Self-stabilising attitude control for spinning tethered formations

The paper analyses the dynamics of a spinning tethered formation where the tethered units are modelled as extended rigid bodies. The system, composed by two platforms linked by a flexible tether a few hundreds of meters long, constitutes the building block of more complex tethered architectures utilised in proposed space interferometry missions. The issue investigated herein is the transfer of a collimated beam from one platform to another in the presence of environmental perturbations and structural vibrations affecting the position and attitude of the two tethered units. We propose to damp residual oscillations and limit the effect of environmental torques with the aid of two passive dampers placed at the tether attachment point. When the damping system is properly tuned, this approach has the considerable advantage of rapidly bringing the system to a minimum energy configuration (zero residual vibrations) without any external control force. Numerical results show the effectiveness of the proposed control strategy and provide an important element towards the implementation of future space-based observatories and formation-flying demonstration mission based on tether-connected architectures.     

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。     

Orbital and relative motion of a tethered satellite system

A simplified model for the orbital and relative motion of a tethered satellite system is presented. The tether acts as a light elastic string with small structural damping but without bending stiffness. Its mass is taken into account in the calculation of the total kinetic and potential energies of the tethered system. This formulation allows the inclusion of the complete gravity gradient influence on the dynamics of the system. The resulting three-dimensional motion is separated in the centre of mass orbital motion on the one hand and the relative motion of the end-bodies on the other. No restrictions on length of the tether or on mass ratio of the end-masses are imposed. It is found that the frequencies and amplitudes of the longitudinal tether oscillations are realistic as long as the tether mass is less than that of the subsatellite.     

改进的绳系卫星系统距离速率控制律

为扩大绳系卫星系统(TSS)控制的稳定域,提出了一种改进距离速率控制算法。根据TSS动力学方程及构造的二阶稳定系统,给出了修正的控制模型。讨论了稳定释放角度和释放/回收速度的影响,并研究了固定绳索长度系留控制方案。算例表明该方法可显著扩大稳定域,提高释放速度。     

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.     

Planar dynamics of variable length multi-tethered spacecraft near collinear Lagrangian points

This paper examines the planar dynamics of a wheel-and-spoke configured multi-spacecraft system, connected together by variable length tethers, near the second Sun–Earth Lagrangian point. The closed form solutions of the system under some simple tether length functions are determined and numerical results for the tether pitch librations under more complex tether length functions are obtained, along with the control effort required to maintain the desired tether librations.     

Planar dynamics of variable length multi-tethered spacecraft near collinear Lagrangian points

This paper examines the planar dynamics of a wheel-and-spoke configured multi-spacecraft system, connected together by variable length tethers, near the second Sun–Earth Lagrangian point. The closed form solutions of the system under some simple tether length functions are determined and numerical results for the tether pitch librations under more complex tether length functions are obtained, along with the control effort required to maintain the desired tether librations.     

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。     

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。     

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。     

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.     

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。     

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.     

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。     

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。     

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.     

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.     

自主机动空间绳网机器人设计与动力学建模

设计了一种新型“平台+绳系+柔性网+自主机动单元”结构的空间机器人系统,较强的机动能力和较大的任务范围使其在空间垃圾清理任务中具有显著的优势。详细描述了自主机动空间绳网机器人的概念、任务过程和特点。为了分析自主机动空间绳网机器人逼近目标过程开始时柔性网网型的变化趋势,采用质量集中法建立了逼近过程的动力学模型,模型中将柔性网离散化为无质量弹性杆和质点的集合,同时考虑了自主控制力的作用。在不同条件下对逼近过程中的网型变化进行了数字仿真,仿真结果表明：逼近过程开始时,自主机动单元无控状态下柔性网将产生收口运动,且收口运动的强弱与自主机动单元和柔性网的初速有关;逼近轨迹也将偏离目标方向。通过自主机动单元的自主控制力能够避免收口运动和逼近方向偏移的产生。     

在轨服务中空间系绳的应用及发展

针对空间系绳在空间在轨服务中的应用与发展问题,在简述空间系绳传统应用及试验情况的基础上,综述了空间绳系机器人、空间绳网机器人两类新在轨应用方式的研究和发展,主要包括动力学建模、结构设计、相对状态测量、逼近/抓捕控制、拖曳变轨等。最后进一步讨论了空间系绳未来的研究方向。