In nature, undulatory swimmers consume minimum energy by adjusting their body's natural frequency to match the tail-beat frequency. Inspired by this, we study the dynamic model of fish body by considering the body shape and the fluid interactions, and develop a soft thunniform robotic fish. The experimental results show that when the driving frequency is close to the natural frequency, the speed of robotic fish reaches the maximum value, approximately 0.25 body length per second. Moreover, an empty space with a different air pressure is embedded into the body of robotic fish to vary its stiffness, and the natural frequency can be adjusted from 2.0 to 2.8 Hz by modulating the air pressure. The results of robotic fish with variable stiffness show that the forward speed and acceleration are increased with natural frequency, and a smaller stiffness of caudal fin contributes to a better propulsive performance. We also predict that the peak speed and acceleration can be obtained simultaneously by adjusting the stiffness of both fish body and caudal fin properly. These results reveal that the swimming abilities of robotic fish are closely related to the driving frequency and the stiffness property.

Biological evidence demonstrates that fish can tune their body stiffness to improve thrust and efficiency during swimming locomotion. However, the stiffness-tuning strategies that maximize swimming speed or efficiency are still unclear. In the present study, a musculo-skeletal model of anguilliform fish is developed to study the properties of variable stiffness, in which the planar serial-parallel mechanism is used to model the body structure. The calcium ion model is adopted to simulate muscular activities and generate muscle force. Further, the relations among the forward speed, the swimming efficiency, and Young’s modulus of the fish body are investigated. The results show that for certain body stiffness, the swimming speed and efficiency are increased with the tail-beat frequency until reaching the maximum value and then decreased. The peak speed and efficiency are also increased with the amplitude of muscle actuation. Anguilliform fish tend to vary their body stiffness to improve the swimming speed and efficiency at a high tail-beat frequency or small amplitude of muscle actuation. Furthermore, the midline motions of anguilliform fish are analyzed by the complex orthogonal decomposition (COD) method, and the discussions of fish motions associated with the variable body stiffness and the tail-beat frequency are also presented. Overall, the optimal swimming performance of anguilliform fish benefits from the matching relationships among the muscle actuation, the body stiffness, and the tail-beat frequency.

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