## 1 Introduction  
Robot manipulators have contributed endless roles in both the industrial automation systems and applied research fields. Recently, studies on parallel robots have attracted a lot of interest in the research community. This is because parallel manipulators have numerous highlighted benefits such as high speed, high stiffness, high-accuracy positioning, high payload capacity and low moving inertia. Parallel manipulators have widely applied in real applications, including precise manufacturing, medical science, humanoid robots, space exploration equipment, and automobile simulators [1]. However, a drawback of parallel robotic manipulators is their limited workspace, especially compared with serial manipulators. Moreover, parallel robotic manipulators are saddled with a complicated dynamic model, singularities, and the forward kinematic problem. Therefore, many field-specific trials are needed to thoroughly handle these disadvantages of parallel robotic manipulators. The path trackingcontrol is then considered for a representative analysis to confirm the effectiveness of the proposed control systems. As reported in the literature, several control methods have been successfully applied to control robot manipulators. Outstanding examples, such as the proportional-integral-derivative (PID) controller [2], Nonlinear PD synchronized control [3], the adaptive switching learning PD control method (ASL-PD) [4], or [5] were reported to control the motion of parallel manipulators. However, these control systems cannot always obtain a prescribed performance due to the presence of external disturbances and uncertainties. Next, numerous advanced control algorithms were introduced, such as the computed torque controllers (CTC) [6; 7; 8], adaptive controllers [9; 10; 11; 12], the model-based iterative learning controller [13], and sliding mode control (SMC) [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. The common property of those controllers is that only local feedback information of each joint will be provided to the control loop of each private actuator without any feedback information from other joints. Therefore, errors generated by external disturbances and dynamic uncertainties in the control loop of each actuator are fixed by this control loop, while other errors do not respond. Additionally, the end-effector trajectory of a parallel robot is driven by all actuators synchronously. For this reason, all joints of the parallel robot should be synchronously driven to improve performance. Recently, studies on the synchronization control of parallel robots have been widely performed. The synchronization controller considers kinematic coupling among the active joints of a parallel robot. Consequently, the tracking performance of the end-effector is enhanced significantly. The synchronization control algorithm was first reported in Reference [26]. This control method has extensively enhanced in References [27; 28] and tracking control for parallel robots [5; 29; 30; 31; 32]. Nonsingular Fast Terminal Sliding mode control (NFTSMC) is one of the most powerful approaches to solving nonlinear systems with uncertain dynamic terms. NFTSMC well handles the disadvantages of both conventional SMC and conventional terminal sliding mode control (TSMC), such as singularity, undefined time convergence, chattering, and slow convergence. NFTSMC has been successfully applied to serial manipulators and parallel manipulators [33; 34; 35; 36; 37; 38; 39; 40]. With NFTSMC, the system states not only achieve fast convergence but also avoids the singularity problem. However, NFTSMC also does not consider kinematic coupling among the active joints of a parallel robot to design the control system. Furthermore, the control input signals of NFTSMC still have chattering by using high-frequency control law. To remove chattering, some effective algorithms were suggested.