Estimate of accuracy of determining the orientation of the star sensor system according to the experimental data

The BOKZ-M60 star sensor (Unit for Measuring Star Coordinates) is intended for determining the parameters of the orientation of the axes of the intrinsic coordinate system relative to the axes of the inertial system by observations of the regions of the stellar sky. It is convenient to characterize an error of the single determination of the orientation of the intrinsic coordinate system of the sensor by the vector of an infinitesimal turn of this system relative to its found position. Full-scale ground-based tests have shown that, for a resting sensor the root-mean-square values of the components of this vector along the axes of the intrinsic coordinate system lying in the plane of the sensor CCD matrix are less than 2″ and the component along the axis perpendicular to the matrix plane is characterized by the root-mean-square value of 15″. The joint processing of one-stage readings of several sensors installed on the same platform allows us to improve the indicated accuracy characteristics. In this paper, estimates of the accuracy of systems from BOKZ-M60 with two and four sensors performed from measurements carried out during the normal operation of these sensors on the Resurs-P satellite are given. Processing the measurements of the sensor system allowed us to increase the accuracy of determining the each of their orientations and to study random and systematic errors in these measurements.     

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°.     

Gravity-oriented satellite dynamics subject to gravitational and active damping torques

The dynamics of the rotational motion of a satellite moving in the central Newtonian field of force over a circular orbit under the effect of gravitational and active damping torques, which depend on the satellite angular velocity projections, has been investigated. The paper proposes a method of determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of damping coefficients and principal central moments of inertia. The conditions of their existence have been obtained. For a zero equilibrium position where the axes of the satellite-centered coordinate system coincide with the axes of the orbital coordinate system, the necessary and sufficient conditions for asymptotic stability are obtained using the Routh–Hurwitz criterion. A detailed analysis of the regions where the conditions of the asymptotic stability of a zero equilibrium position are fulfilled have been obtained depending on three dimensionless parameters of the problem, and the numerical study of the process of attenuation of satellite’s spatial oscillations for various damping coefficients has been carried out. It has been shown that there is a wide range of damping parameters from which, by choosing the necessary values, one can provide the asymptotic stability of satellite’s zero equilibrium position in the orbital coordinate system.     

Modes of uncontrolled rotational motion of the <Emphasis Type="Italic">Progress M-29M</Emphasis> spacecraft

We have reconstructed the uncontrolled rotational motion of the Progress M-29M transport cargo spacecraft in the single-axis solar orientation mode (the so-called sunward spin) and in the mode of the gravitational orientation of a rotating satellite. The modes were implemented on April 3–7, 2016 as a part of preparation for experiments with the DAKON convection sensor onboard the Progress spacecraft. The reconstruction was performed by integral statistical techniques using the measurements of the spacecraft’s angular velocity and electric current from its solar arrays. The measurement data obtained in a certain time interval have been jointly processed using the least-squares method by integrating the equations of the spacecraft’s motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the mathematical model have been estimated. The motion in the sunward spin mode is the rotation of the spacecraft with an angular velocity of 2.2 deg/s about the normal to the plane of solar arrays; the normal is oriented toward the Sun or forms a small angle with this direction. The duration of the mode is several orbit passes. The reconstruction has been performed over time intervals of up to 1 h. As a result, the actual rotational motion of the spacecraft relative to the Earth–Sun direction was obtained. In the gravitational orientation mode, the spacecraft was rotated about its longitudinal axis with an angular velocity of 0.1–0.2 deg/s; the longitudinal axis executed small oscillated relative to the local vertical. The reconstruction of motion relative to the orbital coordinate system was performed in time intervals of up to 7 h using only the angularvelocity measurements. The measurements of the electric current from solar arrays were used for verification.     

Development of a high-precision selenodetic coordinate system for the physical surface of the Moon based on LED beacons on its surface

The paper presents a mathematical algorithm for processing an array of angular measurements of light beacons on images of the lunar surface onboard a polar artificial lunar satellite (PALS) during the Luna–Glob mission and coordinate–time referencing of the PALS for the development of reference selenocentric coordinate systems. The algorithm makes it possible to obtain angular positions of point light beacons located on the surface of the Moon in selenocentric celestial coordinates. The operation of measurement systems that determine the position and orientation of the PALS during its active existence have been numerically simulated. Recommendations have been made for the optimal use of different types of measurements, including ground radio trajectory measurements, navigational star sensors based on the onboard star catalog, gyroscopic orientation systems, and space videos of the lunar surface.     

Measurement of the Quasistatic Component of Microaccelerations Using a Convection Sensor onboard a Satellite

The problem of the interpretation of measurements made by means of a convection sensor is considered. The sensor is a cubic chamber filled by a viscous fluid (gas). Fixed and unequal temperatures are maintained on two opposite sides of the cube; the other sides are perfect heat conductors. Two differential thermocouples are placed inside the chamber to measure the temperature difference at two pairs of fixed points. The sensor is mounted aboard the Earth's satellite. Mathematical models of various degrees of complexity are proposed which describe processes of heat and mass transfer under the action of a quasistatic component of microaccelerations. The results of mathematical simulation of the data of sensor thermocouples presenting a response to the real quasistatic component of microaccelerations which took place aboard the Mirstation are given. It is shown that under usual conditions of an orbital mission the sensor presents a linear low-frequency filter. By combining the data of several identical sensors, tightly arranged and oriented in a certain way, it is possible to measure low-frequency components of the angular acceleration of the satellite and linear microaccelerations at the point of the sensor position.     

星上遥测的精度分析

分析了三轴稳定平台卫星产生遥测测量误差的原因,并对典型星载传感器(热敏电阻、压力变换器、电压)、模拟量通道、A/D变换器等单个误差项目逐一进行了误差分析。根据误差正态分布的特性,得出单个项目的最大测量误差及均方误差,然后合成单个项目的误差,给出整星各种类型被测参数的总误差。最后,根据目前卫星平台的设计现状,提出了进一步提高测量精度的建议。     

一种空间推扫型光学成像系统几何映射方法

卫星光学遥感器在轨成像会受到颤振的影响,因此图像品质受姿态稳定度的影响很大,而高分辨率图像受到平台误差的影响更加明显。通过研究空间相机的几何模型,提出了一种从地球坐标系到空间光学遥感器坐标系之间的转换关系;分析了在轨卫星的姿态误差和运动源,并在几何模型中加入了内外方位元素特征;然后进行了空间TDICCD相机的成像仿真实验。为了在像面上模拟颤振,分别进行不同模态的颤振仿真,并且对视线范围内多模态综合作用进行仿真。仿真实验是基于三个轴系方向的,并且计算了TDICCD仿真图像的几何畸变量,模型中几何畸变量的测量尺度达到亚像素级,结果有利于指导卫星平台和遥感器的参数设计。     

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.     

太阳同步轨道卫星热控分系统分析及优化

定义地心日照轨道坐标系,并在此坐标系下简化卫星与地球相对位置的复杂计算,以及卫星轨道外热流分析过程中相关角度的计算,使轨道外热流的分析仿真更加快速、简洁。以正六棱柱形卫星为例,建立热网络模型,对其表面在一圈轨道内所受的轨道外热流进行仿真,并结合仿真结果计算进出地影区时卫星内部的温度。在此基础上,建立以热控分系统多层隔热材料质量最小化为目标的优化问题;在满足高低温工况卫星内部温度在-10～＋35℃范围内的约束下,对多层隔热材料厚度和散热窗大小进行了优化。     

Nanosatellite <Emphasis Type="Italic">REFLECTOR</Emphasis>: Choice of parameters of the attitude control system

We consider methodological and applied problems of choosing parameters and developing a passive gravity-gradient attitude control system for the REFLECTOR nanosatellite. The attitude control system consists of appropriately distributed satellite mass and additional masses forming the required tensor of inertia, as well as of a set of hysteresis rods manufactured from a magnetically soft material. The combination of these elements allows one, independent of the satellite’s initial angular motion, to maintain its three-axial orientation in the orbital coordinate system with preset performance in precision and fast response. The satellite’s dynamics is investigated using asymptotic and numerical methods. The problems of arrangement of the additional masses and hysteresis rods are discussed, as well as their interaction with magnetizable elements.     

中心刚体-柔性梁系统的旋转运动控制

中心刚体-柔性梁系统是一个典型的刚柔耦合动力学系统,对其动力学与控制的研究一直是国内外的研究热点问题之一。采用一次近似简化模型对中心刚体-柔性梁系统的旋转运动控制进行研究,其中控制律采用变结构控制方法进行设计。切换面的设计采用最优化方法而得出,控制律的设计采用指数趋近律方法。因为所设计的控制律是模态坐标的函数,而模态坐标不可能通过物理测量直接获得,因此给出一个从物理测量中提取模态坐标的滤波器方法。数值仿真结果显示,模态滤波器能够较好地提取出控制律所需的模态坐标;变结构控制能够使得系统达到所期望的运动状态,并可使柔性梁的残余振动得到抑制。     

Determination of the Attitude Motion of a Satellite Based on a Kinematical Model of Motion and Using Data of Measurements of Its Angular Velocity and the Earth’s Magnetic Field Strength

An integral statistical procedure of determination of the attitude motion of a satellite using the data of onboard measurements of angular velocity vectors and the strength of the Earth’s magnetic field (EMF) is suggested. The procedure uses only the equations of kinematics of a solid body and is applicable to determining both controlled and uncontrollable motions of a satellite at any external mechanical moments acting upon it. When applying this procedure, the data of measurements of both types, accumulated during a certain interval of time, are processed jointly. The data of measuring the angular velocity are smoothed by discrete Fourier series, and these series are substituted into kinematical Poisson equations for elements of the matrix of transition from a satellite-fixed coordinate system to the orbital coordinate system. The equations thus obtained represent a kinematical model of the satellite motion. The solution to these equations (which approximate the actual motion of a satellite) is found from the condition of the best (in the sense of the least squares method) fit of the data of measuring the EMF strength vector to its calculated values. The results of testing the suggested procedure using the data of measurements of the angular velocity vectors onboard the Foton-12 satellite and measurements of EMF strengths are presented.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 295–305.Original Russian Text Copyright © 2005 by Abrashkin, Volkov, Voronov, Egorov, Kazakova, Pankratov, Sazonov, Semkin.     

Modeling of the aerodynamic moment acting upon a satellite

We consider the issues of modeling the moments of aerodynamic forces acting upon a satellite with gravitational system of stabilization. It is assumed that satellite orbits are almost circular with heights in the range 550–750 km. Simplified analytical expressions are suggested for the aerodynamic moment in the case when a satellite moves in the regime of gravitational orientation. Accuracy of the obtained expressions is estimated to be compared with that of expressions derived under the assumption of constant coefficient of frontal resistance. An analysis is made of short-periodic variations of the atmosphere density occurring due to orbital motion of a satellite. It is demonstrated that these variations can result in a substantial change of the aerodynamic moment, and their approximation by a truncated Fourier series is suggested. Estimates of the accuracy of the suggested approximation are given.     

遥感小卫星简介——以"北京一号"小卫星为例

高性能对地观测小卫星DMC 4--“北京一号”2005年10月27日在俄罗斯普列谢茨克发射场由宇宙3M火箭成功发射。文章针对小卫星的结构特点和数据特点,指出DMC小卫星图像数据具有获取灵活、重返周期短和大区域覆盖等优势,在地质灾害的调查、监测和预警工作中具有巨大的应用潜力。     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

Theory of physical libration of the Moon with the liquid core: Forced librations

For a two-layer model of the Moon that consists of a solid nonspherical mantle and an ellipsoidal homogeneous liquid core, a theory of forced librations under the effect of gravitational Earth’s moments has been developed. The motion of the Moon over its orbit has been described by the high-accuracy theory of DE/LE-4 orbital motion. Tables have been constructed that present forced librations of the Moon caused by the second harmonic of its force function, in the neighborhood of its motion according to the generalized Cassini laws. Disturbances of the first-order with respect to dynamic compressions of the Moon and its core are obtained in analytical form for Andoyer variables and Poincare variables and for the projection of the angular velocity vector of Moon’s mantle rotation and the Poincare coordinate system (relative to which core’s liquid accomplishes simple motion) on its major central axes of inertia, as well as for the classical variables in the Moon libration theory, etc. Constructed tables of the forced librations theory give the amplitudes and periods of librations and combinations of arguments of the orbital motion theory that correspond to libration parameters. The interpretation of basic variations has been given and a comparison with the previous theories has been carried out, in particular with the modern empirical theory constructed based on the laser observation data.     

Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.     

Orbit design for the Spektr-R spacecraft of the ground-space interferometer

In order to carry out tasks of the RadioAstron mission, a high-apogee orbit was designed. On average, the period of its satellite’s orbit around the Earth is 8.5 days with evolution due to gravitational perturbations produced by the Moon and the Sun. The perigee and apogee of this orbit vary within the limits 7500–70000 km and 270000–333000 km, respectively. The basic evolution of the orbit represents a rotation of its plane around the line of apsides. Over 3 years, the plane normal to the orbit draws on the celestial sphere an oval with a semi-major axis of about 150° and semi-minor axis of about 45°.     

轨道机动时考虑延迟的卫星姿态稳定控制方法

轨道机动时,测量与传输延迟,以及偏心推力对卫星姿态的持续扰动,造成传统的姿态稳定控制方法控制性能下降。为了克服这些问题,设计了对外扰与状态同时估计的闭环-开环预测器。在外扰力矩定常的假设下,给出了此种估计器对状态与外扰的预测都收敛的判定准则。利用估计出的外部扰动前馈补偿推力偏心干扰力矩,同时利用预测出的系统状态设计状态反馈控制器。通过求解两个代数Riccati方程,设计最优状态反馈增益和预测器增益。这种简单的前馈反馈结构具有良好的工程可实现性,同时仿真结果显示,该方法可以有效克服延迟和干扰的影响,提高卫星轨道机动时本体姿态稳定精度。