Dynamic modeling of robotic fish and its experimental validation

In this paper, we present a new dynamic model for a carangiform robotic fish by merging rigid-body dynamics with Lighthill´s large-amplitude elongated-body theory. In addition, we refine the model by introducing an effective approach to the evaluation of time-varying drag force and moment coefficients. It is known that these coefficients vary with the angle of attack, but the angle of attack oscillates constantly for a carangiform robotic fish because of the recoil motion of the body. By examining the individual effects of tail beat bias, frequency, amplitude on the attack angle, we find that the bias has much more dominant impact than the other two factors. Based on this observation, we develop a convenient scheme for determining the drag force and moment coefficients, as a function of the tail beat bias. Experimental results on a robotic fish prototype propelled with a servo-controlled rigid tail have verified the proposed model. In particular, we show that the pressure force at the tail tip, which is often ignored in related literature, plays a significant role in the dynamics. The effectiveness of the proposed scheme for adapting the drag force and moment coefficients is also demonstrated through the comparison with a model that uses constant drag coefficients.