New State Transition Matrices for Relative Motion of Spacecraft Formations in Perturbed Orbits
New State Transition Matrices for Relative Motion of Spacecraft Formations in Perturbed Orbits
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DOI：
10.2514/6.2016-5635
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发表时间：
2016-09
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影响因子：
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通讯作者：
Adam W. Koenig;T. Guffanti;S. D’Amico
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文献类型：
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作者：
Adam W. Koenig;T. Guffanti;S. D’Amico
本文提出了新的状态转移矩阵，该矩阵对两个航天器在任意偏心轨道上的相对运动进行建模，该运动受到 J2 和基于相对轨道元素的三种状态定义的微分阻力的扰动。这些矩阵是通过首先对相对运动方程（包括所有考虑的扰动）执行泰勒展开，然后计算所得线性微分方程的精确封闭式解而导出的。包括特定密度模型和无密度模型的微分阻力配方。特定于密度模型的公式需要大气的先验知识，而无密度模型的公式通过使用一组在飞行中估计的参数来增强相对状态，从而消除了这一要求。由此产生的状态转移矩阵用于将 J2 和微分阻力对先前作品中提供的近圆形轨道中相对运动的影响的几何解释推广到任意偏心轨道。此外，本文通过证明以前的作者使用各种技术导出的许多状态转换矩阵可以通过将本文提出的模型置于更严格的假设下来找到，从而协调了当前的文献。最后，通过与高保真数值轨道传播器的比较来验证所提出的状态转移矩阵。研究发现，包含无密度模型差动阻力的模型比特定于密度模型的模型表现出更好的性能。具体来说，与仅包含 J2 的模型相比，这些状态转换矩阵能够将传播误差减少至少一个数量级，并且能够在广泛的轨道场景下达到或超过文献中类似模型的精度。
This paper presents new state transition matrices that model the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J2 and differential drag for three state definitions based on relative orbital elements. These matrices are derived by first performing a Taylor expansion on the equations of relative motion including all considered perturbations and subsequently computing an exact, closed-form solution of the resulting linear differential equations. Both density-model-specific and density-model-free differential drag formulations are included. Density-model-specific formulations require a-priori knowledge of the atmosphere, while density-model-free formulations remove this requirement by augmenting the relative state with a set of parameters which are estimated in flight. The resulting state transition matrices are used to generalize the geometric interpretation of the effects of J2 and differential drag on relative motion in near-circular orbits provided in previous works to arbitrarily eccentric orbits. Additionally, this paper harmonizes current literature by demonstrating that a number of state transition matrices derived by previous authors using various techniques can be found by subjecting the models presented in this paper to more restrictive assumptions. Finally, the presented state transition matrices are validated through comparison with a high-fidelity numerical orbit propagator. It is found that the models including density-model-free differential drag exhibit much better performance than their density-model-specific counterparts. Specifically, these state transition matrices are able to reduce propagation errors by at least an orderof-magnitude when compared to models including only J2 and are able to match or exceed the accuracy of comparable models in literature over a broad range of orbit scenarios.