Dynamic Modeling of a Robotic Fish Propelled by a Compliant Tail

In this paper, a dynamic model for a robotic fish propelled by a tail with a flexible fin is presented. The robotic fish is composed of two links connected by an actuated joint; the frontal link is rigid and acts as the robotic fish body, while the rear link serves as the tail. The latter comprises a rigid element connected to a flexible caudal fin, whose underwater vibration is responsible for propulsion. The dynamics of the frontal link are described using Kirchhoff´s equations of motion for rigid bodies in quiescent fluids. The tail vibration is modeled using Euler-Bernoulli beam theory and the effect of the encompassing fluid is described using the Morison equation. The thrust production is assessed from static thrust data in terms of the fin-tip displacement; other salient model parameters are estimated through a nonlinear least squares technique. The model is validated against experimental data on circular and S-shaped trajectories. The model can be used for simulation, prediction, design optimization, and control, as it allows for the description of the robot´s motion as a function of the unique input of the system, that is, the servomotor angle. Within the latter application, a heading control algorithm, in which the controller is tuned on the basis of the dynamic model, is presented.