## 1 Introduction  
Literature regarding robotic manipulators has introduced many control systems focused on achieving high performance against various uncertainties, including external noise. These control methods were derived to fundamentally control the motion of robot manipulators, and include the proportional-derivative (PD) controller [1], nonlinear PD controller [2], and the proportional-integral-derivative (PID) controller [3; 4]. The advantages of the cited control systems were to provide a simple and basic approach to implementation, as they do not require an exact dynamic model. However, these systems could not obtain the desired performance in the presence of disturbances and dynamic uncertainties. Several advanced control approaches have been proposed to advance system performance, such as the fuzzy controller [5; 6; 7] and neural network controller [8; 9; 10], but they demand complicated calculations, and the effectiveness of each solution still has several limitations. The control scheme design strategy is based on the robot dynamic model, where the whole dynamic model is computed and compensated explicitly to achieve the desired performance. Therefore, other enhanced methods were suggested to improve the motion tracking for robot manipulators, including a computed torque controller (CTC) [11; 12], adaptive controller [13; 14; 15], and sliding mode controller (SMC) [16; 17; 18; 19; 20]. Among those controllers, SMC has been confirmed to offer high robustness against uncertainties and disturbances for nonlinear systems. Therefore, the SMC has been widely applied in real applications [16; 17; 18; 19; 20]. However, the traditional SMC still possesses drawbacks such as requiring an exact dynamic model, singularity problems, a chattering phenomenon, and finite-time convergence. Some research efforts have focused on overcoming these disadvantages. For the system states to approach the sliding variable within a finite-time, the use of the terminal sliding mode control (TSMC), based on the nonlinear sliding surface, has been reported in the literature [13; 21; 22; 23]. Nonetheless, the TSMC convergence time is slow when compared to the conventional SMC, and still contains a singularity glitch. To solve convergence time and singularity issues, several fast TSMC (FTSMC) [24; 25; 26] and nonsingular TSMC (NTSMC) [27; 28; 29] approaches have been proposed. Practically, private algorithms, such as FTSMC or NTSMC, have only treated an individual weakness or failed to solve the other disadvantages of the classical SMC. Consequently, the nonsingular fast TSMC (NFTSMC) has been introduced [30; 31; 32; 33; 34]. Here, NFTSMC can solve many disadvantages of the classical SMC or other control algorithms based on TSMC. However, chattering behavior has not been removed by applying a high-frequency switching control law to the control input of the above methods, which include TSMC, FTSMC, NTSMC, and NFTSMC. Therefore, some effective techniques have been introduced to handle this topic by application of the saturation function (refer to [35]), full-order sliding mode control (FOSMC) [36; 37], or high-order sliding mode control (HOSMC) [35; 38]. One of the main tasks in the design of a control method based on SMC or TSMC is to develop an exact dynamic model of the robot manipulator, which one does not readily know in advance for real robot systems. To estimate this unknown dynamic model, several computing approaches have been proposed such as neural networks [39; 40; 41] and fuzzy logic systems [42; 43; 44] due to their universal approximation capabilities. While each disadvantage of the classical SMC and TSMC has been treated individually, this report focuses on simultaneous resolution of the disadvantages of SMC and TSMC, including the requirement for an exact dynamic model, as well as the presence of a singularity problem, chattering phenomenon, and finite-time convergence.