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.

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 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.

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.

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.

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.

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.

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.

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.

Structural Analysis About a New Solar Sail

The article presents a structural analysis of a new space probe-solar sail.It was deployed successfully on ground.The loads for an outer space mission was introduced and expressed with equation.As a special state,the largest load around earth was used to analyze the model by the finite element method.Some results about strain and stress was obtained after setting some initial parameters.Compared to the results in the literature,the results presented here are significant.

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 m2/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 ChipSail’s acceleration arising from the sail’s morphing was also analytically modeled.Fabrication and characterization of the sail prototype made of multiple Al/Ni50Ti50 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 90deformation 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.

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.

Design and application of solar sailing: A review on key technologies

Solar sail technology has been proposed and developed for space explorations with advantages of low launch cost,no-propellant consumption,and continuous thrust,which has great potentials in earth polar detection,interstellar explorations and etc.The development of solar sail has made significant progress in structural design,manufacturing,materials,orbit transfer,and stability control in the past few decades,which makes meaningful contributions to astronomy,physics,and aerospace science.Technological breakthroughs of Solar Radiation Pressure(SRP)propulsion and interstellar transfer have been achieved in current solar sail missions.However,there are still many challenges and problems need to be solved.This paper attempts to summarize the research schemes and potential applications of solar sailing in space missions from the viewpoint of key technologies,so as to provide an overall perspective for researchers in this field.Analyses of the key technologies of solar sailing system design are provided.Finally,challenges and prospective development of solar sailing are discussed.

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.

Structural dynamic responses of a stripped solar sail subjected to solar radiation pressure

The stripped solar sail whose membrane is divided into separate narrow membrane strips is believed to have the best structural efficiency.In this paper,the stripped solar sail structure is regarded as an assembly made by connecting a number of boom-strip components in sequence.Considering the coupling effects between booms and membrane strips,an exact and semianalytical method to calculate structural dynamic responses of the stripped solar sail subjected to solar radiation pressure is established.The case study of a 100 m stripped solar sail shows that the stripped architecture helps to reduce the static deflections and amplitudes of the steady-state dynamic response.Larger prestress of the membrane strips will decrease stiffness of the sail and increase amplitudes of the steady-state dynamic response.Increasing thickness of the boom will benefit to stability of the sail and reduce the resonant amplitudes.This proposed semi-analytical method provides an efficient analysis tool for structure design and attitude control of the stripped solar sail.

Review on solar sail technology

This paper reviews solar sail trajectory design and dynamics,attitude control,and structural dynamics.Within the area of orbital dynamics,methods relevant to transfer trajectory design and non-Keplerian orbit generation are discussed.Within the area of attitude control,di erent control strategies,including utilisation of solar radiation pressure and conventional actuators,are discussed.Finally,the methods of modelling structural dynamics during and after deployment are discussed,before considering possible future trends in developing of solar sailing missions.

Solar sailing trajectory optimization with planetary gravity assist

Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.

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.

Control of large angle maneuvers for the flexible solar sail

Solar sail is a new type of spacecraft for deep space exploration,which flies by the pressure of sunlight.The attitude of the sail determines its orbit,so altitude control plays an important role in the mission.However,the large flexible structure leads to some difficulty in attitude control.This paper establishes the reduced dynamic model of a flexible solar sail with foreshortening deformation,and coupling with its attitude and vibration.As usual,large angle maneuvering will lead to the vibration of flexible structure,so the time optimal control of solar sail maneuvering is considered.Bang-Bang control of the solar sail generates large amplitude and sustained vibration,while the combined control based on input shaping can eliminate the vibration efficiently.With the comparison of two reduced models,it is demonstrated that the choice of two models depends on the attention to the stretching deformation.