Abstract: By analyzing the travelling wave propulsion characteristics of dolphins' tails, a travelling wave kinematic feature equation based on the same-frequency feature swing and phase difference factor is proposed, and an average speed control method based on the data-clamping rule is designed. Firstly, the travelling wave propulsion characteristics are analyzed, and it is shown that the kinetic energy mapping principle is also applicable to the travelling wave propulsion mode. A same-frequency feature swing and a phase difference factor are defined to transplant the kinematic feature equation without phase difference to that of the travelling wave propulsion mode. Secondly, a data-clamping design method is proposed to solve the stronger nonlinearity of the obtained equation. By data-clamping based on kinetic energy mapping coefficient, the system will directly reach a small interval around the target speed at the first operation, and all the input and output signals will be clamped within this limited interval. Consequently, the average speed control can be realized by fine-tuning the speed within a small range with iterative learning-identification and repeated control. Simulation and experiment results show that, the kinematic feature equation of the transplanted travelling wave propulsion can be used to guide the robotic dolphins' movement, and the average speed control can be realized by the iterative learning-identification and repeated control method based on the data-clamping design.