Fractional-order fixed-time sliding mode control of robotic manipulators with robust exact differentiator

This paper introduces a robust position tracking control structure of exoskeleton robots (ERs). An open environment and body flexibility are the main challenges in ER control system design. First, a fractional-order nonsingular terminal sliding mode (FONTSM) controller is proposed for a robotic manipulator with uncertainty, where lumped unknown dynamics are computed by time-delay estimation (TDE). Secondly, a robust exact differentiator (RED) is employed as the output feedback observer for the velocity sensorless robotic system. Thirdly, the stability of the FONTSM control system is demonstrated. It is proved that the system error can move to the specified value along the sliding mode surface at a fixed time and can reach the sliding mode surface after a finite time. Finally, simulations on a 2-DOF robotic manipulator show the effectiveness of the fixed-time control strategies. When a combined trigonometric function disturbance is applied, the joint angle error is reduced to 1% by the model-free controller based on output feedback within approximately 1 s.