Robot Manipulator Control Using Backstepping with Lagrange’s Extrapolation and PI Compensator

  • Yassine KaliEmail author
  • Maarouf Saad
  • Jean-Pierre Kenné
  • Khalid Benjelloun
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 175)


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.


Backstepping 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.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yassine Kali
    • 1
    Email author
  • Maarouf Saad
    • 2
  • Jean-Pierre Kenné
    • 2
  • Khalid Benjelloun
    • 1
  1. 1.Ecole Mohammadia d’IngénieursUniversity of Mohammed VRabatMorocco
  2. 2.École de Technologie SupérieureUniversity of QuebecMontrealCanada

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