Spacecraft detumbling using movable telescoping appendages

The dynamics of detumbling a randomly spinning spacecraft using externally mounted, movable telescoping appendages are studied both analytically and numerically. Two types of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. From an application of Lyapunov's second method, boom extension maneuvers can be determined to approach either of two desired final states: close to a zero inertial angular velocity state and a final spin rate about only one of the principal axes. Recovery dynamics are evaluated analytically for the case of symmetrical deployment. Numerical examination of other asymmetrical cases verifies the practicality of using movable appendages to recover a randomly tumbling spacecraft.     

Spacecraft dynamics with regard to elastic gravitational stabilizer deployment

The present paper deals with the study the dynamics of the spacecraft with gyro-gravitational system of stabilization. The deployment of the boom of the gravitational stabilizer commences after placing the spacecraft into the orbit and completion of the preliminary damping, when the gyroscopes are uncaged. Primarily the boom is the pre-stressed tape wound on the special drum. When the drum starts deploying the tape, it turns into the elastic cylindrical rod with the mass at its tip. The objective of the study is the creation of the generalized mathematical model and the conducting of the computer modelling of the spacecraft dynamics. The equations of motion are worked out with the use of the Lagrangian formalism. The numerical simulation of typical modes of system functioning is conducted. It is shown that the folding and the following deployment of the boom result in the turn of the spacecraft by 180° about the axis of the pitch. The results illustrate the behaviour of the main system variables.     

Optimization Problem in Control over a Programmed Turn of a Spacecraft

The problem of spacecraft reorientation from its initial angular position into a desired final position within a given time interval with a minimum value of the angular moment is considered and solved analytically in this work. It is shown that the control over the spacecraft reorientation, optimal in this sense, might be defined in the class of a regular precession performed by the spacecraft. The moment of the start of deceleration is determined from the principles of the terminal control by using real kinematic parameters of apparatus motion, which increases significantly the accuracy of reorientation. The results of mathematical modeling are presented, showing a high efficiency of the proposed way of reorientation.     

速度信息缺失的平动点轨道交会预设性能控制

以平动点轨道的交会对接为研究背景，基于高阶积分链微分器和预设性能控制理论提出了一种仅需相对位置信息的平动点轨道近程交会控制律。首先利用高阶积分链微分器估计两航天器的相对速度状态，并设计预设性能控制器使得两航天器的相对运动状态在预设的边界内渐近收敛到期望状态。然后利用李雅普诺夫函数证明相对运动状态存在扰动时控制器的稳定性。该方法为闭环控制，且与模型无关，容易在线操作。仿真结果表明，在平动点轨道航天器存在未知扰动以及导航制导等不确定的情况下，利用所提交会控制律能够实现追踪航天器与目标航天器交会任务的高精度实时控制，具有较强鲁棒性。     

Impulsive control for angular momentum management of tumbling spacecraft

We discuss an angular momentum control of a tumbling spacecraft. The proposed control method is to apply an impulse by a space robot arm, to measure and control the relative position and attitude between the target spacecraft, and then to apply another impulse until the rotational motion of the target spacecraft is well damped. A discrete controller is designed using the simplified equations of rotational motion through appropriate coordinate transformation. The stationary response under contact model uncertainty is investigated and stability condition is analytically derived. Numerical simulations are given to validate the proposed approach.     

含板类柔性附件的充液航天器动力学研究

对含有板类柔性附件和曲壁轴对称充液储腔的复杂航天器系统进行动力学建模和耦合机理研究。首先，采用Kirchhoff-Love薄板理论对航天器的板类柔性附件进行研究，通过D’Alembert原理得到柔性附件的振动方程，运用模态假设法将混合方程转换为常微分方程。其次，通过推导充液航天器储腔内任意点的运动，得到储腔液体的牵连速度势函数，采用Gauss超几何级数得到液体相对速度势函数的解析形式，通过Hamilton变分原理推导液体晃动的运动方程，以及液体速度势函数模态系数的控制方程。最后采用准坐标Lagrange方程得到耦合航天器系统的状态方程，通过数值仿真校验系统动力学模型的有效性。研究结果表明，刚性平台、液体、柔性附件的相互耦合效应使得航天器系统存在复杂动力学行为，在复杂航天器系统动力学建模过程中需要充分考虑液体晃动和柔性附件振动的影响，柔性附件的安装位置对于耦合航天器系统的动力学行为也有着重要影响。     

轨道交会、悬停及绕飞控制的解析解方法

面向航天器交会对接、编队伴飞以及在轨操控等空间应用的需求,分别对近圆、椭圆轨道上航天器间的相对运动进行了分析与建模,在常值推力作用假设下进行了相对运动的解析求解。采用模型预测的方法获得航天器相对位置和相对速度的预期偏差。通过广义逆变换构造关于预期偏差的最小范数、最小二乘全状态反馈控制器。提出了一种普遍适用于近圆、椭圆轨道,可以实现轨道交会、相对悬停保持和循迹绕飞,对相对位置和相对速度进行同步控制的高精度、高稳定度相对制导律。仿真结果校验了方法的可行性和有效性。     

Optimal control of the deployment process of solar wings on spacecraft

The optimal attitude control problem of spacecraft during the stretching process of solar wings is investigated in this paper. The dynamical equations of the nonholonomic system are derived from the conservation principle of the angular momentum of the multibody system. Attitude control of the spacecraft with internal motion is reduced to a nonholonomic motion planning problem. The spacecraft attitude control is transformed into the steering problem for a drift free control system. The optimal solution for steering a spacecraft with solar wings is presented. The controlled motion of spacecraft is simulated for two cases. The numerical results demonstrate the effectiveness of the optimal control approach.     

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。     

Analysis of evolution of multi-orbit perturbed trajectories of a spacecraft in a central field of attraction

Properties of differential equations of multi-orbit trajectory motion of a spacecraft are investigated analytically. The spacecraft moves under the action of small perturbations (in particular, low thrust) in the plane of a central Newtonian field of attraction. The conditions are specified for existence of a partial singular aperiodic solution, in the neighborhood of which the behavior of osculating elements changes sharply. In this case, phase variables (the angular position of the pericenter and the true anomaly) are found to undergo the sharpest changes. The exact superposition of solutions is suggested for the equations of motion transformed to the form of a quasi-linear, weakly non-stationary system: a partial singular aperiodic solution and fast solutions oscillating around it. Asymptotic representations are obtained for both components of the superposition. They are fairly exact in the region of smallness of perturbing terms at a long variation of the argument.     

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.     

Ballistics, navigation, and motion control for a spacecraft during its landing on the surface of Phobos

Basic concepts and algorithms laid as foundations of the scheme of landing on the Martian moon Phobos (developed for the Phobos-Grunt project) are presented. The conditions ensuring the landing are discussed. Algorithms of onboard navigation and control are described. The equations of spacecraft motion with respect to Phobos are considered, as well as their use for correction of the spacecraft motion. The algorithm of estimation of the spacecraft’s state vector using measurements with a laser altimeter and Doppler meter of velocity and distance is presented. A system for modeling the landing with a firmware complex including a prototype of the onboard computer is described.     

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.     

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.     

带挠性附件卫星的模型化及截断

本文给出了具有中心刚体和P个挠性附件的空间飞行器姿态动力学方程式,并用约束和非约束两种模态展开,得到时域求解的状态方程式和频域中的增广姿态角对控制力矩的逆传递函数阵。推导中考虑了挠性附件对中心刚体的相对运动。本文还给出了两种模态恒等式,其中之一可用来做控制系统分析时截断高阶方程式的截断准则。     

Optimization of passive orbit with the use of gravity maneuver

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions.     

带多充液圆柱贮箱航天器刚-液耦合动力学研究

文中以在低重环境下带多充液圆柱贮箱刚性航天器中刚-液耦合方程的建立和求解为主要研究目的。推导航天器中充液圆柱贮箱内任意点的牵连运动方程,根据壁面边界条件给出了贮箱内液体牵连晃动势的表达式;利用第二类边界条件下的傅立叶-贝塞尔级数展开法对低重力环境下的弯曲自由液面处的复杂动力学边界条件进行处理,建立以液体相对晃动势的模态坐标和晃动波高的模态坐标为状态向量的液体耦合晃动力学方程,通过积分分别得到了耦合晃动力和耦合晃动力矩的解析式;运用准坐标系下的拉格朗日方程建立以航天器主刚体姿态坐标和轨道坐标为状态向量的刚体耦合运动动力学方程,进一步联立上述耦合方程得到航天器整体系统的刚-液耦合动力学状态方程;最后,编制出适用于带多充液圆柱贮箱航天器内刚-液耦合动力学计算的模块化计算程序,通过计算实例验证所编程序的准确性的同时,研究了携带多充液箱航天器系统贮箱布局、外激励方式对航天器刚-液耦合系统动力学特性的影响。     

间接Legendre伪谱法的欠驱动航天器姿态运动轨迹跟踪

针对仅带有两组喷气推力器的非轴对称欠驱动刚性航天器，提出一种基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法。首先采用Legendre伪谱法(LPM)离线规划出系统的最短时间姿态机动参考轨迹。接着将实际运行轨迹与参考轨迹之间的偏差作为变量，根据Pontryagin极小值原理必要条件把系统姿态运动跟踪问题转化为一个两点边值问题(TPBVP)。最后采用 Legendre-Gauss-Lobatto(LGL)点将此两点边值问题离散转化为一个线性方程组来求解，避免了对传统Riccati微分方程的积分运算。数值仿真校验了本文基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法的有效性。     

Determination of kinematic state of an orbiting multibody using GNSS signals

Precise attitude determination of the members of a free-flying multibody system is a not so immediate task, due essentially to the large motion of its appendages coupled with their relevant flexibility effects. In fact, sensors used to this aim in current projects, such as optical encoders usually positioned near the joints of each arm, are almost blind to these effects, and clusters of specific redundant sensors should, therefore, be required in order to reconstruct both elastic deformations and rigid motion.Satellite navigation systems (GNSS) offer a suitable and reliable solution to this problem. To exploit the phase of the signal, instead of the traditional pseudo random code, ensures a very high accuracy of the order of magnitude of centimeter. Such a process requires the solution of an initial ambiguity problem, related to the number of integer wavelength included in the length of the member.The aim of the paper is to investigate the capability of this GNSS based technique to reconstruct the kinematics of a flexible multibody system orbiting around the Earth. This analysis requires a simulation including both the multibody dynamics and the navigation system constellation to define the satellites lines-of-sight at each time step.Concerning multibody equations of motion, a Newtonian formulation is adopted in this work. A special attention is required about the choice of the state variables. As the internal forces are associated to the relative displacements between the bodies, which are small fractions of the distance of the multibody spacecraft from the center of the Earth, the task of obtaining these forces from inertial coordinates could be impossible from a numerical point of view. So, the problem is reformulated in such a way that the equation of motion of the system contains global equations, with no internal forces, and local equations, with internal forces. In the latter, only quantities of the same order of the spacecraft dimensions are present.Accuracies achievable in LEO orbit with current GPS and upcoming Galileo systems are evaluated to show the interest of the proposed technique.     

Dynamics and control of variable-geometry truss structures

Variable-geometry truss structures are likely to be used extensively in the future for in-orbit space construction. This paper considers dynamics formulation and vibration control of such structures. The truss system is modelled as a collection of sub-structures consisting of truss booms, prismatic actuator elements, and in some cases a manipulator at the end. Each truss boom is treated as a separate ‘link’ and its flexibility is modelled using the finite element method. Equations of motion for individual sub-structures are obtained which are then assembled. The non-working constraint forces are eliminated to obtain the equations governing the constrained dynamics of the entire system. For vibration control, the singular perturbation method is employed to construct two reduced-order models, for quasi-static motion and for modal co-ordinates, respectively. Computed torque with PD control is applied to maintain the quasi-static motion, while an optimal LQR method is used for vibration control. Typical simulation results are presented for the planar case.