In order to gradually improve the accuracy and speed of trajectory tracking, a non-singularity fast terminal sliding modecontroller wit In order to gradually improve the accuracy and speed of trajectory tracking, a non-singularity fast terminal slidingmode controller with fuzzy step-down observer backstepping method is proposed for constructing the dynamic model of the roboticarm.The controller adopts a new integral fast terminal sliding mode surface, decomposes the complex nonlinear system intosubsystems not exceeding the order of the system with the backstepping method, and combines the fuzzy system to design a fuzzyreduced-order observer which is used to estimate and compensate the disturbance of the system for the moment of the perturbedobservation, thus ensuring that the system has fast finite-time convergence and non-singularity superior performance.In order toensure the stability of the system, the Lyapunov method is adopted in this paper to prove the stability of the system, and the fast andaccurate tracking of the desired trajectory is shown according to the comparison of different methods.