Energy-storing analysis and fishtail stiffness optimization for a wire-driven elastic robotic fish

The robotic fish with high propulsion efficiency and good maneuverability achieves underwater fishlike propulsion by commonly adopting a motor to drive the fishtail, causing significant fluctuations within motor power due to the uneven swing speed of the fishtail in one swing cycle. Hence, we propose a wire-driven robotic fish with a controlled flexible unit that is a spring-steel-based fishlike tail. This unit can produce elastic deformation to store energy under the action of the wire driving and motor to respond to fluctuations in motor power. Further{more}, we analyze the effects of the energy-storing of the controlled flexible unit on the smoothness of motor power. Based on the developed Lagrangian dynamic model and the cantilever beam model, the power-variance-based nonlinear optimization model for the stiffness of the controlled flexible unit is established to respond to sharp fluctuations in motor power during each fishtail swing cycle. The results validate that the energy-storing of the controlled flexible unit plays a vital role in improving the power fluctuations and maximum frequency of the motor by adjusting its stiffness reasonably, which is beneficial for achieving high propulsion and high speed for robotic fish. Compared with the rigid counterpart that is incapable of storing energy, the energy-storing of the controlled flexible unit is beneficial to increase the maximum frequency of the motor and the average thrust of the fishtail by 0.41 Hz and 0.06 N, respectively.