Experimental investigation of the modes of operation of uncontrolled attitude motion of the Progress spacecraft

Results of in-flight tests of three modes of uncontrolled attitude motion of the Progress spacecraft are described. These proposed modes of experiments related to microgravity are as follows: (1) triaxial gravitational orientation, (2) gravitational orientation of the rotating satellite, and (3) spin-up in the plane of the orbit around the axis of the maximum moment of inertia. The tests were carried out from May 24 to June 1, 2004 onboard the spacecraft Progress M1-11. The actual motion of this spacecraft with respect to its center of mass, in the above-mentioned modes, was determined by telemetric information about an electric current tapped off from solar batteries. The values of the current obtained during a time interval of several hours were processed jointly using the least squares method by integration of the equations of the spacecraft’s attitude motion. The processing resulted in estimation of the initial conditions of motion and of the parameters of mathematical models used. For the obtained motions the quasi-static component of microaccelerations was computed at a point onboard, where installation of experimental equipment is possible.     

航天器环绕小行星Ivar的运动分析

将小行星Ivar近似为三轴椭球体，给出了非球形引力势函数，建立了航天器环绕小行星Ivar的轨道动力学方程。利用Jacobi积分常数绘制了航天器在Ivar周围的零速度曲线，并分析了航天器的可能运动区域，给出了航天器不碰撞小行星Ivar的边界条件及不同偏心率下的近拱点半径。分析了小行星Ivar扁率和椭率对环绕轨道的影响，数学仿真结果表明：在一个轨道周期内，顺行轨道的开普勒能量、轨道角动量、偏心率和近拱点半径变化较大，而逆行轨道的相应参数变化较小。     

考虑太阳帆板振动的空间绳系拖曳动力学与控制

针对使用空间绳网捕获带有太阳帆板等柔性附件的大型失效航天器的碎片清除任务,充分考虑了拖曳过程中柔性附件产生的振动对系统的稳定造成的影响.首先采用凯恩方法建立了失效航天器绳系拖曳系统动力学模型,在建模过程中充分考虑系绳的质量和振动、帆板的振动、系统的轨道运动对姿态的影响等,使动力学模型更加详细和完整,且该动力学模型不受失...     

Analysis of the orbital motion of the asteroid Apophis’ satellite

We have analyzed the orbital disturbed spacecraft motion near an asteroid. The equations of the asteroidocentric spacecraft motion have been used with regard to three perturbations from celestial bodies, the asteroid’s nonsphericity, and solar radiation pressure. It has been shown that the orbital parameters of the main spacecraft and a small satellite with a radio beacon can be selected such that the orbits are rather stable for a fairly long period of time, i.e., a few weeks for the main spacecraft with an orbit initial radius of ~0.5 km and a few years before approaching Apophis with the Earth in 2029, for a small satellite at an orbit initial radius of ~1.5 km. The initial orientation of the spacecraft orbital plane perpendicular to the sunward direction is optimal from the point of view of the stability of the spacecraft flight near an asteroid.     

Robust attitude stabilization of spacecraft subject to actuator failures

A robust nonlinear control scheme is developed to stabilize the 3-axis attitude of the spacecraft for cases where there is no control available on either roll or yaw axis. The stability conditions for robustness against unmatched uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. The properties of the proposed sliding surface are investigated to obtain the domains of sliding mode for the closed-loop system. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.     

Stability of resonance rotation of a satellite with respect to its center of mass in the orbit plane

The stability of resonance oscillations and rotations of a satellite in the plane of its orbit in the case when the difference of the moments of inertia with respect to the principal axes lying in the orbit plane is small is determined at a given rotation number m by the sign of function Φ_m(e), introduced by F.L. Chernous’ko in 1963. In this paper, convenient analytical representations of functions Φ_m(e) are described in the form of integrals and series of Bessel functions regular at e → 1^?. Values of Φ_m(1) are calculated in explicit form. A theorem about the double asymptotic form of functions Φ_m(e) at m → ∞ and e → 1^? is proved by the saddlepoint method.     

万有引力场中带挠性太阳帆板航天器的姿态稳定性

本文讨论带双侧挠性太阳帆板航天器在万有引力场中的姿态运动，建立带挠性帆板航天器的欧拉方程和帆板强迫振动方程。利用Ｇａｌｅｒｋｉｎ方法对动力学方程离散化，利用Ｋｅｌｖｉｎ－Ｔａｉｔ－Ｃｈｅｔａｙｅｖ定量判断航天器在轨道坐标系内相对平衡的稳定性。导出适用于任意阶模态的解析形式稳定性充分条件。     

Stability-based SDRE controller for spacecraft momentum management

Momentum management of spacecraft aims to avoid the angular momentum accumulation of control momentum gyros through real-time attitude adjustment. An attitude control/momentum management controller based on state-dependent Riccati equation is developed for attitude-stabilized spacecraft. The governing equations of the system are formulated as three-axis coupled with full moment of inertia, which fully capture the nonlinearity of the system and are valid for systems with significant products of inertia or strong pitch to roll/yaw coupling. The state-dependent Riccati equation algorithm brings the nonlinear system to a linear structure having state dependent coefficients matrices and minimizing a quadratic-like performance index. The system equations are nondimensionalized, which avoid numerical problems at the same time make the weighting matrix more predictable. To guarantee closed-loop system stability, the state-dependent Riccati equation algorithm is also modified based on pole placement technique. The state-dependent Riccati equation is online calculated through the computational-efficient θ-D technique which reaches a tradeoff between control optimality and computation load. The dynamic characteristics of the system at torque equilibrium attitude are analyzed. Constraints on moment of inertia for successful momentum management are provided. Simulations demonstrate the excellent performance of the controller.     

The Dynamics of a Satellite-Gyrostat with a Single Nonzero Component of the Vector of Gyrostatic Moment

The dynamics of a satellite-gyrostat moving in the central Newtonian force field along a circular orbit is studied. In the particular case when the vector of gyrostatic moment is parallel to one of the satellite’s principal central axes of inertia, all the equilibrium states are determined. For each equilibrium orientation, sufficient conditions of stability are obtained as a result of the analysis of the generalized energy integral, and necessary conditions of stability are determined as a result of analysis of the linearized equations of motion. The evolution of regions of validity for the conditions of stability of equilibrium positions are studied in detail depending on the parameters of the problem. All the bifurcation values of the parameters at which qualitative changes of the regions of stability take place are determined.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 283–294.Original Russian Text Copyright © 2005 by Sarychev, Mirer, Degtyarev.     

Optimal flights to near-Earth asteroid

The spacecraft flights to the Near-Earth asteroid in order to give an impact influence on the asteroid, correct its orbit and prevent the asteroid’s collision with the Earth are analyzed.In the first part, the impulse flights are analyzed in the Lambert approach. There are determined the optimal trajectories maximizing the asteroid deviation from the Earth.In the second part, the flights with the chemical and electric-jet engines are analyzed. The high thrust is used to launch the spacecraft from the geocentric orbit, and the low thrust is applied for the heliocentric motion. On the base of optimal impulse transfer, the optimal low thrust trajectories are determined using Pontryagin maximum principle.The numerical results are given for the flight to the asteroid Toutatis. Parameters of the spacecraft impact on the asteroid are determined. The asteroid deviation from the Earth caused by the spacecraft influence is presented.     

Halo orbits in the vicinity of the L 2 libration point in the Sun-Earth system

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L ₂ libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L ₂ point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L ₂ point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.     

A novel single thruster control strategy for spacecraft attitude stabilization

Feasibility of achieving three axis attitude stabilization using a single thruster is explored in this paper. Torques are generated using a thruster orientation mechanism with which the thrust vector can be tilted on a two axis gimbal. A robust nonlinear control scheme is developed based on the nonlinear kinematic and dynamic equations of motion of a rigid body spacecraft in the presence of gravity gradient torque and external disturbances. The spacecraft, controlled using the proposed concept, constitutes an underactuated system (a system with fewer independent control inputs than degrees of freedom) with nonlinear dynamics. Moreover, using thruster gimbal angles as control inputs make the system non-affine (control terms appear nonlinearly in the state equation). This necessitates the control algorithms to be developed based on nonlinear control theory since linear control methods are not directly applicable. The stability conditions for the spacecraft attitude motion for robustness against uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.     

On the stability of stationary motions of a system of coaxial bodies

We consider the stability of stationary motions of a model of a spacecraft as a system of coaxial bodies with small asymmetry caused by the shift of the axes of dynamic symmetry of bodies relative to the axis of rotation. We determine the stationary motions of the system; their stability is studied with respect to both the projections of angular velocity and the position of the axis of rotation. The sufficient conditions for the stability of these stationary motions are obtained by constructing a Lyapunov function, and the necessary conditions are obtained by analyzing the corresponding linearized equations of perturbed motion.     

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.     

航天器两自由度扫描镜图像运动补偿技术研究

研究航天器的两自由度扫描镜图像运动补偿问题。在姿态估计信息的基础上,给出了一种运动补偿算法。算法中不仅补偿了姿态估计信息,还同时考虑了姿态信息中的长周期系统误差。利用扫描镜在特定工作模式下相对惯性空间的准确定向能力和系统误差的长周期特性,给出了一种系统误差的估计和补偿算法,每隔一定的时间段对系统误差估计值进行更新并加以补偿,进一步提高了扫描精度。基于一颗地球静止轨道卫星的数值仿真结果验证了补偿算法的有效性。     

The Aster project: Flight to a near-Earth asteroid

The information on the project being developed in Brazil for a flight to binary or triple near-Earth asteroid is presented. The project plans to launch a spacecraft into an orbit around the asteroid and to study the asteroid and its satellite within six months. Main attention is concentrated on the analysis of trajectories of flight to asteroids with both impulsive and low thrust in the period 2013-2020. For comparison, the characteristics of flights to the (45) Eugenia triple asteroid of the Main Belt are also given.     

Orbital stability of planar oscillations of a satellite in a circular orbit

We consider the attitude motion of a satellite with a circular orbit in a central Newtonian gravitational field. The satellite is a solid body whose mass geometry is that of a plate. A nonlinear analysis is made of orbital stability of planar oscillations of the satellite at which its middle or major axis of inertia is perpendicular to the orbit plane. At small amplitudes of oscillations the analysis of stability was made analytically, while for arbitrary amplitudes the numerical analysis was performed.     

On the possibility of long-term maintenance of geostationary satellite attitude without using the external information sensors and inertial sensors

The problem of maintaining spacecraft attitude during the loss of information from attitude sensors and inertial sensors is considered. The problem is solved on the basis of the force gyro stabilization principle with producing an angular momentum in the plane of orbit. The redundant mode of attitude maintenance is developed for spacecraft of the Yamal series. The results of testing the mode during the in-flight tests of the Yamal-200 spacecraft are presented.