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Adaptive sliding-mode trajectory tracking control for state constraint master-slave manipulator systems.

David Cruz-Ortiz1, Isaac Chairez2, Alexander Poznyak3

  • 1Department of Bioengineering, UPIBI-Instituto Politécnico Nacional, Av. Acueducto 550, 07340, Mexico City, Mexico.

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Summary

This study introduces an adaptive controller for state-constrained master-slave robotic systems (M-SRS) to achieve precise trajectory tracking. The novel approach ensures finite-time convergence and improved tracking accuracy compared to existing methods.

Keywords:
Master–slave robotic systemOutput feedback controlSliding mode controllerState constraint systemTrajectory tracking problem

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Area of Science:

  • Robotics and Control Systems
  • Applied Mathematics
  • Mechatronics

Background:

  • Master-slave robotic systems (M-SRS) often face challenges with state constraints and bounded uncertainties.
  • Existing control strategies may not adequately address finite-time convergence or state constraint satisfaction in M-SRS.
  • Accurate estimation of articulation velocities is crucial for effective output feedback control in M-SRS.

Purpose of the Study:

  • To propose an adaptive state-dependent gain finite-time convergent controller for state-constrained M-SRS.
  • To ensure trajectory tracking performance while adhering to state constraints.
  • To analyze and prove the finite-time convergence of the sliding surface and asymptotic convergence of the tracking error.

Main Methods:

  • Sliding mode theory fundamentals were employed to design the adaptive controller.
  • A state-dependent adaptive gain was implemented to manage state constraints.
  • Lyapunov stability analysis was utilized to derive gain variation laws and prove convergence properties.
  • A robust and exact differentiator was applied for estimating slave robot articulation velocities.

Main Results:

  • The proposed controller demonstrated finite-time convergence of the sliding surface and asymptotic convergence of the tracking error.
  • Numerical simulations showed a smaller quadratic norm of the tracking error compared to proportional-derivative and conventional sliding mode controllers.
  • The control scheme successfully satisfied state constraints and handled bounded uncertainties.

Conclusions:

  • The developed adaptive finite-time convergent controller effectively addresses trajectory tracking for state-constrained M-SRS.
  • The controller offers superior performance in terms of tracking accuracy and constraint satisfaction.
  • The theoretical stability analysis confirms the robustness and finite-time convergence of the proposed control strategy.