Modeling of LEO orbital debris populations for ORDEM2008

The NASA Orbital Debris Engineering Model, ORDEM2000, is in the process of being updated to a new version: ORDEM2008. The data-driven ORDEM covers a spectrum of object size from 10 μm to greater than 1 m, and ranging from LEO (low Earth orbit) to GEO (geosynchronous orbit) altitude regimes. ORDEM2008 centimeter-sized populations are statistically derived from Haystack and HAX (the Haystack Auxiliary) radar data, while micron-sized populations are estimated from shuttle impact records. Each of the model populations consists of a large number of orbits with specified orbital elements, the number of objects on each orbit (with corresponding uncertainty), and the size, type, and material assignment for each object. This paper describes the general methodology and procedure commonly used in the statistical inference of the ORDEM2008 LEO debris populations. Major steps in the population derivations include data analysis, reference-population construction, definition of model parameters in terms of reference populations, linking model parameters with data, seeking best estimates for the model parameters, uncertainty analysis, and assessment of the outcomes. To demonstrate the population-derivation process and to validate the Bayesian statistical model applied in the population derivations throughout, this paper uses illustrative examples for the special cases of large-size (>1 m, >32 cm, and >10 cm) populations that are tracked by SSN (the Space Surveillance Network) and also monitored by Haystack and HAX radars operating in a staring mode.     

地面等待模型中的旅客延误时间成本分析与仿真

针对多机场地面等待问题MAGHP(Multi Airport Ground Holding Problem),深入研究了影响旅客延误时间的因素,并将其应用于数学模型中目标函数的计算。将航班延误时间转化为旅客延误时间,提出了一个在航班取消情况下减少旅客延误的新方法,并与多机场地面等待模型进行了比较,仿真结果表明,可以大幅度减少旅客延误时间。     

考虑观测的双冲量最优交会研究

针对跟踪星主动交会目标星的轨道转移问题,给出了考虑观测的双冲量最优交会迭代算法。首先对考虑观测的轨道交会问题进行了分析,给出了椭圆转移轨道的存在性判定方法。在此基础上,给出了基于粒子群的优化求解方案。经过对两异面椭圆轨道转移问题的仿真解算,求得了最优交会轨道,验证了算法的正确性。该研究成果可作为工程应用的有益参考,并为其他带约束的轨道交会优化问题提供可行的求解方案。     

Low-thrust transfer to Backflip orbits

The aim of the work is to design a low-thrust transfer from a Low Earth Orbit to a “useful” periodic orbit in the Earth–Moon Circular Restricted Three Body Model (CR3BP). A useful periodic orbit is here intended as one that moves both in the Earth–Moon plane and out of this plane without any requirements of propellant mass. This is achieved by exploiting a particular class of periodic orbits named Backflip orbits, enabled by the CR3BP. The unique characteristics of this class of periodic solutions allow the design of an almost planar transfer from a geocentric orbit and the use of the Backflip intrinsic characteristics to explore the geospace out of the Earth–Moon plane. The main advantage of this approach is that periodic plane changes can be obtained by performing an almost planar transfer. In order to save propellant mass, so as to increase the scientific payload of the mission, a low-powered transfer is considered. This foresees a thrusting phase to gain energy from a departing circular geocentric orbit and a second thrusting phase to match the state of the target Backflip orbit, separated by an intermediate ballistic phase. This results in a combined application of a low-thrust manoeuvre and of a periodical solution in the CR3BP to realize a new class of missions to explore the Earth–Moon neighbourhoods in a quite inexpensive way. In addition, a low-thrust transit between two different Backflip orbits is analyzed and considered as a possible extension of the proposed mission. Thus, also a Backflip-to-Backflip transfer is addressed where a low-powered probe is able to experience periodic excursions above and below the Earth–Moon plane only performing almost planar and very short transfers.     

能量最优与燃料最优Lambert交会问题

Lambert双脉冲交会问题是航天工程中轨道转移和在轨交会等领域的重要问题,而能量最优和燃料最优Lambert交会问题是针对典型应用背景和工程需求衍生的一类Lambert优化问题。针对能量最优与燃料最优Lambert双脉冲交会问题提出一种基于矢量形式的解析计算方法,给出能量最优和燃料最优Lambert交会问题的矢量形式解析解,同时对2种最优交会问题求解的性质与特点进行了分析对比。仿真结果验证了计算的正确性及燃料最优轨道相比能量最优轨道燃料消耗较少的事实。      

一类特殊实对称矩阵的逆特征值问题

讨论如下形式实矩阵的逆特征值问题（1）给定两个互异实数λ,μ和两个n维非零实向量x，y，求矩阵A，使（λ，x）和（μ，y）是A的特征对；（2）给定两个互异实数λ，μ和两个n维非零实向量x，y，求矩阵A和A*，使得（λ，x）和（μ，y）分别是A和A*的特征对．本文给出了问题有解的充要条件，并给出了一些数值例子。     

二维机翼非定常气动力学反命题的变分理论

非定常流动的反命题迄今在世界文献中尚属空白。本文首次对它进行探讨，就二维振荡机翼的非定常气动力学反命的适当提法及其数学模型作了较深的研究，利用变域变分工具成功地建立了相应的变分原理及广义变分原理，为非定常机翼设计及有限元解的应用提供完整周密的理论基础。     

双机平面格斗的一些问题——一种处理“二重角色”的方法

 结合坐标变换和能控区及微分对策方法,本文提出较为细缀的一种处理双机格斗“二重角色”问题的方法。分析了捕捉区、逃避区和危险区,有助于飞行员在空战格斗中采取有利于自己的控制。本文在空战格斗的对策模型中,考虑了双方匀变速运动。     

应用非线性模型预测控制的绳系卫星Halo轨道保持控制

针对哑铃型绳系卫星在圆形限制性三体问题(CRTBP)中的Halo轨道保持控制问题,应用非线性模型预测控制(NMPC)方法设计了Halo轨道保持控制器。首先采用摄动法得到目标Halo轨道,通过跟踪目标轨道上一运动点,将其转化为目标跟踪控制问题,然后设计非线性模型预测控制器对其进行跟踪控制。利用4阶Ronge-Kutta法对原非线性模型进行离散化,将预测控制中的有限时域最优问题转化为非线性规划问题进行求解,得到下一周期的控制量。最后通过数值仿真验证了即使在初始位置偏差较大的情况下,所设计的控制器只需要很少的速度增量就可使绳系卫星系统运动至目标轨道,并精确地保持在目标轨道上。     

A memetic algorithm for path planning of curvature-constrained UAVs performing surveillance of multiple ground targets

The problem of generating optimal paths for curvature-constrained unmanned aerial vehicles （UAVs） performing surveillance of multiple ground targets is addressed in this paper. UAVs are modeled as Dubins vehicles so that the constraints of UAVs＇ minimal turning radius can be taken into account. In view of the effective surveillance range of the sensors equipped on UAVs, the problem is formulated as a Dubins traveling salesman problem with neighborhood （DTSPN）. Considering its prohibitively high computational complexity, the Dubins paths in the sense of terminal heading relaxation are introduced to simplify the calculation of the Dubins distance, and a boundary-based encoding scheme is proposed to determine the visiting point of every target neighborhood. Then, an evolutionary algorithm is used to derive the optimal Dubins tour. To further enhance the quality of the solutions, a local search strategy based on approximate gradient is employed to improve the visiting points of target neighborhoods. Finally, by a minor modification to the individual encoding, the algorithm is easily extended to deal with other two more sophisticated DTSPN variants （multi-UAV scenario and multiple groups of targets scenario）. The performance of the algorithm is demonstrated through comparative experiments with other two state-of-the-art DTSPN algorithms identified in literature. Numerical simulations exhibit that the algorithm proposed in this paper can find high-quality solutions to the DTSPN with lower computational cost and produce significantly improved performance over the other algorithms.