木星探测器轨道计算中的动力学

针对木星探测任务中轨道计算所面临的轨道动力学问题进行研究。首先,对木星探测轨道计算中涉及的时空参考系进行概述,比较了木星动力学时(TDJ)与质心动力学时(TDB)的差异;其次,对木星的定向参数模型及转换关系进行描述,给出了木星天球参考系与固联参考系的转换关系;再次,对木星探测器定轨计算中所需考虑的动力学模型进行讨论,提供了各类摄动加速度计算所需的公式;最后,对木星探测器JUNO的星历数据进行动力学拟合,检验了动力学模型的正确性。     

定时定点月面着陆全程轨道控制设计

针对定时定点月面着陆的目标要求,提出了全程轨道控制设计方法。进行了包括地月转移、近月制动、环月降轨和动力下降的全程轨道控制的分段设计和联合规划,实现在入轨轨道偏差条件下的定时定点月面着陆。分别构建了中途修正、近月制动、环月降轨三段轨道控制的规划变量和目标参数;根据轨道倾角建立了动力下降点与着陆点的匹配转换关系。设计了中途修正、近月制动、环月降轨、动力下降的全程轨道控制策略的联合规划。建立了着陆位置偏差与轨道倾角偏差、着陆时间偏差与轨道半长轴偏差的修正关系,修正设计了中途修正目标倾角和近月制动目标半长轴。仿真算例表明,在入轨偏差轨道条件下,保证了中途修正后的飞行轨道与标称轨道基本一致,实现了与标称状态基本一致的定时定点月面着陆。可应用于月球着陆、月球采样返回以及载人登月等实施月面定时定点着陆任务的轨道设计和控制实施。     

极坐标系连续常值推力机动分析

连续常值推力是空间飞行常用的轨道机动方式,在空间交会与星际航行使命中具有重要的应用价值。其中,小推力适合于地球轨道航天器交会机动,而切向或周向推力以及较大的正径向推力可用于脱离地球引力场的逃逸飞行,执行星际交会使命。应用常推力作用下的极坐标系质心运动方程,对机动推力的量值没有限制;在航天器交会应用中,对相对距离也无要求。这种方法可直接获得向径与速度等轨道参数随时间或极角（绕地心的转动角）的变化,便于分析轨道转移与逃逸运动,有助于飞行使命与运动轨迹的设计。特别是,若机动转移的初轨为圆轨道,在推力较小、飞行时间不长的情况下,应用无量纲形式运动方程,可获得具有工程应用价值的近似解。文章给出一些有关的结果与应用案例。     

TETHERED SATELLITE SYSTEM ANALYSIS (1) — TWO-DIMENSIONAL CASE AND REGULAR DYNAMICS

The study on tethered satellite system (TSS) in two-dimensional in-planar motion is restricted in that the tether is assumed to be massless. The equations of motion are given in a spherical coordinate system to describe the magnitude (tether length) and direction angle of the position vector between the satellites. A length rate control algorithm is adopted, and the controlled motion of the directional angle by the algorithm will have a stable equilibrium state. The equilibrium state is a fixed point if the orbit of the base-satellite is circular, and a limit cycle if the orbit is elliptic. The value and stability of the equilibrium state are determined by the parameters of the control algorithm, and the bifurcation analysis is also given. Two typical TSS missions have been simulated.     

一种空间推扫型光学成像系统几何映射方法

卫星光学遥感器在轨成像会受到颤振的影响,因此图像品质受姿态稳定度的影响很大,而高分辨率图像受到平台误差的影响更加明显。通过研究空间相机的几何模型,提出了一种从地球坐标系到空间光学遥感器坐标系之间的转换关系;分析了在轨卫星的姿态误差和运动源,并在几何模型中加入了内外方位元素特征;然后进行了空间TDICCD相机的成像仿真实验。为了在像面上模拟颤振,分别进行不同模态的颤振仿真,并且对视线范围内多模态综合作用进行仿真。仿真实验是基于三个轴系方向的,并且计算了TDICCD仿真图像的几何畸变量,模型中几何畸变量的测量尺度达到亚像素级,结果有利于指导卫星平台和遥感器的参数设计。     

Near-optimal geostationary transfer maneuvers with cooperative en-route inspection using hybrid optimal control

This research investigates the performance of bi-level hybrid optimal control algorithms in the solution of minimum delta-velocity geostationary transfer maneuvers with cooperative en-route inspection. The maneuvers, introduced here for the first time, are designed to populate a geostationary constellation of space situational awareness satellites while providing additional characterization of objects in lower-altitude orbit regimes. The maneuvering satellite, called the chaser, performs a transfer from low Earth orbit to geostationary orbit, during which it performs an inspection of one of several orbiting targets in conjunction with a ground site for the duration of the target?s line-of-site contact with that site. A three-target scenario is used to test the performance of multiple bi-level hybrid optimal control algorithms. A bi-level hybrid algorithm is then utilized to solve fifteen-, and thirty-target scenarios and shown to have increasing benefit to complete enumeration as the number of targets is increased. Results indicate that the en-route inspection can be accomplished for a small increase in the delta-velocity required for a simple transfer to geostationary orbit given the same initial conditions.     

Optimization of low-thrust orbit transfers with constraints

Approximate numerical methods of optimization are presented for multi-orbit noncoplanar orbit transfers of low-thrust spacecraft. The linear representation of derivatives of boundary parameters is used in the vicinity of a reference trajectory with its discretization into small segments. For each segment a set of pseudo-impulses is introduced, representing possible directions of the thrust vector. In order to solve essentially nonlinear problems, the iterative process of upgrading the reference trajectory is used. At each iteration the linear programming problem of high dimensionality is solved, its boundary conditions being represented in the form of a linear matrix equation. Interval constraints are considered in the form of blocking the propulsion system operation on shadow segments of the orbit, as well as cycling constraints, and constraints on total duration of maneuvers at certain trajectory segments. The results of comparison with solutions obtained by other methods are presented together with examples illustrating the convergence of iterative processes. Optimizations of the trajectories for launching geosynchronous satellites to their orbits and of the trajectories of a noncoplanar transfer from low to high-elliptic Molniya orbit are considered under these constraints.     

北斗系统地固系自主定轨算法

为避免传统惯性系自主定轨算法中的多次坐标转换,针对地固系分布式自主定轨算法原理及其中的关键技术开展研究。给出在地固系中进行自主星历生成的总体框图,推导了地固系自主定轨算法的基本方程,提出一种新的以地固系位置速度为状态量的状态转移矩阵解析计算方法并分析其计算量,证明了地固系自主定轨算法可以进一步降低定轨算法复杂度,且无需上注地球定向参数进行坐标转换。使用仿真数据和真实在轨测量数据的测试结果表明,提出的地固系分布式自主定轨算法与传统算法定轨精度相当,说明了所提算法的可行性,验证了星载自主定轨原型软件的有效性。     

不同推力下的非合作空间目标轨道机动检测

针对非合作空间目标轨道机动检测问题,创新性地提出具备普适性的不同推力下的轨道机动检测算法与检测流程。首先给出不同推力作用下轨道机动动力学模型,在此基础上提出普适性轨道机动检测策略,包括：全模型地基与天基观测数据仿真策略,数据处理软件平台,脉冲推力、连续大推力与连续小推力轨道检测算法与流程,精度评估策略。该策略利用不同推力作用下的检测算法与流程,可以满足多数非合作目标轨道机动检测需求。结合地基与天基观测数据,仿真分析不同推力下的非合作目标轨道机动检测情况与轨道精度恢复情况,结果表明该策略能对轨道机动进行有效检测,为工程实际提供了有益借鉴。     

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.     

三轴稳定通信卫星在地球搜索模式下的陀螺标定

本文介绍三轴稳定通信卫星在转移轨道远地点点火前，在地球搜索模式下的陀螺标定方法和计算公式。此种陀螺标定需进行两次姿态机动，利用太阳敏感器和速率积分陀螺遥测数据标定陀螺的常值漂移。     

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.     

近地轨道卫星的地影预报算法

针对传统地影预报算法计算量大,不适合星载计算机进行地影时刻自主预报的问题,提出一种地影预报星上算法。通过构造降维坐标系将卫星进出地影过程转换为“星-地-日”平面内的几何问题;基于常数变易法推导出阴影条件的隐式解析公式,其方程系数可由实时轨道参数确定。为简化计算,将星上算法设计为双层结构：构造迭代算法,依据实时轨道参数可精确预报卫星在每个节点上的地影时刻;而在任意两个节点之间采用解析算法进行近似预报。仿真结果表明,星上算法的预报精度高且计算量小,适合星载计算机进行地影时刻自主预报。     

嫦娥二号探测器轨道确定与支持

针对嫦娥二号探测器直接进入地月转移轨道、距月面100km高度捕获月球、完成既定任务后飞往日地第二拉格朗日平动点等飞行轨道方面的新特点,分析了定轨预报策略,利用事后精密轨道,全面评估了关键变轨点定轨预报和变轨后快速定轨的精度,其中,近月制动前3h定轨预报至近月点的位置误差为1km,速度误差为 0.3m/s 。利用不同月球引力场模型进行环月轨道精密定轨,根据实测数据残差分析和精密星历比对的结果,采用SGM100h引力场模型的定轨残差均方根最大。此外,针对嫦娥二号扩展任务,分析了不同测轨条件下的定轨精度,测量数据残差分析结果表明,在扩展任务中途修正前的定轨弧段内,测距、时延和时延率数据的残差分别为5m,5ns和1ps/s。     

Decentralized coordinated control for multiple spacecraft formation maneuvers

We investigate the decentralized coordinated control problem by looking into local information exchange among formation flying spacecraft regarding formation maneuvers. The nonlinear dynamics that describes the motion of formation flying spacecraft relative to a reference spacecraft is considered for the general case, in which the reference spacecraft is in an ideal elliptical orbit. With the novel use of consensus algorithms combined with behavior-based control, coordinated formation controllers are proposed for three schemes: (i) with full state feedback; (ii) without velocity measurements; (iii) and with external disturbances and parametric uncertainty. The three algorithms used in the schemes can achieve both formation maneuvering and formation keeping, as well as consider actuator saturation. Numerous simulations demonstrate the effectiveness of the proposed control schemes.     

卫星编队的多冲量轨道机动路径规划方法

基于多冲量轨道机动控制,研究应用微小推力发动机来实现卫星编队轨道机动控制的方法。首先简单介绍轨道机动控制的多冲量次优解的求解方法,并把此方法的改进算法应用于卫星编队的整体轨道机动控制;为降低单次冲量值,应用小推力发动机实现轨道机动,提出了卫星编队多冲量轨道机动的路径规划方法,这种方法把一个多冲量轨道机动过程分成多个来实现;最后,数值仿真结果表明:该方法简便、实用,可以解决单次冲量值过大而不易实现的问题,同时对于轨道摄动因素的影响具有鲁棒性。     

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。     

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.     

Geostationary station acquisition maneuvers for the “CS” spin-stabilized communication satellite

Attitude reorientation maneuvers were conducted three times on the transfer orbit to obtain the apogee kick motor firing attitude of the Medium Capacity Geostationary Communication Satellite for Experimental Purposes (CS) on the third apogee. After two attitude and five orbit maneuvers on the drift orbit, the CS attained geostationary orbit with station keeping accuracy of ±0.1° seven days after launch.     

Optimal control of a spinning double-pyramid Earth-pointing tethered formation

The dynamics and control of a tethered satellite formation for Earth-pointing observation missions is considered. For most practical applications in Earth orbit, a tether formation must be spinning in order to maintain tension in the tethers. It is possible to obtain periodic spinning solutions for a triangular formation whose initial conditions are close to the orbit normal. However, these solutions contain significant deviations of the satellites on a sphere relative to the desired Earth-pointing configuration. To maintain a plane of satellites spinning normal to the orbit plane, it is necessary to utilize “anchors”. Such a configuration resembles a double-pyramid. In this paper, control of a double-pyramid tethered formation is studied. The equations of motion are derived in a floating orbital coordinate system for the general case of an elliptic reference orbit. The motion of the satellites is derived assuming inelastic tethers that can vary in length in a controlled manner. Cartesian coordinates in a rotating reference frame attached to the desired spin frame provide a simple means of expressing the equations of motion, together with a set of constraint equations for the tether tensions. Periodic optimal control theory is applied to the system to determine sets of controlled periodic trajectories by varying the lengths of all interconnecting tethers (nine in total), as well as retrieval and simple reconfiguration trajectories. A modal analysis of the system is also performed using a lumped mass representation of the tethers.