Fixed-time trajectory tracking control for robotic manipulators with disturbances and input saturation constraints

A fixed-time extended state observer (FXESO) is designed to estimate thelumped disturbances, including modeling errors and external disturbances, and theirestimation errors converge to the origin in fixed time. To solve the saturation problemof an actuator, a new fixed-time convergent auxiliary system is built to compensatefor input saturation, and a Gaussian error function is introduced to approximatethe input saturation constraints model.

Then, based on the FXESO and auxiliarydynamic system, a fixed-time nonsingular terminal sliding mode controller is devel-oped. With the proposed control scheme, piecewise continuous functions are adoptedin the controller design to avoid the singularity, and the observer is utilized to min-imize the chattering of the system. The fixed-time stability of the entire closed-loopsystem is demonstrated by Lyapunov theory.