Fishes, with their efficient propulsive systems and wide variety of body shapes, inspire the design of marine robots. To imitate the kinematics of live species for the fish-like robots, some parameters would be extracted by observations from nature. In this article, a summary is presented over the important literature on the kinematics of the body/caudal swimming of fishes. Then, a detailed procedure to extract the kinematic parameters from live species is discussed. In addition, a procedure is presented to account for the length variations of the vertebral column of the live species during their swimming in the modeling of virtual fishes. Different polynomial and exponential amplitude envelope functions associated with single and multiple sinusoidal terms are also adopted to suggest a better kinematic equation for a body/caudal fin swimmer, spiny dogfish shark (Squalus acanthias). A non-linear least-squares algorithm, Trust-Region, is used to fit surfaces on the experimental data. Results show that in general, the accuracy of the kinematic equation is more affected from the sinusoidal term than the amplitude envelope function. Moreover, evaluations offer the third- and fourth-order polynomial amplitude envelope functions with three sinusoidal terms as appropriate and optimal kinematic equations to model the kinematics of the spiny dogfish shark.
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