Study of the mode of angular velocity damping for a spacecraft at non-standard situation

Non-standard situation on a spacecraft (Earth’s satellite) is considered, when there are no measurements of the spacecraft’s angular velocity component relative to one of its body axes. Angular velocity measurements are used in controlling spacecraft’s attitude motion by means of flywheels. The arising problem is to study the operation of standard control algorithms in the absence of some necessary measurements. In this work this problem is solved for the algorithm ensuring the damping of spacecraft’s angular velocity. Such a damping is shown to be possible not for all initial conditions of motion. In the general case one of two possible final modes is realized, each described by stable steady-state solutions of the equations of motion. In one of them, the spacecraft’s angular velocity component relative to the axis, for which the measurements are absent, is nonzero. The estimates of the regions of attraction are obtained for these steady-state solutions by numerical calculations. A simple technique is suggested that allows one to eliminate the initial conditions of the angular velocity damping mode from the attraction region of an undesirable solution. Several realizations of this mode that have taken place are reconstructed. This reconstruction was carried out using approximations of telemetry values of the angular velocity components and the total angular momentum of flywheels, obtained at the non-standard situation, by solutions of the equations of spacecraft’s rotational motion.     

欠驱动航天器飞轮控制方法

针对应用任意剪刀对构型飞轮群的欠驱动刚体航天器姿态控制问题,将飞轮群与航天器看作整体系统进行建模,从整体系统可控性角度分析采用传统模型进行控制系统设计存在的局限性。随后通过对飞轮群角动量集合描述,得出航天器姿态可机动集合。由于飞轮群构型的任意性及航天器的欠驱动特性,导致具有初始角动量的整体系统难以针对系统状态方程采用Lyapunov函数方法进行状态反馈控制器设计,同时为了保证存在外扰动力矩的航天器姿态机动精度,采用非线性预测控制方法实现系统的反馈控制。所提控制算法实现了任意飞轮群剪刀对构型、飞轮群角动量非饱和条件下,任意系统初始角动量欠驱动航天器在姿态可机动集合中的机动控制。仿真结果表明,系统具有良好的控制性能及精度。     

欠驱动挠性航天器的全姿态控制

考虑欠驱动挠性航天器姿态控制问题,其中执行机构配置为两轴喷气和飞轮执行机构。提出了“喷气消旋＋飞轮机动”的分段控制方法,其基本思想是：首先利用喷气推进执行机构使航天器整星角动量趋于零,为飞轮控制做准备;然后利用飞轮执行机构使航天器从任意姿态转向指定姿态并维持。针对“喷气消旋”,说明了提出的控制规律能够保证航天器角动量全局渐近收敛于任意小量;针对“飞轮机动”,证明了航天器全姿态具有大范围渐近稳定性;针对“喷气消旋＋飞轮机动”的完整过程,采用扰动系统理论分析了闭环控制系统的大范围终端有界性。     

欠驱动刚性航天器姿态的非完整运动规划粒子群算法

研究欠驱动刚性航天器姿态的非完整运动规划问题。众所周知航天器利用三个动量飞轮可以控制其姿态和任意定位，当其中一轮失效，航天器动力学方程表现为不可控。在系统角动量为零的情况下，系统的姿态控制问题可转化为无漂移系统的运动规划问题。基于粒子群优化技术设计了欠驱动刚性航天器姿态的非完整运动规划算法。通过数值仿真，并和遗传算法进行了比较，结果表明该方法对欠驱动航天器姿态运动规划是有效的。     

Estimation of residual microaccelerations on board an artificial earth satellite in the monoaxial solar orientation mode

The mode of monoaxial solar orientation of a designed artificial Earth satellite (AES), intended for microgravitational investigations, is studied. In this mode the normal line to the plane of satellite’s solar batteries is permanently directed at the Sun, the absolute angular velocity of a satellite is virtually equal to zero. The mode is implemented by means of an electromechanical system of powered flywheels or gyrodynes. The calculation of the level of microaccelerations arising on board in such a mode, was carried out by mathematical modeling of satellite motion with respect to the center of masses under an effect of gravitational and restoring aerodynamic moments, as well as of the moment produced by the gyrosystem. Two versions of a law for controlling the characteristic angular momentum of a gyrosystem are considered. The first version provides only attenuation of satellite’s perturbed motion in the vicinity of the position of rest with the required velocity. The second version restricts, in addition, the increase in the accumulated angular momentum of a gyrosystem by controlling the angle of rotation of the satellite around the normal to the light-sensitive side of the solar batteries. Both control law versions are shown to maintain the monoaxial orientation mode to a required accuracy and provide a very low level of quasistatic microaccelerations on board the satellite.     

细胞化卫星分布式角动量平衡力矩分配算法

针对细胞化卫星姿态控制系统中细胞模块数量多、控制器细胞通信压力大的问题,提出了一种分布式控制力矩分配算法。该力矩分配算法先将力矩分配问题转化为带耦合等式约束的凸优化问题,然后通过分布式的方式求解该优化问题。在力矩分配过程中,控制器细胞只需要提供期望力矩,因此降低了通信压力。同时,该算法在优化目标函数中引入角动量能力因子,使飞轮细胞可以根据自身的角动量水平决定其力矩输出。数值仿真结果表明,该分布式分配算法可以保证分配后的力矩与期望力矩相等,且实现了平衡飞轮系统角动量的目的,进而可以通过卸载部分细胞的角动量来卸载整个飞轮系统的角动量。     

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.     

使用混合执行机构的快速机动卫星力矩分配算法

针对单框架控制力矩陀螺群（SGCMGs）存在奇异和单框架控制力矩陀螺（SGCMG）存在框架转速死区的问题,研究了SGCMG与飞轮联合作为执行机构的控制力矩分配算法,以SGCMG功耗、飞轮功耗和飞轮角动量的二次型加权矩阵求和为性能指标,提出了一种形式简洁的混合执行机构力矩分配算法,通过分析,证明该分配算法能够有效的避免SGCMGs的奇异;设计了一种SGCMG功耗加权矩阵的调节策略,解决了SGCMG陷入转速死区的问题,设计了一种飞轮角动量加权矩阵的调节策略,通过对加权矩阵的实时调节实现了对飞轮角动量的管理,解决了飞轮转速的饱和与过零问题。数学仿真结果验证了该力矩分配算法的有效性。     

Problems of control of a re-entry vehicle with a moderate lift-to-drag ratio during its entry into the atmosphere

We consider the problems of control of the angular and trajectory motion of the Kliper re-entry vehicle. This spacecraft with a moderate hypersonic lift-to-drag ratio is designed according to the load-carrying frame scheme. Gas-dynamic engines, a split balancing flap, and an air brake are used as mounting devices of control.     

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.     

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.     

A specific case of stability of cylindrical precession of a satellite

In a central Newtonian gravitational field, the motion of a dynamically symmetrical satellite along an elliptical orbit of arbitrary eccentricity is considered. The particular motion of the satellite is known when its axis of symmetry is perpendicular to the orbit plane, and the satellite rotates about this axis with a constant angular velocity (cylindrical precession). A nonlinear analysis of stability of this motion has been performed under the assumption that the geometry of the satellite mass corresponds to a thin plate. At small values of orbit eccentricity e the analysis is analytical, while numerical analysis is used for arbitrary values of e.     

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.     

双体卫星对日定向姿态机动控制

研究了双体卫星(DFP)对日定向姿态机动控制问题。首先分析双体卫星工作机理,建立载荷舱与平台舱姿态模型,推导磁浮机构线圈和磁钢相对距离的数学表达式。提出基于PD控制的载荷舱对日姿态机动、平台舱姿态跟踪以及两舱避碰等控制策略。在此基础上,为提高平台舱姿态跟踪速度,设计反步控制器对平台舱飞轮的动态特性进行补偿。进一步,为提高两舱协同控制性能,对传统PD控制进行改进,提出基于变增益PD控制的载荷舱姿态机动控制律,将两舱相对姿态信息包含在载荷舱对日姿态机动控制律中,有效降低了两舱碰撞风险,提高了两舱姿态机动速度。仿真结果表明,本文控制算法能有效实现双体卫星对日定向,且能避免两舱碰撞。     

一种微型航天器姿态控制系统建模与分析

从航天器微小型化的角度出发，提出了仅利用两个飞轮进行航天器姿态控制的飞轮配置方案。该方案还可以对高速旋转的飞轮所储存的能量进行管理，不需要磁力矩器等额外的卸载装置，从而简化了飞轮姿态控制系统的结构。详细描述了系统的结构和工作原理，推导了航天器姿态控制系统的非线性动力学模型，分析了影响航天器姿态机动性能的主要因素，并通过仿真验证了这种配置方案的有效性。     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

Investigation of CME properties using the data of SDO and PROBA2 spacecraft

Formation and motion (at the initial stage) of six limb CMEs detected in the period June 2010 to June 2011 are investigated using the high-resolution data of the PROBA2 and SDO spacecraft combined with the data of SOHO/LASCO coronagraphs. It is demonstrated that several loop-like structures of enhanced brightness originate in the region of CME formation, and they move one after another with, as a rule, different velocities. These loop-like structures in the final analysis form the frontal structure of CME. Time dependences of the velocity and acceleration of the ejection’s front are obtained for all CMEs under consideration. A conclusion is drawn about possible existence of two classes of CMEs depending on their velocity time profiles. Ejections, whose velocity after reaching its maximum sharply drops by a value of more than 100 km/s and then goes over into a regime of slow change, belong to the first class. Another class of CMEs is formed by ejections whose velocity changes slowly immediately after reaching the maximum. It is demonstrated that the CME’s angular dimension increases at the initial stage of ejection motion up to a factor of 3 with a time scale of doubling the angular size value within the limits 3.5–11 min since the moment of the first measurement of this parameter of an ejection. For three CMEs it is shown that at the initial stage of their motion for a certain time interval they are stronger expanded than grow in the longitude direction.     

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.     

Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

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.     

Practical approaches to handle the singularities of a wrist-partitioned space manipulator

Space robotic systems are expected to play an increasingly important role in the future. However, the control methods based on the inverse kinematics are affected by singularities. In this paper, practical approaches are proposed to solve the problems of a wrist-partitioned space manipulator. For spacecraft-referenced end-point motion control, we presented the singularity separation plus damped reciprocal (SSPDR) method, which separates the singularity parameters from the inverse of the Jacobian, and replaces their reciprocals using the damped reciprocals. For another control strategy, i.e. inertially referenced end-point motion control, including spacecraft attitude-controlled mode and free-floating mode, the linear momentum equation is used to eliminate three independent variables. With modifying some expressions, the SSPDR method is utilized to solve the singularities of spacecraft attitude-controlled space robot. When the space robot is free-floating, the singularities, i.e. the so-called dynamic singularities, cannot be predicted according to its kinematic structure. Combining with the measured angular velocity of the base, the dynamic singularity handling problem is transformed into real-time kinematic singularity avoiding problem, which can be solved by the SSPDR method. Since the SVD decomposition, the estimation of the minimum singularity value, and the calculation of the generalized Jacobian matrix are not required, the algorithm has lower computation load. Another advantage is that, only the accuracy of part velocity components is reduced by adding the damped coefficients. Simulation results verify the proposed approaches.