Differential drag spacecraft rendezvous using an adaptive Lyapunov control strategy

This paper introduces a novel Lyapunov-based adaptive control strategy for spacecraft maneuvers using atmospheric differential drag. The control forces required for rendezvous maneuvers at low Earth orbits can be generated by varying the aerodynamic drag affecting each spacecraft. This can be accomplished, for example, by rotating dedicated sets of drag panels. Thus, the relative spacecraft motion can be controlled without using any propellant since the motion of the panels can be powered by solar energy. A novel adaptive Lyapunov controller is designed, and a critical value for the relative drag acceleration that ensures Lyapunov stability is found. The critical value is used to adapt the Lyapunov controller, enhancing its performance. The method is validated using simulations. The results show that the Adaptive Lyapunov technique outperforms previous control strategies for differential drag based spacecraft maneuvering.     

Optimal trajectories for the aeroassisted flight experiment

This paper deals with the determination of optimal trajectories for the aeroassisted flight experiment (AFE). The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous Earth orbit and LEO denotes a low Earth orbit. Specifically, the AFE spacecraft is released from the Space Shuttle and is accelerated by means of a solid rocket motor toward Earth, so as to achieve atmospheric entry conditions identical with those of a spacecraft returning from GEO. During the atmospheric pass, the angle of attack is kept constant, and the angle of bank is controlled in such a way that the following conditions are satisfied: (a) the atmospheric velocity depletion is such that, after exiting, the AFE spacecraft first ascends to a specified apogee and then descends to a specified perigee; and (b) the exit orbital plane is identical with the entry orbital plane. The final maneuver, not analyzed here, includes the rendezvous with and the capture by the Space Shuttle. In this paper, the trajectories of an AFE spacecraft are analyzed in a 3D space, employing the full system of 6 ODEs describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted in such a way that requirements (a) and (b) are met, while simultaneously minimizing the total characteristic velocity, hence the propellant consumption required for orbital transfer. Two possible transfers are considered: indirect ascent (IA) to a 178 NM perigee via a 197 NM apogee; and direct ascent (DA) to a 178 NM apogee. For both transfers, two cases are investigated: (i) the bank angle is continuously variable; and (ii) the trajectory is divided into segments along which the bank angle is constant. For case (ii), the following subcases are studied; 2, 3, 4 and 5 segments; because the time duration of each segment is optimized, the above subcases involve 4, 6, 8 and 10 parameters, respectively. It is shown that the optimal trajectories of cases (i) and (ii) coalesce into a single trajectory: a two-subarc trajectory, with the bank angle constant in each subarc (bang-bang control). Specifically, the bank angle is near 180° in the atmospheric entry phase (positive lift projection phase) and is near 0° in the atmospheric exit phase (negative lift projection phase). It is also shown that, during the atmospheric pass, the peak values of the changes of the orbital inclination and the longitude of the ascending node are nearly zero; hence, the peak value of the wedge angle (angle between the instantaneous orbital plane and the initial orbital plane) is nearly zero. This means that the motion of the spacecraft is nearly planar in an inertial space.     

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.     

Motion of a descent capsule relative to its center of mass when deploying the orbital tether system

The spatial motion relative to the center of mass is considered for a capsule on an elastic tether, when it is unrolled from a spacecraft by a special program. The spacecraft is in a circular orbit and oriented relative to the local vertical, which is guaranteed by operation of its own stabilization system. Angular motion of the capsule relative to the tether direction is studied, and the main factors influencing the stability of this motion are analyzed. An approximate quasi-linear mathematical model of the capsule attitude motion is obtained, which allows one to estimate the influence of major disturbances of its motion. The results of numerical simulations are presented for characteristic cases of the capsule motion.     

Influence of disturbances on the angular motion of a spacecraft in the powered section of its descent

The motion of a variable-mass spacecraft is considered in the powered section of a descending trajectory. Approximate analytical solutions are obtained for the angles of spatial orientation of the spacecraft, which allows one to analyze the nutation motion and to develop recommendations on the spacecraft’s mass configuration, providing the smallest possible deviations of the longitudinal axis and thrust vector from specified directions. The errors of stabilization of the spacecraft’s longitudinal axis are calculated by means of numerical integration of complete models and using the obtained analytical solutions, the results being in good agreement.     

Informational approaches to angular motion control of spacecraft

Any information concepts may be used for motion control with respect to the center of masses of a reusable transport spacecraft (RTS). Using comparative analysis of the two concepts (the first one, based upon information about attitude parameters with respect to the inertial reference system and the second one, based upon parameters of angular motion with respect to wind-body coordinate system) for specific features of RTS dynamics and control at the stages of orbital flight, atmospheric flight under gas dynamic and aerodynamic control, and landing, paper demonstrates that information on angles of attack, slip and speed roll should be used for angular motion control at this stage of flight.     

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.     

Estimation of the Probability of Capture into a Resonance Mode of Motion for a Spacecraft during Its Descent in the Atmosphere

The estimation of the probability of capture into a resonance mode of motion is considered for a spacecraft with a small asymmetry during its entry into the atmosphere. It is assumed that the initial conditions of spacecraft motion are distributed uniformly in some sufficiently small domain. The problem is solved for the equations of spacecraft motion linear with respect to the angle of attack. An analytical estimate of the probability of the spacecraft capture into the resonance corresponding to an ascending branch of the velocity head is obtained. The emphasis in the analysis of the estimate is made on the effect of the spacecraft asymmetry type on the probability of capture. A comparison of the estimate with the results of numerical computation is carried out. A model problem concerning the construction of the domain of the spacecraft center of mass locations, most dangerous from the point of view of the realization of the stable resonant modes of motion, is solved.     

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

The problem of a rendezvous in the central Newtonian gravitational field is considered for a controlled spacecraft and an uncontrollable spacecraft moving along an elliptic Keplerian orbit. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. In the first variant of the equations of motion a quaternion variable characterizes the orientation of an instantaneous orbit of the spacecraft and the spacecraft location in the orbit, while in the second variant it characterizes the orientation of the plane of the spacecraft instantaneous orbit and the location of a generalized pericenter in the orbit. The quaternion variable used in the second variant of the equations of motion is a quaternion osculating element of the spacecraft orbit. The problem of a rendezvous of two spacecraft is formulated as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle.     

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

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

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。     

带空间机械臂的充液航天器姿态动力学研究

本文研究空间机械臂运动对充液航天器姿态的影响，讨论了利用机械臂调整充液航天器姿态问题、以及机械臂操作与航天器姿态稳定的协调问题。研究表明：影响充液航天器姿态的因素除了机械臂运动的路径，还有机械臂运动的时间、机械臂转角的变化规律、液体的粘性、质量和惯性张量等。其中机械臂运动时间的影响比较明显，而且机械臂运动得越慢对航天器姿态的影响越大。合理地选择机械臂操作时间和机械臂转角变化规律，可以实现机械臂操作     

Some issues of time-optimal control over a spacecraft programmed turn

The problem of optimal turn of a spacecraft from an arbitrary initial position to a final specified angular position in a minimum time is considered and solved. A case is investigated, when the constraint on spacecraft’s angular momentum during the turn is essential. Based on the quaternion method a solution to the posed problem has been found, and an optimal control program is constructed taking the constraints on controlling moment into account. The optimal control is found in the class of regular motions. A condition (calculation expression) is presented for determining the moment to begin braking with the use of measurements of current motion parameters, which considerably improves the accuracy of putting the spacecraft into a preset position. For a dynamically symmetrical spacecraft the solution to the problem of optimal control by the spacecraft spatial turn is presented in analytical form (expressions in elementary functions). An example of mathematical modeling of the spacecraft motion dynamics under optimal control over reorientation is given.     

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.     

微重力环境中重力梯度加速度引起的流体晃动运动

本文研究了关于旋转轴在贮箱的非对称轴上且远离贮箱的几何中心情况下，流体在微重力环境中由重力梯度加速度诱发的晃动特性，建立了问题的数学模型并对模型进行了数值模拟。以高级Ｘ射线天文物理实验卫星（简称ＡＸＡＦ─Ｓ）作为研究对象，获得了由旋转运动引起的重力梯度加速度的数学表达式。晃动问题的数值计算以与卫星固连的非惯性坐标系为基础，目的是寻求一种较为易处理且适合于流体力学方程的边界和初始条件。通过数值计算获得了流体作用于卫星贮箱上的力和力矩。     

共面快速受控绕飞轨迹设计与控制

绕飞运动在航天器在轨服务与在轨支援、辅助航天员舱外活动、航天器编队飞行、空间交会对接等空间活动中具有重要应用。分析了快速受控绕飞的可行性和主要过程，建立了适用于目标航天器运行在圆轨道上的共面快速绕飞和进入绕飞与退出绕飞的轨迹设计模型，采用多速度脉冲控制方法和等角度，等时间控制方式对绕飞轨迹进行控制。仿真计算结果表明所提出的快速受控绕飞轨迹设计模型和控制方法可以实现对圆轨道目标航天器的共面快速受控绕飞。     

POES companion: Objectives, methodology, and benefits

POES Companion is a small satellite that would carry an atmospheric sounding instrument identical to one on a nearby operational polar orbiting spacecraft. The spacing between the two satellites would be controlled and variable. The mission is designed to establish the upper bound on the distance between the two satellites within which data from the instruments are statistically equivalent, and further would demonstrate that two neighboring spacecraft can be managed safely and efficiently. POES Companion will validate new Companion options outlined in this paper that could substantially reduce costs attributable to satellite-based atmospheric sounders for both operational and research programs.     

航天器大气进入过程制导方法综述

研究承担进入任务的升阻比小于0.5的小升阻比航天器,基于对该类航天器大气进入制导方法的调研,分别以地球大气再入和火星大气进入过程为例,分析了进入制导需满足的各种约束和待解决的技术难题,并对大气进入制导控制方法的研究现状进行了阐述,对不同方法的优缺点进行了对比研究分析和归纳总结,对未来研究发展方向进行了展望。     

航天员舱外相对航天器运动轨迹摄动研究

用轨道根数描述载人航天器运动,在其轨道坐标系(LVLH)中,建立了含地球J2项引力和大气阻力摄动加速度的航天员质心相对航天器的运动模型。在参考轨道存在小偏心率时,对基于圆参考轨道假设推导的航天器编队飞行的线性时变系统状态矩阵进行了修正。仿真结果表明:对偏心率为0.002的航天器轨道,修正后模型所得航天员相对轨迹摄动量在离舱300 s后达到0.8%,是修正前模型的5倍,但计算量增加不超过5%,更适于航天员舱外飞行和近距离编队飞行建模。     

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。