A novel trajectory planning method for a robotic fish

Recently, there has been a growing interest in biomimetic underwater vehicles. Although a lot of research has been conducted in the area of dynamics and kinematics of robotic fish, most of the approaches solve the inverse problem by finding the required force the caudal fin should produce, in order for the robotic fish to follow a trajectory. Others use predefined undulatory body motions which usually approximate paths of simple planar geometrical shapes, such as circles and straight lines. The attempts cannot conclude a priori if a robotic fish can actually follow the given trajectory. More importantly, they cannot derive caudal fin trajectories that will ensure that the fish will follow a given planar trajectory. In this paper we present a novel and universal methodology for finding how the caudal fin of a robotic fish should move, so that the robotic fish follows any planar trajectory. Also, we identify the sufficient conditions, which must be satisfied to predict a priori, whether the robotic fish is able to follow a given trajectory. To the best of the knowledge of the authors, this is the first time that such a methodology is presented. Finally, experimental results are provided, showing the merits of the developed method.