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To acquire fast and high-precision trajectory tracking performances of the end effector, a robust adaptive nonsingular fast terminal sliding mode control law based on the radial basis function neural network is proposed, in which the priori model information of cable-driven parallel robots is not required. The proposed scheme combines the radial basis function neural network method with a nonsingular fast terminal sliding mode control structure, which contains three terms (the radial basis function neural network term, the hyperbolic tangent function term, and the robust control term), and it can not only weaken the chattering phenomenon but also increase the system robustness. Under the proposed scheme, the finite-time stability of the closed-loop system in the presence of external disturbances is demonstrated by the Lyapunov theorem. 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