Discrete Vortex Method-Based Fish-Like Locomotion Modeling

In nature, fish can achieve efficient swimming through vortex control, which is also a crucial factor in the propulsion of biomimetic robotic fish. Existing analytical models of robotic fish generally do not consider vortices. In addition, numerical methods for solving fluid dynamics are complex and computationally intensive. In this article, based on the discrete vortex method (DVM), the point vortex circulation caused by tail oscillation is calculated and an accurate and efficient dynamic model for robotic fish is established. Specifically, for a single-joint robotic fish, the hydrodynamic forces on the tail are analyzed using the DVM and calculated using the unsteady Bernoulli equation. And for the fish head, the simplified Morison equation is adopted to analyze the inertial forces and drag forces. Then, the dynamics of the entire robotic fish are derived using the Newton-Euler method, allowing for the calculation of position, velocity, forces, and wake circulation at each moment. As a result, the vortex structure obtained from the proposed method exhibits characteristics of a reverse Karman vortex street, similar to previous DPIV results and computational fluid dynamics (CFD) simulations. Furthermore, the simulated speeds closely match the experimental results with an average absolute error of 16.73%, which reduces the error by 2.95% compared to the conventional quasi-steady lift and drag model. Meanwhile, our method requires much less time consumption compared to the CFD method, making it convenient for application in the control and optimization of robotic fish.