Target-tracking control design for a robotic fish with caudal fin

In this paper we propose a novel target-tracking control scheme for a carangiform robotic fish based on a faithful dynamic model that combines rigid-body dynamics with Lighthill's large-amplitude elongated-body theory. We first average the dynamic model under periodic tail-actuation, which results in an average model with tail-beat patterns (bias, frequency, and amplitude) as new control inputs that are nonlinearly coupled. By introducing two new state variables, the orientation angle error and the distance between the robotic fish body and the target location, we derived the dynamic equations for these variables, which are then used in backstepping-based controller design. A hybrid controller is proposed, where the switching is determined by whether the orientation error is above a threshold value. Using Lyapunov analysis, we show that the trajectory of the robotic fish will converge to the target point if the given condition is satisfied. Finally, the effectiveness of the proposed control strategy is demonstrated through simulation results.