This paper describes an impedance controller that uses the fast terminal sliding mode and adaptive neural networks. The proposed controller improves the dynamic trajectory performance and force tracking accuracy of robotic manipulators in three-dimensional uncertain environments. The key idea of the controller is that the improved adaptive nonsingular fast terminal sliding mode (ANFTSMC) uses integral control to eliminates chattering without affecting the tracking performance. Also, adaptive neural networks are introduced into the sliding mode controller to provide a local approximation in the dynamic model of the robotic manipulator, and the stability is guaranteed through the Lyapunov theory. Finally, combined with impedance control, the operation of the robotic manipulator is simulated in environments containing various obstacle types, and experimental validation has demonstrated the effectiveness and superiority of the proposed control scheme.