Backstepping control for a two-link manipulator with appointed-time convergence

Area of Science:

• Robotics
• Control Systems Engineering
• Applied Mathematics

Background:

• Two-link manipulators are fundamental in robotics, requiring precise control for complex tasks.
• Existing control methods often provide estimated or unbounded convergence times.
• Trajectory tracking errors and external disturbances pose significant challenges in manipulator control.

Purpose of the Study:

• To develop a novel backstepping control law for a two-link manipulator.
• To achieve precise appointed-time convergence, allowing exact determination of convergence time.
• To constrain trajectory tracking errors and suppress external disturbances.

Main Methods:

• A novel backstepping control law is designed.
• An appointed-time prescribed performance function is utilized to constrain errors.
• A disturbance observer and switching sliding mode control are integrated to handle external disturbances.
• Lyapunov stability analysis is employed to verify controller stability.

Main Results:

• The proposed control law guarantees appointed-time convergence, with a precisely obtainable convergence time.
• Trajectory tracking errors are effectively constrained beforehand.
• External disturbances are successfully suppressed.
• Numerical simulations confirm the efficacy and stability of the proposed control scheme.

Conclusions:

• The novel backstepping control law offers superior performance in terms of precise convergence time and error constraint for two-link manipulators.
• The integration of appointed-time functions and disturbance observers provides a robust solution for real-world robotic applications.
• This approach advances the field of finite-time control in robotics.