Tracking Finite-Time Prescribed Performance Fractional Power Rate Reaching Law Sliding-Mode Control For a 4-DOF Robot Manipulator

Accurate trajectory tracking control with finite-time convergence is essential for many robot manipulator applications, such as manufacturing and surgery. It ensures rapid response and swift adaptation to dynamic and changing environments. It minimizes energy consumption, enhances safety, and leads to quicker task completion. However, attaining high trajectory tracking accuracy during the steady-state phase and a smooth and rapid transient response presents a significant challenge, especially when dealing with external disturbances and uncertainty in robot parameters. This article proposes a control strategy named the finite-time prescribed performance fractional power rate reaching law sliding-mode controller to enhance the performances of the power rate reaching law sliding-mode control (PLSMC) for a trajectory tracking application in the robot's joint space. The controller design incorporates two techniques, which are the fractional calculus (FC) to address the robustness of the PLSMC and a new finite-time prescribed performance function (FTPPF) to enhance the transient response and ensure finite-time convergence of the controller. Using FC creates a flexible control structure that enhances tracking performance, reduces chattering, and increases the controller's robustness against disturbances. The proposed FTPPF guarantees minimal overshoot and convergence of the error in a limited duration, regardless of the robot's initial position. The sliding surface is designed based on the fractional derivative of the transformed error calculated from the proposed FTPPF. The transformed error guarantees that FTPPF constantly bounds the tracking error. The Lyapunov principle is employed to demonstrate the asymptotic stability of the error dynamic. Experimental outcomes indicate that the suggested controller outperforms the PLSMC regardless of the presence or absence of disturbances, enhancing the transient and the steady-state response and more efficiently rejecting disturbances.