Time-optimal rendezvous transfer trajectory for restricted cone-angle range solar sails

The advantage of solar sails in deep space exploration is that no fuel consumption is required. The heliocentric distance is one factor influencing the solar radiation pressure force exerted on solar sails. In addition, the solar radiation pressure force is also related to the solar sail orientation with respect to the sunlight direction. For an ideal flat solar sail, the cone angle between the sail normal and the sunlight direction determines the magnitude and direction of solar radiation pressure force. In general, the cone angle can change from 0° to 90°. However, in practical applications, a large cone angle may reduce the efficiency of solar radiation pressure force and there is a strict requirement on the attitude control. Usually, the cone angle range is restricted less more than an acute angle （for example, not more than 40°） in engineering practice. In this paper, the time-optimal transfer trajectory is designed over a restricted range of the cone angle, and an indirect method is used to solve the two point boundary value problem associated to the optimal control problem. Relevant numerical examples are provided to compare with the case of an unrestricted case, and the effects of different maximum restricted cone angles are discussed. The results indicate that （1） for the condition of a restricted cone-angle range the transfer time is longer than that for the unrestricted case and （2） the optimal transfer time increases as the maximum restricted cone angle decreases.

Trajectory optimization and applications using high performance solar sails

The high performance solar sail can enable fast missions to the outer solar system and produce exotic non-Keplerian orbits.As there is no fuel consumption,mission trajectories for solar sail spacecraft are typically optimized with respect to flight time.Several investigations focused on interstellar probe missions have been made,including optimal methods and new objective functions. Two modes of interstellar mission trajectories,namely 'direct flyby' and 'angular momentum reversal trajectory',are compared and discussed.As a foundation,a 3D non-dimensional dynamic model for an ideal plane solar sail is introduced as well as an optimal control framework.A newly found periodic double angular momentum reversal trajectory is presented,and some properties and potential applications of this kind of inverse orbits are illustrated.The method how to achieve the minimum periodic inverse orbit is also briefly elucidated.

Displaced orbits generated by solar sails for the hyperbolic and degenerated cases

Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill＇s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail＇s attitude and lightness number is obtained, which verifies that the controller is realizable.

Quasi-periodic orbits of small solar sails with time-varying attitude around Earth–Moon libration points

This paper proposes new quasi-periodic orbits around Earth–Moon collinear libration points using solar sails.By including the time-varying sail orientation in the linearized equations of motion for the circular restricted three-body problem(CR3BP),four types of quasi-periodic orbits(two types around L1 and two types around L2)were formulated.Among them,one type of orbit around L2 realizes a considerably small geometry variation while ensuring visibility from the Earth if(and only if)the sail acceleration due to solar radiation pressure is approximately of a certain magnitude,which is much smaller than that assumed in several previous studies.This means that only small solar sails can remain in the vicinity of L2 for a long time without propellant consumption.The orbits designed in the linearized CR3BP can be translated into nonlinear CR3BP and high-fidelity ephemeris models without losing geometrical characteristics.In this study,new quasi-periodic orbits are formulated,and their characteristics are discussed.Furthermore,their extendibility to higher-fidelity dynamic models was verified using numerical examples.

Dynamic analysis of spinning solar sails at deployment process

The spinning deployment process of solar sails is analyzed in this study. A simplified model is established by considering the out-of-plane and in-plane motions of solar sails. The influences of structure parameters, initial conditions, and feedback control parameters are also analyzed.A method to build the geometric model of a solar sail is presented by analyzing the folding process of solar sails. The finite element model of solar sails is then established, which contains continuous cables and sail membranes. The dynamics of the second-stage deployment of solar sails are simulated by using ABAQUS software. The influences of the rotational speed and out-of-plane movement of the hub are analyzed by different tip masses, initial velocities, and control parameters.Compared with the results from theoretical models, simulation results show good agreements.

Angular velocity determination of spinning solar sails using only a sun sensor

The direction of the sun is the easiest and most reliable observation vector for a solar sail running in deep space exploration. This paper presents a new method using only raw measurements of the sun direction vector to estimate angular velocity for a spinning solar sail. In cases with a constant spin angular velocity, the estimation equation is formed based on the kinematic model for the apparent motion of the sun direction vector; the least-squares solution is then easily calculated. A performance criterion is defined and used to analyze estimation accuracy. In cases with a variable spin angular velocity, the estimation equation is developed based on the kinematic model for the apparent motion of the sun direction vector and the attitude dynamics equation. Simulation results show that the proposed method can quickly yield high-precision angular velocity estimates that are insensitive to certain measurement noises and modeling errors.

Feasibility analysis of the angular momentum reversal trajectory via hodograph method for high performance solar sails

In this paper a new phase space of hodograph method is adopted to investigate and better understand the two-dimensional angular momentum reversal(H-reversal) trajectories for high performance solar sails within a fixed cone angle.As the hodograph method and the H-reversal trajectory are not very common,both of them are briefly introduced.The relationship between them are constructed and addressed with a sample trajectory.How the phase space varies according to the sail quality and the fixed sail cone angle is also studied.Through variation of the phase space,the minimum sail lightness number can be obtained by solving a set of algebraic equations instead of a parameter optimization problem.For a given sail lightness number,there are three types of the two-dimensional possible heliocentric motion,including the spiral inward trajectories towards the Sun,the H-reversal trajectories and the directly outward escape trajectories.The boundaries that separate these different groups are easily determined by using the phase space.Finally,the method and procedures to achieve the feasible region of the H-reversal trajectory with required perihelion distance are presented in detail.

Shape memory composite structures for self-deployable solar sails

Shape memory composites(SMCs)combine mechanical performances of composite materials with functional behavior of shape memory polymers.They can be used to produce the external frame of self-deployable solar sails with very low weight in comparison with traditional composite booms.Furthermore,heat activation is necessary for deploying instead of complex mechanical devices.In this study,the mechanical behavior of a solar sail with SMC frame is simulated by means of finite element modeling.Design considerations are made on sail deployment configuration,size/weight ratio of solar sails,and SMC properties.An experimental activity has been also performed to provide suitable candidates for the composite laminates of the SMC structure.Mechanical and instrumented recovery tests have been carried out on 2-plies carbon-fiber laminates with a shape memory interlayer.

Self-excited oscillation of spinning solar sails utilizing solar radiation pressure

The present paper proposes a control method to excite spinning solar sail membranes for three-dimensional use.Using optical property switching,the input is given as the change in magnitude of the solar radiation pressure.The resonance point of this system varies with the vibration state due to its nonlinearity and the change in equilibrium state.To deal with this,a state feedback control law that automatically tracks the resonance point is developed in the present study.The proposed method enables decentralized control of the actuators on the sail,each of which determines the control input independently using only the information of vibration state.The proposed method is validated using numerical simulations.The results show that the nonlinear system behaves differently from the linear system,and the vibration grows using the decentralized control regardless of resonance point variation.

Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method

The spinning solar sail of large scale has been well developed in recent years. Such a solar sail can be considered as a rigid-flexible multibody system mainly composed of a spinning central rigid hub, a number of flexible thin tethers, sail membranes, and tip masses. A simplified interplanetary kite-craft accelerated by radiation of the Sun （IKAROS） model is established in this study by using the absolute-coordinate-based （ACB） method that combines the natural coordinate formulation （NCF） describing the central rigid hub and the absolute nodal coordinate formulation （ANCF） describing flexible parts. The initial configuration of the system in the second-stage deployment is determined through both dynamic and static analyses. The huge set of stiff equations of system dynamics is solved by using the generalized-alpha method, and thus the deployment dynamics of the system can be well understood.

Solar radiation pressure used for formation flying control around the Sun-Earth libration point

Solar radiation pressure is used to control the formation flying around the L2 libration point in the Sun-Earth system. Formation flying control around a halo orbit requires a very small thrust that cannot be satisfied by the latest thrusters. The key contribution of this paper is that the continuous low thrust is produced by solar radiation pressure to achieve the tight formation flying around the libration point. However, only certain families of formation types can be controlled by solar radiation pressure since the direction of solar radiation pressure is restricted to a certain range. Two types of feasible formations using solar radiation pressure control are designed. The conditions of feasible formations are given analytically. Simulations are presented for each case, and the results show that the formations are well controlled by solar radiation pressure.

Utilization of an H-reversal trajectory of a solar sail for asteroid deflection

Near Earth Asteroids have a possibility of impacting the Earth and always represent a threat. This paper proposes a way of changing the orbit of the asteroid to avoid an impact. A solar sail evolving in an H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of the solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact the target asteroid along an H-reversal trajectory. The impact velocity depends on two important parameters： the minimum solar distance along the trajectory and lightness number of the solar sail. A larger lightness number and a smaller solar distance lead to a higher impact velocity. Finally, the deflection capability of a solar sail impacting the asteroid along the H-reversal trajectory is discussed. The results show that a 10kg solar sail with a lead-time of one year can move Apophis out of a 600-m keyhole area in 2029 to eliminate the possibility of its resonant return in 2036.

Solar sail time-optimal interplanetary transfer trajectory design

The fuel consumption associated with some interplanetary transfer trajectories using chemical propulsion is not affordable. A solar sail is a method of propulsion that does not consume fuel. Transfer time is one of the most pressing problems of solar sail transfer trajectory design. This paper investigates the time-optimal interplanetary transfer trajectories to a circular orbit of given inclination and radius. The optimal control law is derived from the principle of maximization. An indirect method is used to solve the optimal control problem by selecting values for the initial adjoint vari- ables, which are normalized within a unit sphere. The conditions for the existence of the time-optimal transfer are dependent on the lightness number of the sail and the inclination and radius of the target orbit. A numerical method is used to obtain the boundary values for the time-optimal transfer trajectories. For the cases where no time-optimal transfer trajectories exist, first-order necessary conditions of the optimal control are proposed to obtain feasible solutions. The results show that the transfer time decreases as the minimum distance from the Sun decreases during the transfer duration. For a solar sail with a small lightness number, the transfer time may be evaluated analytically for a three-phase transfer trajectory. The analytical results are compared with previous results and the associated numerical results. The transfer time of the numerical result here is smaller than the transfer time from previous results and is larger than the analytical result.

An integrated simulation system for operating solar sail spacecraft

An integrated simulation system for solar sail spacecraft with individually controllable elements(SSICE)is investigated in this paper,including the modelling of power management,thermal control,attitude control,umbra prediction,and orbit prediction subsystems.Considering the self-control and reactivity subsystems,an agent based method is applied to develop the subsystem models.Each subsystem is an individual agent component,which manages itself autonomously and reacts to the requirements from other agents.To reduce computing burden on a specified computer and improve the suitability and flexibility of the integrated simulation system,a distributed framework is employed in the system by deploying agent components on different computers.The data transmission among agents is based on the transmission control protocol/Internet protocol(TCP/IP).A practical example of sun pointing is used to test the operating effect of the integrated system and the working condition of subsystems.The simulation results verify that the integrated system has higher sun pointing accuracy,quicker dynamical response to variations of the lighting,attitude and temperature and fewer computing resources with effective and accurate subsystems.The integrated system proposed in this paper can be applied to solar sail design,operation,and mission planning.

Dynamic Analysis and Parametric Optimization of Telescopic Tubular Mast Applied on Solar Sail

Large-scale solar sails can provide power to spacecraft for deep space exploration.A new type of telescopic tubular mast(TTM)driven by a bistable carbon fiber-reinforced polymer tube was designed in this study to solve the problem of contact between the sail membrane and the spacecraft under light pressure.Compared with the traditional TTM,it has a small size,light weight,high extension ratio,and simple structure.The anti-blossoming and self-unlocking structure of the proposed TTM was described.We aimed to simplify the TTM with a complex structure into a beam model with equal linear mass density,and the simulation results showed good consistency.The dynamic equation was derived based on the equivalent model,and the effects of different factors on the vibration characteristics of the TTM were analyzed.The performance parameters were optimized based on a multiobjective genetic algorithm,and prototype production and load experiments were conducted.The results show that the advantages of the new TTM can complete the deployment of large-scale solar sails,which is valuable for future deep space exploration.

Design of Near-optimal Earth Escape Orbits for Solar Sail Spacecraft

With the increase of the interest in solar sailing, it is required to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. In this paper, a technique for escaping the Earth by using a solar sail is developed and numerically simulated. The spacecraft is initially in a geosynchronous transfer orbit (GTO). Blended solar sail analytical control law, explicitly independent of time, are then presented, which provide near-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller. This control law is investigated from a range of initial conditions and is shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the blending solar sail analytical control law is suitable for solar sail on-board autonomously control system.

Design,modeling and experimental investigation of a novel solar sail with high area-to-mass ratios for efficient solar sailing

Solar sailing is a promising propellant-free approach to propelling spacecraft in space.However, the propelling efficiency of conventional solar sail spacecraft is limited by their areato-mass ratios. This paper proposes a novel design of micro solar sails with area-to-mass ratios above 100 m^(2)/kg for next-generation chip-scale spacecraft. Bilayer thin films developed by Microelectromechanical Systems(MEMS) technologies were patterned into grid microstructures, and theoretical analysis of a sail prototype was conducted. The electro-thermal and thermo-mechanical models of the solar sail in geospace were established by taking effects of Joule heating, solar radiation, and thermal re-emission into consideration, enabling rapid prediction of its threedimensional(3-D) reconfiguration from the as-released two-dimensional(2-D) microstructure.Adjustment of the Chip Sail's acceleration arising from the sail's morphing was also analytically modeled. Fabrication and characterization of the sail prototype made of multiple Al/Ni_(50)Ti_(50) bilayer beams were accomplished. In-situ SEM imaging of the sail prototype in vacuum chamber witnessed an active and continuous 3-D reconfiguration under Joule heating, and over 90° deformation was detected by applying a DC voltage of 0.078 V. Theoretical and experimental work on the solar sail with at least 10 times higher area-to-mass ratios than conventional ones will lay a solid foundation for efficient solar sailing.

Coupled trajectory and attitude stability of displaced orbits

Coupled trajectory and attitude stability of displaced solar orbits is studied by using sailcraft with a kind of two-folding construction with two unequal rectangular plates forming a right angle. Three-dimensional coupled trajectory and attitude equations are developed for the coupled dynamical system, and the results show that all three types of displaced solar orbits widely referenced can be achieved through selecting an appropriate size of the two-folding sail. An anal- ysis of the corresponding linear stability of the trajectory and attitude coupled system is carried out, and both trajectory and attitude linearly stable orbits are found to exist in a small range of parameters, whose non-linear stability is then examined via numerical simulations. Finally, passively stable orbits are found to have weak stability, and such passive means of station-keeping are attractive and useful in practice because of its simplicity.

Formation around planetary displaced orbit

The paper investigates the relative motion around the planetary displaced orbit. Several kinds of displaced orbits for geocentric and martian cases were discussed. First, the relative motion was linearized around the displaced orbits. Then, two seminatural control laws were investigated for each kind of orbit and the stable regions were obtained for each case. One of the two control laws is the passive control law that is very attractive for engineering practice. However, the two control laws are not very suitable for the Martian mission. Another special semi-natural control law is designed based on the requirement of the Martian mission. The results show that large stable regions exist for the control law.

Optimization of body configuration and joint-driven attitude stabilization for transformable spacecraft under solar radiation pressure

The solar sail is one of the most promising space exploration systems due to its theoretically infinite specific impulse achieved through solar radiation pressure(SRP).Recently,researchers have proposed“transformable spacecraft”capable of actively reconfiguring their body configurations using actuatable joints.Transformable spacecraft,if used similarly to solar sails,are expected to significantly enhance orbit and attitude control capabilities owing to their high redundancy in control degrees of freedom.However,controlling them becomes challenging due to their large number of inputs,leading previous researchers to impose strong constraints to limit their potential control capabilities.This study focuses on novel attitude control techniques for transformable spacecraft under SRP.We developed two methods,namely,joint angle optimization to obtain arbitrary SRP force and torque,and momentum damping control driven by joint angle actuation.Our proposed methods are formulated in a general manner and can be applied to any transformable spacecraft comprising front faces that can predominantly receive the SRP on each body.The validity of our proposed method is confirmed through numerical simulations.Our study contributes to making most of the high control redundancy of transformable spacecraft without the need for expendable propellants,thus significantly enhancing the orbit and attitude control capabilities.