Non-singular terminal sliding-mode control for a manipulator robot using a barrier Lyapunov function

Area of Science:

• Robotics
• Control Systems Engineering
• Applied Mathematics

Background:

• Robot manipulators require precise trajectory tracking for complex tasks.
• Ensuring full-state constraints (position and velocity) during operation is critical but challenging.
• Existing sliding mode controllers often struggle to satisfy these constraints robustly.

Purpose of the Study:

• To design a robust finite-time controller for robot manipulators that guarantees trajectory tracking under full-state constraints.
• To introduce a novel control strategy that ensures permanent satisfaction of position and velocity constraints.
• To validate the controller's effectiveness through numerical simulations and experimental evaluation.

Main Methods:

• Development of a constrained non-singular terminal sliding mode (CNTSM) controller.
• Integration of a gain self-adapting tuning method for finite-time convergence.
• Utilization of a barrier Lyapunov function for finite-time stability analysis.
• Employing an adaptive super-twisting algorithm as a robust differentiator for tracking error estimation.

Main Results:

• The CNTSM controller achieved finite-time convergence to the sliding surface and reference trajectories.
• The controller successfully maintained permanent satisfaction of position and velocity constraints.
• Numerical and experimental results demonstrated superior tracking performance compared to classical non-singular terminal sliding mode controllers.
• The proposed controller effectively handled uncertainties in the robot manipulator's inertia and Coriolis matrices.

Conclusions:

• The proposed CNTSM controller offers a robust solution for finite-time trajectory tracking of robot manipulators with full-state constraints.
• The CNTSM controller provides enhanced performance and constraint satisfaction over traditional methods.
• This design advances the field of constrained control for robotic systems.