A Study on the Dynamic Modeling, Swimming-Speed Analysis, and Control of the Fish Robot with a Flexible Tail
웬 피 루안
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Fish robot has been the subject of many studies in recent years, but most of them were analyzed, controlled or optimized using multi-joint rigid-bar models. Attention is rarely paid to the flexible tail. The flexible tail not only has better performance in terms of thrust force and propulsion efficiency, but also the mechanisms were simpler and more mechanically robust than multi-joint rigid-bar system. Firstly, the purpose of this paper presented a dynamic modeling of a fish robot with a uniform flexible tail case and a non-uniform one case. In the first case, the uniform flexible tail was simplified as a slewing beam actuated by a driving moment. The governing equation was derived by using the Euler-Bernoulli theory. In order to simplify this equation, the hydrodynamic forces, including reactive force and resistive force were estimated. It is a fourth-order in space and second-order in time Partial Differential Equation (PDE) of the lateral movement function with constant coefficients. Its analytical solution was then derived by using the modal analysis method. This solution described the relationship between the driving moment and the lateral movement of the flexible tail. Simulation and experiments were carried out and compared. It was proved that this dynamic model well explains the real behavior of a fish robot with a uniform flexible tail. The main difference between the first case and the second one is that the coefficients of the PDE were not constants because of the non-uniform shape. Solving this PDE is generally complex. In our proposed method, these coefficients were approximated by exponential functions from which an analytical solution was derived. It describes the lateral movement of the non-uniform flexible tail as a function of material, geometrical and actuator properties. Comparison between simulation and experiments proved that the proposed model is suitable for predicting the real behavior of a fish robot with a non-uniform flexible tail. Secondly, design and fabrication of a fish robot were presented. The influences of the driving moment and the tail's stiffness on the thrust, the swimming-speed, and the Froude efficiency were then analyzed. In addition, the optimal driving moment was also determined for obtaining the maximum swimming-speed. Finally, the descent operation mode of the fish robot was investigated by adding inclined pectoral fins. By using a neural network model and PID based controller, the fish robot was controlled to track desired trajectories.