Abstract
A robust nonlinear backstepping technique with Lagrange’s extrapolation and PI compensator is proposed in this chapter for high accuracy trajectory tracking of robot manipulators with uncertain dynamics and unexpeted disturbances. The proposed controller is synthesized by using Lagrangian extrapolation method with PI compensator to estimate the uncertainties and disturbances and to deal with the effect of hard nonlinearities caused by the estimation error while nonlinear backstepping technique is used to ensure good tracking. The stability analysis is accomplished recursively using appropriate Lyapunov functions candidate. As a result, the proposed control technique shows better performances via experimental results on a 7-DOF robot arm in comparison with the classical backstepping and sliding mode control.
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References
Al-Hadithi, B. M., Matía, F., & Jiménez, A. (2007). Fuzzy controller for robot manipulators (pp. 688–697). Berlin/Heidelberg: Springer.
Chen, S.-H., & Fu, L.-C. (2015). Observer-based backstepping control of a 6-DOF parallel hydraulic manipulator. Control Engineering Practice, 36, 100–112.
Choi, J. Y., & Farrell, J. (2000). Observer-based backstepping control using online approximation. American Control Conference, 5, 3646–3650.
Fierro, R., & Lewis, F. L. (1998). Control of a nonholonomic mobile robot using neural networks. IEEE Transactions on Neural Networks, 9(4), 589–600.
Hu, Q., Xu, L., & Zhang, A. (2012). Adaptive backstepping trajectory tracking control of robot manipulator. Journal of the Franklin Institute, 349(3), 1087–1105.
Jagannathan, S., & Lewis, F. (1998). Robust backstepping control of robotic systems using neural networks. Journal of Intelligent and Robotic Systems, 23, 105–128.
Kali, Y., Saad, M., Benjelloun, K., & Fatemi, A. (2017). Discrete-time second order sliding mode with time delay control for uncertain robot manipulators. Robotics and Autonomous Systems, 94, 53–60.
Khalil, H. (1992). Nonlinear systems. New York: Macmillan Publishing Company.
Kokotovic, P., Krstic, M., & Kanellakopoulos, I. (1995). Nonlinear and adaptive control design. New York: Wiley.
Lewis, F., Abdallah, C., & Dawson, D. (1993). Control of robot manipulators. New York: Macmillan Publishing Company.
Liu, J., & Wang, X. (2012). Advanced sliding mode control for mechanical systems. Berlin/Heidelberg: Springer.
Shieh, H.-J., & Hsu, C.-H. (2008). An adaptive approximator-based backstepping control approach for piezoactuator-driven stages. IEEE Transactions On Industrial Electronics, 55, 1729–1738.
Skjetne, R., & Fossen, T. (2004). On integral control in backstepping: Analysis of different techniques. In American Control Conference, Boston, Massachusetts.
Slotine, J., & Li, W. (1991). Applied nonlinear control. Taipei: Prentice-Hall International.
Spong, M., Hutchinson, S., & Vidyasagar, M. (2005). Robot modeling and control. Wiley.
Su, C.-Y., Li, G., Li, Z., & Su, H. (2015). Fuzzy approximation-based adaptive backstepping control of an exoskeleton for human upper limbs. IEEE Transactions on Fuzzy Systems, 23, 555–566.
Tan, Y., Chang, J., Tan, H., & Jun, H. (2000). Integral backstepping control and experimental implementation for motion system. In IEEE International Conference on Control Applications, Anchorage, AK.
Toumi, K., & Ito, O. (1990). A time delay controller for systems with unknown dynamics. ASME Journal of Dynamic System, Measurement and Control, 112, 133–141.
Utkin, V. (1992). Sliding mode in control and optimization. Berlin: Springer.
Utkin, V., Guldner, J., & Shi, J. (1999). Sliding mode control in electromechanical systems (2nd ed.). Boca Raton, London.
Weisheng, C., Ge, S., Jian, W., & Maoguo, G. (2015). Globally stable adaptive backstepping neural network control for uncertain strict-feedback systems with tracking accuracy known a priori. IEEE Transactions on Neural Networks and Learning Systems, 26, 1842–1854.
Wilson, J., Charest, M., & Dubay, R. (2016). Non-linear model predictive control schemes with application on a 2 link vertical robot manipulator. Robotics and Computer-Integrated Manufacturing, 41, 23–30.
Yaramasu, V., & Wu, B. (2014). Model predictive decoupled active and reactive power control for high-power grid-connected four-level diode-clamped inverters. IEEE Transactions on Industrial Electronics, 61(7), 3407–3416.
Yoo, B. K., & Ham, W. C. (2000). Adaptive control of robot manipulator using fuzzy compensator. IEEE Transactions on Fuzzy Systems, 8, 186–199.
Zhou, J., & Er, M. J. (2007). Adaptive output control of a class of uncertain chaotic systems. Systems and Control Letters, 56(6), 452–460.
Zhou, J., & Wen, C. (2008). Adaptive backstepping control of uncertain systems. Berlin: Springer.
Acknowledgements
The authors are grateful to Nabil Derbel (University of Sfax, Tunisia), Jawhar Ghommam (University of Tunis, Tunisia) and Quanmin Zhu (University of the West of England) for the opportunity to contribute to the New developments and advances in the field of Robotics.
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Kali, Y., Saad, M., Kenné, JP., Benjelloun, K. (2019). Robot Manipulator Control Using Backstepping with Lagrange’s Extrapolation and PI Compensator. In: Derbel, N., Ghommam, J., Zhu, Q. (eds) New Developments and Advances in Robot Control. Studies in Systems, Decision and Control, vol 175. Springer, Singapore. https://doi.org/10.1007/978-981-13-2212-9_6
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DOI: https://doi.org/10.1007/978-981-13-2212-9_6
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