Optimal guidance based on receding horizon control for low-thrust transfer to libration point orbits

This paper addresses the design and computation of a guidance law for a transfer mission from an orbit near the Earth to a halo orbit around the libration point L₂ in the Sun–Earth system. The guidance law, which is designed based on receding horizon control and compensates for launch velocity errors that are introduced by inaccuracies of the launch vehicle, is solved using the generating function method. During the design of the closed-loop guidance law, the entire transfer mission, which is considered a nonlinear optimal control problem, is evaluated to obtain a nominal reference trajectory. Using the launch velocity errors and the uncertainty of the model, a spacecraft controlled by the proposed guidance law tracks the reference trajectory. Furthermore, the original Riccati differential equation in the receding horizon control algorithm is replaced by an equivalent convenient form of the Riccati differential equation that is based on the generating function. The high-efficiency solution of the equivalent equation avoids the online direct integration of the original Riccati differential equation, which significantly increases the computational efficiency for the receding horizon control problem. Numerical simulations using a nonlinear bicircular four-body model demonstrate the capabilities of the proposed receding horizon guidance law for the transfer mission. In addition, the generating function method improves the computational efficiency by at least one order of magnitude over the backward sweep method in solving the receding horizon control problem.     

“嫦娥二号”卫星CCD立体相机的关键技术

文章介绍了中国两次绕月探测中 CCD 立体相机所采用的技术与创新,并与国际同类相机所获取的图像进行了比较;在此基础上详细介绍了“嫦娥二号”(CE-2)卫星CCD立体相机的综合创新集成技术--“单镜头两视角同轨立体成像、时间延迟积分图像传感器（TDICCD）推扫、速高比补偿”,并从工程目标与科学目标出发进行探测灵敏度及成像动态范围的需求分析;根据需求分析确定了总体技术方案,包括光、机、电的优化设计以及对月探测中首次采用TDICCD的技术困难与对策;特别讨论了速高比补偿的方案及实施途径,并进行了在轨试验验证。文章最后分别给出了虹湾地区成像分辨率为1.3m以及全月面分辨率为7m 的代表性图像,图像清晰、层次丰富,显示出中国在对月立体成像技术上取得了显著进步。     

A rendezvous navigation algorithm for orbit determination, based on visual measurements by space vehicle crew members

At present, various radio navigation systems are employed during the automated approach of a transport vehicle to a space station. Experience has shown that emergency situations can occur in which it is necessary to revert to manual override of the automatic approach.Such situations have indeed occurred during flight operations of the space station Mir. The crews of the transport vehicles and the Mir used manual steering more than 30 times for successful docking, and four times for approach to the station.Successful manual steering demands absolute understanding of the relative orbit parameters. The decisive task of the crew is to determine these relative parameters. This is possible using visual observations from either the transport vehicle or the station using simple and reliable instruments. This article explains the algorithm for determining the relative orbits from visual crew observations, based on similarities of relative orbit families.     

On prediction of re-entry time of an upper stage from GTO

The evolution of objects in geostationary transfer orbit (GTO) is determined by a complex interplay of atmospheric drag and luni-solar gravity. These orbits are highly eccentric (eccentricity >0.7) and have large variations in velocity and perturbations during a revolution. The periodic changes in the perigee altitudes of these orbits are mainly due to the gravitational perturbations of the Sun and the Moon. The re-entry time of the objects in such orbits is sensitive to the initial conditions. The aim of this paper is to study the re-entry time of the cryogenic stage of the Indian geo-synchronous launch vehicle, GSLV-F04/CS, which has been decaying since 2 September 2007 from initial orbit with eccentricity equal to 0.706. Two parameters, initial eccentricity and ballistic coefficient, are chosen for optimal estimation. It is known that the errors are more in eccentricity for the observations based on two line elements (TLEs). These two parameters are computed with response surface method using a genetic algorithm for the selected eight different zones, based on rough linear variation of the mean apogee altitude during 200 days orbit evolution. The study shows that the GSLV-F04/CS will re-enter between 5 December 2010 and 7 January 2011. The methodology is also applied to study the re-entry of six decayed objects (cryogenic stages of GSLV and Molniya satellites). Good agreement is noticed between the actual and the predicted re-entry times. The absolute percentage error in re-entry prediction time for all the six objects is found to be less than 7%. The present methodology is being adopted at Vikram Sarabhai Space Centre (VSSC) to predict the re-entry time of GSLV-F04/CS.     

贩毒吸毒的微分方程模型及定性分析

贩毒吸毒是人类丑恶行为表现出的社会丑恶现象，在人类正常的生活环境中时有发生。特别近年来有的国家或地区呈现流行的趋势，各国对此都十分关注。建立三个描述贩毒吸毒社会丑恶现象的微分方程模型。借助于微分方程定性论的基本理论，分析微分方程模型基本理论，分析贩毒吸毒流行的趋势，流行的结局，得到基本符合实际的效果。     

地球静止轨道卫星撞击解体的数值模拟

分析了地球静止轨道（GE0）环内的物体现状,引入美国家航空航天局（NASA）的标准解体模型,给出了卫星撞击解体算法,编写了数值仿真软件,仿真研究了GEO卫星撞击解体形成碎片的特征及其轨道分布。结果表明：撞击会产生大量碎片,对空间环境造成长期的严重危害。研究结果对分析卫星撞击解体特性、保护空间环境有一定的参考价值。     

基于三阶解析解的小行星平衡点附近halo轨道确定方法研究

尽管周期解的存在性已经被证明,但要在给定的动力学系统中寻找到满足一定精度要求的周期解依然是一件极富挑战性的工作.提出如下方法确定小行星平衡点附近精确的周期轨道(halo轨道).首先扩展运动方程:将小行星平衡点附近轨道运动方程的右端项在平衡点处展成三阶幂级数.从而将非线性运动学方程扩展为拟线性微分方程.然后求近似解析解:应用Lindstedt-Poincaré方法求解扩展后的运动方程组,将周期解和其运动频率展开成三阶幂级数,并将二者代人扩展后的拟线性微分方程中.这样就可以得到三个不同阶的线性运动方程,逐次求解三个微分方程并消除解中的永年项即可得到hal.轨道的三阶解析解.最后微分校正:将周期轨道在三阶解析解附近线性化,得到状态转移矩阵,并使用状态转移矩阵和轨道终端状态的偏差修正轨道初值,从而得到满足精度要求的精确引力场中的halo轨道.     

OTV在空间攻防体系中的发展研究

轨道转移飞行器(OTV)是在轨道之间进行物质、能量转移的一类飞行器的总称.本文通过对OTV的概述,从其技术特点出发,介绍其在空间攻防体系中的应用和关键技术,最后对我国OTV的发展规划作了简要的剖析.     

Impact of GPS antenna phase center variations on precise orbits of the GOCE satellite

The first European Space Agency Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) has been launched on March 17, 2009. The 12-channel dual-frequency Global Positioning System receiver delivers 1 Hz data and provides the basis for precise orbit determination (POD) on the few cm-level for such a very low orbiting satellite (254.9 km). As a member of the European GOCE Gravity Consortium, which is responsible for the GOCE High-level Processing Facility (HPF), the Astronomical Institute of the University of Bern (AIUB) provides the Precise Science Orbit (PSO) product for the GOCE satellite. The mission requirement for 1-dimensional POD accuracy is 2 cm. The use of in-flight determined antenna phase center variations (PCVs) is necessary to meet this requirement. The PCVs are determined from 154 days of data and the magnitude is up to 3-4 cm. The impact of the PCVs on the orbit determination is significant. The cross-track direction benefits most of the PCVs. The improvement is clearly seen in the orbit overlap analysis and in the validation with independent Satellite Laser Ranging (SLR) measurements. It is the first time that SLR could validate the cross-track component of a LEO orbit.