The use of a movable telescoping end mass system for the time-optimal control of spinning spacecraft

The time-optimal control of a spin-stabilized spacecraft with a movable telescoping appendage (boom), is considered analytically and numerically. The motion of a control mass at the end of the boom is determined such that the terminal time will be minimized for two-axis control of a symmetric spacecraft. The equations of rotational motion are linearized about the desired state of spin about the symmetry axis. The equations for the transverse angular velocity components have the form of a coupled two dimensional harmonic oscillator with boom motion as a control force. The control function which brings the system to the desired state is known to be a series of positive and negative pulses. If the initial state is such that the system can be driven to rest in a single switch, the responses, switching and final times, and required boom motion may be determined analytically. Some typical numerical results based on these solutions are discussed.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: III

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

带挠性附件的航天器系统动力学特性研究

本文研究了带挠性附件的航天器系统动力学特性。带挠性附件的航天器系统建模为刚性主体带挠性附件（挠性附件的末端带有刚性质量），根据拟坐标下的Ｌａｇｒａｎｇｅ定理建立了主刚体姿态运动与挠性附件振动相互耦合的动力学状态方程。针对一类带挠性附件的航天器系统编制了有关计算软件，利用该软件以ＳＣＯＬＥ模型（ＳＣＯＬＥ是ＳｐａｃｅｃｒａｆｔＣｏｎｔｒｏｌＬａｂｏｒａｔｏ－ｒｙＥｘｐｅｒｉｍｅｎｔ的缩写，其系统构形可参见文献［２］［３］）为例进行动力学分析，我们得到了与ＮＡＳＡ有关报告几乎完全一样的结果。本项研究为一类带挠性附件的航天器控制系统设计提供了一种合适的动力学理论模型。     

Spacecraft dynamics with regard to elastic gravitational stabilizer deployment

The present paper deals with the study the dynamics of the spacecraft with gyro-gravitational system of stabilization. The deployment of the boom of the gravitational stabilizer commences after placing the spacecraft into the orbit and completion of the preliminary damping, when the gyroscopes are uncaged. Primarily the boom is the pre-stressed tape wound on the special drum. When the drum starts deploying the tape, it turns into the elastic cylindrical rod with the mass at its tip. The objective of the study is the creation of the generalized mathematical model and the conducting of the computer modelling of the spacecraft dynamics. The equations of motion are worked out with the use of the Lagrangian formalism. The numerical simulation of typical modes of system functioning is conducted. It is shown that the folding and the following deployment of the boom result in the turn of the spacecraft by 180° about the axis of the pitch. The results illustrate the behaviour of the main system variables.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: II

The problem of a rendezvous in the central Newtonian gravitational field is considered for a controlled spacecraft and an uncontrollable spacecraft moving along an elliptic Keplerian orbit. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. In the first variant of the equations of motion a quaternion variable characterizes the orientation of an instantaneous orbit of the spacecraft and the spacecraft location in the orbit, while in the second variant it characterizes the orientation of the plane of the spacecraft instantaneous orbit and the location of a generalized pericenter in the orbit. The quaternion variable used in the second variant of the equations of motion is a quaternion osculating element of the spacecraft orbit. The problem of a rendezvous of two spacecraft is formulated as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle.     

大型空间结构的自适应控制

本文将Bar-Kana等人的模型参考自适应控制法(MRAC)用于柔性结构的自适应控制中,原方法要求系统的输入维数等于输出维数。对于柔性的大型空间结构(LSS),观测量的数目往往大于输入量的数目。本文采用组合LSS各观测点的信号,形成综合输出矢量Y_P,以满足自适应控制系统中,用较少的控制输入达到控制LSS结构中较多观测点的要求。为了克服跟踪误差,本文建议用最优返馈增益阵作为输出阵C_P,并采用LQR理论以求C_P。 本文将大型空间结构的实例简化成离散模型,进行模拟计算,计算结果说明系统有较好的跟踪特性,当LSS的柔度变化较大时,系统具有跟踪的鲁棒性。     

航天器薄壳柔性附件展开耦合行为特性研究

为研究大范围运动柔性附件几何非线性和耦合效应与中心刚体的精确动力学行为,以薄壳结构柔性附件为研究对象,引入非线性应变和位移关系,利用虚功原理推导了做大范围运动带柔性附件航天机构的完整非线性动力学模型,所构建的模型包含了非线性几何变形及附加非线性项。针对线性和非线性模型,相应开展了大范围运动航天机构刚柔耦合数值分析。结果表明,随着转速增大,线性与非线性模型动力学特性产生根本差异,指出线性模型忽略了非线性耦合项的不足,而非线性模型可精确地预测大范围运动带柔性附件航天机构动力学行为。结论对航天机构定向和跟踪操作的动力学与控制具有重要的理论价值及工程实际意义。     

挠性航天器伸展动力学分析

本文导出了带挠性伸展附件航天器姿态动力学方程，研究了附件伸展和振动对姿态动力学的影响。对于附件按指数规律伸展情况，以及附件长度的次方随时间线性变化情况，给出了姿态角速率的渐近公式。     

On plane oscillations of a pendulum with variable length suspended on the surface of a planet’s satellite

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We discuss how the change in length of a pendulum can be used to compensate its oscillations. We wrote equations of motion, indicated a rule for the change in length of a pendulum, at which it has equilibrium positions relative to the coordinate system rotating together with the Moon and Earth. We study the necessary conditions for the stability of these motions. Chaotic dynamics of the pendulum is studied numerically and analytically.     

航天器挠性附件刚柔耦合动力学建模与仿真

大型挠性航天器在进行轨道机动或姿态调整等大范围刚体运动时,将与其挠性附件的变形运动发生强烈的耦合,传统的零次近似动力学模型已不能正确揭示此时系统的动力学行为。现针对带梁式挠性附件的航天器,在计及挠性附件变形位移场耦合作用的基础上,通过Lagrange方程建立了航天器的刚柔耦合一次近似动力学模型,并利用Wilson-θ方法进行了数值仿真。仿真结果说明,在航天器经历大范围刚体运动时,该动力学模型能够正确预示挠性附件的动力学行为;挠性附件的振动频率随着大范围刚体运动速度的增加而增大,出现了动力刚化现象。     

空间飞行器对接动力学研究

异体同构周边式对接机构是目前飞船对接已经采用了的一种对接机构。本文详细地分析了具有这种对接机构的飞船的对接动力学。对接过程分三个阶段进行,捕获与接触;调整对接环;对接成功后的飞船姿态调整。 本文根据Jourdain—Bertrand原理推导并给出这三个阶段的对接动力学模型。同时,给出一组数字仿真结果。     

带挠性附件的航天器结构-姿态耦合动力学

用Lagrange方程建立了基于混合坐标法的带挠性附件航天器结构-姿态动力学模型,对挠性附件结构的振动特性及其与航天器的耦合关系进行了理论分析,提出了航天器结构-姿态联合仿真分析的方法,并以某卫星天线为挠性附件结构,仿真分析了天线结构的振动特性及其对姿态控制系统的影响.结果表明:提出的航天器结构-姿态联合仿真方法能有效...     

Spacecraft Injection into a Heliocentric Terrestrial Orbit

We consider the problem of injection of a spacecraft into the heliocentric Earth's orbit ahead and/or behind the Earth by 60° and 120° in heliographic longitude. The range of solar and astrophysical problems for which these orbits are necessary is reviewed. The variants of injection into heliocentric orbits work from a low around-Earth orbit with one turn-on of the engine in this orbit and one turn-on at the end of the injection trajectory. In this case, it turns out to be more profitable to put spacecraft into orbit for three or even four revolutions of the Earth about the Sun. The velocities necessary for the start from a low around-Earth orbit, the velocities at the final point of injection, and the fuel mass (relative to the spacecraft mass) necessary for injection are estimated. The problems for which injection to similar orbits is executed, using the low-thrust engine and with a combined regime of injection, are also considered.     

基于多柔体动力学的飞行器多目标优化设计

研究了柔性航天器总体设计中基于结构与姿态控制的多目标优化问题。利用拉格朗日 方程建立了刚柔耦合系统动力学模型,提出以附件质量和微分矩阵最大实特征值为目标函数 的多目标优化问题;采用非支配排序进化求解算法（NSGA-II）,对某柔性航天器进行了多目 标优化分析设计;最优决策为具有一定规律性的空间曲线,该优化结果对柔性卫星的总体分 析设计具有一定的指导意义。
     

Ultralight deployable booms for solar sails and other large gossamer structures in space

Future solar sail spacecraft which do not need any rocket motors and propellants are a promising option for long-term exploration missions in the solar system. However, they will require ultralight reflective foils and deployable booms which will allow for the unfolding of huge sails. The achievement of an acceptable ratio of reflective sail area and structural mass, which results in a still small, but significant acceleration under the photon pressure of sunlight, is extremely challenging. The same challenging deployment technique is required for the unfolding of large reflector membranes or antennas (gossamer structures). The key elements are the booms which must be stowable in a very small envelope before they reach their destination in space. Such booms were developed by DLR and have been successfully tested under zero-g-conditions during a parabolic flight campaign in February 2009. It could be convincingly demonstrated that the unfolding process is both controllable and reproducible. The booms consisted of two co-bonded omega-shaped carbonfiber half shells with 0.1 mm wall thickness each and had a weight of only 62 g per meter. Two different deployment technologies were tested, one based upon an inflatable 12 μm thick polymer hose inside the boom, the other one using an electromechanical uncoiling device at the tip of each boom. In the latter case, the uncoiling devices will radially fly away from the spacecraft, such that they become “expendable deployment mechanisms” and their mass does not count any more for the spacecraft mass that needs to be accelerated or actively controlled.     

航天器附件展开动力学仿真

用Newton-Euler法建立了中心刚体带挠性附件的航天器动力学方程, 进行挠性附件展开的动力学仿真,研究附件展开对主体姿态的影响。当航天器 附件展开机构失效时,利用航天器姿态抖动来帮助展开附件。本文用ADAMS软 件建立了航天器的虚拟物理模型,用ADAMS和Matlab/Simulink联合仿真了航 天器姿态抖动过程。仿真结果表明此方法是有效的。     

基于内模原理的复杂挠性卫星姿态控制研究

首先对具有运动挠性附件的航天器的姿态动力学模型进行了简要讨论和分析,证明了对于受步进扰动的复杂挠性卫星系统,采用输出反馈PD控制仅能得到一致有界稳定的结论。为了获得闭环系统的渐近稳定性能,进一步构造了具有内模补偿的PD控制系统,并且根据Lyapunov理论给出了严格证明。基于美国GOES 8号静止轨道气象卫星公布的动力学参数,对PD控制及含有内模补偿的PD控制两类控制器进行了仿真对比,以校验所设计控制系统的有效性。最后,进行了总结并提出进一步的研究设想。     

How we will go to Mars

This article studies the efficiency of ejecting waste generated by the life support system (LSS) of a manned spacecraft to reduce initial mass on low earth orbit. The spacecraft is used for a long-duration interplanetary mission and is equipped with either a chemical or a nuclear-thermal propulsion system. For this study we simulate an optimal control problem for a given spacecraft maneuver. An impulsive approximation of the optimal interplanetary spacecraft trajectory is assumed, which allows us to reduce the general optimal control problem to hierarchic structure of 'outer' and 'inner' subproblems. This structure is analyzed using the Pontryagin's Maximum principle. Numerical results, illustrating the efficiency of waste ejection are shown for typical Earth-Mars transfer trajectories. This results confirm in theory that using a waste ejection system makes an early manned Mars mission possible without having to design and build new, advanced biological LSS.     

Dual attitude and parameter estimation of passively magnetically stabilized nano satellites

The attitude determination capability of a nano satellite is limited by a lack of traditional high performance attitude sensors, a result of having small budgets for mass and power. Attitude determination can still be performed on a nano satellite with low fidelity sensors, but an accurate model of the spacecraft attitude dynamics is required. The passive magnetic stabilization systems commonly employed in nano satellites are known to introduce uncertainties in the parameters of the attitude dynamics model that cannot easily be resolved prior to launch. In this paper, a batch estimation problem is formulated that simultaneously solves for the attitude of the spacecraft and performs parameter estimation on the magnetic properties of the magnetic materials using only a measurement of the solar vector. The estimation technique is applied to data from NASA Ames Research Center's O/OREOS nano satellite and the University of Michigan's RAX-1 nano satellite, where clear differences are detected between the magnetic properties as measured before launch and those that fit the observed data. To date this is the first known on-orbit verification of the attitude dynamics model of a passively magnetically stabilized spacecraft.     

Optimization Problem in Control over a Programmed Turn of a Spacecraft

The problem of spacecraft reorientation from its initial angular position into a desired final position within a given time interval with a minimum value of the angular moment is considered and solved analytically in this work. It is shown that the control over the spacecraft reorientation, optimal in this sense, might be defined in the class of a regular precession performed by the spacecraft. The moment of the start of deceleration is determined from the principles of the terminal control by using real kinematic parameters of apparatus motion, which increases significantly the accuracy of reorientation. The results of mathematical modeling are presented, showing a high efficiency of the proposed way of reorientation.