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As a static network, the slow learning of back propagation (BP) neural network is an insurmountable disadvantage facing dynamic system identification. In contrast, dynamic neural network provides a potential choice, representing the development direction of neural network modeling, identification and control. Based on dynamic Elman network, a new learning neural network structure, called fast learning neural network, is proposed in this paper. It not only conforms to the basic characteristics of biological neural network, but also has the advantages of simple algorithm, fast learning convergence and high identification accuracy of linear and non-linear systems. Based on the experimental data, this network is applied to the identification of the motion model of modular robots to obtain the non-linear kinematics model of robots. Therefore, this kind of neural network is very suitable for robot kinematics model identification and motion control. The simulation results show that it is appropriate to identify the kinematics model and control the motion of the robot based on fast learning neural network; and the combination of fast learning and ELM network speeds up the training efficiency. [ABSTRACT FROM AUTHOR]