Uncontrolled Attitude Motion of the Foton-12 Satellite and Quasi-Steady Microaccelerations onboard It

The results of determination of the uncontrolled attitude motion of the Foton-12 satellite (placed in orbit on September 9, 1999, terminated its flight on September 24, 1999) are presented. The determination was carried out by the onboard measurement data of the Earth's magnetic field strength vector. Intervals with a duration of several hours were selected from data covering almost the entire flight. On each such interval the data were processed simultaneously using the least squares method by integrating the satellite's equations of motion with respect to the center of mass. The initial conditions of motion and the parameters of the mathematical model employed were estimated in processing. The results obtained provided for a complete representation of the satellite's motion during the flight. This motion, beginning with a small angular velocity, gradually sped up. The growth of the component of the angular velocity with respect to the longitudinal axis of the satellite was particularly strong. During the first several days of the flight this component increased virtually after every passage through the orbit's perigee. As the satellite's angular velocity increased, its motion became more and more similar to the regular Euler precession of an axisymmetric rigid body. In the last several days of flight the satellite's angular velocity with respect to its longitudinal axis was about 1 deg/s and the projection of the angular velocity onto the plane perpendicular to this axis had a magnitude of approximately 0.15 deg/s. The deviation of the longitudinal axis from the normal to the orbit plane did not exceed 60°. The knowledge of the attitude motion of the satellite allowed us to determine the quasi-steady microacceleration component onboard it at the locations of the technological and scientific equipment.     

Analysis of Low-Frequency Microaccelerations onboard the Foton-11Satellite

The method and the results of investigating the low-frequency component of microaccelerations onboard the Foton-11satellite are presented. The investigation was based on the processing of data of the angular velocity measurements made by the German system QSAM, as well as the data of measurements of microaccelerations performed by the QSAM system and by the French accelerometer BETA. The processing was carried out in the following manner. A low-frequency (frequencies less than 0.01 Hz) component was selected from the data of measurements of each component of the angular velocity vector or of the microacceleration, and an approximation was constructed of the obtained vector function by a similar function that was calculated along the solutions to the differential equations of motion of the satellite with respect to its center of mass. The construction was carried out by the least squares method. The initial conditions of the satellite motion, its aerodynamic parameters, and constant biases in the measurement data were used as fitting parameters. The time intervals on which the approximation was constructed were from one to five hours long. The processing of the measurements performed with three different instruments produced sufficiently close results. It turned out to be that the rotational motion of the satellite during nearly the entire flight was close to the regular Eulerian precession of the axially symmetric rigid body. The angular velocity of the satellite with respect to its longitudinal axis was about 1 deg/s, while the projection of the angular velocity onto the plane perpendicular to this axis had an absolute value of about 0.2 deg/s. The magnitude of the quasistatic component of microaccelerations in the locations of the accelerometers QSAM and BETA did not exceed 5 × 10^–5–10^–4m/s²for the considered motion of the satellite.     

Determination of attitude motion of the Foton M-2 satellite using the data of onboard measurements of its angular velocity

We present the resutls of a prompt determination of the uncontrolled attitude motion of the Foton M-2 satellite, which was in orbit from May 31 to June 16, 2005. The data of onboard measurements of the angular velocity vector were used for this determination. The measurement sessions were carried out once a day, each lasting 83 min. Upon terminating a session, the data were transmitted to the ground to be processed using the least squares method and integrating the equations of motion of the satellite with respect to its center of mass. As a result of processing, the initial conditions of motion during a session were estimated, as well as parameters of the mathematical model used. The satellite’s actual motion is determined for 12 such sessions. The results obtained in flight completely described the satellite’s motion. This motion, having begun with a small angular velocity, gradually became faster, and in two days became close to the regular Euler precession of an axisymmetric solid body. On June 14, 2005 the angular velocity of the satellite with respect to its longitudinal axis was approximately 1.3 degrees per second, and the angular velocity projection onto a plane perpendicular to this axis had a magnitude of about 0.11 degrees per second. The results obtained are consistent with more precise results obtained later by processing the data on the Earth’s magnetic field measured on the same satellite, and they complement the latter in determination of the motion in the concluding segment of the flight, when no magnetic measurements were performed.     

Determination of attitude motion of the <Emphasis Type="Italic">Foton M-3</Emphasis> satellite according to the data of onboard measurements of the Earth’s magnetic field

The results of reconstruction of rotational motion of the Foton M-3 satellite during its uncontrolled flight in September 2007 are presented. The reconstruction was performed by processing the data of onboard measurements of the Earth’s magnetic field obtained by the DIMAC instruments. The measurements were carried out continuously throughout the flight, but the processing technique dealt with the data portions covering time intervals of a few orbital revolutions. The data obtained on each such interval were processed jointly by the least squares method with using integration of the equations of satellite motion relative to its center of mass. When processing, the initial conditions of motion and the used mathematical model’s parameters were estimated. The results of processing 16 data sets gave us complete information about the satellite motion. This motion, which began at a low angular velocity, had gradually accelerated and in five days became close to the regular Euler precession of an axisymmetric solid body. At the end of uncontrolled flight the angular velocity of the satellite relative to its lengthwise axis was 0.5 deg/s; the angular velocity projection onto the plane perpendicular to this axis had a magnitude of about 0.18 deg/s.     

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.     

Determination of the Quasistatic Component of Microaccelerations at the MirStation

We describe the determination of the quasistatic component of microaccelerations, as it was done during the space experiments with the instruments DACON and ALICE-2. This component was calculated using the telemetric information related to the motion of the station with respect to its center of mass. The information consists of the values of the station angular velocity vector and the quaternion which specifies its orientation, determined at discrete instants of time. The quaternion is determined with a step of about 1 min, the angular velocity with a step of about 10 s. The information is used in the following manner. At first, the quaternion components corresponding to some time interval are smoothed by splines. Then, employing the obtained splines and kinematic equations, the angular velocity and acceleration of the station are calculated on this interval. Finally, the microacceleration is calculated as a function of time at the point of the location of the instrument. The data of measurements of the angular velocity are used for the purpose of control. As a rule, the available telemetric information allows one to find the quasi-static component for the entire time interval of carrying out the experiment. Examples of determination of this component for some experiments are presented. A comparison with the results of calculating the microacceleration quasistatic component by other methods is made.     

Motion sickness susceptibility during rotation at 30 rpm in free-fall parabolic flight

Free fall per se whether in parabolic or orbital flight may be regarded as a "partial" motion environment with respect to eliciting motion sickness, requiring an additional component to render this environment "complete" or stressful. Parabolic flight in toto falls in the category of a "complete" motion environment in that some persons became motion sick with head fixed and eyes closed. In the present experiment we selected subjects who were symptom free or nearly symptom free in the KC-135 with head fixed. All tests were conducted with the subject rotating at 30 rpm in a rotating litter chair, and comparisons were made between head-fixed and head-moving conditions (right-left) in the free-fall phase of parabolic flight and under simulated free-fall phases in the laboratory. With head fixed most subjects were insusceptible; with head moving left-right susceptibility was slightly higher in the laboratory than aloft. An additional comparison was made correlating susceptibility in the free-fall phases of parabolic flight with susceptibility to experimental motion sickness in Skylab. In both situations cross-coupled angular accelerations were generated by executing head and body movements out of the plane of rotation. In parabolic flight 9 of 15 subjects reached an endpoint just short of frank motion sickness. In the Skylab workshop all eight of the astronauts tested were symptom free at the end of the test. The explanation for the difference in susceptibility rests in two factors: (1) Basic susceptibility in free fall is lower than on the ground, and (2) in Skylab the astronauts who needed to adapt had achieved this goal prior to the first test on Mission-Day 8.     

Asymptotic study of a complete magnetic attitude control cycle providing a single-axis orientation

The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms.     

Determination of parameters of attitude motion of a small communication satellite using the data of measurements of current of solar panels

A communication satellite (small spacecraft) injected into a geosynchronous orbit is considered. Flywheel engines are used to control the rotational spacecraft motion. The spacecraft after the emergency situation has passed into a state of uncontrolled rotation. In this case, no direct telemetric information about parameters of its rotational motion was accessible. As a result, the problem arose to determine the rotational satellite motion according to the available indirect information: current taken from the solar panels. Telemetric measurements of solar panel current obtained on the time interval of a few hours were simultaneously processed by the least squares method integrating the equations of rotational satellite motion. We present the results of processing 10 intervals of the measurement data allowing one to determine the real rotational spacecraft motion and to estimate the total angular momentum of flywheel engines.     

The Mode of Gravitational Orientation for the International Space Station

The results of the determination of the uncontrolled attitude motion of the International Space Station during its unmanned flight in 1999 are presented. The data of onboard measurements of three components of the angular velocity are used for this determination. These data covering an interval of slightly less than one orbit were jointly processed by the least squares method, by integrating the equations of motion of the station relative to its center of mass. As a result of this processing, the initial conditions of the motion and the parameters of the mathematical model used were estimated. The actual motion of the station has been determined for 20 such intervals during April–November. Throughout these intervals, the station rotated about the axis of the minimum moment of inertia, the latter executing small oscillations relative to the local vertical. Such a mode, known as the mode of gravitational orientation of a rotating satellite or the mode of generalized gravitational orientation, was planned before the flight. The measurements were made to verify it. The quasistatic component of the microaccelerations aboard the station is estimated for this mode.     

空间机械臂非完整运动规划的遗传算法研究

带空间机械臂航天器系统在无外力矩作用时，系统相对于总质心的动量矩守恒而变为非完整系统。由于非完整约束的不可积性，非完整系统的运动规划与控制比一般系统要困难得多。现利用非完整特性研究了自由漂浮空间机械臂的三维姿态运动控制问题。首先导出带空间机械臂的航天器三维姿态运动数学模型，并将系统的控制问题转化为无漂移系统的非完整运动规划问题。在运动规划中，根据最优控制原理和优化理论，提出基于遗传算法的最优运动规划数值算法。通过数值仿真，表明该方法对空间机械臂及航天器三维姿态运动的非完整运动规划是有效的。     

Orbital and angular motion construction for low thrust interplanetary flight

Low thrust interplanetary flight is considered. Firstly, the fuel-optimal control is found. Then the angular motion is synthesized. This motion provides the thruster tracking of the required by optimal control direction. And, finally, reaction wheel control law for tracking this angular motion is proposed and implemented. The numerical example is given and total operation time for thrusters is found. Disturbances from solar pressure, thrust eccentricity, inaccuracy of reaction wheels installation and errors of inertia tensor are taken into account.     

控制力矩陀螺群奇异角动量超曲面仿真分析

用角动量超曲面仿真分析了控制力矩陀螺构型奇异的产生机理。基于控制力矩陀螺群动力学总角动量和输出控制力矩,讨论了典型构型奇异存在的状况,并确定了奇异点存在的判断依据,对五棱锥构型的显奇异和隐奇异进行了角动量超曲面仿真,发现能通过零运动脱离奇异状态的隐奇异点,为控制力矩陀螺群的操纵律设计提供了重要依据。控制系统数学仿真结果表明该分析法有效。     

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.     

The use of a movable telescoping end mass system for the time-optimal control of spinning spacecraft

The time-optimal control of a spin-stabilized spacecraft with a movable telescoping appendage (boom), is considered analytically and numerically. The motion of a control mass at the end of the boom is determined such that the terminal time will be minimized for two-axis control of a symmetric spacecraft. The equations of rotational motion are linearized about the desired state of spin about the symmetry axis. The equations for the transverse angular velocity components have the form of a coupled two dimensional harmonic oscillator with boom motion as a control force. The control function which brings the system to the desired state is known to be a series of positive and negative pulses. If the initial state is such that the system can be driven to rest in a single switch, the responses, switching and final times, and required boom motion may be determined analytically. Some typical numerical results based on these solutions are discussed.     

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.     

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.     

视觉导引的无人直升机自主着舰系统仿真

对于无人直升机着舰问题,提出了基于视觉导引的自主着舰方案;建立了一套无人直升机自主着舰仿真系统;建立了舰船运动模型,无人直升机六自由度非线性全量模型;设计了着舰特征图案,通过摄像机模型获取舰船上的特征图案;提出快速四点算法实现3D位姿估算,并以此构建视觉信息识别系统,识别直升机与舰船相对运动参数;通过分层控制思想,实现基于视觉信息导引着舰。在此基础上形成仿真闭环,对无人直升机定点自主着舰的全过程进行仿真验证。     

Vestibular factors influencing the biomedical support of humans in space

This paper will describe the biomedical support aspects of humans in space with respect to the vestibular system. The vestibular system is thought to be the primary sensory system involved in the short-term effects of space motion sickness although there is increasing evidence that many factors play a role in this complex set of symptoms. There is the possibility that an individual's inner sense of orientation may be strongly coupled with the susceptibility to space motion sickness. A variety of suggested countermeasures for space motion sickness will be described. Although there are no known ground-based tests that can predict space motion sickness, the search should go on. The long term effects of the vestibular system in weightlessness are still relatively unknown. Some preliminary data has shown that the otoconia are irregular in size and distribution following extended periods of weightlessness. The ramifications of this data are not yet known and because the data was obtained on lower order animals, definitive studies and results must wait until the space station era when higher primates can be studied for long durations. This leads us to artificial gravity, the last topic of this paper. The vestibular system is intimately tied to this question since it has been shown on Earth that exposure to a slow rotating room causes motion sickness for some period of time before adaptation occurs. If the artificial gravity is intermittent, will this mean that people will get sick every time they experience it? The data from many astronauts returning to Earth indicates that a variety of sensory illusions are present, especially immediately upon return to a 1-g environment. Oscillopsia or apparent motion of the visual surround upon head motion along with inappropriate eye motions for a given head motion, all indicate that there is much to be studied yet about the vestibular and CNS systems reaction to a sudden application of a steady state acceleration field like 1-g. From the above information it is obvious that the vestibular system does have unique requirements when it comes to the biomedical support of space flight. This is not to say that other areas such as cardiovascular, musculo-skeletal, immunological and hematological systems do not have their own unique requirements but that possible solutions to one system can provide continuing problems to another system. For example, artificial gravity might be helpful for long term stabilization of bone demineralization or cardiovascular deconditioning but might introduce a new set of problems in orientation, vestibular conflict and just plain body motion in a rotating space vehicle.     

J2项摄动条件下线性化的编队卫星动力学方程

考虑J2项摄动力对参考卫星轨道的绝对影响和对伴随卫星轨道的相对影响,应用拉格朗日方法,在笛卡尔坐标系下,给出了一组考虑J2项摄动的线性化的编队卫星相对动力学方程。该方程考虑了J2项摄动力带来的相对运动平面内外的耦合和短周期项的影响,有效地提高了相对动力学模型的精度。仿真结果表明,该方程组可有效地描述J2项摄动条件下编队卫星的相对运动,其误差只有二体非线性模型的10%,利用其设计的水平圆编队半径的相对误差不超过1%,并且由于是线性化的微分方程描述,可方便地应用到编队卫星导航、制导与控制系统的设计中。