498–1522 (1999).Google Scholar
5. Barambones, O. and Etxebarria, V., “Robust neural control for robotic manipulators,” Automatica 38 (2), 235–242 (2002).Google Scholar
6. Pan, H. and Xin, M., “Nonlinear robust and optimal control of robot manipulators,” Nonlinear Dynamics 76 (1), 237–254 (2014).Google Scholar
7. Fateh, M. M., “Proper uncertainty bound parameter to robust control of electrical manipulators using nominal model,” Nonlinear Dyn. 61 (4), 655–666 (2010).Google Scholar
8. Ortega, R. and Spong, M. W., “Adaptive motion control of rigid robots: A tutorial,” Automatica 25 (6), 877–888 (1989).Google Scholar
9. Sciavicco, L. and Siciliano, B., Modelling and Control of Robot Manipulators (Springer Science & Business Media, McGraw-Hill, New York, NY, USA, 2012).Google Scholar
10. Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control, vol. 3 (Wiley, New York, 2006).Google Scholar
11. Burkan, R., “Modelling of bound estimation laws and robust controllers for robustness to parametric uncertainty for control of robot manipulators,” J. Intell. Robotic Syst. 60 (3), 365–394 (2010).Google Scholar
12. Fu, L. C., “Robust adaptive decentralized control of robot manipulators,” IEEE Trans. Automat. Control 37 (1), 106–110 (1992).Google Scholar
13. Colbaugh, R. and Glass, K., “Decentralized adaptive control of electrically-driven manipulators,” Comput. Electric. Eng. 22 (6), 383–401 (1996).Google Scholar
14. Su, Y. X. and Zheng, C. H., “Global asymptotic tracking of robot manipulators with a simple decentralised non-linear PD-like controller,” IET Control Theory Appl. 4 (9), 1605–1611 (2010).Google Scholar
15. Yang, Z. J., Fukushima, Y. and Qin, P., “Decentralized adaptive robust control of robot manipulators using disturbance observers,” IEEE Trans. Control Syst. Technol. 20 (5), 1357–1365 (2012).Google Scholar
16. Khorashadizadeh, S. and Fateh, M. M., (2017). “Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion,” Robotica 35 (2), 310–336 (2012).Google Scholar
17. Seraji, H., “Decentralized adaptive control of manipulators: Theory, simulation, and experimentation,” IEEE Trans. Robot. Autom. 5 (2), 183–201 (1989).Google Scholar
18. Ahmadipour, M., Khayatian, A. and Dehghani, M., “Adaptive control of rigid-link electrically-driven robots with parametric uncertainties in kinematics and dynamics and without acceleration measurements,” Robotica 32 (7), 1153–1169 (2014).Google Scholar
19. Kwan, C., Lewis, F. L. and Dawson, D. M., “Robust neural-network control of rigid-link electrically-driven robots,” IEEE Trans. Neural Netw. 9 (4), 581–588 (1998).Google Scholar
20. Fateh, M. M., Ahmadi, S. M. and Khorashadizadeh, S., “Adaptive RBF network control for robot manipulators,” J. AI Data Mining 2 (2), 159–166 (2014).Google Scholar
21. Huang, S. N., Tan, K. K. and Lee, T. H., “Adaptive neural network algorithm for control design of rigid-link electrically-driven robots,” Neurocomputing 71 (4), 885–894 (2008).Google Scholar
22. Ahanda, J. J. B. M., Mbede, J. B., Melingui, A. and Essimbi, B., “Robust adaptive control for robot manipulators: Support vector regression-based command filtered adaptive backstepping approach,” Robotica 36 (4), 516–534 (2018).Google Scholar
23. Izadbakhsh, A. and Khorashadizadeh, S., “Robust task-space control of robot manipulators using differential equations for uncertainty estimation,” Robotica 35 (9), 1923–1938 (2017).Google Scholar
24. Fateh, M. M., “On the voltage-based control of robot manipulators,” Int. J. Control, Autom. Syst. 6 (5), 702–712 (2008).Google Scholar
25. Fateh, M. M., “Robust control of flexible-joint robots using voltage control strategy,” Nonlinear Dyn. 67 (2), 1525–1537 (2012).Google Scholar
26. Cho, Y. W., Seo, K. S. and Lee, H. J., “A direct adaptive fuzzy control of nonlinear systems with application to robot manipulator tracking control,” Int. J. Control, Autom. Syst. 5 (6), 630–642 (2007).Google Scholar
27. Baigzadehnoe, B., Rahmani, Z., Khosravi, A. and Rezaie, B., “On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach,” ISA Trans. 70, 432–446 (2017).Google Scholar
28. Nazmara, G., Fateh, M. M. and Ahmadi, S. M., “A model-reference impedance control of robot manipulators using an adaptive fuzzy uncertainty estimator,” Int. J. Comput. Intell. Syst. 11 (1), 979–990 (2018).Google Scholar
29. Zeng, W. and Wang, C., “Learning from NN output feedback control of robot manipulators,” Neurocomputing 125, 172–182 (2014).Google Scholar
30. Tang, Z. L., Ge, S. S., Tee, K. P. and He, W., “Adaptive neural control for an uncertain robotic manipulator with joint space constraints,” Int. J. Control 89 (7), 1428–1446 (2016).Google Scholar
31. Ahmadi, S. M. and Fateh, M. M., “Task-space control of robots using an adaptive Taylor series uncertainty estimator,” Int. J. Control (2018). doi.org/10.1080/00207179.2018.1429673Google Scholar
32. Ahmadi, S. M. and Fateh, M. M., “Task-space asymptotic tracking control of robots using a direct adaptive Taylor series controller,” J. Vibration Control (2018). doi.org/10.1177/1077546318758800.Google Scholar
33. Wang, L. X., A Course in Fuzzy Systems and Control (Prentice-Hall press, UK, 1997).Google Scholar
34. Christensen, O. and Christensen, K. L., Approximation Theory: From Taylor Polynomials to Wavelets (Springer Science & Business Media, Birkhauser, Boston, MA, USA, 2004).Google Scholar
35. Rudin, W., Principles of Mathematical Analysis, vol. 3 (McGraw-hill, New York, 1964).Google Scholar
36. Sharma, R., Gaur, P. and Mittal, A. P., “Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload,” ISA Trans. 58, 279–291 (2015).Google Scholar