绳系卫星系统的运动与控制

绳系卫星系统的运动与控制分析,是绳系卫星应用的基础。本文的数学模型考虑了作用在子星、主星及系绳上的空气阻力以及在伸展与收回阶段主星与系绳之间的质量传递,给出了相应的具体的计算式。应用该数学模型,本文对现有的几种主要控制法,进行了模拟计算,作出评审意见。     

绳系空间太阳能电站动力学响应分析

利用绝对节点坐标方法研究绳系空间太阳能电站在轨飞行的太阳能电池板动力响应。通过勒让德变换引入广义动量,在约束哈密尔顿体系下建立轨道、姿态和弹性振动耦合的动力学方程。基于祖冲之类方法的思想,结合辛龙格-库塔方法对微分-代数方程进行数值求解。数值算例说明本文建模方法和数值算法都是有效的,能很好地保持系统约束和能量。最后分析了绳长、平台系统的质量、轨道高度对于梁中点挠度和轴向平均应变的影响。     

Optimal control of a spinning double-pyramid Earth-pointing tethered formation

The dynamics and control of a tethered satellite formation for Earth-pointing observation missions is considered. For most practical applications in Earth orbit, a tether formation must be spinning in order to maintain tension in the tethers. It is possible to obtain periodic spinning solutions for a triangular formation whose initial conditions are close to the orbit normal. However, these solutions contain significant deviations of the satellites on a sphere relative to the desired Earth-pointing configuration. To maintain a plane of satellites spinning normal to the orbit plane, it is necessary to utilize “anchors”. Such a configuration resembles a double-pyramid. In this paper, control of a double-pyramid tethered formation is studied. The equations of motion are derived in a floating orbital coordinate system for the general case of an elliptic reference orbit. The motion of the satellites is derived assuming inelastic tethers that can vary in length in a controlled manner. Cartesian coordinates in a rotating reference frame attached to the desired spin frame provide a simple means of expressing the equations of motion, together with a set of constraint equations for the tether tensions. Periodic optimal control theory is applied to the system to determine sets of controlled periodic trajectories by varying the lengths of all interconnecting tethers (nine in total), as well as retrieval and simple reconfiguration trajectories. A modal analysis of the system is also performed using a lumped mass representation of the tethers.     

绳系卫星系统复杂模型研究

对绳系卫星系统提出一种仿真度更高的动力学模型，着重研究状态保持阶段的子星的振荡与姿态运动。主星设为质点，与系统质心相合，作圆轨道运动；子星取为三维刚体，系绳采用株式模型。除绳系统动能、引力位能及系绳弹性势能外，还考虑了系绳的结构阻尼，以及由系绳外皮包引起的弯曲力矩与扭转力矩。计算机辅助推导参与模拟计算程序设计。     

空间绳系机器人抓捕非合作目标的质量特性参数辨识

针对空间绳系机器人抓捕非合作目标/空间垃圾后需要对其进行回收/拖曳的精确控制问题,提出了一种利用抓捕后保持阶段的振动特性辨识目标参数的方法。首先,根据质量特性参数辨识的需要,推导了系统的动力学模型。不同于以往将本体卫星和被抓捕目标简化为质点的动力学模型,本文针对任意的目标抓捕位置,在考虑重力梯度影响的基础上,利用拉格朗日法获得系统各广义坐标的动力学公式。然后,分析非合作目标和系绳在后抓捕保持阶段的姿态运动。最后,在非合作目标与本体卫星没有任何信息交互的情况下,利用后抓捕阶段目标卫星和系绳特有的振动,并使用具有鲁棒性可遗忘因子的递推最小二乘法,提出了包括转动惯量和质心到任意抓捕点距离在内的质量特性参数辨识算法。     

Tether-platform coupled control

From the control point of view, tethered systems pose several challenges, the major one pertaining to the regulation of the unstable system dynamics during the retrieval phase. On the other hand, the system configuration permits design of controllers using length rate, tension and offset schemes, which are not feasible with other satellites. Here “offset” refers to the time dependent variation of the tether attachment point at the platform end. The present paper studies several applications of the offset scheme in controlling the tethered systems. To that end, planar equations of motion of a space platform based Tethered Satellite System (TSS) are derived by the Lagrangian procedure. This is followed by representative results aimed at the offset control of platform pitch, tether attitude and vibration motions. The offset scheme is used for simultaneous control of platform and tether pitch motion. Finally the attention is directed towards simultaneous regulation of the platform pitch and longitudinal tether vibration. The numerical results clearly show considerable promise for the offset control scheme in regulating tether, platform and combined tether-platform dynamics.     

Mechanics of very long tethered systems

A space elevator has been proposed as an alternate method for launching satellites; however, the materials available now are not strong enough to support the stress generated in the structure. On the other hand, with the existing technology, a partial elevator is feasible. In this paper, the mechanics of a very long tethered system that functions as a partial elevator is studied. For such a system, the center of mass, center of gravity, and center of orbit are not coincident; disregarding this distinction can lead to erroneous results. A relation between these three points is presented in this paper. A consistent stress distribution along the tether is obtained by taking into account the distinction between these points. Dynamics of the system consisting of two end bodies, the tether (with mass), and a climber is examined. The equations of motion are derived using the Lagrangian formulation and analyzed numerically.     

绳系卫星安全捕获策略下的释放最优控制

安全捕获是绳系卫星系统空间应用的一个重要拓展。考虑系绳质量、系统质心变化及状态、控制约束,采用基于Lagrange方程的圆轨道条件下空间绳系网捕系统三维动力学模型。建立了安全捕获模型,推导得到零相对速度条件下的安全捕获末端条件。为保证方法的适用性,将基于Legendre伪谱法的连续时间最优控制问题离散为标准的非线性动态规划问题。最后在考虑释放控制前初始面外角偏差为5°的情况下,通过数值仿真验证了方法的有效性。仿真结果表明：对于远距离释放条件下的安全捕获,系统质心变化不容忽视;最小能量与绳长加速度约束下的控制响应相比最小时间与面内角约束要更平滑。     

Motion of a descent capsule relative to its center of mass when deploying the orbital tether system

The spatial motion relative to the center of mass is considered for a capsule on an elastic tether, when it is unrolled from a spacecraft by a special program. The spacecraft is in a circular orbit and oriented relative to the local vertical, which is guaranteed by operation of its own stabilization system. Angular motion of the capsule relative to the tether direction is studied, and the main factors influencing the stability of this motion are analyzed. An approximate quasi-linear mathematical model of the capsule attitude motion is obtained, which allows one to estimate the influence of major disturbances of its motion. The results of numerical simulations are presented for characteristic cases of the capsule motion.     

Satellite pitch and roll attitude maneuvers through very short tethers

Explored here is the feasibility of achieving satellite pitch and roll attitude maneuvers through tethers. The proposed tethered satellite system (TSS) comprises of four identical tethers connecting the auxiliary mass to the satellite at its four distinct off-centered and equiangularly spaced points. The open-loop tether length control laws have been developed in order to achieve arbitrary pitch and roll attitude slewing maneuvers. Numerical simulation of the nonlinear governing equations of motion for these tether length variations establishes the feasibility of executing fixed as well as chase-slewing maneuvers. Nearly passive nature of the proposed mechanism using very short tethers along with small auxiliary mass needed makes the concept particularly attractive for future space missions.     

TETHERED SATELLITE SYSTEM ANALYSIS (1) — TWO-DIMENSIONAL CASE AND REGULAR DYNAMICS

The study on tethered satellite system (TSS) in two-dimensional in-planar motion is restricted in that the tether is assumed to be massless. The equations of motion are given in a spherical coordinate system to describe the magnitude (tether length) and direction angle of the position vector between the satellites. A length rate control algorithm is adopted, and the controlled motion of the directional angle by the algorithm will have a stable equilibrium state. The equilibrium state is a fixed point if the orbit of the base-satellite is circular, and a limit cycle if the orbit is elliptic. The value and stability of the equilibrium state are determined by the parameters of the control algorithm, and the bifurcation analysis is also given. Two typical TSS missions have been simulated.     

绳系太阳能发电卫星姿态机动的主动振动控制

针对绳系太阳能发电卫星大角度回转机动时太阳能板的振动抑制问题,提出了主姿态控制和基于绳中张力的主动振动控制技术相结合的复合控制方法。建立了绳系太阳能发电卫星系统的动力学方程,并基于任务函数控制算法设计了主控制器保证卫星姿态的渐近稳定和挠性结构振动的衰减性;考虑到绳的非线性特性,基于任务函数控制算法设计了绳系卫星系统的主动振动抑制辅助控制器来抑制挠性结构的振动。设计的同时证明了系统的稳定性。将该方法应用于绳系卫星的大角度单轴回转机动的仿真研究,结果表明:该方法不仅能够使绳系卫星完成姿态机动,而且能够有效地抑制太阳能板的振动。     

Electrodynamic Tethered Deorbit System Dynamics and Performance Analysis

Electrodynamic tethered deorbit technology is a novel way to remove abandoned spacecrafts like upper stages or unusable satellites. This paper investigates and analyses the deorbit performance and mission applicability of the electrodynamic tethered system. To do so, the electrodynamic tethered deorbit dynamics with multi-perturbation is firstly formulated, where the Earth magnetic field, the atmospheric drag, and the Earth oblateness effect are considered. Then, the key system parameters, including payload mass, tether length and tether type, are analyzed by numerical simulations to investigate their influences on the deorbit performance and to give the setting principles for choosing system parameters. Based on this and given an appropriate group of system parameters, numerical simulations are undertaken to study the impact of the mission parameters, including orbit height and orbit inclination, and thus to investigate the mission applicability of the electrodynamic tethered deorbit technology.     

Stability of a ring of connected satellites

The motion of a large number of artificial satellites connected in a ring one after another by tethers of variable length is considered. Every satellite is supposed to have a control system programmed according to some tether tension law as a function of the distance between tethered satellites. The effect of the tension control law on the stability of stationary rotation of this ring is investigated. The final stability condition includes two requirements: 1) the nominal tether tension should be less than a definite limit equal, up to numerical coefficient, to one satellite weight divided by the number of satellites; 2) tether tension should decrease (or remain constant) with the increase of the distance between tethered satellites. In dynamics the artificial rings of this kind are much like their natural prototype—meteor rings. On the other hand, the investigation of the artificial rings contributes to developing an unexpected view upon meteor rings, suggesting a model of an imaginary equivalent string.     

辐射开环空间绳系机器人编队动力学及控制

提出了一种新型辐射开环空间绳系机器人编队系统,其在编队稳定性、任务灵活性及燃料消耗等方面具有明显的优势。针对辐射开环空间绳系机器人编队系统自旋运动过程中的构型误差控制问题,首先建立了编队系统的自旋动力学模型;然后分析了空间绳系机器人的绳系拉力和空间平台的自旋扭矩对编队系统自旋运动中出现的构型误差的控制能力;设计了一种依靠空间绳系机器人绳系拉力和空间平台自旋扭矩作为控制量,对构型误差进行控制的协调控制方法;最后通过数字仿真进行了校验和分析。仿真结果表明：设计的协调控制方法能够明显改善编队系统自旋运动中构型误差的控制效果。     

Analysis of the dynamics of the deployed aerodynamic space tether system

An analysis of the motion of a deployed space system that consists of two end bodies connected by a tether has been considered. One of the bodies has a relatively large ballistic coefficient that ensures aerodynamic braking or the stabilization of the motion of the entire system in relatively low near-Earth orbits. The deployment of this system mainly occurs due to the action of aerodynamic forces. Several ways of deploying the system have been analyzed, including (1) the uncontrolled release of the tether with hardly any braking; (2) deployment with constant braking force; (3) the dynamic control law without feedback, when the resistance force varies according to a set program; (4) a kinematic control law with feedback when programs are set for varying the velocity and length of the tether release. To analyze the dynamics of the system, a mathematical model of motion has been constructed in which the motion of the end bodies relative to their centers of mass is taken into account.     

空间非合作目标物柔性捕获技术进展

分类探讨了近年来出现的多种空间柔性捕获技术的原理及性能特点，给出了一些具有代表性的案例，结果表明：空间绳系捕获技术在理论及试验研究方面都相对成熟，是未来行之有效、可工程实现的柔性捕获方式之一。重点针对空间非合作目标物捕获中容易出现的翻滚问题，对比分析现有的几种常用的接触式消旋方法，分析表明能同时实现捕获+消旋的一步式消旋法更具有应用前景。以空间绳系捕获技术作为空间柔性捕获的代表，对其捕获后的空间绳系组合体动力学模型建立过程中的系绳模型进行了综述，指出了各种系绳模型的优缺点及适用条件。对系绳控制机构进行了分类综述，给出了设计系绳控制机构需重点关注的问题。最后对空间绳系捕获技术的发展方向做了展望。     

绳系卫星的一种新型高阶滑模控制器设计

针对绳系卫星轨道转移控制问题,给出绳系卫星在轨机动模型并将面内运动处理为典型的欠驱动形式;为实现对面内摆角的跟踪控制,定义滑模面并建立积分链系统,设计一种新型高阶滑模系绳张力控制律,得到无抖振控制量,这种控制律在保证高精度跟踪的前提下,有效避免了控制抖振现象;关于滑模面的高阶滑模运动建立后,在平衡点对闭环系统线性化,根据劳斯判据,闭环系统在平衡点是局部渐近稳定的。最后,通过仿真分析,验证了所提出控制算法的有效性。     

Safety implications of unscheduled situations in the operation of tethered satellite systems from the international space station

Space based experiments involving the use of tethers were examined with a view to identifying the implications of unscheduled events such as tether severance and interference between the tether and other hardware. It is the authors opinion that these type of events, which have important consequences for the operation of tethers in space, have received insufficient consideration in the extensive literature on the subject. In particular, the investigation of the interference event appears to be completely new. The examination focussed on tether experiments planned for the forthcoming International Space Station (ISS). Results were obtained through the use of a highspeed, non-linear, computer simulation model specifically designed for use with tethered satellite systems. Simulations showed that both severance and interference were possible during retrieval of the tether, particularly if ‘skip-rope’ motion is initiated. The motion following each of these incidents is predicted and shows that these unscheduled events are potentially very hazardous for the ISS. While the results of these simulations are not directly applicable to specific operations on the ISS, they fulfill the primary purpose of this paper which is the demonstration of this new technology.     

Modifying the atlas of low lunar orbits using inert tethers

For long enough tethers, the coupling of the attitude and orbital dynamics may show non-negligible effects in the orbital motion of a tethered satellite about a central body. In the case of fast rotating tethers the attitude remains constant, on average, up to second order effects. Besides, for a tether rotating in a plane parallel to the equatorial plane of the central body, the attitude–orbit coupling effect is formally equal to the perturbation of the Keplerian motion produced by the oblateness of the central body and, therefore, may have a stabilizing effect in the orbital dynamics. In the case of a tethered satellite in a low lunar orbit, it is demonstrated that feasible tether lengths can help in modifying the actual map of lunar frozen orbits.