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.     

Control of the deployment of an orbital tether system that consists of two small spacecraft

Control of an orbital tether system that consists of two small spacecraft has been considered. The proposed control laws are based on the modification of well-known programs for the deployment of tether system systems under the assumption that the masses of spacecraft and the tether are comparable in magnitude. To construct nominal deployment programs, we have developed a mathematical model of the motion of the given system in an orbital moving coordinate system taking into account the specific features of this problem. The performance of the proposed deployment programs is assessed by a mathematical model of the orbital tether system with distributed parameters written in the geocentric coordinate system. The test calculations involve a linear regulator that implements feedback on the tether length and velocity.     

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     

绳系卫星系统中的周期运动

在椭圆轨道上飞行的绳系卫星系统的重要特征是系绳的方向角具有周期性运动，称为驻环。不稳定的驻环导致全系统的不稳定性。本文给出系统运动的数学模型、距离速率控制方法、求解驻环的数值迭代算法、驻环的稳定性和吸引域以及控制参数平面上驻环存在的区界和计算机仿真结果     

YES2 optimal trajectories in presence of eccentricity and aerodynamic drag

YES2 (launching 2007) aims to demonstrate a tether-assisted re-entry concept, whereby payload will be returned to Earth using momentum provided from a swinging tether. Deployment takes place in two phases: (1) deployment of 3.5 km of tether to the local vertical and hold, and (2) deployment to 30 km for a swinging cut. Optimal trajectories are determined for both phases after comparing the effect of different cost functions on the deployment dynamics. Closed-loop control is provided by linearizing the dynamics around the optimal trajectories and solving a receding horizon control problem for a set of linear feedback gains. The controllers are tested in a flexible tether model with large disturbances to the hardware model and environmental variables. Closed-loop simulations show that the system can be controlled quite well using only feedback of length and length rate.     

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。     

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.     

有分布质量系绳的卫星系统的动力学

以一组偏微分方程建立起的数学模型和采用距离速率控制算法来描述系统的受控运动。创建的递推算法用于计算系统的定常运动和称驻形。根据求解小偏差运动方程和通过边界条件求解特征根以判定驻形的稳定性。给出了模拟结果。     

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.     

Experiments and numerical simulations of an electrodynamic tether deployment from a spool-type reel using thrusters

The amount of space debris is ever increasing, and pollution of the space environment has become a serious problem that can no longer be ignored. Consequently, the active removal of large space debris from crowded economically useful orbits should begin as soon as possible. The Japan Aerospace Exploration Agency has been investigating an active debris removal system that employs highly efficient electrodynamic tether (EDT) technology for orbital transfer. This study investigates the tether deployment from a spool-type reel using thrusters by means of numerical simulations of an EDT system. The thrusters are used in order to ensure the deployment of a tether with the length of several kilometers. In the simulations using a multiple mass tether model, the key parameters are estimated from various on-ground experiments. By means of the numerical simulations, the dynamics of tether deployment is studied and requirements of thruster needed for the deployment, such as the thrust forces and the periods of thruster activation, are clarified.     

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.     

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.     

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.     

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.     

Qualification and in-flight demonstration of a European tether deployment system on YES2

This paper highlights the design, qualification and mission performance of the tether deployer system on the second Young Engineers’ Satellite (YES2), that featured a tethered momentum transfer. The deployer is designed with a broad range of near-term tether applications in mind. The system contains the tether, including features to enhance safety and wound up in controlled manner onto a spool core, optical deployment sensors, a “barberpole” friction brake controlled by a stepper motor and a triple tether cutter system. To initiate the deployment a spring-based ejection system was developed, and to apply accurate momentum transfer a timer and release system is present on the subsatellite side. A small, 6 kg re-entry capsule was developed as subsatellite. On September 25th, 2007, YES2 deployed a 32 km tether in orbit and gathered a wealth of data. Confidence is gained from the mission results for use of the deployer in future missions.     

空间碎片绳网捕获拖曳恒张力控制

针对空间绳网系统捕获空间碎片后，在轨道转移过程中的精确控制问题，提出一种使用常值拉力将空间碎片拖曳至坟墓轨道的方法。首先，采用牛顿欧拉法建立绳系组合体动力学模型；其次，通过李雅普诺夫方法证明仅使用恒张力即可实现拖曳过程的稳定控制；再次，提出采用常值拉力切换控制律抑制空间碎片的姿态章动，采用基于相平面控制原理的控制律抑制绳系组合体面内面外摆动，规避在轨道转移过程中系绳松弛造成缠绕、系绳张力过大造成断裂或两星接近发生碰撞等风险。最后，通过拖曳离轨全过程仿真分析，校验了所提出控制方法的有效性。     

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。     

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.