Dynamic Modeling of Three-Dimensional Swimming for Biomimetic Robotic Fish

This paper presents a three-dimensional, dynamic model of robotic fish which synthesizes both the carangiform and anguilliform swimming modes. The designed robotic fish is composed of three parts: stiff anterior body with a pair of pectoral fins for up-and-down motion, flexible rear body, and an oscillating lunate caudal fin. We use unsteady flow theory to analyze the motion of the anterior part and the links, and adopt experimental result from oscillating foil for the caudal fin. So the dynamic equation of each part can be obtained, and by summing up these equations, the dynamic equation for total swimming robot can be derived. The desired propulsive characteristics including forward velocity, sway velocity, pitch velocity, three velocity of Eulerian angles of the stiff anterior body, motion trajectory as well as propulsive efficiency can then be obtained by solving ordinary differential equation. The circular motion, based on asymmetrical kinematics of flexible rear body, can be achieved by adding different deflections to the oscillatory links. Comparisons between simulation results and real experiments are then conducted and discussed. A good agreement on dynamic characteristics demonstrates the validity of the proposed model