A combined Averaging-Shooting Approach for the Trim Analysis of Hovering Insects/Flapping-Wing Micro-Air-Vehicles
A combined Averaging-Shooting Approach for the Trim Analysis of Hovering Insects/Flapping-Wing Micro-Air-Vehicles
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DOI：
10.2514/6.2017-1734
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发表时间：
2017-01
影响因子：
3.4
通讯作者：
Ahmed M. Hassan;H. Taha
中科院分区：
文献类型：
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作者：
Ahmed M. Hassan;H. Taha
由于翅膀相对于身体的振荡运动，生物飞行器及其人造仿生飞行器扑翼微型飞行器(FWMAV)的飞行动力学通常被描述为多体、非线性时间周期(NLTP)系统模型，其平衡和稳定性分析具有相当大的挑战性。在这项工作中，我们考虑了两自由度FWMAV的NLTP系统模型，该模型被限制为沿垂直轨道移动。我们结合了时序微积分、几何控制和平均等工具，为悬停时的FWMAV的平衡提供了严格的数学分析，即放松了在分析FWMAV和昆虫的平衡和稳定性时通常采用的单体和直接平均假设。我们还利用优化打靶法对所得到的周期轨道进行了数值捕捉，并对所得结果进行了验证。最后，我们为NLTP系统的平衡和稳定性分析提供了一种组合的平均-打靶法，该方法(I)不同于典型的打靶法，不需要初始猜测；(Ii)提供比解析平均方法更准确的结果，从而放松了对难以处理的高阶平均动力学的需要；以及(Iii)与数值打靶法相比，允许对系统动力学进行更深入的研究。
Because of the wing oscillatory motion with respect to the body, the flight dynamics of biological flyers as well as their man-made mimetic vehicles, flapping-wing microair-vehicles (FWMAVs), are typically represented by multi-body, nonlinear time-periodic (NLTP) system models whose balance and stability analyses are quite challenging. In this work, we consider a NLTP system model for a two-degree-of-freedom FWMAV that is confined to move along vertical rails. We combine tools from chronological calculus, geometric control, and averaging to provide a mathematically rigorous analysis for the balance of FWMAVs at hover; that is, relaxing the single-body and direct averaging assumptions that are commonly adopted in analyzing balance and stability of FWMAVs and insects. We also use optimized shooting to numerically capture the resulting periodic orbit and verify the obtained results. Finally, we provide a combined averaging-shooting approach for the balance and stability analysis of NLTP systems that (i) unlike typical shooting methods, does not require an initial guess; (ii) provides more accurate results than the analytical averaging approaches, hence relaxing the need for intractable high-order averaged dynamics; and (iii) allows a deeper scrutiny of the system dynamics, in contrast to numerical shooting methods.