Families of halo orbits in the elliptic restricted three-body problem for a solar sail with reflectivity control devices

Solar sail halo orbits designed in the Sun-Earth circular restricted three-body problem (CR3BP) provide inefficient reference orbits for station-keeping since the disturbance due to the eccentricity of the Earth’s orbit has to be compensated for. This paper presents a strategy to compute families of halo orbits around the collinear artificial equilibrium points in the Sun-Earth elliptic restricted three-body problem (ER3BP) for a solar sail with reflectivity control devices (RCDs). In this non-autonomous model, periodic halo orbits only exist when their periods are equal to integer multiples of one year. Here multi-revolution halo orbits with periods equal to integer multiples of one year are constructed in the CR3BP and then used as seeds to numerically continue the halo orbits in the ER3BP. The linear stability of the orbits is analyzed which shows that the in-plane motion is unstable while the out-of-plane motion is neutrally stable and a bifurcation is identified. Finally, station-keeping is performed which shows that a reference orbit designed in the ER3BP is significantly more efficient than that designed in the CR3BP, while the addition of RCDs improve station-keeping performance and robustness to uncertainty in the sail lightness number.     

姿态角幅值约束下的太阳帆Lissajous轨道保持控制

太阳帆航天器以两姿态角作为轨道控制输入时, 其轨道动力学方程具有非仿射非线性特性. 通过人工平动点处线性化获得的线性系统可完成太阳帆航天器轨道保持控制器的分析与设计. 由于线性近似模型为有误差模型, 存在近似有效范围约束, 表现为轨道高度约束和姿态角幅值约束. 本文研究了姿态角幅值约束对线性近似模型有效性的影响, 通过计算给出满足近似误差要求的姿态角幅值约束. 当控制输入存在幅值约束时, 控制器轨道修正能力受到束缚. 通过研究姿态角幅值约束下的最大允许入轨误差, 设计了最大允许入轨误差下线性二次型调节器(LQR)用于轨道保持控制, 并将控制器应用于太阳帆日地三体系统非线性模型中, 实现了日地人工L₁点Lissajous轨道最大允许入轨误差的控制收敛和良好精度下的轨道保持控制.      

Influence of optical parameters on a solar sail motion

Detailed dynamic modeling of a solar sail requires recording of solar radiation pressure influence. A photon-solar sail is determined by the thrust value and the direction. We define the solar sail’s reflectivity depending on the film materials, the sail design and temperature, the thickness of multiple layers, and degradation factor, with a reasonable degree of accuracy. Thus, this work is devoted to the identification of optical characteristics of thin multilayer films in space flight conditions, i.e. to finding its reflectance, absorbance, and transmittance. In particular, the paper asks whether the solar sail simulates by a mathematical model of the optical characteristics of a multilayer epitaxial thin film. The temperature change effect and optical properties of solar sail degradation are considered as well. Solar sail flight from Earth to Mercury is designed as a simulation of the flight change in optical parameters.     

基于参考轨道的Walker星座相对相位保持策略

针对高轨道Walker全球星座相对相位保持问题,在分析星座几何结构演化规律基础上,提出了一种基于动态调整参考轨道的星座相对相位保持策略.该参考轨道的半长轴取星座所有卫星的平均轨道半长轴的平均值,通过计算各卫星相对参考轨道的相对相位偏差以及变化率,而后根据有关维持的约束条件来选择合适的卫星进行站点保持,使得所有卫星的相对参考轨道的相位偏差不超过允许值.当一旦有卫星进行了站点保持,则参考轨道就重新统计确定.文章通过一个12颗MEO卫星构成的Walker-δ星座的分析算例,表明这种相对保持策略可以减少星座的站点维持次数.本文提出的方法可以为我国今后卫星导航星座的维持提供参考.     

太阳帆航天器悬浮轨道动力学与控制

基于线性动力学模型和非线性动力学模型,研究了太阳帆航天器日心悬浮轨道保持与控制问题.首先,推导出了柱坐标形式的太阳帆动力学方程,并在参考悬浮轨道附近线性化以建立状态方程,然后对状态方程进行可控性分析.通过合理选择控制变量加权矩阵R,用线性二次型调节器(LQR)对线性模型进行控制.将得到的控制律代入非线性模型中进行验证,表明该控制律渐近稳定,并且具有良好的控制精度,可实现太阳帆悬浮轨道控制.      

Extrasolar space exploration by a solar sail accelerated via thermal desorption of coating

For extrasolar space exploration it might be very convenient to take advantage of space environmental effects such as solar radiation heating to accelerate a solar sail coated by materials that undergo thermal desorption at a particular temperature. Thermal desorption can provide additional thrust as heating liberates atoms, embedded on the surface of the solar sail. We are considering orbital dynamics of a solar sail coated with materials that undergo thermal desorption at a specific temperature, as a result of heating by solar radiation at a particular heliocentric distance, and focus on two scenarios that only differ in the way the sail approaches the Sun. For each scenario once the perihelion is reached, the sail coat undergoes thermal desorption. When the desorption process ends, the sail then escapes the Solar System having the conventional acceleration due to solar radiation pressure. We study the dependence of a cruise speed of a solar sail on perihelion of the orbit where the solar sail is deployed. The following scenarios are considered and analyzed: (1) Hohmann transfer plus thermal desorption. In this scenario the sail would be carried as a payload to the perihelion with a conventional propulsion system by a Hohmann transfer from Earth’s orbit to an orbit very close to the Sun and then be deployed. Our calculations show that the cruise speed of the solar sail varies from 173?km/s to 325?km/s that corresponds to perihelion 0.3?AU and 0.1 AU, respectively. (2) Elliptical transfer plus Slingshot plus thermal desorption. In this scenario the transfer occurs from Earth’s orbit to Jupiter’s orbit; then a Jupiter’s fly-by leads to the orbit close to the Sun, where the sail is deployed and thermal desorption comes active. In this case the cruise speed of the solar sail varies from 187?km/s to 331?km/s depending on the perihelion of the orbit. Our study analyses and compares the different scenarios in which thermal desorption comes beside traditional propulsion systems for extrasolar space exploration.     

地月平动点中继应用轨道维持

地月平动点中继应用轨道对于月球背面探测具有十分重要的应用价值,由于地月平动点的不稳定性,必须进行轨道维持。文章研究了真实力模型下月球平动点中继应用轨道的维持。首先,基于限制性三体问题下平动点轨道的运动特性,研究了平动点轨道维持的数学模型与维持策略,提出了平动点轨道维持的连续环绕控制方法,并给出了轨道维持的Halo和Lissajous两种控制方式;其次,充分考虑各天体和光压摄动下,采用数值手段研究了不同幅值的地月平动点周期中继应用轨道的维持间隔与速度增量等。研究结果表明:Lissajous控制方式适用于月球平动点中继应用轨道的维持,在给定测控精度条件下,维持间隔约7.4d,速度增量优于20m/s/a。该方法已经成功应用于我国"嫦娥2号"日地平动点任务和"嫦娥5T1"地月平动点任务并获得了良好的控制效果,还可直接应用于我国未来"嫦娥4号"等月球背面探测任务。     

太阳帆航天器行星际轨道转移优化算法

研究基于遗传算法的太阳帆行星际转移轨道的全局优化问题.通过极小值原理推导了太阳帆全局优化控制律,并以太阳帆飞行时间最短为优化目标函数,运用遗传算法对发射时间、到达时间和协态变量初值进行参数优化设计.为了解决轨道转移这一多约束优化问题,在遗传算法中加入动态罚函数.在此理论基础上作了从地球同步轨道出发到火星同步轨道转移和从地球出发与火星交会两个算例,仿真结果表明了该方法在太阳帆转移轨道全局优化中的有效性.     

Spinning solar sail orbit steering via spin rate control

The orbit of a solar sail can be controlled by changing the attitude of the spacecraft. In this study, we consider the spinning solar power sail IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun), which is managed by Japan Aerospace Exploration Agency (JAXA). The IKAROS attitude, i.e., the direction of its spin-axis, is nominally controlled by the rhumb-line control method. By utilizing the solar radiation torque, however, we are able to change the direction of the spin-axis by only controlling its spin rate. With this spin rate control, we can also control indirectly the solar sail’s trajectory. The main objective of this study is to construct the orbit control strategy of the solar sail via the spin-rate control method. We evaluate this strategy in terms of its propellant consumption compared to the rhumb-line control method. Finally, we present the actual flight attitude data of IKAROS and the change of its trajectory.     

Improving magnetosphere in situ observations using solar sails

Past and current magnetosphere missions employ conventional spacecraft formations for in situ observations of the geomagnetic tail. Conventional spacecraft flying in inertially fixed Keplerian orbits are only aligned with the geomagnetic tail once per year, since the geomagnetic tail is always aligned with the Earth-Sun line, and therefore, rotates annually. Solar sails are able to artificially create sun-synchronous orbits such that the orbit apse line remains aligned with the geomagnetic tail line throughout the entire year. This continuous presence in the geomagnetic tail can significantly increase the science phase for magnetosphere missions. In this paper, the problem of solar sail formation design is explored using nonlinear programming to design optimal two-craft, triangle, and tetrahedron solar sail formations, in terms of formation quality and formation stability. The designed formations are directly compared to the formations used in NASA’s Magnetospheric Multi-Scale mission.     

End-to-end trajectory design for a solar-sail-only pole-sitter at Venus,Earth, and Mars

The concept of a pole-sitter has been under investigation for many years, showing the capability of a low-thrust propulsion system to maintain a spacecraft at a static position along a planet’s polar axis. From such a position, the spacecraft has a view of the planet’s polar regions equivalent to that of the low- and mid-latitudes from geostationary orbit. Previous work has hinted at the existence of pole-sitters that would only require a solar sail to provide the necessary propulsive thrust if a slight deviation from a position exactly along the polar axis is allowed, without compromising on the continuous view of the planet’s polar region (a so-called quasi-pole-sitter). This paper conducts a further in-depth analysis of these high-potential solar-sail-only quasi-pole-sitters and presents a full end-to-end trajectory design: from launch and transfer to orbit design and orbit control. The results are the next steppingstone towards strengthening the feasibility and utility of these orbits for continuous planetary polar observation.     

太阳帆推进任务的快速仿真方法

研究太阳帆的力学特性和轨道控制设计方法,导出太阳帆的无奇点控制律.提出通过STK中MATLAB语言编写的嵌入式脚本（Plug in Script）来将由控制律得到的光压力加速度矢量,添加到STK轨道计算力学模型中,从而进行轨道控制的方法.仿真结果表明,对于常规方法难以进行仿真分析的航天器动力学模型（如太阳帆）,所提出的方法能快速灵活地支持其相应的任务,并增强任务场景的可视化,从而实现利用STK丰富的功能特性进行复杂航天任务的设计、分析和验证.     

太阳帆飞行器轨道动力学分析

通过分析对轨道要素影响最大的加速度分量,使太阳帆总是位于光压力沿这个加速度方向的分量最大的方位。通过分析轨道要素调整时的相互影响关系,提出了同时修正多种轨道偏差的控制方案。对处于地球静止轨道上太阳帆飞行器的轨道调整进行了数值仿真。结果证明利用太阳光压力进行轨道调整是可行的,而且有利的太阳方位是进行快速有效的轨道调整的必要条件。     

On-orbit verification of fuel-free attitude control system for spinning solar sail utilizing solar radiation pressure

This paper introduces a new attitude control system for a solar sail, which leverages solar radiation pressure. This novel system achieves completely fuel-free and oscillation-free attitude control of a flexible spinning solar sail. This system consists of thin-film-type devices that electrically control their optical parameters such as reflectivity to generate an imbalance in the solar radiation pressure applied to the edge of the sail. By using these devices, minute and continuous control torque can be applied to the sail to realize very stable and fuel-free attitude control of the large and flexible membrane. The control system was implemented as an optional attitude control system for small solar power sail demonstrator named IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun). In-orbit attitude control experiments were conducted, and the performance of the controller was successfully verified in comparison with the ground-based analytical performance estimation.     

V型轮控系统卫星东西位置保持策略优化方法研究

以某在轨GEO卫星为研究对象,探讨了适用于V型轮控系统特点的东西位置保持策略．首先分析了V型轮控系统的工作原理,提出了轮控过程中推力器效率的标定方法和喷气卸载对轨道影响的数学模型;然后深入分析了轮控过程中姿态控制对卫星东西位置保持环及偏心率的影响,提出了延长位保周期的控制策略,并在实际任务中获得了较好的效果．     

Optimal steering law of refractive sail

The interaction between electromagnetic waves and matter is the working principle of a photon-propelled spacecraft, which extracts momentum from the solar radiation to obtain a propulsive acceleration. An example is offered by solar sails, which use a thin membrane to reflect the impinging photons. The solar radiation momentum may actually be transferred to matter by means of various optical phenomena, such as absorption, emission, or refraction. This paper deals with the novel concept of a refractive sail, through which the Sun’s light is refracted by crossing a film made of polymeric micro-prisms. The main feature of a refractive sail is to give a large transverse component of thrust even when the sail nominal plane is orthogonal to the Sun-spacecraft line. Starting from the recent literature results, this paper proposes a semi-analytical thrust model that estimates the characteristics of the propulsive acceleration vector as a function of the sail attitude angles. Such a mathematical model is then used to analyze a simplified Earth-Mars and Earth-Venus interplanetary transfer within an optimal framework.     

On the stabilizing effect of Solar Radiation Pressure in the Earth-Moon system

Solar sails change the natural dynamics of systems: Trajectories that are driven by gravitational forces can be displaced and changed because of the effect of Solar Radiation Pressure (SRP). Moreover, if the lightness number of the sail is large enough, the instability of certain orbits can be diminished and even removed. In this paper we modify two models for the motion of a probe in the Earth-Moon system that include the effect of Sun’s gravity to take also into account the effect of SRP. These models, the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP), are periodic perturbations of the Earth-Moon Restricted Three Body Problem (RTBP). The models are modified to consider the effect of the SRP upon a solar sail. We provide examples of periodic orbits that are stabilized (or made less unstable) due to the effect of SRP.     

Solar sail near the Sun: Point-like and extended models of radiation source

Some modifications of solar sail radiation pressure forces on a plate and on a sphere for use in the numerical simulation of ‘local-optimal’ (or ‘instantaneously optimal’) trajectories of a spacecraft with a solar sail are suggested. The force model development is chronologically reviewed, including its connection with solar sail surface reflective and thermal properties. The sail surface is considered as partly absorbing, partly reflective (specular and diffuse), partly transparent. Thermal balance is specified because the spacecraft moves from circular Earth orbit to near-Sun regions and thermal limitations on the sail film are taken into account. A spherical sail-balloon can be used in near-Sun regions for scientific research beginning with the solar-synchronous orbit and moving outward from the Sun. The Sun is considered not only as a point-like source of radiation but also as an extended source of radiation which is assumed to be consequently as a point-like source of radiation, a uniformly bright flat solar disc and uniformly bright solar sphere.     

Solar sail optimal control with solar irradiance fluctuations

The optimization of a solar sail-based orbital transfer amounts to searching for the control law that minimizes the flight time. In this context, the optimal trajectory is usually determined assuming constant solar properties. However, the total solar irradiance undergoes both long-term (solar cycles) and short-term variations, and recent analyses have shown that this may have an impact on solar sailing for missions requiring an accurate thrust modulation. In this regard, the paper discusses a strategy to overcome such an issue by suitably adjusting the thrust vector in order to track a reference, optimal, transfer trajectory. In particular, the sail propulsive acceleration magnitude is modified by means of a set of electrochromic material panels, which change their optical properties on application of a suitable electric voltage. The proposed control law is validated with a set of numerical simulations that involve a classical Earth-Mars, orbit-to-orbit, heliocentric transfer.     

Shape optimization of a three-dimensional membrane-structured solar sail using an angular momentum unloading strategy

A shape of the satellite’s solar sail membrane is essential for unloading angular momentum in the three-axis stabilized attitude control system because the three-dimensional solar sail can receive solar radiation pressure from arbitrary directions. In this paper, the objective is the shape optimization of a three-dimensional membrane-structured solar sail using the angular momentum unloading strategy. We modelled and simulated the solar radiation pressure torque, for unloading angular momentum. Using the simulation system, since the unloading angular momentum rate is maximized, the shape of the three-dimensional solar sail was optimized using a Genetic algorithm and Sequential Quadratic Programming. The unloading velocity in the optimized shaped solar sail was greatly improved with respect to a conventional flat or pyramid solar sail.