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首页> 外文期刊>Celestial Mechanics and Dynamical Astronomy >Application of Hamiltonian structure-preserving control to formation flying on a J2-perturbed mean circular orbit
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Application of Hamiltonian structure-preserving control to formation flying on a J2-perturbed mean circular orbit

机译：哈密​​顿保结构控制在扰动J 2 平均圆轨道上的编队飞行中的应用

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The bounded quasi-periodic relative trajectories are investigated in this paper for on-orbit surveillance, inspection or repair, which requires rapid changes in formation configuration for full three-dimensional imaging and unpredictable evolutions of relative trajectories for non-allied spacecraft. A linearized differential equation for modeling J 2 perturbed relative dynamics is derived without any simplified treatment of full short-period effects. The equation serves as a nominal reference model for stationkeeping controller to generate the quasi-periodic trajectories near the equilibrium, i.e., the location of the chief. The developed model exhibits good numerical accuracy and is applicable to an elliptic orbit with small eccentricity inheriting from the osculating conversion of orbital elements. A Hamiltonian structure-preserving controller is derived for the three-dimensional time-periodic system that models the J 2-perturbed relative dynamics on a mean circular orbit. The equilibrium of the system has time-varying topological types and no fixed-dimensional unstable/stable/center manifolds, which are quite different from the two-dimensional time-independent system with a permanent pair of hyperbolic eigenvalues and fixed-dimensions of unstable/stable/ center manifolds. The unstable and stable manifolds are employed to change the hyperbolic equilibrium to elliptic one with the poles assigned on the imaginary axis. The detailed investigations are conducted on the critical controller gain for Floquet stability and the optimal gain for the fuel cost, respectively. Any initial relative position and velocity leads to a bounded trajectory around the controlled elliptic equilibrium. The numerical simulation indicates that the controller effectively stabilizes motions relative to the perturbed elliptic orbit with small eccentricity and unperturbed elliptic orbit with arbitrary eccentricity. The developed controller stabilizes the quasi-periodic relative trajectories involved in six foundational motions with different frequencies generated by the eigenvectors of the Floquet multipliers, rather than to track a reference relative configuration. Only the relative positions are employed for the feedback without the information from the direct measurement or the filter estimation of relative velocity. So the current controller has potential applications in formation flying for its less computation overload for on-board computer, less constraint on the measurements, and easily-achievable quasi-periodic relative trajectories.
机译：本文对有界的准周期相对轨迹进行了研究，以进行在轨监视，检查或维修，这要求对编队构型进行快速更改以进行完整的三维成像，并且对非盟军航天器的相对轨迹进行不可预测的演变。推导了用于建模J 2 扰动的相对动力学的线性微分方程，而没有对完整的短周期效应进行任何简化处理。该方程式作为驻地控制器的标称参考模型，用于在平衡附近（即主管的位置）生成准周期轨迹。所开发的模型具有良好的数值精度，并且适用于从轨道元素的密切转换继承而来的小离心率的椭圆轨道。推导了三维时间周期系统的哈密顿结构保持控制器，该模型对平均圆轨道上受J 2 扰动的相对动力学建模。系统的平衡具有随时间变化的拓扑类型，没有固定维的不稳定/稳定/中心流形，这与具有永久双曲特征值对和二维不稳定/维固定维的二维与时间无关的系统大不相同。稳定/中央歧管。不稳定和稳定的流形用于将双曲平衡更改为椭圆形，其中极点位于虚轴上。分别针对Floquet稳定性的关键控制器增益和燃油成本的最佳增益进行了详细研究。任何初始相对位置和速度都会导致围绕受控椭圆平衡的有限轨迹。数值模拟表明，该控制器有效地稳定了相对于小偏心度的摄动椭圆轨道和相对于任意偏心度的无扰动椭圆轨道的运动。所开发的控制器稳定了由Floquet乘数的特征向量生成的具有不同频率的六个基本运动中涉及的准周期相对轨迹，而不是跟踪参考相对配置。仅将相对位置用于反馈，而没有来自直接测量或相对速度的滤波器估计的信息。因此，当前的控制器在编队飞行中具有潜在的应用，因为它对车载计算机的计算负担较小，对测量的约束较少，并且易于实现的准周期相对轨迹。

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