Robot Manipulator Control Using Backstepping with Lagrange’s Extrapolation and PI Compensator
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.
KeywordsBackstepping Lagrange’s extrapolation PI compensator Uncertain robot manipulators Lyapunov Trajectory tracking
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.
- Choi, J. Y., & Farrell, J. (2000). Observer-based backstepping control using online approximation. American Control Conference, 5, 3646–3650.Google Scholar
- Lewis, F., Abdallah, C., & Dawson, D. (1993). Control of robot manipulators. New York: Macmillan Publishing Company.Google Scholar
- Skjetne, R., & Fossen, T. (2004). On integral control in backstepping: Analysis of different techniques. In American Control Conference, Boston, Massachusetts.Google Scholar
- Spong, M., Hutchinson, S., & Vidyasagar, M. (2005). Robot modeling and control. Wiley.Google Scholar
- 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.Google Scholar
- Utkin, V., Guldner, J., & Shi, J. (1999). Sliding mode control in electromechanical systems (2nd ed.). Boca Raton, London.Google Scholar