Dynamics Modeling and Oscillation Control of a Biomimetic Fish-tail Robot Based on a Three-element Model
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摘要: 随着仿生水下机器人技术的发展, 基于气动驱动的仿生鱼尾机器人因其高灵活性和低噪声特性受到广泛关注. 然而, 气动软体驱动器固有的非线性迟滞效应与柔顺特性为鱼尾的精确动力学建模与摆动控制带来挑战. 为此, 针对气动仿生鱼尾机器人建立包含弹簧、质量与阻尼的三元动力学模型, 并通过实验数据实现参数辨识, 有效描述该机器人的复杂非线性动力学行为. 进而提出一种前馈—反馈复合控制方法, 利用逆动力学方法, 基于所建立的模型生成前馈输入以提升响应速度, 结合PID反馈抑制建模误差与外部扰动, 同时基于Lyapunov理论证明系统的渐近稳定性. 实验结果表明, 在定频正弦、变幅变频及随机轨迹等多种工况下, 该方法均显著优于传统PID控制, 具有更高的跟踪精度与动态适应能力, 同时, 反馈补偿与参数辨识也被证明对提升跟踪性能具有关键作用. 水下实验进一步验证所提方法对辨识误差、未建模动态及外部扰动的适应能力.Abstract: With the development of biomimetic underwater robotics, pneumatic-driven biomimetic fish-tail robots have attracted widespread attention due to their high flexibility and low noise characteristics. However, the inherent nonlinear hysteresis and compliant properties of pneumatic soft actuators pose significant challenges for accurate dynamic modeling and precise oscillation control of the fish tail. To address these problems, a three-element dynamic model incorporating spring, mass, and damping is established for the pneumatic biomimetic fish-tail robot, and model parameters are identified by using experimental data, effectively characterizing the complex nonlinear dynamic behavior of the robot. Furthermore, a feedforward-feedback composite control method is proposed, in which the inverse dynamic approach is employed to generate feedforward inputs based on the established model to enhance response speed, while PID feedback is used to suppress modeling errors and external disturbances. The asymptotic stability of the closed-loop system is rigorously proven by using Lyapunov theory. Experimental results demonstrate that, under various operating conditions including constant-frequency sine waves, variable-amplitude-variable-frequency signals, and random trajectories, the proposed method significantly outperforms conventional PID control, achieving higher tracking accuracy and superior dynamic adaptability. Meanwhile, feedback compensation and parameter identification are also critical for improving tracking performance. Underwater experiments further validate the adaptability of the proposed method to parameter identification errors, unmodeled dynamics, and external disturbances.
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图 5 比例压力调节阀扫频特性测试
Fig. 5 Sweep frequency characteristic test of proportional pressure regulating valve
图 6 仿生鱼尾机器人开环控制实验数据
Fig. 6 Open-loop control experimental data for the biomimetic fish-tail robot
图 7 仿生鱼尾机器人的三元模型结构
Fig. 7 Three-element model structure of the biomimetic fish-tail robot
图 8 三种模型输出与实验数据的拟合对比
Fig. 8 Comparison of the fitting for three model outputs with experimental data
图 10 正弦波轨迹跟踪控制的实验结果
Fig. 10 Experimental results of sine wave trajectory tracking control
图 11 变幅变频波轨迹跟踪控制的实验结果
Fig. 11 Experimental results of variable amplitude and frequency wave trajectory tracking control
图 12 随机波轨迹跟踪控制的实验结果
Fig. 12 Experimental results of random wave trajectory tracking control
表 1 参数辨识结果
Table 1 Parameter identification results
参数 辨识结果 单位 $ M $ 0.0076 kg $ C $ 0.4597 N·s/m $ K $ 3.9949 N/m $ F_1 $ 147.1144 N/$ 10^5 $ Pa 
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表 2 不同模型的拟合效果对比
Table 2 Comparison of fitting effects among different models
方法 $ e_{\mathrm rmsp} $ $ e_{\mathrm mp} $ 三元模型 1.16% 16.85% Bouc-Wen模型 5.34% 16.87% Prandtl-Ishlinskii模型 5.97% 18.93%
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