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.     

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.     

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.     

A hybrid attitude controller consisting of electromagnetic torque rods and an active fluid ring

In this paper, a novel hybrid actuation system for satellite attitude stabilization is proposed along with its feasibility analysis. The system considered consists of two magnetic torque rods and one fluid ring to produce the control torque required in the direction in which magnetic torque rods cannot produce torque. A mathematical model of the system dynamics is derived first. Then a controller is developed to stabilize the attitude angles of a satellite equipped with the abovementioned set of actuators. The effect of failure of the fluid ring or a magnetic torque rod is examined as well. It is noted that the case of failure of the magnetic torque rod whose torque is along the pitch axis is the most critical, since the coupling between the roll or yaw motion and the pitch motion is quite weak. The simulation results show that the control system proposed is quite fault tolerant.     

Characterization of the optimal mass problem for aerobraking tethers

In the aerobraking tether concept, a probe, connected to an orbiter by a long, thin tether, passes through the atmosphere of a target planet to provide a desired velocity change, while keeping the orbiter above the sensible atmosphere. In earlier work, simple analytic models have been developed which accurately describe the characteristics of the mass-optimal tether. In this paper these models are generalized so that design of the spacecraft and the aerobraking maneuver can be completely characterized by four independent parameters. By comparing the tether mass (e.g. for aerocapture) with the propellant mass required to capture the orbiter, we show that aerobraking tethers have a clear advantage for a wide range of maneuvers.     

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。     

敏捷卫星偏流角计算模型研究

TDICCD相机成像时为保证图像品质,要求对偏流角进行修正。文章针对敏捷卫星任意姿态角建立了在星下点成像、俯仰姿态机动后成像、滚动姿态机动后成像,以及滚动加俯仰姿态机动后成像几种情况下偏流角计算模型,并对模型进行了仿真计算。结果表明,敏捷卫星姿态目标计算当中,有必要考虑姿态机动带来的偏流角控制目标变化,以保证姿态控制精度。文章对敏捷卫星的偏流角控制设计、计算和测试验证工作有参考价值。     

Refined dynamical analysis of multi-tethered satellite formations

The dynamics of a multi-tethered satellite formation is considered here, in order to derive a minimum complexity model that successfully represents its dynamics under the action of gravity gradient force and tether tension, where tethers are modeled by means of a sequence of point-masses and massless springs (bead model). The results thus obtained are compared with those derived for a simple, massless tether model, in order to highlight the effects of tether mass on the resulting open-loop behavior. The analysis is performed by means of numerical simulation of the considered models. Once the dynamic behavior of the formation is identified for the nominal values of tether characteristics, the problems raised by the presence of tether mass are highlighted and possible solutions are outlined, when possible. A parametric analysis with respect to the tether linear mass, damping and stiffness is also discussed.     

Coupling between structural deformation and attitude motion of large planar space structures suspended by multi-tethers

A planar space structure suspended by multi-tethers is one candidate for large and lightweight structures. For such flexible structures, coupling phenomena between structural deformation and attitude motion must be considered. In the present paper, the dynamic characteristics of a planar structure suspended by multi-tethers are investigated. Simulation results reveal that the coupling occurs for low tether stiffness. In addition, it is shown that the coupling can also occur if a number of the tethers become slack. Thermal deformation of the planar structure is one cause of tether slack. Thermal deformation and the induced attitude motion are also investigated. It is shown that roll and yaw motions become unstable due to thermal deformation. Finally, we modify the condition of the connection between sub-panels in order to reduce the overall thermal deformation, and it is confirmed that large deformation can be inhibited by the modification.     

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.     

Electric sail,photonic sail and deorbiting applications of the freely guided photonic blade

We consider a freely guided photonic blade (FGPB) which is a centrifugally stretched sheet of photonic sail membrane that can be tilted by changing the centre of mass or by other means. The FGPB can be installed at the tip of each main tether of an electric solar wind sail (E-sail) so that one can actively manage the tethers to avoid their mutual collisions and to modify the spin rate of the sail if needed. This enables a more scalable and modular E-sail than the baseline approach where auxiliary tethers are used for collision avoidance. For purely photonic sail applications one can remove the tethers and increase the size of the blades to obtain a novel variant of the heliogyro that can have a significantly higher packing density than the traditional heliogyro. For satellite deorbiting in low Earth orbit (LEO) conditions, analogous designs exist where the E-sail effect is replaced by the negative polarity plasma brake effect and the photonic pressure by atmospheric drag. We conclude that the FGPB appears to be an enabling technique for diverse applications. We also outline a way of demonstrating it on ground and in LEO at low cost.     

Ground assisted rendezvous with geosynchronous satellites for the disposal of space debris by means of Earth-oriented tethers

Previous studies have shown that extended length Earth-oriented tethers in the geosynchronous (GEO) region can be used to re-orbit satellites to disposal orbits. One such approach involves the extension of a GEO based tether, collection of a debris object, and retraction of the tether, which transfers the retracted configuration to a higher energy orbit for debris disposal. The re-extension of the tether after debris disposal returns the configuration to the near-GEO altitude. The practical feasibility of such a system depends on the ability to collect GEO debris objects, attach them to a deployed tether system, and retract the tethers for transfer to the disposal orbits.This study addresses the collection and delivery of debris objects to the deployed tether system in GEO. The investigation considers the number, type and the characteristics of the debris objects as well as the collection tug that can be ground controlled to detect, rendezvous and dock with the debris objects for their delivery to the tethers system.A total of more than 400 objects are in drift orbits crossing all longitudes either below or above the geostationary radius. More than 130 objects are also known to librate around the stable points in GEO with periods of libration up to five or more years. A characterization of the position and velocity of the debris objects relative to the collection tug is investigated. Typical rendezvous performance requirements for uncooperative GEO satellites are examined, and the similarities with other approaches such as the ESA's CX-OLEV commercial mission proposal to extend the life of geostationary telecommunication satellites are noted.     

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.     

空间系绳的安全性设计准则探讨

系绳的安全性设计是成功实施空间系绳试验非常重要的一环。文章首先介绍了空间系绳的发展状况,然后对已有的系绳材料与结构作了详细的介绍与分析,并通过对国外历次空间系绳试验的总结,给出了从安全性角度如何选择系绳的考虑因素。     

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.     

再论空间系绳在回收容器返回中的应用

在已有的研究结果的基础上，对空间系绳在回收容器回中的应用，作了进一步分析，包括从回收容器离开空间站至回收容器从系绳上脱落的系绳伸展运动，（２）从系绳脱落的回收容器的返回运动，（３）释放容器后的系绳的收回运动。对回收容器的动态释放，除了两阶段指数型伸展程序外，还提出了另外两种导致系绳后摆的方式。对静态释放与动态释放，不仅对系绳长度，而且对系绳张力作了计算与分析。为了系绳收回过程的稳定，不仅要施加张力     

静止轨道卫星姿态偏置对天线方向图影响的分析

地球静止轨道（GEO）卫星通常具备滚动、俯仰姿态偏置能力,即卫星滚动或俯仰姿态控制目标角度不是0°,而是某一设定角度,以便卫星定点位置改变时也能确保天线方向图覆盖满足要求。文章对某GEO卫星姿态偏置后对天线方向图及卫星其它性能的影响进行了分析,给出了卫星姿态偏置情况下天线覆盖区域的计算方法,在计算时考虑了卫星轨道倾角的影响。分析结果表明：由于卫星天线方向图设计时均有一定的设计裕度,卫星定点位置发生变化时,通过进行姿态偏置,可使其天线方向图满足用户使用要求,卫星在轨测试及运行结果也验证了这一结论。     

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。     

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.     

Tethers and debris mitigation

In recent years, the use of tethers has been proposed for reduction of space debris either through momentum transfer or use of electrodynamic effects. Tethers have been shown to at least theoretically allow for quick, elegant and cost-effective deorbit of defunct satellites or spent stages. On the other hand, the large risk that tethers themselves may pose to other satellites in orbit has been recognized as well. The large collision area of tethers, combined with operational hazards and meteoroid risk may result in a large orbital exposure. For example, in 1997, the ESA/Dutch 35-km tether deployment of YES from TEAMSAT was inhibited after an analysis of the collision risk for the case the tether operation would fail. The question rises how these two points of view compare to eachother. This paper intends to highlight a representative selection of the proposed tether applications while taking into account the added risks caused by the tethers themselves.Typical applications from recent literature will be briefly described, such as an Ariane 502 spent stage re-entry from GTO and the concept of deboost of defunct satellites by interaction of a conductive tether with the Earth magnetic field.Mass savings of the tethered sytems versus conventional equivalents will be evaluated.Based on a crude risk analysis, involving elements such as mission complexity, dynamic stability, meteoroid risk and orbital life time, a general outline of limiting factors can be given for the various applications. Special attention is reserved for implementation of mechanisms that help reduce this tether risk, such as the DUtether (Tether Degradable by Ultraviolet), utilization of airdrag and solar pressure, the effect of residual current in bare tethers, tether retrieval etc.It is proposed how a net tether-induced mitigation can be compared to that of conventional alternatives, i.e. deboost by rocket engine or a completely passive approach.This comparison is put in the perspective of an ever-increasing occupation of the space environment.It is concluded that tethers can in fact help mitigate the debris risk and that for each application a useful niche can be defined. It is argued that eliminating pollution directly after use of the precious resource of space is not only good custom, but also an important way to make the risk of debris controllable and independent of future trends. Although tethers may have large exposure in terms of area-time product, they deliver a quick cleaning service that may be appreciated by the future users of space.