小推力轨道保持方法

对小推力轨道保持方法进行了研究。用快、慢变量控制器分别控制轨道要素的快慢变量,基于推导的经典轨道要素与2个推力方向角和最佳变轨位置的关系,给出了最优推力方向角的解析表达式。用Lyapunov反馈控制实现卫星轨道机动的轨道转移,并引入相位调整,实现了卫星的站位保持。仿真结果表明:基于Lyapunov的反馈控制可实现小推力轨道的转移和保持。     

Design of optimal earth pole-sitter transfers using low-thrust propulsion

Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which solar electric propulsion is used to transfer the spacecraft to the pole-sitter orbit. The objective is to minimize the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits manifold-like trajectories that wind onto the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral, which provides further mass savings, but at the cost of an increased time of flight.     

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。     

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.     

Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

General solution for the optimal trajectory of an AFE-type spacecraft

The aeroassisted flight experiment (AFE) refers to an experimental spacecraft to be launched and then recovered by the Space Shuttle. It simulates a transfer from a geosynchronous Earth orbit (GEO) to a low Earth orbit (LEO). In this paper, with reference to an AFE-type spacecraft, an actual GEO-to-LEO transfer is considered under the following assumptions: the GEO and LEO orbital planes are identical; both the initial and final orbits are circular; the initial phase angle is given, while the final phase angle is free. The aeroassisted orbital transfer trajectory involves three branches: a preatmospheric branch, GEO-to-entry; an atmospheric branch, entry-to-exit; a post-atmospheric branch, exit-to-LEO. The optimal trajectory is determined by minimizing the total characteristic velocity. The optimization is performed with respect to the velocity impulses at GEO, LEO, and the time history of the angle of bank during the atmospheric pass. It is assumed that the entry path inclination is free and that the angle of attack is constant, = 17.0 deg. The sequential gradient-restoration algorithm is used to compute the optimal trajectory and it is shown that the best atmospheric pass is to be performed with constant angle of bank. The resulting optimal trajectory constitutes an ideal nominal trajectory for the generation of guidance trajectories for two reasons: the fact that the low value of the characteristic velocity is accompanied by relatively low values of the peak heating rate and the peak dynamic pressure; and the simplicity of the control distribution, requiring constant angle of bank.     

Optimal impulse point-to-elliptical orbit transfers of a spacecraft

The paper deals with energetically optimal multi-impulse transfer of a spacecraft in the central Newtonian gravity field near a planet. At the initial state of the transfer the distance from the spacecraft to the center of attraction, its radial and transversal velocity projections are known. At the end of the transfer the spacecraft must be located in the elliptical orbit with the given area and energy constants. The distance from the spacecraft to the center of attraction is bounded above and below, the transfer time being unspecified. The initial orbit intersects the inner boundary of the given ring.All the optimal solutions have been obtained by analytical way. A number of new solutions has been found for the given problem in comparison with the case of the transfer from the orbit at the free initial point.Up to five impulses can be applied on the optimal trajectories. The numerical simulation of the problem is carried out. It shows that all obtained solutions give not only local but global optimal energetic input on the corresponding conditions.     

太阳帆日心定点悬浮转移轨道设计

研究了太阳帆航天器日心定点悬浮轨道(HFDO)的转移轨道设计问题,以球坐标形式建立了太阳帆的动力学模型,基于该模型给出在日心悬浮轨道基础上实现定点悬浮的条件,提出了一种实现日心定点悬浮的转移轨道设计方法。首先,确定定点悬浮的位置;然后,设计经过该位置的绕日极轨轨道;最后,实施轨道减速实现定点悬浮,并给出了解析形式的轨道控制律。结合太阳极地观测任务,设计了定点悬浮在太阳北极1AU处的太阳帆转移轨道。仿真结果表明:该轨道转移方案总耗时3.5年,太阳帆定点到黄北极距日心1AU处,此后只要保持太阳光垂直照射帆面,即可维持稳定的悬浮状态。     

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 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.     

一类椭圆轨道交会中的动力学方程研究

研究了一类追踪器和目标器轨道半长轴相差不大、轨道面外的距离相差不大的小偏心率椭圆交会的动力学问题.首先选择合适的圆轨道上的点建立参考系,推导出针对圆轨道参考系的无量纲化线性定常方程,并获得相应的相对状态;接着讨论该方程在小偏心椭圆轨道两冲量交会中的应用;最后进行数值仿真,验证动力学方程和制导策略,并与CW方程及制导策略的相关仿真进行比较.仿真结果表明本文给出的动力学方程的精度优于CW方程,能有效解决这类椭圆交会问题.     

Spacecraft formation flying: A review and new results on state feedback control

This paper presents a review of previous work within the field of spacecraft formation flying, including modeling approaches and controller design. In addition, five new approaches for tracking control of relative translational motion between two spacecraft in a leader–follower formation are derived. One PD controller with feedback linearisation is derived and shown to result in an exponentially stable equilibrium point of the closed loop system. Four nonlinear controllers are derived and proved by using Lyapunov theory and Matrosov's theorem to leave the closed loop system uniformly globally asymptotically stable. Results from the simulation of the system with the derived controllers are presented, and compared with respect to power consumption and tracking performance.     

基于转移时间约束的异面圆锥曲线变轨算法

在圆锥曲线转移轨道Lagrange方程的基础上,分析了双曲线和多圈飞行椭圆轨道的转移时间与半长轴的几何关系,以及椭圆转移问题的虚焦点位置对长程、短程轨道的约束.给出了一种与初始速度方向相关的转移角定义,以及一种基于Lagrange方程的圆锥曲线变轨计算方法,随后提出了一种以半长轴为迭代变量的变轨算法.通过异面椭圆和双曲线转移两个实例,验证了该算法与Vaughan算法具有相同结果,并具有明确的几何意义.     

一种挠性航天器的对偶四元数姿轨耦合控制方法

为解决复杂的挠性航天器的姿轨控制问题,对于挠性航天器的姿轨耦合动力学建模与控制展开研究。基于对偶四元数原理,推导给出一套挠性航天器的姿轨一体化动力学模型。此种模型能够紧凑描述航天器的轨道和姿态,且能够自动引入航天器平动、转动与挠性附件振动三者之间的关联耦合作用。基于此模型设计了一种自适应位置姿态跟踪控制器,该控制器能够在航天器质量特性参数未知的情况下,对其位置和姿态进行轨迹跟踪控制,并使位置和姿态误差收敛。该自适应控制器还可对航天器上挠性附件对系统的耦合作用进行估计,进而在控制输出中对其进行补偿,提高卫星控制系统的稳定性。通过仿真对控制律进行校验,结果表明该控制律对挠性航天器控制效果良好,具有一定的工程应用参考价值。     

编队飞行自主控制的自适应方法

自主的高精度相对控制是实现卫星编队任务的关键技术,自主性要求控制器尽可能只利用星载设备所能提供的测量信息以减少星间通信量,高精度要求控制器连续的消除干扰力、期望轨迹推演以及参考星轨道控制与机动所造成的跟踪误差,为此,本文推导了描述星间相对运动的完整动力学模型以及对期望轨迹的跟踪误差模型,基于Lyapunov方法设计了自适应控制器,并证明了此控制器可以保证闭环系统的最终跟踪误差小于指定的界。本文给出的控制器仅需要星间的相对位置和相对速度测量,不需要主星的轨道参数、轨道位置和轨道机动信息,从而具有较高的自主性。仿真结果表明本文给出的控制器可以完成对期望轨迹的跟踪。     

飞行器围绕小行星的轨道运动

分析了飞行器围绕小行星轨道运动的特点，介绍了所建立的表述这一问题的理论基础。采用三种不同方法从几个侧面揭示了这一问题的本质特征。给出了所完成的研究这一问题的进展、结果和相互联系，其中包括轨道摄动、共振运动和周期轨道运动。这一问题的核心和难点是轨道的稳定性问题。     

How we will go to Mars

This article studies the efficiency of ejecting waste generated by the life support system (LSS) of a manned spacecraft to reduce initial mass on low earth orbit. The spacecraft is used for a long-duration interplanetary mission and is equipped with either a chemical or a nuclear-thermal propulsion system. For this study we simulate an optimal control problem for a given spacecraft maneuver. An impulsive approximation of the optimal interplanetary spacecraft trajectory is assumed, which allows us to reduce the general optimal control problem to hierarchic structure of 'outer' and 'inner' subproblems. This structure is analyzed using the Pontryagin's Maximum principle. Numerical results, illustrating the efficiency of waste ejection are shown for typical Earth-Mars transfer trajectories. This results confirm in theory that using a waste ejection system makes an early manned Mars mission possible without having to design and build new, advanced biological LSS.     

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.     

组合体与飞船联合轨道维持

通过组合体与飞船联合轨道维持解决了组合体和飞船轨道多特征参数的控制问题。建立了升交点经度、轨道高度和偏心率的控制方程以及基于时间关联特性的升交点赤经和制动点高度耦合控制方程和偏心率保持的双冲量耦合控制方程。结合组合体与飞船的飞行特点,制定了组合体轨道维持实现升交点赤经和轨道偏心率以及飞船轨道维持实现制动点高度的联合控制策略。耦合控制方程使得组合体和飞船轨道维持的控制量分配合理,融合了各次控制之间存在的耦合影响,设计了联合轨道维持策略迭代计算流程。基于神舟九号交会对接飞行过程,通过多组仿真算例校验了组合体与飞船轨道多特征参数的联合优化控制,具有较好的工程应用价值。