This paper proposes a non-singular fast terminal sliding mode control method for a binocular active vision platform of a picking robot with unknown dynamics. The method uses radial basis function (RBF) neural networks to achieve trajectory tracking accuracy and enhance robustness against external interference. A non-singular fast terminal sliding mode controller is designed for the system’s convergence within a limited time. An adaptive neural network approximates the unknown nonlinear function of the dynamic model. Stability and finite-time convergence of the closed-loop system are established using Lyapunov theory. Experimental verification on the binocular vision platform demonstrates position and speed errors converging to the desired trajectory within 2 and 1 second, respectively. Moreover, when subjected to external interference, the position and velocity errors converge within 0.1 seconds. Simulation experiments confirm the method’s effectiveness in improving convergence speed, trajectory tracking accuracy, and robustness against external interference, while reducing system chattering.