Fractional Exponential Reaching Law Sliding Mode Control for a Robot Manipulator Tracking Application

This paper proposes a control strategy for a robot manipulator with four Degrees Of Freedom (DOF) that takes advantage of sliding mode control theory, exponential reaching law, and fractional calculus. Tracking the joint space trajec-tories with precision is the goal of the proposed Fractional Exponential reaching law Sliding Mode Control (FrExpSMC). Utilizing fractional calculus in the sliding surface enhances the robustness of the exponential reaching mode against external disturbances. The fractional calculus expression of the sliding surface ensures a finite time convergence of the controller and provides the controller with a fast response in the transient phase. The proposed control approach's efficiency and performances are demonstrated by simulation on a model of a 4-DOF robot manipulator and compared to the conventional sliding mode control. The stability of the closed-loop system is proved using Lyapunov theory. The results indicate that the recommended control outperforms the conventional sliding mode control in both tracking performance and robustness against step disturbances.