###### Abstract  
This paper comes up with a novel Fast Terminal Sliding Mode Control (FTSMC) for robot manipulators. First, to enhance the response, fast convergence time, against uncertainties, and accuracy of the tracking position, the novel Fast Terminal Sliding Mode Manifold (FTSMM) is developed. Then, a Supper-Twisting Control Law (STCL) is applied to combat the unknown nonlinear functions in the control system. By using this technique, the exterior disturbances and uncertain dynamics are compensated more rapidly and more correctly with the smooth control torque. Finally, the proposed controller is launched from the proposed sliding mode manifold and the STCL to provide the desired performance. Consequently, the stabilization and robustness criteria are guaranteed in the designed system with high-performance and limited chattering. The proposed controller runs without a precise dynamic model, even in the presence of uncertain components. The numerical examples are simulated to evaluate the effectiveness of the proposed control method for trajectory tracking control of a 3-Degrees of Freedom (DOF) robotic manipulator. super-twisting control law; robot manipulators; fast terminal sliding mode control 20202  
when it uses a linear sliding manifold. As a result of the linear sliding manifold, the SMC only ensures asymptotic convergence [15]. Therefore, in case that the pressure of a large control force is unavailable, the asymptotic stability status is less likely to converge fast with high-precision control. Terminal Sliding Mode Control (TSMC) [16; 17] is proposed to solve convergence problems in finite time, enhancing the transient performance. However, in several situations, TSMC does not offer the desired performance with initial state variables far from the equilibrium point. Additionally, it has not solved the chattering and slow convergence, as well as creating a new problem that is the singularity phenomenon. To resolve the issues of SMC and TSMC in a synchronized manner, Nonsingular Fast Terminal Sliding Mode Control (NFTSMC) has been evolved successfully in robotic systems [10; 12; 18; 19; 20; 21; 22; 23; 24]. It thoroughly solves the problems, including singularity, convergence in finite-time, and slow convergence. Unfortunately, the chattering has not yet been addressed as these controllers still use a robust reaching control law to deal with uncertain components, and also require the upper limit value of unknown components. For chattering, many solutions have been proposed that can be mentioned, such as the Boundary Layer Method (BLM) [6; 25; 26], the Adaptive Super-Twisting Method (ASTM) [27], the Second-Order SMC (SOSMC) or the Third-Order SMC (TOSMC) [28; 29; 30; 31], the Full-Order SMC (FOSMC) [32; 33; 34; 35], and the Fuzzy-SMC (F-SMC) [36; 37; 38; 5]. For the requirement of the upper limit value of unknown components, many control methods were based on a combination of Neural Networks (NNs), Fuzzy Logic Systems (FLSs), or Adaptive Control Laws (ALCs) with NFTSMC. Although the behavior of unknown components can be well learned by NNs or FLSs. However, it increases the complexity of the control method design because there are more parameters to be adjusted. ACLs are more applicable than the other two methods because they use simple and effective updating rules. Based on the mentioned analysis, our paper attempts to propose an advanced Fast Terminal Sliding Mode Control (FTSMC) with contributions for robot manipulators: (1) inherits the benefits of the FTSMC and Supper-Twisting Control Law (STCL) in the characteristics of robustness towards the existing uncertainties, finite-time convergence, singularity elimination, estimation capability, and good transient performance; (2) proposes a new Fast Terminal Sliding Mode Manifold (FTSMM) and provides sufficient evidence of finite-time convergence; (3) further improves the precision in the trajectory tracking control; (4) the control torque commands are smooth with less oscillation. The rest of our paper has the following arrangement.