考虑J2项摄动的星座相对运动控制

利用轨道某些要素(偏心率，升交点赤经和倾角)的差别可以构成由一颗中心星和几个环绕星组成的近距离星座。在理想中心引力场下，环绕星运行轨迹在水平面投影可以呈现封闭圆形。在地球引力摄动时，这种空间形状将逐渐发散。为此，本文考虑J2项摄动的影响，设计了对其具有鲁棒性的环绕星相对轨道；进而导出了带有J2项摄动的环绕星相对运动方程，并给出了基于惯性笛卡尔坐标系运动学变量的相对轨道控制方法。分析和仿真结果表明，这种控制方法能够实现星座相对运动的高精度控制。     

Research on constellation refueling based on formation flying

A new scheme for refueling satellite constellation is proposed in this paper. Compared with the traditional research, where the satellite refueling is implemented through spacecraft rendezvous and docking, the new pattern studied here is based on formation flying, and it is more feasible, safer and more reliable. On the grounds of the proposed pattern, two refueling strategies are studied. The first is called single supplier refueling (SSR) based on formation flying. In this scenario, one fuel-sufficient satellite called a supplier, departs from its parking orbit, and after a series of orbit maneuvers, arrives at the target constellation that consists of multiple fuel-deficient satellites called workers. It then transfers equal fuel to each worker within the prescribed mission time. The second strategy is called double suppliers refueling (DSR) based on formation flying. This time two suppliers take charge of refueling half of the workers respectively in the same way as SSR. Using a genetic algorithm, the orbit of a supplier with a minimum consumption of fuel can be obtained once the mission time is fixed. Simulation results indicate that DSR is superior to SSR and that this dominance will be more distinct as the number of workers increases and the mission time decreases.     

Attitude stabilization of a satellite by magnetic coils

Stabilization problem for a satellite is considered. The only measurement is of the geomagnetic field in the satellite coordinates. The control is carried out by a magnetic moment of current coils (magnetorquers) mounted on the satellite body. The stabilizer constructed in this work solves the problems of magnetic and gravitational stabilization. Qualitative analysis and results of numerical simulation are presented. The results of simulation show that the proposed stabilization system is reliable, and has an appropriate accuracy and does not need powerful sources of energy, and therefore can be used for attitude control of small satellites.     

近地卫星磁测自主导航算法研究

地磁场具有较为完善的数学模型，而地磁场矢量是卫星位置的函数，利用三轴磁强计的测量信息即可实现近地卫星的自主导航。本文提出了采用UKF(Unscented Kalman Filter)滤波作为处理磁测自主导航问题的滤波算法。基于unscented变换，UKF滤波算法能够给出更精确的均值和协方差的估计，从而带来更高的精度。本文以地磁场矢量为测量量，进行了数学仿真。仿真结果表明：经UKF滤波后，卫星总的位置误差在1km(3σ)以内。通过比较可知，该方法比传统的扩展Kalman滤波(EKF)有更好的收敛性和更高的精度。     

用于对地观测定位的编队飞行卫星群轨道构形设计

编队飞行卫星群是一组小卫星,它们具有短的相对距离、相等的轨道半长轴和微小差别的其它轨道要素,它们形成相互伴随运动,并且具有一定的构形。提出将编队飞行卫星群的轨道设计技术应用于对地观测定位卫星系统中。根据设想的要求,针对由四颗伴随卫星围绕基准卫星(或一个虚拟的中心)飞行的轨道设计案例,初步分析了编队飞行卫星群的构形保持,地球引力和大气阻力的摄动影响等问题。     

Spin-stabilized satellite magnetic attitude control scheme without initial detumbling

The angular motion of an axisymmetrical satellite equipped with an active magnetic attitude control system is considered. The dynamics of the satellite are analytically studied on the whole control loop. The control loop is as follows: preliminary reorientation along with nutation damping, spinning about the axis of symmetry, then precise reorientation of the axis of symmetry in inertial space. Reorientation starts right after separation from the launch vehicle. Active magnetic attitude control system time-response with respect to its parameters is analyzed. It is proven that low-inclined orbit forces low control system time-response. Comparison with the common control scheme shows the time-response gain. Numerical analysis of the disturbances effect is carried out and good pointing accuracy is proved.     

A simplified technique for determining the rotational motion of a satellite based on the onboard measurements of the angular velocity and magnetic field of the Earth

The mathematical model, which allowed us to reconstruct the rotational motion of the Bion M-1 and Foton M-4 satellites by processing the measurements of onboard magnetometers and the angular velocity sensor, is sufficiently detailed and accurate. If we slightly lower the requirements for accuracy and transfer to a rougher model, i.e., we will not update the biases in measurements of the angular velocity component, then the measurement processing technique can be significantly simplified. The volume of calculations in minimizing the functional of the least-square technique is reduced; the most complicated part of calculations is performed using the standard procedure of computational linear algebra. This simplified technique is described below, and the examples of its application for reconstructing the rotational motion of the Foton M-4 satellite are presented. A noticeable distinction in the reconstructions of motion, constructed by simplified and more exact techniques, is revealed in processing the measurements over time intervals longer than 4 hours.     

Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

Autonomous guidance and control of Earth-orbiting formation flying spacecraft: Closing the loop

Previous work on autonomous formation flying guidance and control identified three key challenges to overcome in order to obtain a fully autonomous guidance and control loop: an accurate but simple model of relative motion about elliptical and perturbed orbits, an efficient way of performing conflicting requirements trade-off with power-limited on-board computers, and finally an optimal or near-optimal control algorithm easy to implement on a flight computer. This paper first summarizes recent developments on each of these subject that help to overcome these challenges, developments which are then used as building blocks for an autonomous formation flying guidance and control system. This system autonomously performs trade-offs between conflicting requirements, i.e. minimization of fuel cost, formation accuracy and equal repartition of the fuel expenditure within the formation. Simulation results show that a complete guidance and control loop can be established using mainly analytical results and with very few numerical optimization which facilitates on-board implementation.     

A mechanism for generating magnetic field by vortex processes in stellar plasma

The difference in viscous properties of proton and electron gases in fully ionized hydrogen plasma is shown to result in a possibility of generation in this plasma of the magnetic field, even if initially there was no field. As an example, a simplified planar stationary model of a magnetohydrodynamic process of the eddy sink type is considered. It is demonstrated that the intensity of the generated magnetic field strongly depends on plasma temperature, so that the range T = 100000–500000 K corresponds to the range of maximum magnetic induction B = 50–2700 G. Such values are frequently observed in ordinary stars, in particular, in solar flares.     

Influence of sensor and actuator errors on impulsive satellite formation control methods

This paper investigates how sensor and actuator errors are impacting formation control accuracy and propellant consumption of a two-satellite formation in a low Earth orbit. Realistic relative navigation errors are implemented, based on the results from the PRISMA mission, as well as realistic actuator uncertainty and actuator constraints. Two impulsive control methods are investigated. The first method is based on a controller that is implemented onboard PRISMA and the second method uses linear programming to arrive at a model predictive controller. The control methods are tested in a simulation environment and are subjected to orbital perturbations and realistic sensor errors and actuator errors. Both control methods are able to maintain the desired relative geometry of a projected circular orbit in the presence of the errors. The PRISMA control method demonstrates lower propellant consumption, while the model predictive controller shows better control accuracy. The results show that, based on the used scenario, sensor errors dominate both the formation control accuracy and propellant consumption. The versatility of the model predictive controller is demonstrated in a challenging formation control scenario including formation maintenance and formation reconfiguration tasks.     

Planar oscillations of a vibrating dumbbell-like body in a central field of forces

The problem of planar motions of a dumbbell-like body of variable length in a central field of Newtonian attraction is considered both in the exact formulation and in satellite approximation. In the satellite approximation the true anomaly of the center of mass is used as an independent variable, which has allowed us to represent the equation of planar oscillations of the dumbbell in the form similar to the Beletskii equation. Some exact solutions to the inverse problem are given both in the complete formulation and in satellite approximation. Under an assumption of small orbit eccentricity and amplitude of the dumbbell vibrations the conditions of existence are found for families of almost periodic motions and splitting separatrices. The phenomena of alternation of regular and chaotic motions are established numerically, as well as chaos suppression with increasing frequency of vibrations. Using the method of averaging the stabilization of tangent equilibria is proved to be impossible.     

Motion of three viscoelastic planets in the field of their mutual attraction forces

Translational-rotational motion of three planets modeled by viscoelastic balls in the gravitational field of mutual attraction is studied in this paper. The system of equations of motion for the mechanical system under consideration is deduced from the d’Alembert-Lagrange variational principle. Using the method of separation of motions, an approximate system of ordinary differential equations, describing the translational-rotational motion of the planets, is obtained with taking into account perturbations caused by elasticity and dissipation. The found steady-state motion of the system is an analog to triangular libration points in the classical three-body problem.     

Numerical simulation on antenna temperature field of complex structure satellite in solar simulator

A thermal network model is developed for studying the temperature variation of complicated structure satellite surfaces. The solar incident areas, the infrared and solar radiation transfer coefficients among surfaces are numerically simulated by means of Monte Carlo ray tracing (MCRT) method in model. The non-uniformity and the instability of solar radiation, which plays the important roles in simulating outer-space heat flux designation parameters by solar simulator, are studied for analysis variation of antenna temperature fields in detail. Results showed non-uniformity irradiation effects are greater than those of instability for this kind of geometry sheltering structure.     

Neutral surfaces of coronal magnetic field and solar filaments

The shape of solar filaments is compared with the projection of parts of the neutral surface of the coronal magnetic field within a certain range of heights at different aspects of observation due to the rotation of the Sun. Neutral surfaces are calculated in the potential approximation from the photospheric data. The comparison shows that the material of filaments is concentrated mainly near the neutral surface of the potential field. The traces of the neutral surface section by the horizontal plane serve as polarity inversion lines (PILs) of the vertical field at the given height. In projection onto the disk, a lower edge of the filament with the intermediate barbs protruding on each side is delineated by the PIL at the low height, while an upper edge touches the high-height PIL. All material of the filament is enclosed in the space between these two lines. Although in reality the magnetic field structure near filaments differs very strongly from the potential field structure, their neutral surfaces can be similar and close, especially at low heights. This fact is probably the cause of the observed correlation. It can be used to determine the height of the upper edge of filaments above the photosphere in the case of observations only on the disk.     

Study of a bunch of three algorithms for magnetic control of attitude and spin rate of a spin-stabilized satellite

We consider the angular motion of an axi-symmetrical satellite equipped with an active magnetic attitude control system. Dynamics of the satellite is studied on the entire control loop, consisting of a bunch of three successively used algorithms. The control cycle includes the stages of nutation damping, spinning up the satellite about its symmetry axis, and reorienting the symmetry axis into a preset direction in the inertial space. The results are confirmed by numerical simulations.     

Estimating the accuracy of the technique of reconstructing the rotational motion of a satellite based on the measurements of its angular velocity and the magnetic field of the Earth

The paper has studied the accuracy of the technique that allows the rotational motion of the Earth artificial satellites (AES) to be reconstructed based on the data of onboard measurements of angular velocity vectors and the strength of the Earth magnetic field (EMF). The technique is based on kinematic equations of the rotational motion of a rigid body. Both types of measurement data collected over some time interval have been processed jointly. The angular velocity measurements have been approximated using convenient formulas, which are substituted into the kinematic differential equations for the quaternion that specifies the transition from the body-fixed coordinate system of a satellite to the inertial coordinate system. Thus obtained equations represent a kinematic model of the rotational motion of a satellite. The solution of these equations, which approximate real motion, has been found by the least-square method from the condition of best fitting between the data of measurements of the EMF strength vector and its calculated values. The accuracy of the technique has been estimated by processing the data obtained from the board of the service module of the International Space Station (ISS). The reconstruction of station motion using the aforementioned technique has been compared with the telemetry data on the actual motion of the station. The technique has allowed us to reconstruct the station motion in the orbital orientation mode with a maximum error less than 0.6° and the turns with a maximal error of less than 1.2°.     

Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).