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Robust task-space control of robot manipulators using differential equations for uncertainty estimation

Published online by Cambridge University Press:  08 September 2016

Alireza Izadbakhsh  and
Saeed Khorashadizadeh
Alireza Izadbakhsh*
Affiliation:
Department of Electrical Engineering, College of Engineering, Garmsar branch, Islamic Azad University, Garmsar, Iran
Saeed Khorashadizadeh
Affiliation:
Department of Electrical Engineering, Faculty of Engineering, University of Birjand, Birjand, Iran E-mail: s_khorashadi@yahoo.com
*
*Corresponding author. E-mail: izadbakhsh_alireza@hotmail.com
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Summary

Most control algorithms for rigid-link electrically driven robots are given in joint coordinates. However, since the task to be accomplished is expressed in Cartesian coordinates, inverse kinematics has to be computed in order to implement the control law. Alternatively, one can develop the necessary theory directly in workspace coordinates. This has the disadvantage of a more complex robot model. In this paper, a robust control scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator kinematics and dynamics, actuator dynamics and nor computing inverse kinematics. The control design procedure is based on a new form of universal approximation theory and using Stone–Weierstrass theorem, to mitigate structured and unstructured uncertainties associated with external disturbances and actuated manipulator dynamics. It has been assumed that the lumped uncertainty can be modeled by linear differential equations. As the method is Model-Free, a broad range of manipulators can be controlled. Numerical case studies are developed for an industrial robot manipulator.

Keywords

Model-free controlElectrically driven robot manipulatorDifferential equationsRobust control
Type
Articles
Information
Robotica , Volume 35 , Issue 9 , September 2017 , pp. 1923 - 1938
Copyright
Copyright © Cambridge University Press 2016 

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References

1. Spong, M. W., “On the robust control of robot manipulators,” IEEE Trans. Autom. Control 37, 1782–1786 (1992).CrossRefGoogle Scholar
2. Bascetta, L. and Rocco, P., “Revising the robust control design for rigid robot manipulators,” IEEE Trans. Robot. 26, 180–187 (2010).Google Scholar
3. Fateh, M. M. and Khorashadizadeh, S., “Optimal Robust voltage control of electrically driven robot manipulators,” Nonlinear Dyn. 70, 1445–1458 (2012).Google Scholar
4. Izadbakhsh, A. and Fateh, M. M., “Robust Lyapunov-based control of flexible-joint robots using voltage control strategy,” Arab J. Sci. Eng. 39, 3111–3121 (2014).Google Scholar
5. Huang, A.-C. and Chien, M.-C., Adaptive Control of Robot Manipulators: A Unified Regressor Free Approach, World Scientific Publishing Co. Pte. Ltd. Singapore (World Science, 2010).CrossRefGoogle Scholar
6. Islam, S. and Liu, P., “Robust sliding mode control for robot manipulators,” IEEE Trans. Ind. Electron. 58, 2444–2453 (2011).Google Scholar
7. Kim, E., “Output feedback tracking control of robot manipulators with model uncertainty via adaptive fuzzy logic,” IEEE Trans. Fuzzy Syst. 12, 368–378 (2004).CrossRefGoogle Scholar
8. Fateh, M. M. and Khorashadizadeh, S., “Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty,” Nonlinear Dyn. 69, 1465–1477 (2012).CrossRefGoogle Scholar
9. Puga-Guzmán, S., Valenzuela, J. M. and Santibáñez, V., “Adaptive neural network motion control of manipulators with experimental evaluations,” The Sci. World J., doi: 10.1155/2014/694706 (2014).Google Scholar
10. Wang, L. X., A Course in Fuzzy Systems and Control (Prentice-Hall, New York, 1997)Google Scholar
11. Izadbakhsh, A., “Robust control design for rigid-link flexible-joint electrically driven robot subjected to constraint: Theory and experimental verification,” Nonlinear Dyn. 85, 751–765 (2016).CrossRefGoogle Scholar
12. Chien, M.-C. and Huang, A.-C., “Adaptive impedance controller design for flexible-joint electrically-driven robots without computation of the regressor matrix,” Robotica 30, 133–144 (2012).Google Scholar
13. Tsai, Y. C. and Huang, A.-C., “FAT based adaptive control for pneumatic servo system with mismatched uncertainties,” Mech. Syst. Sig. Process. 22, 1263–1273 (2008).Google Scholar
14. Huang, A.-C. and Kuo, Y. S., “Sliding control of nonlinear systems containing time-varying uncertainties with unknown bounds,” Int. J. Control 74, 252–264 (2001).Google Scholar
15. Chien, M.-C. and Huang, A.-C., “Adaptive impedance control of robot manipulators based on function approximation technique,” Robotica 22, 395–403 (2004).Google Scholar
16. Huang, A.-C., Wu, S. C. and Ting, W. F., “An FAT-based adaptive controller for robot manipulators without regressor matrix: Theory and experiments,” Robotica 24, 205–210 (2006).Google Scholar
17. Khorashadizadeh, S. and Fateh, M. M., “Uncertainty estimation in robust tracking control of robot manipulators using the fourier series expansion,” Robotica DOI: http://dx.doi.org/10.1017/S026357471500051X (2015).Google Scholar
18. Khorashadizadeh, S. and Fateh, M. M., “Adaptive Fourier Series-Based Control of Electrically Driven Robot Manipulators,” The 3rd International Conference on Control, Instrumentation, and Automation (ICCIA), (Tehran, 2013) pp. 213–218.CrossRefGoogle Scholar
19. Khorashadizadeh, S. and Fateh, M. M., “Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation,” Nonlinear Dyn. 79, 1151–1161 (2014).CrossRefGoogle Scholar
20. Talole, S. E., Kolhe, J. P. and Phadke, S. B., “Extended-state-observer-based control of flexible-joint system with experimental validation,” IEEE Trans. Ind. Electron. 57, 1411–1419 (2010).CrossRefGoogle Scholar
21. Cheah, C. C., Liu, C. and Slotine, J. J. E., “Adaptive jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models,” IEEE Trans. Autom. Control 51, 1024–1029 (2006).CrossRefGoogle Scholar
22. Izadbakhsh, A. and Fateh, M. M., “Real-time robust adaptive control of robots subjected to actuator voltage constraint,” Nonlinear Dyn. 78, 1999–2014 (2014).CrossRefGoogle Scholar
23. Moreno-Valenzuela, J., Campa, R. and Santibáñez, V., “Model-based control of a class of voltage-driven robot manipulators with non-passive dynamics,” Comput. Electr. Eng. 39, 2086–2099 (2013).Google Scholar
24. Orrante-Sakanassi, J., Santibañez, V. and Moreno-Valenzuela, J., “Stability analysis of a voltage-based controller for robot manipulators,” Int. J. Adv. Robot. Syst. doi: 10.5772/53894 (2013).Google Scholar
25. Khatib, O., “A unified approach for motion and force control of robot manipulators: The operational space formulation,” IEEE J. Robot. Autom. 3, 43–53 (1987).CrossRefGoogle Scholar
26. Izadbakhsh, A. and Rafiei, S. M. R., “Endpoint perfect tracking control of robots-a robust non inversion-based approach,” Int. J. Control Autom. Syst. 7, 888–898 (2009).Google Scholar
27. Izadbakhsh, A., Akbarzadeh Kalat, A., Fateh, M. M. and Rafiei, S.M.R., “A robust anti-windup control design for electrically driven robots-theory and experiment,” Int. J. Control Autom. Syst. 9, 1005–1012 (2011).Google Scholar
28. Izadbakhsh, A. and Rafiei, S. M. R., “Robust Control Methodologies for Optical Micro Electro Mechanical System-New Approaches and Comparison,” 13th Power Electronics and Motion Control Conference on EPE-PEMC, (Poznan, 2008) pp. 2102–2107.Google Scholar
29. Rudin, W., Principles of Mathematical Analysis, McGraw-Hill Education; 3rd edition (January 1, 1976).Google Scholar
30. Izadbakhsh, A., “Closed-form Dynamic Model of Puma560 Robot Arm,” Proceedings of the 4th International Conference on Autonomous Robots and Agents, (Wellington, 2009) pp. 675–680.Google Scholar
31. Corke, P., “The Unimation Puma Servo System,” CSIRO Division of Manufacturing Technology, (1994) p. 38.Google Scholar
32. Corke, P. and Armstrong-Helouvry, B., “A Search for Consensus Among Model Parameters Reported for the Puma560 Robot,” IEEE International Conference on Robotics and Automation, (San Diego, CA, 1994) pp. 1608–1613.Google Scholar