An improved kinematic model for fishlike swimming based on Lissajous method

To study the mechanism of fish swimming with high efficiency and fast speed, it´s of great importance to analyze the swimming image and establish an accurate kinematic model. However, according to the current model based on the traveling wave equation, the body length and moving directions of every part of fish will change when it swims with large undulating amplitude. By analyzing the images of the real fish swimming postures, it can be known that the movement of each particle on the fish body satisfies the Lissajous equation with the ratio of the horizontal harmonic frequency and the vertical one of 2 to 1. As a result, the improved kinematic model is established based on the Lissajous method and has been verified successfully. The results show that the latter model has higher approximation accuracy, which can reduce the error value down to 17% of the former. And it would provide an accurate reference path for further study on the hydrodynamics of the robotic fish.