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In this paper, a novel compliant joint with two identical torsion springs is proposed for a biomimetic multi-joint robotic fish, which enables imitatation of the swimming behavior of live fish. More importantly, a dynamic model based on the Lagrangian dynamic method is developed to explore the compliant passive mechanism. In the dynamic modeling, a simplified Morrison equation is utilized to analyze the hydrodynamic forces. Further, the parameter identification technique is employed to estimate numerous hydrodynamic parameters. The extensive experimental data with different situations match well with the simulation results, which verifies the effectiveness of the obtained dynamic model. Finally, motivated by the requirement for performance optimization, we firstly take advantage of a dynamic model to investigate the effect of joint stiffness and control parameters on the swimming speed and energy efficiency of a biomimetic multi-joint robotic fish. The results reveal that phase difference plays a primary role in improving efficiency and the compliant joint presents a more significant role in performance improvement when a smaller phase difference is given. Namely, at the largest actuation frequency, the maximum improvement of energy efficiency is obtained and surprisingly approximates 89%. Additionally, the maximum improvement in maximum swimming speed is about 0.19 body lengths per second. These findings demonstrate the potential of compliance in optimizing joint design and locomotion control for better performance.

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