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.

在本文中，为仿生多关节机器鱼提出了一种具有两个相同扭力弹簧的新型柔性关节，可以模仿活鱼的游泳行为。更重要的是，开发了基于拉格朗日动力学方法的动力学模型来探索顺应被动机制。在动态建模中，使用简化的莫里森方程来分析水动力。此外，参数识别技术被用来估计大量的水动力参数。大量不同情况下的实验数据与仿真结果吻合良好，验证了所得动力学模型的有效性。最后，在性能优化需求的推动下，我们首先利用动态模型来研究关节刚度和控制参数对仿生多关节机器鱼游泳速度和能量效率的影响。结果表明，相位差在提高效率方面起主要作用，当相位差较小时，柔顺接头在性能提高方面的作用更为显着。也就是说，在最大驱动频率下，获得了最大的能量效率改进，并且令人惊讶地接近 89%。此外，最大游泳速度的最大提高约为每秒 0.19 个身体长度。这些发现证明了合规性在优化关节设计和运动控制以获得更好性能方面的潜力。