Rotational Motion Of Satellite Research Articles

Attenuation of Target Satellite's Rotational Motion by a Free-Flying Space Robot with Nonlinear Model Predictive Control

Attenuation of Target Satellite's Rotational Motion by a Free-Flying Space Robot with Nonlinear Model Predictive Control

Periodic Approximation of the Rotational Motion of the Photon-12 Satellite

The results of repeated processing of magnetic measurements carried out on the Photon-12 satellite (which was in orbit from September 9 to 24, 1999) are described. The processing was performed in order to reconstruct the uncontrolled rotational motion of this satellite. In re-processing, the simplified mathematical model of rotational motion was used. The actual orbit of a satellite (the apogee height is 380 km, the perigee height is 220 km) is replaced by a circular orbit; the expression for the aerodynamic moment acting on a satellite is simplified. The system of differential equations underlying the new model is autonomous and proved to be sufficiently accurate to reconstruct the satellite motion based on magnetic measurements in the case in which the satellite angular velocity was not very low and grew gradually. In the last third of the flight, when the satellite motion became virtually stable and had a sufficiently high angular velocity, this system could be reduced to a generalized-conservative system. Such a reduction makes more definite the set of its solutions suitable for approximate description of the actual motion of a satellite. In some segments of motion, the combining of which covers about 3 days, it was possible to use, for this purpose, the periodic solutions continued from the Lyapunov periodic solutions.

The Rotational Motion Simulation of AIST Small Spacecraft Prototype Based on Current Values From Solar Battery Panels and on a Hardware-software Stand

The functioning of space technique is associated with remote maintenance of operable state of onboard systems and software. If an element fails, problems arise in analyzing the state, ascertaining the reasons for the failure and restoring the element functional using available hardware-in-the-loop and algorithmic tools. The paper concentrates on currents analysis from solar battery panels of AIST small spacecraft in order to evaluate the parameters of the satellite's rotational motion after a significant break-down of the electrical battery. At the same time, the scientific equipment and onboard measurement instruments proved to be practically inoperative due to the lack of power supply. After the break-down of the electrical battery, magnetorquers and measurement instruments could not perform their function. A backup orientation system was not provided. The raw data for estimating the angular velocity vector was the current values from solar battery panels. However, in order to obtain an acceptable estimate of the angular velocity vector, more accurate current measurements are required than it implemented onboard the small spacecraft. To simulate the small spacecraft rotational motion and compare results with estimates obtained from telemetric data analysis, HIL US-03 hardware-software stand for simulation of the small spacecraft systems was used.

Satellite angular motion classification for active on-orbit debris removal using robots

PurposeThis paper aims to present a novel method for identification and classification of rotational motion for uncontrolled satellites. These processes are shown in context of close proximity orbital operations. In particular, it includes a manipulator arm mounted on chaser satellite and used to capture target satellites. In such situations, a precise extrapolation of the target’s docking port position is needed to determine the manipulator arm motion. The outcome of this analysis might be used in future debris removal or servicing space missions.Design/methodology/approachNonlinear, and in some special cases, chaotic nature of satellite rotational motion was considered. Four parameters were defined: range of motion toward docking port, dominant frequencies, fractal dimension of the motion and its time dependencies.FindingsThe qualitative analysis was performed for presented cases of spacecraft rotational motion and for each case the respective parameters were calculated. The analysis shows that it is possible to detect the type of rotational motion.Originality/valueA novel procedure allowing to estimate the type of satellite rotational motion based on fractal approach was proposed.

Эволюция вращательного движения спутника с гибкими вязкоупругими стержнями на эллиптической орбите

The rotational motion of an artificial satellite in the central Newtonian force field is investigated. The satellite is modeled as a symmetric solid with rigid viscoelastic rods rigidly attached along the symmetry axis and with a spherical inertia tensor. A limited statement of the problem is considered: the center of mass of the satellite moves along a given Keplerian elliptic orbit. As is known, some artificial Earth satellites (AES) have whip radio antennas for a length of hundreds of meters. The problem considered in this paper is a model for studying the rotational motion of this type of satellites. To solve this problem, the method of separation of motions and averaging is used for mechanical systems with an infinite number of degrees of freedom. We obtain an averaged system of differential equations in the Andoyer variables, which describes the evolution of the satellite's rotational motion. Partial solutions of the evolutionary system of the equations are found. For each such class of solutions phase portraits are built. It is shown that in the process of dissipative evolution caused by energy dissipation in rods, the angle between the vector of the angular momentum of the satellite's rotational motion and the normal to the orbital plane decreases to zero. Besides, new classes of stationary motions are found: the axis of symmetry of the satellite makes an arbitrary angle with the normal to the orbit plane, or the module of the angular velocity of the satellite rotation does not depend on the orbital angular velocity of the radius vector of its center of mass.

Rotational motion of Foton M-4

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.

Reconstruction of spacecraft rotational motion using a Kalman filter

Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.

Determining the rotational motion of the Bion M-1 satellite with the GRAVITON instrument

Actual controlled rotational motion of the Bion M-1 satellite is reconstructed for the modes of the orbital and single-axis solar orientation. The reconstruction was performed using data of onboard measurements of the vectors of angular velocity and the Earth’s magnetic field (EMF) strength. The reconstruction procedure is based on the kinematic equations of the rotational motion of a solid body. In the framework of this procedure, measurement data for two types collected at a certain time interval are processed jointly. Measurements of angular velocity are interpolated by piecewise–linear functions, which are substituted in the kinematic differential equations for quaternion giving the transition from the satellite instrument coordinate system to the inertial (the second geoequatorial) coordinate system. Thus the obtained equations represent the kinematic model of the satellite rotational motion. The solution to these equations approximating the actual motion is derived from the condition of the best (in the sense of the least-square method) matching measurement data of the EMF strength vector with the calculated values. The described procedure allows us to reconstruct the actual rotational satellite motion using one solution to kinematic equations over time intervals with durations of more than 5 h. Found reconstructions were used to calculate the residual microaccelerations.

Integrated SVD/EKF for Small Satellite Attitude Determination and Rate Gyro Bias Estimation

In this study an integrated singular value decomposition (SVD)/ Extended Kalman filter (EKF) attitude determination system is presented, in which the SVD and EKF algorithms are combined to estimate the attitude angles and angular velocities and gyro biases, respectively. As a reference directions for SVD, the unit vectors toward the Sun and Earth's Magnetic Field are used. The Euler angles produced SVD are provided as input to the EKF along with angular rate data. The parameters of satellite's rotational motion and rate gyro biases are estimated using EKF. In comparison to more traditional approaches, this preprocessing step significantly reduces the complexity of filter design by allowing the use of linear measurement equations.

The use of refined model of aerodynamic moment in the problem of reconstruction of the Foton satellite rotational motion

A new mathematical model of the uncontrolled rotational motion of the Foton satellite is presented. The model is based on the Euler dynamic equations of rigid body motion and takes into account the action upon the satellite of four external mechanical moments: gravitational, restoring aerodynamic, moment with constant components in the satellite-fixed coordinate system, and moment arising due to interaction of the Earth’s magnetic field with the satellite’s proper magnetic moment. To calculate the aerodynamic moment a special geometrical model of the outer satellite shell is used. Detailed form of the formulas giving above-mentioned moments in the equations of satellite motion is agreed with the form of the considered motion. Model testing is performed by determining with its help the rotational motion of the Foton M-2 satellite (it was in orbit from May 31, 2005 to June 16, 2005) using the data of the onboard measurements of the Earth’s magnetic field strength. The use of the new model has led to a relatively small improvement in the accuracy of the motion determination, but allowed us to obtain physically real estimates of some parameters.

Resonance in Satellite’s Motion Under Air Drag

This article studies the attitude motion of a satellite in a circular orbit under the influence of central body of mass M and its moon of mass m, whose orbit is assumed to be circular and coplanar with the orbit of the satellite. The body is assumed to be tri-axial body with principal moments of inertia A < B < C at its centre of mass, C is the moment of inertia about the spin axis which is perpendicular to the orbital plane. These principal axes are taken as the co-ordinate axes x, y, z; the z axis being perpendicular to the orbital plane. We have studied the rotational motion of satellite in the circular orbit under the influence of aerodynamic torque. Using BKM method, it is observed that the amplitude of the oscillation remains constant upto the second order of approximation. The main and the parametric resonance have been shown to exist and have been studied by BKM method. The analysis regarding the stability of the stationary planar oscillation of a satellite near the resonance frequency shows that the discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation.

Low-Frequency Microaccelerations onboard the Foton-11 Satellite

We analyze the microacceleration measurements carried out onboard the Foton-11 satellite with the three-component accelerometer BETA. The microaccelerations were recorded virtually throughout the entire orbital flight of the Foton-11 satellite. The data obtained were analyzed in the following way. First they were used to determine the actual rotational motion of the satellite for several arbitrarily selected time intervals 4 h long. This problem was solved by constructing the approximation of the microacceleretation low-frequency component (previously determined from the data) by its calculated analog computed along the solutions to differential equations of rotational motion of the satellite. The approximation was made by the least squares method. As a result, those mathematical model parameters and the solutions to equations of motion were found that gave the best consistency of the microacceleretation low-frequency component and its calculated analog. Then the spectral analysis of the low-frequency component and its calculated analog was made. It was shown that, although basic harmonics of these functions coincided sufficiently well, some harmonics of the low-frequency component failed to be interpreted in terms of the satellite's rotational motion.

Quasistatic Microaccelerations onboard the Foton Satellite during Its Flight at High-Altitude Orbits

The level of quasistatic microaccelerations onboard the Foton-M satellite is predicted for its flights in two orbits: the planned orbit with the altitudes in perigee hπ = 262 km and in apogee hα = 304 km and the orbit with hπ = 262 km and hα = 350 km. The prediction is based on mathematical simulation of the satellite motion with respect to its center of mass under the action of gravitational and aerodynamic moments. The model is represented by the system of equations of the satellite rotational motion. Parameters of this system are chosen from the condition of coincidence of the motion of preceding Foton satellites (hπ ≈ 220 km and hα ≈ 400 km) calculated using this model with the results of determination of actual rotational motion of the Foton-11 and Foton-12 satellites. With the help of the model thus calibrated, a calculation is made of the rotational motion of the Foton-M satellite and of the quasistatic microaccelerations onboard it. As is shown by the results of simulation, the use of the first and the second orbits will result in reductions of microaccelerations by 30% and 60%, respectively.

An Analysis of the Low-Frequency Component in Measurements of Angular Velocity and Microacceleration onboard the Foton-12 Satellite

We compare the results of two methods used to determine the angular velocity of the Foton-12 satellite and the low-frequency component of microaccelerations onboard it. The first method is based on reconstruction of the satellite's rotational motion using the data of onboard measurements of the strength of the Earth's magnetic field. The motion (time dependence of the orientation parameters and angular velocity) was found from the condition of best approximation of the measurement data by the functions calculated along the solutions to equations of attitude motion of the satellite. The solutions found were used to calculate the quasistatic component of microaccelerations at certain points of the satellite, in particular, at the point of location of an accelerometer of the QSAM system. Filtration of the low-frequency component of the angular velocity and microacceleration from the data of measurements by a sensor of angular velocity and by the accelerometer of this system served as a second method. The filtration was made using the discrete Fourier series. A spectral analysis of the functions representing the results of determining the angular velocity and microacceleration by both methods is performed. Comparing the frequencies and amplitudes of the harmonic component of these functions allowed us to estimate the accuracy of measurements made by the QSAM system in the low-frequency range.

Attitude determination and control system design of the ITU-UUBF LEO1 satellite

In this paper an attitude determination and control system for ITU-UUBF LEO1 satellite is proposed. To determine the attitude of the satellite this system uses algebraic method (2-vector algorithm). As a reference direction, the unit vectors toward the Sun and the Earth's center, and the Earth's magnetic field are used. Thus, it includes three different 2-vector algorithms based on using Earth's magnetic field–Sun vector, Earth's magnetic field–nadir vector, and nadir vector–Sun vector couples. A redundant data processing algorithm based on maximum likelihood was designed. The parameters of satellite's rotational motion are estimated using extended Kalman filter (EKF). For control purposes an EKF-based PD controller is designed. To reveal the performance of the designed system a simulation is made.

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.

Evolution of Rotational Motion of a Symmetrical Satellite with Viscoelastic Rods

We study the motion of a symmetrical satellite with a pair of flexible viscoelastic rods in a central Newtonian gravitational field. A restricted problem formulation is considered, when the satellite's center of mass moves along a fixed circular orbit. A small parameter e is introduced which is inversely proportional to the stiffness of flexible elements. Another small parameter μ is equal to the ratio of the squared orbital angular velocity and the squared magnitude of the initial angular velocity of the satellite. In order to describe the satellite rotational motion relative to the center of mass, we use the canonical Andoyer variables. In the undisturbed formulation of the problem, i.e., at e = 0 and μ = 0, these variables are the action–angle variables. Equations describing the evolution of motion are derived by an asymptotic method which combines the method of separating motions for systems with an infinite number of degrees of freedom and the Krylov–Bogolyubov method for systems with fast and slow variables. The manifolds of stationary motions are found, and their stability is investigated on the basis of equations in variations. Phase portraits are constructed which describe the rotational motion of a satellite at the stage of slow dissipative evolution.

On the Dynamics of the LAGEOS-I Spin Vector: High Precision Direct Observations and Comparisons to Theoretical Modeling

AbstractLAGEOS I is a high-density geodetic satellite launched by NASA on 4 May 1976 (Johnson et al., 1976). Using a network of laser ranging stations, GSFC/NASA has maintained extremely accurate information on the orbital motions of LAGEOS I, and the later LAGEOS II and on the time-dependent evolution of their orbital parameters. The development of short-pulse laser ranging systems, and better models for atmospheric refractive effects, have dramatically improved the ability to locate the spacecraft or measure geodetic position and terrestrial crustal motion, but these systems do not measure the satellite rotational motion or gyroscopic effects, thought initially unimportant. Primarily as a result of technical strides in orbit determination, it is now recognized that the spin-motion is critical to understanding weak but important interactions with the environment.