Hydrodynamic modeling of pectoral fin having varying thickness for biomimetic fish robot

Pectoral fin types of biological fish have an enormous diversity, and they play an essential role in locomotion of fish. The adaptation to shapes and movement mechanism of pectoral fin types helps swimming motion of the main body effectively, that results in the high flexibility and maneuverability of locomotion. This paper proposes a hydrodynamic model of a type of flexible pectoral fin (FPF), which can be used to increase the robotic fish motion efficient and reduce the consumed energy. The pectoral fin has the symmetrical shape and varying thickness along the symmetrical axis. Based on the Lagrange energetic method, Assumed Mode Method (AMM), and Rayleigh-Ritz method, the mathematical model of deformation and estimated thrust of the pectoral fin is described explicitly. The effect of inertia and damping factors are modeled by the Morison force. The numerical simulations and some initial experiments are demonstrated to verify the agreement of theoretical and empirical model. The proposed model is expected to support in issues of modeling whole of robotic fish and control design effectively.