ABSTRACT ATTITUDE TRACKING CONTROL FOR SPACECRAFT FORMATION FLYING

CALL FOR PAPERSThe 22nd AAS/AIAA Space Flight Mechanics MeetingFrancis Marion Hotel, Charleston, South CarolinaABSTRACT DEADLINE:The 22nd Space Flight Mechanics Meeting will be held January 29 – February 2, 2012 at the Francis Ma-rion Hotel in Charleston, South Carolina. The conference is organized by the American Astronautical So-ciety (AAS) Space Flight Mechanics Committee and co-sponsored by the American Institute of Aeronau-tics and Astronautics (AIAA) Astrodynamics Technical Committee. Manuscripts are solicited on topics related to space-flight mechanics and astrodynamics, including but not necessarily limited to:October 3, 2011• Asteroid and non-Earth orbiting missions• Atmospheric re-entry guidance and control• Attitude dynamics, determination and control• Attitude-sensor and payload-sensor calibration• Dynamical systems theory applied to space flight prob-lems• Dynamics and control of large space structures and tethers• Earth orbital and planetary mission studies• Flight dynamics operations and spacecraft autonomy • Orbit determination and space-surveillance tracking • Orbital debris and space environment• Orbital dynamics, perturbations, and stability• Rendezvous, relative motion, proximity missions, and formation flying• Reusable launch vehicle design, dynamics, guidance, and control• Satellite constellations• Space situational awareness and conjunction analysis • Spacecraft guidance, navigation and control (GNC) • Trajectory / mission / maneuver design and optimiza-tionManuscripts will be accepted based on the quality of the extended abstract, the originality of the work and/or ideas, and the anticipated interest in the proposed subject. Submissions that are based on experi-mental results or current data, or report on ongoing missions, are especially encouraged.Complete manuscripts are required before the conference. English is the conference working language. SPECIAL SESSIONSProposals are being considered for suitable special sessions, such as topical panel discussions, invited ses-sions, workshops, mini-symposia, and technology demonstrations. A proposal for a panel discussion should include the session title, a brief description of the discussion topic(s), and a list of the speakers and their qualifications. For an invited session, workshop, mini-symposium, or demonstration, a proposal should include the session title, a brief description, and a list of proposed activities and/or invited speakers and paper titles. Prospective special-session organizers should submit their proposals to the Technical Chairs.BREAKWELL STUDENT TRAVEL AWARDThe AAS Space Flight Mechanics Committee announces the John V. Breakwell Student Travel Award. This award provides travel expenses for up to three (3) U.S. and Canadian students presenting at this con-ference. Students wishing to apply for this award are strongly advised to submit their completed manu-script by the abstract submittal deadline. The maximum coverage per student is limited to $1000. Details and applications may be obtained via .INFORMATION FOR AUTHORSBecause the submission deadline of October 3, 2011 has been fully extended for the convenience of con-tributors, there are no plans to defer this deadline due to the constraints of the conference planning sche-dule. Notification of acceptance will be sent via email by November 14, 2011. Detailed author instruc-tions will be sent by email following acceptance. By submitting an abstract, the author affirms that the manuscript’s majority content has not been previously presented or published elsewhere.Authors may access the web-based abstract submittal system using the link available via the official web-site . During the online submission process, authors are expected to provide: 1. a paper title, as well as the name, affiliation, postal address, telephone number, and email address of thecorresponding author and each co-author,2. an extended abstract in the Portable Document File (PDF) format of at least 500 words that includes thetitle and authors, and provides a clear and concise statement of the problem to be addressed, the pro-posed method of solution, the results expected or obtained, and an explanation of its significance to as-trodynamics and/or space-flight mechanics, with pertinent references and supporting tables and figures as necessary, and,3. a condensed abstract (100 words) to be included in the conference program, which is directly typed intothe text box provided on the web page and avoids the use of special symbols or characters, such as Greek letters.Foreign contributors requiring an official letter of acceptance for a visa application should contact the Technical Chairmen by email at their earliest opportunity.Technology Transfer Notice - Technology transfer guidelines substantially extend the time required to review abstracts and manuscripts by private enterprises and government agencies. To preclude late sub-missions and withdrawals, it is the responsibility of the author(s) to determine the extent of necessary ap-provals prior to submitting an abstract.No-Paper/No-Podium Policy – A complete manuscript must be electronically uploaded to the web site prior to the conference in PDF format, be no more than twenty (20) pages in length, and conform to the AAS manuscript format. If a complete manuscript is not received on time, then its presentation at the con-ference shall be forfeited; and if a presentation is not made by an author at the conference, then the manu-script shall be omitted from published proceedings.Questions concerning the submission of manuscripts should be addressed to the technical chairs:AAS Technical ChairMr. James McAdamsJohns Hopkins University Applied Physics Laboratory 11100 Johns Hopkins RoadLaurel, MD 20723-6099(240) 228-8685 (voice)Jim.McAdams@ AIAA Technical ChairMr. David McKinleya.i. solutions, Inc.10001 Derekwood Lane, Suite 215 Lanham, MD 20706(410) 980-2904 (voice)david.mckinley@All other questions should be directed to the General Chairs:AAS General ChairDr. Matthew Berry Analytical Graphics, Inc. 220 Valley Creek Boulevard Exton, PA 19341(610) 981-8213 (voice) mberry@ AIAA General ChairMr. Keith L. Jenkins, Esq.Keith L. Jenkins., Registered Patent Attorney, LLC 44075 W. Neely DriveMaricopa, AZ 85138(480) 390-6179 (voice)keith@。

一种非线性系统自适应跟踪控制器设计作者：易鸿来源：《现代电子技术》2013年第06期摘要：为了处理闭环系统遇外界强干扰时出现不稳定的问题，提出一种非线性系统自适应跟踪控制设计方案该设计方法。

主要利用比例和积分结构，这种结构将系统中不确定项由单位分解逼近，同时这种结构的鲁棒跟踪控制器也使系统在干扰波动影响下保持很好的跟踪效果。

其结果使闭环系统所有的状态与跟踪误差收敛到原点的一个很小的范围，通过仿真实验表明这种控制器设计可行并且有效。

关键词：单位分解；非线性系统； PI控制；模糊逻辑；自适应跟踪控制器中图分类号： TN911⁃34； TB18 文献标识码： A 文章编号： 1004⁃373X（2013）06⁃0007⁃030 引言自适应控制的基本思想是：在控制系统的运行过程中，系统本身不断地测量被控系统的状态、性能和参数，从而认识或掌握系统当前的运行指标并与期望的指标相比较，进而做出决策，来改变控制器的结构、参数或根据自适应规律来改变控制作用，以保证系统运行在某种意义下的最优或次优状态。

自适应控制系统主要由控制器、被控对象、自适应器及反馈控制回路和自适应回路组成。

与常规的反馈控制系统比较，自适应控制系统有三个显著特点：控制器可调，增加了自适应回路，适用对象。

因设计的原理和结构的不同，自适应控制系统大致可分为如下几种主要形式：变增益控制、模型参考自适应控制系统、自校正控制系统。

本文研究针对非线性控制中出现的一些问题，提出一种基于单位分解的变结构自适应控制，利用单位分解作为万能逼近器的设计思想逼近非线性系统的未知函数，有效地减少自适应律个数和解决系统变量个数增加而导致的维数灾难问题。

这种设计方法一方面有效抵消的外部干扰，另一方面也较好解决了传统模糊自适应控制带来的维数灾难问题。

1 问题描述4 结语本文针对传统模糊自适应控制的维数灾难问题，提出了一种基于单位分解的的自适应控制方案。

方案选用单位分解逼近非线性系统中的不确定项，用较少的开覆盖完成控制目标，是自适应机构在一定程度上得到简化，节省了控制算法的计算量。

第42卷第1期航天返回与遥感2021年2月SPACECRAFT RECOVERY & REMOTE SENSING11多源信息融合在空间态势感知领域的应用与发展王兴龙 蔡亚星 陈士明 陈余军（中国空间技术研究院通信与导航卫星总体部，北京 100094）摘要在当前复杂多样的航天任务领域中，多源信息融合技术的重要性日益突出。

文章以多源信息融合技术为核心，调研分析了其在空间态势感知领域的应用现状与发展前景；概述了多源信息融合的定义、模型和理论研究现状；归纳了空间态势感知的信息源种类和典型传感器；分析了基于多源信息融合的典型空间态势感知系统，包括美国空间监视网（SSN）、“轨道瞭望”（OrbitOutlook）计划、“印记”（Hallmark）计划和欧盟空间监视与跟踪系统（EUSST）等；最后对多源信息融合在空间态势感知领域的发展前景进行了展望。

文章研究结果可为中国空间态势感知和多源信息融合技术发展提供参考。

关键词多源信息融合空间态势感知航天应用发展中图分类号: V11文献标志码: A 文章编号: 1009-8518(2021)01-0011-10DOI: 10.3969/j.issn.1009-8518.2021.01.002Application and Development of Multi-source Information Fusion inSpace Situational AwarenessWANG Xinglong CAI Yaxing CHEN Shiming CHEN Yujun（Institute of Telecommunication and Navigation Satellites, China Academy of Space Technology, Beijing 100094, China）Abstract The multi-source information fusion technology is expected to play an increasingly important role in current various space missions. This paper focuses on the multi-source information fusion technology and analyzes its application and development in space situational awareness. Firstly, the definition, model and theoretical research of multi-source information fusion are introduced. The information source kinds and the typical sensors of space situational awareness are summarized. Then, the foreign typical space situational awareness systems based on multi-source information fusion are analyzed, such as USA Space Surveillance Network (SSN), OrbitOutlook, Hallmark and European Union Space Surveillance and Tracking Framework (EUSST). Finally, the future development of multi-source information fusion in space situational awareness is prospected. The results of this paper can provide references for the development of China space situational awareness and multi-source information fusion technologies.Keywords multi-source information fusion; space situational awareness; space application; development 0 引言随着人类空间活动的不断增加，地球周围空间产生了大量人造物体，包括航天器、火箭末级和空间收稿日期：2020-12-05引用格式：王兴龙, 蔡亚星, 陈士明, 等. 多源信息融合在空间态势感知领域的应用与发展[J]. 航天返回与遥感, 2021, 42(1): 11-20.WANG Xinglong, CAI Yaxing, CHEN Shiming, et al. Application and Development of Multi-source Information Fusion in Space Situational Awareness[J]. Spacecraft Recovery & Remote Sensing, 2021, 42(1): 11-20. (in Chinese)12航天返回与遥感2021年第42卷碎片等，这些空间物体在给人类带来便利的同时，也影响着人类的空间活动。

基于组合导航系统的数值积分粒子滤波算法摘要本研究工作中，我们研究数值积分粒子滤波器（CPF）算法来计算GPS / INS组合导航系统的估值。

GPS/ INS组合导航系统的误差模型是非线性的。

CPF算法是建立在数值积分卡尔曼滤波器（CKF）和粒子滤波器（PF）之上的，并且具有两者的优点。

因此CPF可以为高维非线性滤波器问题提供一个系统的解决方案。

CPF通过模拟的方式来展现。

模拟结果表明，当与次优技术例如数值积分卡尔曼滤波器（CKF）比较时，这种方法具有优越的性能，因为在这种情况下CKF有大的初始偏差。

模拟的结果表明，该改进的CPF的表现超越了传统的非线性滤器。

该研究为工程设计和改进提供了支持。

关键字：数值积分规则数值积分卡尔曼滤波（CKF）数值积分粒子滤波器（CPF）组合导航1、引言滤波器在实际系统起着非常重要的作用。

在现实世界中，几乎所有的系统都具有非线性特性。

只有深刻领会非线性系统的本质，合理建立系统模型和非线性网络滤波方法才能有效地帮助分析和解决各种在工程实践中遇到的问题。

卡尔曼滤波器（KF）是用于估算线性系统[1]的最优滤波器。

该GPS / INS导航系统通常采用卡尔曼滤波器来估计所述系统的状态[2，3]。

卡尔曼滤波器的简单计算，递归结构和数学严谨的推导，使其适用和吸引大量实际应用的使用。

然而，许多现实世界的系统都是非线性的。

扩展卡尔曼滤波器（EKF）的开发来帮助这些非线性系统。

但是扩展卡尔曼滤波器是一种次优的非线性滤波器，由于当是线性系统[4，5]时截断了高阶项。

EKF的计算时间类似于卡尔曼滤波器[6]的。

数值积分卡尔曼滤波器（CKF）是没有非线性模型[7]的直链化非线性滤波连接的方法。

在CKF算法是公正和最小方差，这比GPS / INS 动态系统[8] EKF方法更好。

在CKF中被建议使用贬低线性偏置的非线性测量方程[9]。

物理系统往往受到意想不到的偏差或失误[10]。

其结果是，有一个方法，来维持一个精确的和可靠的解决方案[11]是重要的。

双目视觉识别柚子轴线姿态的一种方法云双;张秋菊【摘要】Recognizing the fruit posture was often needed in the applications of fruit sorting, testing and robotic fruit-picking. Based on the binocular stereo vision technology, a method of finding the three-dimensional orientation of the grapefruit axis by searching for the fruit boundary shape with photographic geometry principle was presented. The effectiveness of the method was proved by the experimental results.%在水果分选、检测以及水果采摘机器人中,需要识别目标物体的姿态信息.文中讨论了一种利用双目立体视觉技术,通过寻找柚子边界形状并结合摄影几何原理寻找其轴线三维姿态的方法,实验验证了该方法的有效性.【期刊名称】《江南大学学报（自然科学版）》【年(卷),期】2012(011)001【总页数】5页(P33-37)【关键词】像面轴线;空间交汇;水果姿态【作者】云双;张秋菊【作者单位】江南大学机械工程学院,江苏无锡214122;江南大学机械工程学院,江苏无锡214122【正文语种】中文【中图分类】TP39近年来，在水果品质自动检测、水果分级分选方面，机器视觉系统得到了越来越多的应用［1-4］。

在水果采摘、分拣和加工中应用机器人技术正在成为实现水果加工自动化的一大发展趋势，不仅可以改善水果加工卫生条件，还可以减轻劳动强度和提高劳动效率。

采用机械手取代人工操作，获取水果位姿信息是非常关键的。

第42卷第1期航天返回与遥感2021年2月SPACECRAFT RECOVERY & REMOTE SENSING21星上智能信息处理技术发展趋势分析与若干思考乔凯1智喜洋*2王达伟2胡建明2韩奇超2张勇1（1 北京跟踪与通信技术研究所，北京 100094）（2 哈尔滨工业大学空间光学工程研究中心，哈尔滨 150001）摘要星上智能信息处理的主要任务是接收天基探测载荷数据，并在星上完成数据压缩、复杂海空环境下高价值目标的发现、识别与跟踪等工作，达到降低下传数据率、支持天基广域探测与全自主即时态势感知等目的。

文章回顾了美国、德国等航天强国光学卫星的星上信息处理技术的发展现状，梳理总结了该技术的发展思路与关键指标。

在此基础上，结合星上信息处理技术的应用现状，着重从天基光学探测应用需求出发，提出星上智能信息处理关键技术与能力的发展建议，为推进未来海空目标多源探测与信息融合处理技术创新与持续发展提供支撑。

关键词天基探测海空目标星上智能信息处理态势感知航天遥感中图分类号: V443+.5文献标志码: A 文章编号: 1009-8518(2021)01-0021-07DOI: 10.3969/j.issn.1009-8518.2021.01.003Analysis and Some Thoughts on the Development Trend of the on-board Intelligent Information Processing TechnologyQIAO Kai1 ZHI Xiyang*2 WANG Dawei2HU Jianming2 HAN Qichao2 ZHANG Yong1（1 Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094）（2 Research Center of Space Optical Engineering, Harbin Institute of Technology, Harbin, 150001)Abstract The main task of intelligent information processing is to receive satellite detection payload data, and complete data compression, target discovery, recognition and tracking tasks on board, so as to achieve the purpose of reducing down transmission data rate and supporting space-based wide-area awareness of high-value sea-aero targets. This paper reviews the development history and current situation of the on-board information processing technology of optical satellites in the United States, Germany and other aerospace powers, and then summarizes the development approaches and key indicators of this technology. On this basis, combined with the application status and application requirements of optical satellite intelligent detection, the development suggestions of key technologies and capabilities on on-board intelligent information processing are put forward, which can provide support for the innovation and sustainable development of multi-mode detection and information fusion processing technology for sea-aero targets in the future.Keywords space-based detection; sea-aero target; on-board intelligent information processing; situation awareness; space remote sensing收稿日期：2021-01-12基金项目：国家自然科学基金（61975043）引用格式：乔凯, 智喜洋, 王达伟, 等. 星上智能信息处理技术发展趋势分析与若干思考[J]. 航天返回与遥感, 2021, 42(1): 21-27.QIAO Kai, ZHI Xiyang, WANG Dawei, et al. Analysis and Some Thoughts on the Development Trend of the on-board Intelligent Information Processing Technology[J]. Spacecraft Recovery & Remote Sensing, 2021, 42(1): 21-27. (in Chinese)22航天返回与遥感2021年第42卷0 引言基于卫星平台的天基光学探测具有观测范围广、空间与时间分辨率高、可全天候工作等独特优势，已成为海空目标精准识别、持续监视的必要手段，是实现广域海空监管的有效途径，在交通运输、海洋执法、国防安全等领域有着重要应用[1]。

Vol.18　No.5　6 航　天　器　工　程SPACECRA FT EN GIN EERIN G 第18卷　第5期　2009年9月Open Loop T racking for Yinghuo 21Martian OrbiterPIN G Jinsong SHAN G Kun Q IAN Zhihan YE Shuhua HON G Xiaoyu ZHAN G Sujun J IAN Nianchuan WAN G Mingyuan YAN Jianguo SUN Jing SHI Xian HUAN G Qian DA I Chunli FUN G Leewo YAN Haojian WAN G Guangli L IU Qinghui L I Jinling L I Huihua ZH EN G Weimin HU Xiaogong WAN G Weihua HUAN G Y ong WAN G Wenbin J IAN G Dongrong FAN Qingyuan GOU Wei HAN Tingting(Shanghai Ast ronomical Observatory ,Shanghai 200030,China )Abstract :The 1st Chinese Mars p robe ,Y inghuo 21,is planned to be launched in Octo ber 2009,toget her wit h t he Russia Phobos 2Grunt landing mission.YH 21will explore t he space weat her of t he Mars ,and test t he deep space communication and navigation techniques.Different f rom com 2mon deep space mission ,t he ast ronomical Very Long Baseline Interferometry (VLBI ),open loop t racking met hod ,like DOR/DOR ,seam beam VLBI and one 2way Doppler will be used to deter 2mine t he S/C orbit and position.K ey w ords :Mars exploration ;Y inghuo 21;open loop ;VLB I收稿日期:2009207201;修回日期:2009207215基金项目:中俄萤火一号火星探测项目;国家863计划资助课题(2008AA12A209,2008AA12A210)、国家自然科学基金课题(10973031)、中科院重要方向性项目(K J CX22TW 2T1322)作者简介:平劲松(1968-),男,博士,中科院天文创新基地《现代地壳运动监测与地球参考系》团组首席研究员,博士生导师,中科院2004年度“百人计划入选者”,主要从事行星科学、大气科学、大气电离层、月球行星(深空)探测等领域和方向的研究。

a r X i v :g r -q c /0411082v 1 16 N o v 2004Laser Ranging to the Moon,Mars and BeyondSlava G.Turyshev,James G.Williams,Michael Shao,John D.AndersonJet Propulsion Laboratory,California Institute of Technology,4800Oak Grove Drive,Pasadena,CA 91109,USAKenneth L.Nordtvedt,Jr.Northwest Analysis,118Sourdough Ridge Road,Bozeman,MT 59715USA Thomas W.Murphy,Jr.Physics Department,University of California,San Diego 9500Gilman Dr.,La Jolla,CA 92093USA Abstract Current and future optical technologies will aid exploration of the Moon and Mars while advancing fundamental physics research in the solar system.Technologies and possible improvements in the laser-enabled tests of various physical phenomena are considered along with a space architecture that could be the cornerstone for robotic and human exploration of the solar system.In particular,accurate ranging to the Moon and Mars would not only lead to construction of a new space communication infrastructure enabling an improved navigational accuracy,but will also provide a significant improvement in several tests of gravitational theory:the equivalence principle,geodetic precession,PPN parameters βand γ,and possible variation of the gravitational constant G .Other tests would become possible with an optical architecture that would allow proceeding from meter to centimeter to millimeter range accuracies on interplanetary distances.This paper discusses the current state and the future improvements in the tests of relativistic gravity with Lunar Laser Ranging (LLR).We also consider precision gravitational tests with the future laser rangingto Mars and discuss optical design of the proposed Laser Astrometric Test of Relativity (LATOR)mission.We emphasize that already existing capabilities can offer significant improvements not only in the tests of fundamental physics,but may also establish the infrastructure for space exploration in the near future.Looking to future exploration,what characteristics are desired for the next generation of ranging devices,what is the optimal architecture that would benefit both space exploration and fundamental physics,and what fundamental questions can be investigated?We try to answer these questions.1IntroductionThe recent progress in fundamental physics research was enabled by significant advancements in many technological areas with one of the examples being the continuing development of the NASA Deep Space Network –critical infrastructure for precision navigation and communication in space.A demonstration of such a progress is the recent Cassini solar conjunction experiment[8,6]that was possible only because of the use of Ka-band(∼33.4GHz)spacecraft radio-tracking capabilities.The experiment was part of the ancillary science program–a by-product of this new radio-tracking technology.Becasue of a much higher data rate transmission and, thus,larger data volume delivered from large distances the higher communication frequency was a very important mission capability.The higher frequencies are also less affected by the dispersion in the solar plasma,thus allowing a more extensive coverage,when depp space navigation is concerned.There is still a possibility of moving to even higher radio-frequencies, say to∼60GHz,however,this would put us closer to the limit that the Earth’s atmosphere imposes on signal transmission.Beyond these frequencies radio communication with distant spacecraft will be inefficient.The next step is switching to optical communication.Lasers—with their spatial coherence,narrow spectral emission,high power,and well-defined spatial modes—are highly useful for many space applications.While in free-space,optical laser communication(lasercomm)would have an advantage as opposed to the conventional radio-communication sercomm would provide not only significantly higher data rates(on the order of a few Gbps),it would also allow a more precise navigation and attitude control.The latter is of great importance for manned missions in accord the“Moon,Mars and Beyond”Space Exploration Initiative.In fact,precision navigation,attitude control,landing,resource location, 3-dimensional imaging,surface scanning,formationflying and many other areas are thought only in terms of laser-enabled technologies.Here we investigate how a near-future free-space optical communication architecture might benefit progress in gravitational and fundamental physics experiments performed in the solar system.This paper focuses on current and future optical technologies and methods that will advance fundamental physics research in the context of solar system exploration.There are many activities that focused on the design on an optical transceiver system which will work at the distance comparable to that between the Earth and Mars,and test it on the Moon.This paper summarizes required capabilities for such a system.In particular,we discuss how accurate laser ranging to the neighboring celestial bodies,the Moon and Mars,would not only lead to construction of a new space communication infrastructure with much improved navigational accuracy,it will also provide a significant improvement in several tests of gravitational theory. Looking to future exploration,we address the characteristics that are desired for the next generation of ranging devices;we will focus on optimal architecture that would benefit both space exploration and fundamental physics,and discuss the questions of critical importance that can be investigated.This paper is organized as follows:Section2discusses the current state and future per-formance expected with the LLR technology.Section3addresses the possibility of improving tests of gravitational theories with laser ranging to Mars.Section4addresses the next logical step—interplanetary laser ranging.We discuss the mission proposal for the Laser Astrometric Test of Relativity(LATOR).We present a design for its optical receiver system.Section5 addresses a proposal for new multi-purpose space architecture based on optical communica-tion.We present a preliminary design and discuss implications of this new proposal for tests of fundamental physics.We close with a summary and recommendations.2LLR Contribution to Fundamental PhysicsDuring more than35years of its existence lunar laser ranging has become a critical technique available for precision tests of gravitational theory.The20th century progress in three seem-ingly unrelated areas of human exploration–quantum optics,astronomy,and human spaceexploration,led to the construction of this unique interplanetary instrument to conduct very precise tests of fundamental physics.In this section we will discuss the current state in LLR tests of relativistic gravity and explore what could be possible in the near future.2.1Motivation for Precision Tests of GravityThe nature of gravity is fundamental to our understanding of the structure and evolution of the universe.This importance motivates various precision tests of gravity both in laboratories and in space.Most of the experimental underpinning for theoretical gravitation has come from experiments conducted in the solar system.Einstein’s general theory of relativity(GR)began its empirical success in1915by explaining the anomalous perihelion precession of Mercury’s orbit,using no adjustable theoretical parameters.Eddington’s observations of the gravitational deflection of light during a solar eclipse in1919confirmed the doubling of the deflection angles predicted by GR as compared to Newtonian and Equivalence Principle(EP)arguments.Follow-ing these beginnings,the general theory of relativity has been verified at ever-higher accuracy. Thus,microwave ranging to the Viking landers on Mars yielded an accuracy of∼0.2%from the gravitational time-delay tests of GR[48,44,49,50].Recent spacecraft and planetary mi-crowave radar observations reached an accuracy of∼0.15%[4,5].The astrometric observations of the deflection of quasar positions with respect to the Sun performed with Very-Long Base-line Interferometry(VLBI)improved the accuracy of the tests of gravity to∼0.045%[45,51]. Lunar Laser Ranging(LLR),the continuing legacy of the Apollo program,has provided ver-ification of GR improving an accuracy to∼0.011%via precision measurements of the lunar orbit[62,63,30,31,32,35,24,36,4,68].The recent time-delay experiments with the Cassini spacecraft at a solar conjunction have tested gravity to a remarkable accuracy of0.0023%[8] in measuring deflection of microwaves by solar gravity.Thus,almost ninety years after general relativity was born,Einstein’s theory has survived every test.This rare longevity and the absence of any adjustable parameters,does not mean that this theory is absolutely correct,but it serves to motivate more sensitive tests searching for its expected violation.The solar conjunction experiments with the Cassini spacecraft have dramatically improved the accuracy in the solar system tests of GR[8].The reported accuracy of2.3×10−5in measuring the Eddington parameterγ,opens a new realm for gravitational tests,especially those motivated by the on-going progress in scalar-tensor theories of gravity.1 In particular,scalar-tensor extensions of gravity that are consistent with present cosmological models[15,16,17,18,19,20,39]predict deviations of this parameter from its GR value of unity at levels of10−5to10−7.Furthermore,the continuing inability to unify gravity with the other forces indicates that GR should be violated at some level.The Cassini result together with these theoretical predictions motivate new searches for possible GR violations;they also provide a robust theoretical paradigm and constructive guidance for experiments that would push beyond the present experimental accuracy for parameterized post-Newtonian(PPN)parameters(for details on the PPN formalism see[60]).Thus,in addition to experiments that probe the GR prediction for the curvature of the gravityfield(given by parameterγ),any experiment pushingthe accuracy in measuring the degree of non-linearity of gravity superposition(given by anotherEddington parameterβ)will also be of great interest.This is a powerful motive for tests ofgravitational physics phenomena at improved accuracies.Analyses of laser ranges to the Moon have provided increasingly stringent limits on anyviolation of the Equivalence Principle(EP);they also enabled very accurate measurements fora number of relativistic gravity parameters.2.2LLR History and Scientific BackgroundLLR has a distinguished history[24,9]dating back to the placement of a retroreflector array onthe lunar surface by the Apollo11astronauts.Additional reflectors were left by the Apollo14and Apollo15astronauts,and two French-built reflector arrays were placed on the Moon by theSoviet Luna17and Luna21missions.Figure1shows the weighted RMS residual for each year.Early accuracies using the McDonald Observatory’s2.7m telescope hovered around25cm. Equipment improvements decreased the ranging uncertainty to∼15cm later in the1970s.In1985the2.7m ranging system was replaced with the McDonald Laser Ranging System(MLRS).In the1980s ranges were also received from Haleakala Observatory on the island of Maui in theHawaiian chain and the Observatoire de la Cote d’Azur(OCA)in France.Haleakala ceasedoperations in1990.A sequence of technical improvements decreased the range uncertainty tothe current∼2cm.The2.7m telescope had a greater light gathering capability than thenewer smaller aperture systems,but the newer systemsfired more frequently and had a muchimproved range accuracy.The new systems do not distinguish returning photons against thebright background near full Moon,which the2.7m telescope could do,though there are somemodern eclipse observations.The lasers currently used in the ranging operate at10Hz,with a pulse width of about200 psec;each pulse contains∼1018photons.Under favorable observing conditions a single reflectedphoton is detected once every few seconds.For data processing,the ranges represented by thereturned photons are statistically combined into normal points,each normal point comprisingup to∼100photons.There are15553normal points are collected until March2004.Themeasured round-trip travel times∆t are two way,but in this paper equivalent ranges in lengthunits are c∆t/2.The conversion between time and length(for distance,residuals,and dataaccuracy)uses1nsec=15cm.The ranges of the early1970s had accuracies of approximately25cm.By1976the accuracies of the ranges had improved to about15cm.Accuracies improvedfurther in the mid-1980s;by1987they were4cm,and the present accuracies are∼2cm.One immediate result of lunar ranging was the great improvement in the accuracy of the lunarephemeris[62]and lunar science[67].LLR measures the range from an observatory on the Earth to a retroreflector on the Moon. For the Earth and Moon orbiting the Sun,the scale of relativistic effects is set by the ratio(GM/rc2)≃v2/c2∼10−8.The center-to-center distance of the Moon from the Earth,with mean value385,000km,is variable due to such things as eccentricity,the attraction of the Sun,planets,and the Earth’s bulge,and relativistic corrections.In addition to the lunar orbit,therange from an observatory on the Earth to a retroreflector on the Moon depends on the positionin space of the ranging observatory and the targeted lunar retroreflector.Thus,orientation ofthe rotation axes and the rotation angles of both bodies are important with tidal distortions,plate motion,and relativistic transformations also coming into play.To extract the gravitationalphysics information of interest it is necessary to accurately model a variety of effects[68].For a general review of LLR see[24].A comprehensive paper on tests of gravitationalphysics is[62].A recent test of the EP is in[4]and other GR tests are in[64].An overviewFigure1:Historical accuracy of LLR data from1970to2004.of the LLR gravitational physics tests is given by Nordtvedt[37].Reviews of various tests of relativity,including the contribution by LLR,are given in[58,60].Our recent paper describes the model improvements needed to achieve mm-level accuracy for LLR[66].The most recent LLR results are given in[68].2.3Tests of Relativistic Gravity with LLRLLR offers very accurate laser ranging(weighted rms currently∼2cm or∼5×10−11in frac-tional accuracy)to retroreflectors on the Moon.Analysis of these very precise data contributes to many areas of fundamental and gravitational physics.Thus,these high-precision studies of the Earth-Moon-Sun system provide the most sensitive tests of several key properties of weak-field gravity,including Einstein’s Strong Equivalence Principle(SEP)on which general relativity rests(in fact,LLR is the only current test of the SEP).LLR data yielded the strongest limits to date on variability of the gravitational constant(the way gravity is affected by the expansion of the universe),and the best measurement of the de Sitter precession rate.In this Section we discuss these tests in more details.2.3.1Tests of the Equivalence PrincipleThe Equivalence Principle,the exact correspondence of gravitational and inertial masses,is a central assumption of general relativity and a unique feature of gravitation.EP tests can therefore be viewed in two contexts:tests of the foundations of general relativity,or as searches for new physics.As emphasized by Damour[12,13],almost all extensions to the standard modelof particle physics(with best known extension offered by string theory)generically predict newforces that would show up as apparent violations of the EP.The weak form the EP(the WEP)states that the gravitational properties of strong and electro-weak interactions obey the EP.In this case the relevant test-body differences are their fractional nuclear-binding differences,their neutron-to-proton ratios,their atomic charges,etc. General relativity,as well as other metric theories of gravity,predict that the WEP is exact. However,extensions of the Standard Model of Particle Physics that contain new macroscopic-range quantumfields predict quantum exchange forces that will generically violate the WEP because they couple to generalized‘charges’rather than to mass/energy as does gravity[17,18]. WEP tests can be conducted with laboratory or astronomical bodies,because the relevant differences are in the test-body compositions.Easily the most precise tests of the EP are made by simply comparing the free fall accelerations,a1and a2,of different test bodies.For the case when the self-gravity of the test bodies is negligible and for a uniform external gravityfield, with the bodies at the same distance from the source of the gravity,the expression for the Equivalence Principle takes the most elegant form:∆a= M G M I 2(1)(a1+a2)where M G and M I represent gravitational and inertial masses of each body.The sensitivity of the EP test is determined by the precision of the differential acceleration measurement divided by the degree to which the test bodies differ(position).The strong form of the EP(the SEP)extends the principle to cover the gravitational properties of gravitational energy itself.In other words it is an assumption about the way that gravity begets gravity,i.e.about the non-linear property of gravitation.Although general relativity assumes that the SEP is exact,alternate metric theories of gravity such as those involving scalarfields,and other extensions of gravity theory,typically violate the SEP[30,31, 32,35].For the SEP case,the relevant test body differences are the fractional contributions to their masses by gravitational self-energy.Because of the extreme weakness of gravity,SEP test bodies that differ significantly must have astronomical sizes.Currently the Earth-Moon-Sun system provides the best arena for testing the SEP.The development of the parameterized post-Newtonian formalism[31,56,57],allows one to describe within the common framework the motion of celestial bodies in external gravitational fields within a wide class of metric theories of gravity.Over the last35years,the PPN formalism has become a useful framework for testing the SEP for extended bodies.In that formalism,the ratio of passive gravitational to inertial mass to thefirst order is given by[30,31]:M GMc2 ,(2) whereηis the SEP violation parameter(discussed below),M is the mass of a body and E is its gravitational binding or self-energy:E2Mc2 V B d3x d3yρB(x)ρB(y)EMc2 E=−4.64×10−10andwhere the subscripts E and m denote the Earth and Moon,respectively.The relatively small size bodies used in the laboratory experiments possess a negligible amount of gravitational self-energy and therefore such experiments indicate nothing about the equality of gravitational self-energy contributions to the inertial and passive gravitational masses of the bodies [30].TotesttheSEP onemustutilize planet-sizedextendedbodiesinwhichcase theratioEq.(3)is considerably higher.Dynamics of the three-body Sun-Earth-Moon system in the solar system barycentric inertial frame was used to search for the effect of a possible violation of the Equivalence Principle.In this frame,the quasi-Newtonian acceleration of the Moon (m )with respect to the Earth (E ),a =a m −a E ,is calculated to be:a =−µ∗rM I m µS r SEr 3Sm + M G M I m µS r SEr 3+µS r SEr 3Sm +η E Mc 2 m µS r SEMc 2 E − E n 2−(n −n ′)2n ′2a ′cos[(n −n ′)t +D 0].(8)Here,n denotes the sidereal mean motion of the Moon around the Earth,n ′the sidereal mean motion of the Earth around the Sun,and a ′denotes the radius of the orbit of the Earth around the Sun (assumed circular).The argument D =(n −n ′)t +D 0with near synodic period is the mean longitude of the Moon minus the mean longitude of the Sun and is zero at new Moon.(For a more precise derivation of the lunar range perturbation due to the SEP violation acceleration term in Eq.(6)consult [62].)Any anomalous radial perturbation will be proportional to cos D .Expressed in terms ofη,the radial perturbation in Eq.(8)isδr∼13ηcos D meters [38,21,22].This effect,generalized to all similar three body situations,the“SEP-polarization effect.”LLR investigates the SEP by looking for a displacement of the lunar orbit along the direction to the Sun.The equivalence principle can be split into two parts:the weak equivalence principle tests the sensitivity to composition and the strong equivalence principle checks the dependence on mass.There are laboratory investigations of the weak equivalence principle(at University of Washington)which are about as accurate as LLR[7,1].LLR is the dominant test of the strong equivalence principle.The most accurate test of the SEP violation effect is presently provided by LLR[61,48,23],and also in[24,62,63,4].Recent analysis of LLR data test the EP of∆(M G/M I)EP=(−1.0±1.4)×10−13[68].This result corresponds to a test of the SEP of∆(M G/M I)SEP=(−2.0±2.0)×10−13with the SEP violation parameter η=4β−γ−3found to beη=(4.4±4.5)×10−ing the recent Cassini result for the PPN parameterγ,PPN parameterβis determined at the level ofβ−1=(1.2±1.1)×10−4.2.3.2Other Tests of Gravity with LLRLLR data yielded the strongest limits to date on variability of the gravitational constant(the way gravity is affected by the expansion of the universe),the best measurement of the de Sitter precession rate,and is relied upon to generate accurate astronomical ephemerides.The possibility of a time variation of the gravitational constant,G,wasfirst considered by Dirac in1938on the basis of his large number hypothesis,and later developed by Brans and Dicke in their theory of gravitation(for more details consult[59,60]).Variation might be related to the expansion of the Universe,in which case˙G/G=σH0,where H0is the Hubble constant, andσis a dimensionless parameter whose value depends on both the gravitational constant and the cosmological model considered.Revival of interest in Brans-Dicke-like theories,with a variable G,was partially motivated by the appearance of superstring theories where G is considered to be a dynamical quantity[26].Two limits on a change of G come from LLR and planetary ranging.This is the second most important gravitational physics result that LLR provides.GR does not predict a changing G,but some other theories do,thus testing for this effect is important.The current LLR ˙G/G=(4±9)×10−13yr−1is the most accurate limit published[68].The˙G/G uncertaintyis83times smaller than the inverse age of the universe,t0=13.4Gyr with the value for Hubble constant H0=72km/sec/Mpc from the WMAP data[52].The uncertainty for˙G/G is improving rapidly because its sensitivity depends on the square of the data span.This fact puts LLR,with its more then35years of history,in a clear advantage as opposed to other experiments.LLR has also provided the only accurate determination of the geodetic precession.Ref.[68]reports a test of geodetic precession,which expressed as a relative deviation from GR,is K gp=−0.0019±0.0064.The GP-B satellite should provide improved accuracy over this value, if that mission is successfully completed.LLR also has the capability of determining PPNβandγdirectly from the point-mass orbit perturbations.A future possibility is detection of the solar J2from LLR data combined with the planetary ranging data.Also possible are dark matter tests,looking for any departure from the inverse square law of gravity,and checking for a variation of the speed of light.The accurate LLR data has been able to quickly eliminate several suggested alterations of physical laws.The precisely measured lunar motion is a reality that any proposed laws of attraction and motion must satisfy.The above investigations are important to gravitational physics.The future LLR data will improve the above investigations.Thus,future LLR data of current accuracy would con-tinue to shrink the uncertainty of˙G because of the quadratic dependence on data span.The equivalence principle results would improve more slowly.To make a big improvement in the equivalence principle uncertainty requires improved range accuracy,and that is the motivation for constructing the APOLLO ranging facility in New Mexico.2.4Future LLR Data and APOLLO facilityIt is essential that acquisition of the new LLR data will continue in the future.Accuracies∼2cm are now achieved,and further very useful improvement is expected.Inclusion of improved data into LLR analyses would allow a correspondingly more precise determination of the gravitational physics parameters under study.LLR has remained a viable experiment with fresh results over35years because the data accuracies have improved by an order of magnitude(see Figure1).There are prospects for future LLR station that would provide another order of magnitude improvement.The Apache Point Observatory Lunar Laser-ranging Operation(APOLLO)is a new LLR effort designed to achieve mm range precision and corresponding order-of-magnitude gains in measurements of fundamental physics parameters.For thefirst time in the LLR history,using a3.5m telescope the APOLLO facility will push LLR into a new regime of multiple photon returns with each pulse,enabling millimeter range precision to be achieved[29,66].The anticipated mm-level range accuracy,expected from APOLLO,has a potential to test the EP with a sensitivity approaching10−14.This accuracy would yield sensitivity for parameterβat the level of∼5×10−5and measurements of the relative change in the gravitational constant,˙G/G, would be∼0.1%the inverse age of the universe.The overwhelming advantage APOLLO has over current LLR operations is a3.5m astro-nomical quality telescope at a good site.The site in southern New Mexico offers high altitude (2780m)and very good atmospheric“seeing”and image quality,with a median image resolu-tion of1.1arcseconds.Both the image sharpness and large aperture conspire to deliver more photons onto the lunar retroreflector and receive more of the photons returning from the re-flectors,pared to current operations that receive,on average,fewer than0.01 photons per pulse,APOLLO should be well into the multi-photon regime,with perhaps5–10 return photons per pulse.With this signal rate,APOLLO will be efficient atfinding and track-ing the lunar return,yielding hundreds of times more photons in an observation than current√operations deliver.In addition to the significant reduction in statistical error(useful).These new reflectors on the Moon(and later on Mars)can offer significant navigational accuracy for many space vehicles on their approach to the lunar surface or during theirflight around the Moon,but they also will contribute significantly to fundamental physics research.The future of lunar ranging might take two forms,namely passive retroreflectors and active transponders.The advantages of new installations of passive retroreflector arrays are their long life and simplicity.The disadvantages are the weak returned signal and the spread of the reflected pulse arising from lunar librations(apparent changes in orientation of up to10 degrees).Insofar as the photon timing error budget is dominated by the libration-induced pulse spread—as is the case in modern lunar ranging—the laser and timing system parameters do√not influence the net measurement uncertainty,which simply scales as1/3Laser Ranging to MarsThere are three different experiments that can be done with accurate ranges to Mars:a test of the SEP(similar to LLR),a solar conjunction experiment measuring the deflection of light in the solar gravity,similar to the Cassini experiment,and a search for temporal variation in the gravitational constant G.The Earth-Mars-Sun-Jupiter system allows for a sensitive test of the SEP which is qualitatively different from that provided by LLR[3].Furthermore,the outcome of these ranging experiments has the potential to improve the values of the two relativistic parameters—a combination of PPN parametersη(via test of SEP)and a direct observation of the PPN parameterγ(via Shapiro time delay or solar conjunction experiments).(This is quite different compared to LLR,as the small variation of Shapiro time delay prohibits very accurate independent determination of the parameterγ).The Earth-Mars range would also provide for a very accurate test of˙G/G.This section qualitatively addresses the near-term possibility of laser ranging to Mars and addresses the above three effects.3.1Planetary Test of the SEP with Ranging to MarsEarth-Mars ranging data can provide a useful estimate of the SEP parameterηgiven by Eq.(7). It was demonstrated in[3]that if future Mars missions provide ranging measurements with an accuracy ofσcentimeters,after ten years of ranging the expected accuracy for the SEP parameterηmay be of orderσ×10−6.These ranging measurements will also provide the most accurate determination of the mass of Jupiter,independent of the SEP effect test.It has been observed previously that a measurement of the Sun’s gravitational to inertial mass ratio can be performed using the Sun-Jupiter-Mars or Sun-Jupiter-Earth system[33,47,3]. The question we would like to answer here is how accurately can we do the SEP test given the accurate ranging to Mars?We emphasize that the Sun-Mars-Earth-Jupiter system,though governed basically by the same equations of motion as Sun-Earth-Moon system,is significantly different physically.For a given value of SEP parameterηthe polarization effects on the Earth and Mars orbits are almost two orders of magnitude larger than on the lunar orbit.Below we examine the SEP effect on the Earth-Mars range,which has been measured as part of the Mariner9and Viking missions with ranging accuracy∼7m[48,44,41,43].The main motivation for our analysis is the near-future Mars missions that should yield ranging data, accurate to∼1cm.This accuracy would bring additional capabilities for the precision tests of fundamental and gravitational physics.3.1.1Analytical Background for a Planetary SEP TestThe dynamics of the four-body Sun-Mars-Earth-Jupiter system in the Solar system barycentric inertial frame were considered.The quasi-Newtonian acceleration of the Earth(E)with respect to the Sun(S),a SE=a E−a S,is straightforwardly calculated to be:a SE=−µ∗SE·r SE MI Eb=M,Jµb r bS r3bE + M G M I E b=M,Jµb r bS。

第24卷　第6期2005年12月 飞行器测控学报Journa l of Spacecraft TT&C Technology Vol.24　No.6Dec.2005深空测控通信的特点和主要技术问题3刘嘉兴(西南电子技术研究所・四川成都・610036)摘　要　分析研究了深空测控通信的特点,对频段提高、灵敏度提高、G/T值提高、E I RP提高、编码增益提高、定轨精度提高、极窄带锁相、低门限接收和调制/解调方式等主要技术问题进行了探讨。

关键词　深空探测;深空网(DS N);测控通信技术;定轨中图分类号:V1文献标识码:AFeatures and Ma i n Techn i cal Issues i n Deep SpaceTT&C and Teleco mmun i cati on Syste m sL I U J ia2xing(Southwest I nstitute of Electr onic Technol ogy,Chengdu,Sichuan Pr ovince610036)Abstract　This paper analyses the features of deep s pace tracking,tele metry,contr ol and telecommunicati on(TTC&T)syste m s and discusses the main techniques t o i m p r ove receiver sensitivity,frequency bands,G/T,E I RP,coding gain,orbit deter m inati on accuracy and narr ow2band P LL and modulati on/demodulati on.Key words　Deep Space Exp l orati on;Deep Space Net w ork(DS N);TTC&T Technol ogy;O rbit Deter m inati on0　引 言深空探测是指对月球和月球以远的天体和空间进行的探测,实施探测的航天器称为深空探测器,对其测控通信的系统称为深空测控通信系统,它包括深空测控通信地面站和空间应答机两大部分。

多智能体的鲁棒自适应有向三角编队控制朱亚东;杜晋;王芹【摘要】针对一类具有不确定性和外部干扰的三个智能体系统，提出了基于距离的分散自适应有向编队控制策略。

利用模糊系统的逼近能力对单个智能体的不确定动态进行逼近，同时通过参数自适应估计消除了逼近误差和外部干扰对系统的影响；进一步，引入势能函数避免个体之间的碰撞。

通过Babalat引理能够证明所提控制算法能够保证期望的三角队形且每个智能体都能达到期望的速度。

%In this paper, a decentralized adaptive control scheme of directed triangle formation based on interagent distances is worked out for three multi-agent systems with uncertain nonlinear dynamics and external disturbances. Uncertain dynamics terms are approximated by the first type fuzzy systems. At the same time, the effects of approximation error and external disturbances are eliminated by using the adaptive estimation ofpa- rameter. Furthermore, the inter-agent potential functions are introduced to avoid the collision between each a- gent. By the Babalat＇ s lemma, the proposed control algorithms can not only accomplish the desired formation but also ensure that speeds of all agents converge to a common value during the motion.【期刊名称】《扬州职业大学学报》【年(卷),期】2011(015)002【总页数】5页(P29-33)【关键词】多智能体系统;分散自适应控制;有向编队控制【作者】朱亚东;杜晋;王芹【作者单位】扬州职业大学,江苏扬州225009;扬州职业大学,江苏扬州225009;扬州职业大学,江苏扬州225009【正文语种】中文【中图分类】TP27320世纪90年代后期，多智能体的编队控制研究获得了深入的发展，相关研究成果在协同搜寻、营救、导航和多机器人规划、水下航行器控制及空间航行器的控制方面发挥了很大的作用[1－3]。