Task space control of the robot manipulators with adaptive fuzzy global fast terminal sliding mode control in presence of dynamic and kinematic uncertainties

Summary Basic features such as convergence time and speed, number‐action control coefficients, free chattering, and proof of stability are significant in the design process and sliding mode control (SMC) efficiency. In this article, we propose an adaptive fuzzy global fast terminal SMC (AFGFTSMC) to handle the mentioned features in the task space control of the robot manipulator in the presence of dynamic and kinematic uncertainties. First, perturbed joint space dynamic equations of the system are transferred to task space, and a broad range of uncertainties are considered there. Then, a global fast terminal SMC (GFTSMC) is proposed for robot manipulators in task space, in which a flexible sliding surface improves the convergence time. Next, to have an intelligent adjustment of the sliding surface coefficients, which leads to a much faster convergence rate, a fuzzy approximator with just seven fuzzy rules is presented. In the following, to access the boundaries of the existing uncertainties, an adaptive fuzzy approximator is proposed, which has five fuzzy rules and only one adaptive law, increases the system's robustness, and eliminates the effect of chattering. Mathematical proof shows that the task space closed‐loop control system under the proposed AFGFTSMC and in the presence of dynamic and kinematic uncertainties has a finite‐time global asymptotic stability. The theoretical evidence and simulation results, which are conducted on a 2‐link robot manipulator, confirm the good efficiency of the proposed controller.