In this study, we investigate the modeling framework for a robotic fish actuated by a flexible caudal fin, which is filled with electrorheological (ER) fluid and thus enables tunable stiffness. This feature can be used in optimizing the robotic fish speed or maneuverability in different operating regimes. The robotic fish is assumed to be anchored and the flexible tail undergoes undulation activated by a servomotor at the base. Lighthill’s large-amplitude elongated-body theory is used to calculate the hydrodynamic force on the caudal fin, and Hamilton’s principle is used to derive the dynamic equations of motion of the caudal fin. The dynamic equations are then discritized using the finite element method, to obtain an approximate numerical solution. In particular, simulation is conducted to understand the influence of the applied electric field on the stiffness and thrust performance of the caudal fin.

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