Development and Stiffness Optimization for a Flexible-Tail Robotic Fish

The integral flexible tail has the potential advantage of lifelike undulating motion. However, due to the complex manufacturing process and difficult modification of structural parameters, its application in robotic fish encounters many challenges. Combining rigid structure and flexible material, this letter proposes a passive flexible fish tail, which can achieve continuous movement and high swimming frequency with simple but effective structure. First, with the full consideration of bending deformation of the spring steels, a dynamic model is established. Next, a passive fitting method is particularly applied to imitate the traveling wave model of the carangiform fish. More importantly, a calculation model, which can be used to acquire the theoretical ranges of the stiffness of spring steels, is derived based on the bending model of the cantilever beam subjected to the concentrated force and moment. Finally, the extensive simulation and experiments validate the effectiveness of the proposed methods, and the designed robotic fish can achieve 0.77 m/s (i.e., 1.12 BL/s) at a swimming frequency of 2.5 Hz. The obtained results can provide a valuable sight for improving the swimming performance of the robotic fish.