Determination of kinematic state of an orbiting multibody using GNSS signals

Precise attitude determination of the members of a free-flying multibody system is a not so immediate task, due essentially to the large motion of its appendages coupled with their relevant flexibility effects. In fact, sensors used to this aim in current projects, such as optical encoders usually positioned near the joints of each arm, are almost blind to these effects, and clusters of specific redundant sensors should, therefore, be required in order to reconstruct both elastic deformations and rigid motion.Satellite navigation systems (GNSS) offer a suitable and reliable solution to this problem. To exploit the phase of the signal, instead of the traditional pseudo random code, ensures a very high accuracy of the order of magnitude of centimeter. Such a process requires the solution of an initial ambiguity problem, related to the number of integer wavelength included in the length of the member.The aim of the paper is to investigate the capability of this GNSS based technique to reconstruct the kinematics of a flexible multibody system orbiting around the Earth. This analysis requires a simulation including both the multibody dynamics and the navigation system constellation to define the satellites lines-of-sight at each time step.Concerning multibody equations of motion, a Newtonian formulation is adopted in this work. A special attention is required about the choice of the state variables. As the internal forces are associated to the relative displacements between the bodies, which are small fractions of the distance of the multibody spacecraft from the center of the Earth, the task of obtaining these forces from inertial coordinates could be impossible from a numerical point of view. So, the problem is reformulated in such a way that the equation of motion of the system contains global equations, with no internal forces, and local equations, with internal forces. In the latter, only quantities of the same order of the spacecraft dimensions are present.Accuracies achievable in LEO orbit with current GPS and upcoming Galileo systems are evaluated to show the interest of the proposed technique.     

Optimal control of the deployment process of solar wings on spacecraft

The optimal attitude control problem of spacecraft during the stretching process of solar wings is investigated in this paper. The dynamical equations of the nonholonomic system are derived from the conservation principle of the angular momentum of the multibody system. Attitude control of the spacecraft with internal motion is reduced to a nonholonomic motion planning problem. The spacecraft attitude control is transformed into the steering problem for a drift free control system. The optimal solution for steering a spacecraft with solar wings is presented. The controlled motion of spacecraft is simulated for two cases. The numerical results demonstrate the effectiveness of the optimal control approach.     

微重力环境中重力梯度加速度引起的流体晃动运动

本文研究了关于旋转轴在贮箱的非对称轴上且远离贮箱的几何中心情况下，流体在微重力环境中由重力梯度加速度诱发的晃动特性，建立了问题的数学模型并对模型进行了数值模拟。以高级Ｘ射线天文物理实验卫星（简称ＡＸＡＦ─Ｓ）作为研究对象，获得了由旋转运动引起的重力梯度加速度的数学表达式。晃动问题的数值计算以与卫星固连的非惯性坐标系为基础，目的是寻求一种较为易处理且适合于流体力学方程的边界和初始条件。通过数值计算获得了流体作用于卫星贮箱上的力和力矩。     

柔性绳网动力学建模与天地差异性分析

采用有限元模型研究了柔性绳网系统的动力学特性。针对空间绳网直接弹射展开方式,首先将绳网离散为若干单元,各单元处理为非线性“半阻尼弹簧”模型,然后分别计算各单元所受气动力和重力,最终建立绳网系统多柔体动力学模型。基于所建立的动力学模型分别对柔性绳网在地面和太空展开的动力学过程进行了仿真分析,研究了绳网在展开面积、空间位形和飞行距离等方面的天地差异性及其动力学机理,为未来空间绳网系统的分析设计提供理论参考。     

空间站大型柔性伸展机构的动力学仿真

本文研究了考虑构件柔性效应对空间站大型伸展机构的动力学问题，在采用柔性多体系统单向递推组集建模方法的基础上建立了任意拓扑结构的柔性多体系统的动力学方程。本文头等讨论了切割铰约束方程的建立和直接违约校正方法。数值仿真结果表明了柔性效应对空间站展开机构动力学的影响。     

Magnetobraking for Mars return vehicles

It is proposed that magnetobraking may be used to dissipate hyperbolic excess velocity from a spacecraft returning from Mars to Earth orbit. In magnetobraking, an electrodynamic tether is deployed from the spacecraft. The Earth's magnetic field produces a force on electrical current in the tether, which can be used to either brake or accelerate the spacecraft without expenditure of reaction mass. The peak acceleration on the Mars return is 0.007 m/s², and the amount of braking possible is dependent on the density and current-carrying capacity of the tether, but is independent of length. Since energy is produced as the spacecraft velocity decreases, no on-board power source is required. As the spacecraft approaches the Earth, the magnetic field increases and the power produced by the tether increases, reaching a maximum of about 800 W per kg of spacecraft mass at closest approach.     

Two-craft tether formation relative equilibria about circular orbits and libration points

The relative equilibria of a two spacecraft tether formation connected by line-of-sight elastic forces moving in the context of a restricted two-body system and a circularly restricted three-body system are investigated. For a two spacecraft formation moving in a central gravitational field, a common assumption is that the center of the circular orbit is located at the primary mass and the center of mass of the formation orbits around the primary in a great-circle orbit. The relative equilibrium is called great-circle if the center of mass of the formation moves on the plane with the center of the gravitational field residing on it; otherwise, it is called a nongreat-circle orbit. Previous research shows that nongreat-circle equilibria in low Earth orbits exhibit a deflection of about a degree from the great-circle equilibria when spacecraft with unequal masses are separated by 350 km. This paper studies these equilibria (radial, along-track and orbit-normal in circular Earth orbit and Earth–Moon Libration points) for a range of inter-craft distances and semi-major axes of the formation center of mass. In the context of a two-spacecraft Coulomb formation with separation distances on the order of dozens of meters, this paper shows that the equilibria deflections are negligible (less than 10^?6°) even for very heterogeneous mass distributions. Furthermore, the nongreat-circle equilibria conditions for a two spacecraft tether structure at the Lagrangian libration points are developed.     

航天器柔性多体系统动力学的高效建模方法

以航天器为工程背景,提出了一种高效建模方法。文中采用有限元离散和模态叠加法描述部件的弹性变形。用铰链相对坐标建立了相邻柔性体之间的递推运动学方程。利用递推运动学方程、柔性体的牛顿—欧拉方程和铰链的约束特性,构造了单链多体系统动力学问题的递推算法。对树状多体系统的拓扑结构进行了研究,提出了研究树状多体系统动力学问题的求解过程控制方法,从而实现了树状多体系统与链式多体系统的统一,使得对单链多体系统建立的递推动力学方程能够直接用于求解树状多体系统的动力学问题。     

Planetary Defense From Space: Part 1-Keplerian Theory

A system of two space bases housing missiles is proposed to achieve the Planetary Defense of the Earth against dangerous asteroids and comets. We show that the layout of the Earth–Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth).

We show that placing bases of missiles at L1 and L3 would cause those missiles to deflect the trajectory of asteroids by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that the confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement.

An additional remark is that the theory developed in this paper is just a beginning of a larger set of future research work. In fact, while in this paper we only develop the Keplerian analytical theory of the Optimal Planetary Defense achievable from the Earth–Moon Lagrangian points L1 and L3, much more sophisticated analytical refinements would be needed to:

1. Take into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3;

2. add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth–Moon system or from the surface of the Moon itself;

3. encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see “which asteroids could be diverted by which missiles”, even in the very simplified scheme outlined here.

Outlined for the first time in February 2002, our Confocal Planetary Defense concept is a Keplerian Theory that proved simple enough to catch the attention of scholars, representatives of the US Military and popular writers. These developments could possibly mark the beginning of an “all embracing” mathematical vision of Planetary Defense beyond all learned activities, dramatic movies and unknown military plans covered by secret.     

TiO2光催化薄膜在空间污染防护 应用中的探索

文章采用溶胶凝胶法在JGS1石英玻璃上制备了TiO₂薄膜,并对其晶体结构与光催化性能之间的关系进行了研究,探讨了紫外光辐照下TiO₂薄膜对大分子链硅油光催化效果。结果表明:经500 ℃热处理后的TiO₂薄膜为锐钛矿结构,具有较高的光催化活性;在253 nm紫外光辐照下,TiO₂薄膜对大分子链硅油表现出较好的光催化降解效果。该研究将为空间环境下飞行器光学表面污染净化材料的开发提供有益参考。     

基于Fe3O4陶粒的密封舱微波辐射空气净化技术

着眼于开发满足生物安全性的密封舱空气净化技术,制备Fe₃O₄陶粒吸波材料,并探讨基于该吸波材料的微波辐射过程对不同种类生物气溶胶的灭活特性。验证实验显示:灭活效果随着微波辐射时间的延长而增强;微波辐射对不同种类生物气溶胶的灭活率依次为大肠杆菌＞杂色曲霉菌＞枯草芽孢杆菌＞枯草芽孢杆菌孢子。分析发现:添加Fe₃O₄陶粒使微波辐射对生物气溶胶的灭活增强是微波热效应、非热效应以及O?和?OH的氧化作用共同所致;Fe₃O₄陶粒还可降低48.56%～59.23%的单位微波能耗。基于Fe₃O₄陶粒的微波辐射技术可有效用于我国载人航天器（含空间站）发射前的舱内空气净化除菌。     

带多充液圆柱贮箱航天器刚-液耦合动力学研究

文中以在低重环境下带多充液圆柱贮箱刚性航天器中刚-液耦合方程的建立和求解为主要研究目的。推导航天器中充液圆柱贮箱内任意点的牵连运动方程,根据壁面边界条件给出了贮箱内液体牵连晃动势的表达式;利用第二类边界条件下的傅立叶-贝塞尔级数展开法对低重力环境下的弯曲自由液面处的复杂动力学边界条件进行处理,建立以液体相对晃动势的模态坐标和晃动波高的模态坐标为状态向量的液体耦合晃动力学方程,通过积分分别得到了耦合晃动力和耦合晃动力矩的解析式;运用准坐标系下的拉格朗日方程建立以航天器主刚体姿态坐标和轨道坐标为状态向量的刚体耦合运动动力学方程,进一步联立上述耦合方程得到航天器整体系统的刚-液耦合动力学状态方程;最后,编制出适用于带多充液圆柱贮箱航天器内刚-液耦合动力学计算的模块化计算程序,通过计算实例验证所编程序的准确性的同时,研究了携带多充液箱航天器系统贮箱布局、外激励方式对航天器刚-液耦合系统动力学特性的影响。     

用Kane方法建立的空间站大型伸展机构柔性多体动力学模型

本文采用Ｋａｎｅ方法建立了空间站大型伸展机构柔性多体系统动力学模型。该模型考虑了系统的轨道运动、姿态运动、构件伸展运动和构件弹性运动，通过约束矩阵建立系统的约束关系，所得方程具有程式化特点，便于计算机编程。该模型还可适用于空间飞行器、地面车辆、复杂机械等多体系统。     

Optimization of space orbits design for Earth orbiting missions

In Earth orbiting space missions, the orbit selection dictates the mission parameters like the ground resolution, the area coverage, and the frequency of coverage parameters. To achieve desired mission parameters, usually Earth regions of interest are identified and the spacecraft is maneuvered continuously to visit only these regions. This method is expensive, it requires a propulsion system onboard the spacecraft, working throughout the mission lifetime. It also requires a longer time to cover all the regions of interest, due to the very weak thrust forces compared to that of the Earth's gravitational field. This paper presents a methodology to design natural orbits, in which the regions of interest are visited without the use of propulsion systems, depending only on the gravitational forces. The problem is formulated as an optimization problem. A genetic algorithm along with a second order gradient method is implemented for optimization. The design process takes into consideration the gravitational second zonal harmonic, and hence allows for the design of repeated Sun-synchronous orbits. The field of view of the payload is also taken into consideration in the optimization process. Numerical results are presented that demonstrates the efficiency of the proposed method.     

可变构型复合柔性结构航天器动力学建模研究

针对中心刚体加复合柔性结构类航天器采用混合坐标法和子结构模态综合法，建立了可变构型复合柔性结构航天器低阶动力学模型。获得的柔性动力学方程及其各类耦合系数矩阵，适用于全星级可变构型系统和部件级复合柔性附件系统的控制系统设计与仿真，该模型具有阶数低和工程实用的特点。     

Vibration control of a flexible space manipulator during on orbit operations

Space manipulators are complex systems, composed by robotic arms accommodated on an orbiting platform. They can be used to perform a variety of tasks: launch of satellites, retrieval of spacecraft for inspection, maintenance and repair, movement of cargo and so on. All these missions require extreme precision. However, in order to respect the mass at launch requirements, manipulators arms are usually very light and flexible, and their motion involves significant structural vibrations, especially after a grasping maneuver. In order to fulfill the maneuvers of space robotic systems it is hence necessary to properly model the forces acting on the space robot, from the main terms, such as the orbital motion, to the second order perturbations, like the gravity gradient and the orbital perturbations; also flexible excitation of the links and of the joints can be of great importance in the manipulators dynamics. The case is furthermore complicated by the fact that the manipulator, together with its supporting spacecraft, is an unconstrained body. Therefore the motion of any of its parts affects the entire system configuration. The governing equations of the dynamics of such robotic systems are highly nonlinear and fully coupled. The present paper aims at designing and studying active damping strategies and relevant devices that could be used to reduce the structural vibrations of a space manipulator with flexible links during its on orbit operations. In particular an optimized adaptive vibration control via piezoelectric devices is proposed. The number of piezoelectric devices, their placement and operational mode should be correctly chosen in order to obtain maximum performance in terms of elastic oscillations reduction and power consumption. Even though an optimal placement cannot have a universal validity, since it depends on the type of maneuver and on the overall inertial and geometrical characteristics, an approach to solve the problem is proposed.     

Applications of multi-body dynamical environments: The ARTEMIS transfer trajectory design

The application of forces in multi-body dynamical environments to permit the transfer of spacecraft from Earth orbit to Sun–Earth weak stability regions and then return to the Earth–Moon libration (L₁ and L₂) orbits has been successfully accomplished for the first time. This demonstrated that transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecrafts into Earth–Moon libration orbits by means of these applications.     

Rosetta: The ESA comet rendezvous mission

Rosetta was selected in November 1993 for the ESA Cornerstone 3 mission, to be launched in 2003, dedicated to the exploration of the small bodies of the solar system (asteroids and comets). Following this selection, the Rosetta mission and its spacecraft have been completely reviewed: this paper presents the studies performed the proposed mission and the resulting spacecraft design.

Three mission opportunities have been identified in 2003–2004, allowing rendezvous with a comet. From a single Ariane 5 launch, the transfer to the comet orbit will be supported by planetary gravity assists (two from Earth, one from Venus or Mars); during the transfer sequence, two asteroid fly-bys will occur, allowing first mission science phases. The comet rendezvous will occur 8–9 years after launch; Rosetta will orbit around the comet and the main science mission phase will take place up to the comet perihelion (1–2 years duration).

The spacecraft design is driven (i) by the communication scenario with the Earth and its equipment, (ii) by the autonomy requirements for the long cruise phases which are not supported by the ground stations, (iii) by the solar cells solar array for the electrical power supply and (iv) by the navigation scenario and sensors for cruise, target approach and rendezvous phases. These requirements will be developed and the satellite design will be presented.     

General background and approach to multibody dynamics for space applications

Multibody dynamics for space applications is dictated by space environment such as space-varying gravity forces, orbital and attitude perturbations, control forces if any. Several methods and formulations devoted to the modeling of flexible bodies undergoing large overall motions were developed in recent years.Most of these different formulations were aimed to face one of the main problems concerning the analysis of spacecraft dynamics namely the reduction of computer simulation time. By virtue of this, the use of symbolic manipulation, recursive formulation and parallel processing algorithms were proposed. All these approaches fall into two categories, the one based on Newton/Euler methods and the one based on Lagrangian methods; both of them have their advantages and disadvantages although in general, Newtonian approaches lend to a better understanding of the physics of problems and in particular of the magnitude of the reactions and of the corresponding structural stresses. Another important issue which must be addressed carefully in multibody space dynamics is relevant to a correct choice of kinematics variables. In fact, when dealing with flexible multibody system the resulting equations include two different types of state variables, the ones associated with large (rigid) displacements and the ones associated with elastic deformations. These two sets of variables have generally two different time scales if we think of the attitude motion of a satellite whose period of oscillation, due to the gravity gradient effects, is of the same order of magnitude as the orbital period, which is much bigger than the one associated with the structural vibration of the satellite itself. Therefore, the numerical integration of the equations of the system represents a challenging problem.This was the abstract and some of the arguments that Professor Paolo Santini intended to present for the Breakwell Lecture; unfortunately a deadly disease attacked him and shortly took him to death, leaving his work unfinished. In agreement with Astrodynamics Committee it was decided to prepare a paper based on some research activities that Paolo Santini performed during almost 50 years in the aerospace field. His researches spanned many arguments, encompassing flexible space structures, to optimization, stability analysis, thermal analysis, smart structure, etc. just to mention the ones more related to the space field (Paolo Santini was also one the pioneers of the studies of composite wing structures, aeroelasticity and unsteady aerodynamics for aeronautical applications). Following notes have been prepared by Paolo Gasbarri who was one of Paolo Santini collaborators for almost 15 years, they will attempt to offer a sketch of Professor Santini's activity by focusing on three main topics: the stability of flexible spacecrafts, the dynamics of multibody systems and the use of the smart structure technology for the space applications.     

Manufacture in space: the MINOS system

The manufacture in Space of products for use on Earth is a possibility for the 1990s. The MINOS project is based on the idea of a free-flyer station for the current medium-level production of either unique products (which cannot be made on Earth), or of economic yields of products which cannot be obtained in sufficient quantities on Earth.At present, only the main system may be defined from general specifications: electrical power (10 kW), residual acceleration (10^?5 g), processing cycle duration (10 hr).The launch vehicle is Ariane I and its improved versions (models II, III and IV).The outer structure of the spececraft is described with solar panels, energy storage (battery and inertial storage) and control systems.The definition of orbital parameters capable of accommodating the basis specifications, especially the high energy level and the re-entry conditions on the Guiana base, is a major problem. The re-entry vehicle is studied from a pure ballistic trajectory point of view. From the results of orbital performance, the mass of the spacecraft and also the mass of the ascent vehicle are evaluated. For this latter value, its determination is directly related to the cost of space-processed materials.A general overview is given of the other spacecraft sub-systems such as satellite tracking, communications, ground stations, resources requirements, telemetry, onboard computing system etc.