Control Oriented Modeling and Singular Perturbation Analysis in Flapping-wing Flight
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摘要: 针对扑翼飞行中的周期性和时标不一现象, 以及扑翼飞行实际控制中的问题, 本文基于奇异摄动理论, 提出了一种针对扑翼周期系统的稳定性分析方法. 具体而言, 首先建立了扑翼飞行器的多刚体模型, 为后文对翅翼动力学的奇异摄动分析铺平道路; 其次, 对多刚体模型进行简化, 抽象出扑翼飞行动力学的核心问题, 并针对实际控制中的问题, 提出了利用奇异摄动理论分析扑翼飞行周期稳定性的方法, 指出了其相对于其他方法的优越性; 最后, 在自制的四自由度扑翼飞行器完成了真实的飞行实验, 验证了所提方法的有效性.Abstract: In view of the periodicity and the time scale difference in flapping flight, as well as the practical problems in the control of flapping flight, a singular perturbation theory based system stability analysis method for periodic flapping-wing motions is proposed in this paper. Firstly, a multi-rigid body model of flapping wing vehicle is established, which paves the way for the singular perturbation analysis of flapping wing dynamics. Secondly, the multi rigid body model is simplified, and the core problem of flapping wing flight dynamics is abstracted. By using the singular perturbation theory, the stability of flapping wing flight periodic orbit is analyzed, and its superiority compared with other methods is discussed. Finally, the experiments of real flight are conducted in the self-made four degrees of freedom flapping wing aircraft, which verify the effectiveness of the proposed method.
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图 1 不同种类扑翼飞行多刚体模型中的坐标系建立
Fig. 1 The coordinate setup in the multi-rigid body dynamics of different flapping wing flights
图 2 翅翼两级连杆系统中各刚体坐标系之间的旋转平移示意图
Fig. 2 The schematic for the rotations and the translations between different frames of a two-link wing
图 3 扑动翅翼周期轨道控制示意图
Fig. 3 The schematic for the control of flapping-wing periodic orbit
图 4 四自由度扑翼飞行器示意图 ((a)惯性坐标系与机体坐标系设置; (b)翅翼驱动与控制机构; (c1)无偏转的翅翼姿态; (c2)偏转后的翅翼姿态; (d1) 无偏转的尾翼姿态; (d2) 偏转后的尾翼姿态)
Fig. 4 The schematic for the 4-DoF flapping wing vehicle ((a) Inertial coordinate system and body coordinate system setup; (b) Flapping wings actuation and control mechanism; (c1) Flapping wings in default state; (c2) Flapping wings in deflection state; (d1) Tail in default state; (d2) Tail in deflection state)
图 5 运动捕捉系统辅助的四自由度扑翼飞行器实际飞行
Fig. 5 The real flight of the developed 4-DoF flapping wing system with the help of the motion capture system
图 6 不同两翼转角差下悬停飞行时的控制输入与机体姿态
Fig. 6 The control inputs and fuselage attitudes in the hovering flight with different two-wings deflection-angle deviations
图 8 由翅翼偏转引起的绕z轴周期变化的力矩 ((a)在不同偏转角下力矩的周期变化; (b)转角差值为−0.3倍最大转角的力矩多周期统计特性; (c)转角差值为0.3倍最大转角时的力矩多周期统计特性)
Fig. 8 The periodically changing torque around z-axis induced by the wings deflection ((a) Periodic variation of torque under different deflection angles; (b) Statistical characteristics of the torque with the deflection angle of −0.3 limit angle; (c) Statistical characteristics of the torque with the deflection angle of 0.3 limit angle)
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