Configuration space and stability analysis of solar sail near-vertical earth-trailing orbits

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L₁ sail-based vertical orbits.     

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.     

Solar-photon sail hovering orbits about single and binary asteroids

Solar-photon sails can be useful for missions towards and about asteroids. Indeed, for the interplanetary transfer phase, missions to asteroids often require a large variation in inclination and solar-photon sails perform very well for such high energy missions. In the same way, solar-photon sails are also expected to perform well in the phase about the asteroid. This paper studies single and binary asteroids’ hovering regions by using a sailcraft. In order to consider a sailcraft with its own mass and shape, the mutual polyhedral method (usually used to study asteroid dynamics) is used; therefore, the sailcraft is designed by means of tetrahedra. The procedure to obtain the hovering regions about a single asteroid is presented and an accurate analysis of the control variables is carried out. Moreover, control torques required to maintain hovering orbits are obtained by considering the gravitational torques acting on the sailcraft due to the asteroid. In the end, the theory for hovering orbits is extended to binary-asteroid systems and applied to the binary system 1999 KW4.     

Application of a modified generalized sail model on a solar sail with wrinkles

In this paper, we present an analysis of effect of wrinkles on the solar sail performance. We describe different analytical, semi-analytical and numerical approaches to the calculation of general large-scale curvature of a solar sail as well as parameters of so-called wrinkled domains, and introduce the impact of such wrinkles on the thrust and torque of the solar sail. Finally, we present a model of an optically-orthotropic surface for such non-ideal sail, providing a connection with the Generalized Sail Model, and other solar sail thrust models.     

Status of solar sail technology within NASA

In the early 2000s, NASA made substantial progress in the development of solar sail propulsion systems for use in robotic science and exploration of the solar system. Two different 20-m solar sail systems were produced. NASA has successfully completed functional vacuum testing in their Glenn Research Center’s Space Power Facility at Plum Brook Station, Ohio. The sails were designed and developed by Alliant Techsystems Space Systems and L’Garde, respectively. The sail systems consist of a central structure with four deployable booms that support each sail. These sail designs are robust enough for deployment in a one-atmosphere, one-gravity environment and are scalable to much larger solar sails – perhaps as large as 150 m on a side. Computation modeling and analytical simulations were performed in order to assess the scalability of the technology to the larger sizes that are required to implement the first generation of missions using solar sails. Furthermore, life and space environmental effects testing of sail and component materials was also conducted.     

Dynamical analysis of a spinning solar sail

This paper discusses the orbit and attitude dynamics of a solar sail, and gives the sufficient conditions of a stable orbit and attitude coupled system. The stability of the coupled system is determined by the orbit stability and attitude stability. Based on the sufficient conditions, a spin-stabilized solar sail of cone configuration is proposed to evolve in the heliocentric displaced orbit. For this kind of configuration, the attitude is always stable by spinning itself. The orbit stability depends on the orbit parameters of the heliocentric displaced orbit, the ratio of the orbit radius to displaced distance and orbit angular velocity. If the center of mass and center of pressure overlap, it can be proved that the coupled system is stable when the orbit parameters are chosen in the stable region. When the center of mass and center of pressure offset exists, the stability of the coupled system can not be judged. A numerical example is given and the result shows that both the orbit and attitude are stable for the case.     

Attitude stability criteria of axisymmetric solar sail

Passive attitude stability criteria of a solar sail whose membrane surface is axisymmetric are studied in this paper under a general SRP model. This paper proves that arbitrary attitude equilibrium position can be designed through adjusting the deviation between the pressure center and the mass center of the sail. The linearized method is applied to inspect analytically the stability of the equilibrium point from two different points of views. The results show that the attitude stability depends on the membrane surface shape and area. The results of simulation with full dynamic equations confirm that the two stability criteria are effective in judging the attitude stability for axisymmetric solar sail. Several possible applications of the study are also mentioned.     

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.     

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.     

Numerical techniques for generating and refining solar sail trajectories

Like all applications in trajectory design, the design of solar sail trajectories requires a transition from analytical models to numerically generated realizations of an orbit. In astrodynamics, three numerical strategies are often employed. Differential correctors (also known as shooting methods) are perhaps the most common techniques. Finite-difference methods and collocation schemes are also employed and are successful in generating trajectories with pseudo-continuous control histories. These three numerical techniques are employed here to generate periodic trajectories displaced below the Moon in a circular restricted three-body system. All these approaches reveal trajectory options within the design space for solar sail applications.     

Analysis of the solar sail deformation based on the point cloud method

The deformation of the solar-sail membrane is an important factor for causing inaccuracies in the solar-sail missions. This paper describes the solar sail under deformation by using a new modelling technique based on point cloud and triangular mesh generation. Two types of deformation, stemming from wrinkling and billowing, are modelled. The changes in the solar radiation pressure force and the moment caused by deformation are calculated and compared to the ideal non-deformed case. The heliocentric spiral trajectory and the orbital angular momentum reversal trajectory are taken as examples to quantify the influence of the deformation from an orbit point of view. Additionally, point cloud simplification, based on the normal vector and bounding box, is utilized to simplify the original deformed-sail model. It involves a reasonable reduction and renewal of the points in the model considering the variation of surface curvature. The simplification and its modelling accuracy are numerically investigated as well as computational efficiency.     

Optimal solar sail trajectory approximation with finite Fourier series

The heliocentric transfer of a solar sail-based spacecraft is usually studied from an optimal perspective, by looking for the control law that minimizes the total flight time. The optimal control problem can be solved either with an indirect approach, whose solution is difficult to obtain due to its sensitivity to an initial guess of the costates, or with a direct method, which requires a good estimate of a feasible (guess) trajectory. This work presents a procedure to generate an approximate optimal trajectory through a finite Fourier series. The minimum time problem is solved using a nonlinear programming solver, in which the optimization parameters are the coefficients of the Fourier series and the positions of the spacecraft along the initial and target orbits. Suitable constraints are enforced on the direction and magnitude of the sail propulsive acceleration vector in order to obtain feasible solutions. A comparison with the numerical results from an indirect approach shows that the proposed method provides a good approximation of the optimal trajectory with a small computational effort.     

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.     

Hierarchical global search for fuel-optimal impulsive transfers between lunar libration orbits

The attention to the periodic orbit in the Earth-Moon restricted three-body system continues to grow due to its special environment and locations. This research investigates the feasibility of constructing fuel-optimal single and multiple impulse transfers between unstable periodic orbits at L₁ and L₂ points. Invariant manifolds, which could provide the appropriate initial trajectories for optimization, are analyzed deeply to enable previously unknown orbit options and potentially to reduce mission cost. A global search strategy based on comparing the orbital state of the unstable and stable manifolds, incorporated with low-thrust techniques, is performed to seek a suitable matching point for maneuver application. Then the sequential quadratic programming (SQP) is adopted to further optimize the velocity increment and obtain the single/multiple impulse optimal transfers. The associated constraint gradients are derived to achieve higher accuracy and rapidity of the algorithm. To highlight the effectivity of the transfer scheme, three-dimensional low-energy transfers between different types and spatial regions of performing single and multiple impulses are explored. The total Delta-V required varies between a few meters per second and tens of meters per second, and the related flight time is about several weeks, mainly depending on the energy of periodic orbits and the invariant manifold structure. The results obtained in this paper can provide a useful reference for the selection of escape and capture site along the manifolds, maneuver magnitude and transfer time.     

A torus-shaped solar sail accelerated via thermal desorption of coating

A torus-shaped sail consists of a reflective membrane attached to an inflatable torus-shaped rim. The sail’s deployment from its stowed configuration is initiated by introducing inflation pressure into the toroidal rim with an attached circular flat membrane coated by heat-sensitive materials that undergo thermal desorption (TD) from a solid to a gas phase. Our study of the deployment and acceleration of the sail is split into three steps: at a particular heliocentric distance a torus-shaped sail is deployed by a gas inflated into the toroidal rim and the membrane is kept flat by the pressure of the gas; under heating by solar radiation, the membrane coat undergoes TD and the sail is accelerated via TD of coating and solar radiation pressure (SRP); when TD ends, the sail utilizes thrust only from SRP. We study the stability of the torus-shaped sail and deflection and vibration of the flat membrane due to the acceleration by TD and SRP.     

Durability characterization of mechanical interfaces in solar sail membrane structures

The construction of a solar sail from commercially available metallized film presents several challenges. The solar sail membrane is made by seaming together precut lengths of ultrathin metallized polymer film into the required geometry. This assembled sail membrane is then folded into a small stowage volume prior to launch. The sail membranes must have additional features for connecting to rigid structural elements (e.g., sail booms) and must be electrically grounded to the spacecraft bus to prevent charge build up. Space durability of the material and mechanical interfaces of the sail membrane assemblies will be critical for the success of any solar sail mission. In this study, interfaces of polymer/metal joints in a representative solar sail membrane assembly were tested to ensure that the adhesive interfaces and the fastening grommets could withstand the temperature range and expected loads required for mission success. Various adhesion methods, such as surface treatment, commercial adhesives, and fastening systems, were experimentally tested in order to determine the most suitable method of construction.     

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.     

Integrated guidance and control for solar sail station-keeping with optical degradation

Current control approaches for solar sail station-keeping on libration point orbits have not considered the degradation of the sail’s optical properties. However, significant optical degradation could lead to poor station-keeping performance or even complete failure. This paper presents an integrated guidance and control strategy to address this problem by updating the reference orbit based on in situ estimation. An exponential optical degradation model is incorporated into the solar radiation acceleration model, and an on-line reference orbit update approach is incorporated into the station-keeping, coupled with an active disturbance rejection controller. The reflection coefficient is estimated on-line and the reference orbit is updated discretely when the optical properties have degraded by a prescribed amount. This strategy provides discrete updates to the reference orbits such that the perturbation due to the optical degradation is maintained within a small range. These smaller perturbations can be dealt with by the controller’s robustness and station-keeping can be sustained for long durations even in the presence of large optical degradation.     

平动点周期轨道间小推力转移的Gauss伪谱法

针对三体问题共线平动点附近周期轨道间的小推力转移问题,构造了一种新的形状函数,在此基础上提出了一种基于Gauss伪谱法的优化设计方法。首先,建立小推力轨道转移动力学模型,参考初始轨道和目标轨道的类型,构造一种新的形状函数以近似小推力转移轨道。为满足不同的约束要求,提出了振幅和相位按多项式变化的假设,推导了小推力转移轨道的近似解析解;然后利用Gauss伪谱法将小推力轨道转移的最优控制问题转化为非线性规划问题,并对推导的近似解析解进行解算和处理,为Gauss伪谱法求解非线性规划问题提供较为有效的控制变量的初始猜测值;最后以地月系统L₁点附近Halo轨道间的小推力转移问题为例进行了仿真分析。仿真结果表明,小推力转移轨道近似解析解具备有效性和普适性,使得Gauss伪谱法的迭代效率提高55%以上,同时也表明Gauss伪谱法可有效解决平动点周期轨道间的小推力转移轨道优化设计问题。