Periodic attitude motions along planar orbits in the elliptic restricted three-body problem

A way to improve the accuracy of the three-body problem model is taking into account the eccentricity of primary attractors. Elliptic Restricted Three-Body Problem (ER3BP) is a model for studying spacecraft trajectory within the three-body problem such that the orbital eccentricity of primaries is reflected in it. As the principal cause of perturbation in the employed dynamical model, the primaries eccentricity changes the structure of orbits compared to the ideal Circular Restricted Three-Body Problem (CR3BP). It also changes the attitude behavior of a spacecraft revolving along periodic orbits in this regime. In this paper, the coupled orbit-attitude dynamics of a spacecraft in the ER3BP are exploited to find precise periodic solutions as the spacecraft is considered to be in planar orbits around Lagrangian points and Distant Retrograde Orbits (DRO). Periodic solutions are repetitious behaviors in which spacecraft whole dynamics are repeated periodically, these periodic behaviors are the main interest of this study because they are beneficial for future mission designs and allow delineation of the system’s governing dynamics. Previous studies laid the foundation for spacecraft stability analysis or studying pitch motion of spacecraft in the ER3BP regime. While in this paper, at first, initial guesses for correction algorithms were derived through verified search methods, then correction algorithms were used to refine calculated orbit-attitude periodic behaviors. Periodic orbits and full periodic solutions are portrayed and compared to previous studies and simpler models. Natural periodic solutions are valuable information eventuate in the longer functional lifetime of spacecraft. Since the problem assumption considered in this paper is much closer to real mission conditions, these results may be the means to use natural bounded motions in the actual operational environment.     

Adaptive sliding mode control of spacecraft attitude-orbit dynamics on SE(3)

In this paper, to solve the problem of parameters uncertainty in spacecraft tracking control, an adaptive controller based on sliding mode is proposed for the relative spacecraft attitude-orbit dynamics on the Lie group SE(3). The dynamic equations of relative attitude orbit error for two spacecraft are established in the framework of Lie group SE(3). Considering the uncertainty of spacecraft parameters, a formal decomposition of known and unknown parameters, the state variables and control variables is firstly made in the original system. An online estimator is designed to evaluate the unknown parameters. A sliding mode controller is developed to actuate the spacecraft to track the target spacecraft. Then a Lyapunov function of tracking error and parameters estimated error is designed to prove the stability of the closed-loop system. Finally, the simulation results and analysis are presented to verify the effectiveness and feasibility of the proposed method.     

常值径向推力下的飞行器运动轨迹

研究了初始停泊轨道为椭圆时,空间飞行器在常值径向推力下运动的有界性和周期性.首先建立了飞行器运动的动力学方程,并通过能量积分和角动量积分进行了简化.然后将有界性的研究转化为一个一元三次不等式的求解,并在此基础上针对不同的初始真近点角分别进行了研究,得到了运动的边界和有界性条件.接下来利用椭圆积分研究了运动的周期性,分别研究了径向运动、极角转动以及整体运动的周期性.最后用数值算法得到了运动的周期轨道.     

End-to-end trajectory design for a solar-sail-only pole-sitter at Venus,Earth, and Mars

The concept of a pole-sitter has been under investigation for many years, showing the capability of a low-thrust propulsion system to maintain a spacecraft at a static position along a planet’s polar axis. From such a position, the spacecraft has a view of the planet’s polar regions equivalent to that of the low- and mid-latitudes from geostationary orbit. Previous work has hinted at the existence of pole-sitters that would only require a solar sail to provide the necessary propulsive thrust if a slight deviation from a position exactly along the polar axis is allowed, without compromising on the continuous view of the planet’s polar region (a so-called quasi-pole-sitter). This paper conducts a further in-depth analysis of these high-potential solar-sail-only quasi-pole-sitters and presents a full end-to-end trajectory design: from launch and transfer to orbit design and orbit control. The results are the next steppingstone towards strengthening the feasibility and utility of these orbits for continuous planetary polar observation.     

遗传算法在星座多星接近轨道优化中的应用

以三颗非共轨的Walker星座卫星为研究对象, 对航天器无需变轨与其接近的可能性进行研究. 将Lambert方法得到的航天器轨道作为初始轨道, 利用遗传算法对初始轨道进行优化. 对初始轨道在参考时刻位置和速度的改变量进行编码,形成对应的种群. 以航天器与星座卫星之间的最近距离为适应度函数, 通过种群的繁殖得到优化结果. 结合仿真算例, 分析了最小二乘算法和遗传算法在轨道优化中的优劣以及接近过程中轨道摄动的影响. 结果表明, 遗传算法适用于所提出的轨道改进问题. 研究结果可为单航天器无需变轨对星座多星接近问题提供理论依据.      

一种短航程再入解析预测校正制导方法

针对载人探月飞船高速再入返回问题,提出了一种短航程低过载的再入解析预测校正制导方法。引入大升阻比航天器滑翔式再入的概念,通过设定再入过程中滑翔段轨迹形式,利用轨迹参数描述滑翔段轨迹,推导出预测航程的解析公式。为使终端误差满足要求,通过试位法校正轨迹参数,并换算得到倾侧角制导指令。在偏差条件下进行仿真,实现了飞船2100km任务航程下400~450s内以低于6.5g₀的过载再入,结果表明,所提制导方法具有较高的精度和较强的鲁棒性,为载人探月飞船应急快速返回提供了参考思路。      

显示多体动力学方程自动编制技术

为高效得到复杂柔性多体航天器的动力学方程解析表达式,研究了系统动力学方程自动编制技术。首先,基于Kane方法推导了构型简单的链状多体系统动力学显式方程;然后,根据方程中各项物理意义和分布规律,开发了适用于树状构型多体航天器的解析动力学方程输出程序,并运用Latex软件对输出文本进行二次编译,增强输出复杂数学公式的可读性。所得方法极大地简化了对此类航天器的建模工作。     

Attitude stability and periodic attitudes of rigid spacecrafts on the stationary orbits around asteroid 216 Kleopatra

In this work, equilibrium attitude configurations, attitude stability and periodic attitude families are investigated for rigid spacecrafts moving on stationary orbits around asteroid 216 Kleopatra. The polyhedral approach is adopted to formulate the equations of rotational motion. In this dynamical model, six equilibrium attitude configurations with non-zero Euler angles are identified for a spacecraft moving on each stationary orbit. Then the linearized equations of attitude motion at equilibrium attitudes are derived. Based on the linear system, the necessary conditions of stability of equilibrium attitudes are provided, and stability domains on the spacecraft’s characteristic plane are obtained. It is found that the stability domains are distributed in the first and third quadrants of the characteristic plane and the stability domain in the third quadrant is separated into two regions by an unstable belt. Subsequently, we present the linear solution around a stable equilibrium attitude point, indicating that there are three types of elemental periodic attitudes. By means of numerical approaches, three fundamental families of periodic solutions are determined in the full attitude model.     

Spacecraft fuel-optimal and balancing maneuvers for a class of formation reconfiguration problems

This paper presents fuel optimal and balancing methodologies for reconfiguring multiple spacecraft in formation subject to a Newtonian gravity field. For a kind of continuous-thrust propulsion system, a fuel-optimal control problem is formulated to minimize the integral squared control subject to the linearized Hill or Clohessy–Wiltshire dynamics of relative motion with respect to a circular reference orbit. Palmer’s analytical solution for general reconfiguration is adapted to maneuvers between projected circular orbits, resulting in the optimal fuel consumption index as a function of configuration parameters such as orbit radius, phase angle, and transfer time. Parametric analyses reveal unique characteristics of individual fuel optimality and gross fuel consumption: for an arbitrary selection of initial/terminal orbit radii, (i) there exist special transfer times such that individual fuel consumption is optimally uniform for all phase angles, and (ii) the total fuel expenditure for a group of three or more spacecraft is invariant for the relatively same configuration with respect to the departure phase. These results serve to effectively design fuel balancing strategies for formation reconfiguration of multiple spacecraft.     

电磁航天器编队位置跟踪自适应协同控制

通过引入一致性理论针对电磁航天器编队相对位置协同控制问题设计了自适应协同控制器。分析了电磁航天器编队的基本原理,建立了电磁航天器编队相对运动精确的非线性动力学方程。基于电磁力远场计算模型的不确定性,对相对运动动力学模型进行了修正。在电磁力计算模型不确定和航天器间存在通信时延的条件下,对位置跟踪控制的目标设计了自适应协同控制器。考虑到电磁航天器磁矩产生能力的不同,给出了通过优化进行磁矩分配的方案。通过仿真表明:所设计的自适应协同控制器不仅实现了对期望轨迹的准确跟踪,而且相比人工势函数法,暂态维持编队构型的能力提高了4.9倍,并且所给出的磁矩分配方案实现了磁矩的合理分配。     

Surface shape control of integrated paraboloid space reflector consisting of sub-reflectors exploiting modulated solar pressure

Reflectors are very critical space elements and can be used not only as solar collectors/reflectors, telecommunication radio antennas and telescopes but also for dual-usage such as solar sails and solar concentrators to probe and sublimate materials from asteroids when actively controlling the surface shape. In this paper, the surface shape of a slack reflector with negligible elastic deformations will be controlled to be a paraboloid by actively modulating the solar radiation pressure (SRP) force using reflectivity control devices (RCDs) across the reflector. Nonlinear static equilibrium equations for an arbitrary infinitesimal within the reflector along the radial, circumferential and transverse directions are established considering the external modulated SRP force and internal tensions respectively. The coupled radial stress differential governing equation and reflectivity algebraic equation are obtained for the paraboloid reflector by the help of the formulation of an inverse problem based on equilibrium equations previously established. Some analytical and numerical analysis for reflectors with ideal and non-perfect SRP force models are performed respectively. The conclusions concerning about how to control the reflector’s surface shape successfully using allowed reflectivity, resulting in reasonable stress range, moreover, how to get the feasible solutions influenced by the reflector’s size parameters, are all based on the presented analytical and numerical analysis.     

航天器相对运动的两点边界值问题解析解

针对无摄椭圆轨道,推导了表示真实相对位置速度的状态转移矩阵,进而推导出了相对运动两点边界值问题的一阶解析解。所得结果不仅可指定转移时间、还可在时间范围内进行全局的燃料优化或在时间和燃料两者间折中;对于周期和非周期的相对运动均适用。仿真结果表明此解的归一化精度达到10^－6。进一步的仿真发现相对转移过程的燃料消耗会随目标轨道偏心率的增加而增加;随长半轴的增加而减少;随初始真近点角的增加呈现周期性变化;随着转移时间增加,燃料消耗的总趋势是减少的。     

Necessary conditions for the optimality of singular arcs of spacecraft trajectories subject to multiple gravitational bodies

This document analyzes the optimality of intermediate thrust arcs (singular arcs) of spacecraft trajectories subject to multiple gravitational bodies. A series of necessary conditions for optimality are formally derived, including the generalized Legendre–Clebsch condition. As the order of singular optimality turns out to be two, an explicit formula for the singular optimal control is also presented. These analytical outcomes are validated by showing that they are identical to Lawden’s classical result if the equations of motion are reduced for a central gravity field. Practical utility is demonstrated by applying these analytical derivations to a candidate optimal trajectory near the Moon subject to solar and Earth perturbation. While the candidate optimal trajectory turns out to be bang-singular-bang, the intermediate thrust arc satisfies all the necessary conditions for optimality.     

Optimal guidance and collision avoidance for docking with the rotating target spacecraft

The guidance and control strategy for spacecraft rendezvous and docking are of vital importance, especially for a chaser spacecraft docking with a rotating target spacecraft. Approach guidance for docking maneuver in planar is studied in this paper. Approach maneuver includes two processes: optimal energy approach and the following flying-around approach. Flying-around approach method is presented to maintain a fixed relative distance and attitude for chaser spacecraft docking with target spacecraft. Due to the disadvantage of energy consumption and initial velocity condition, optimal energy guidance is presented and can be used for providing an initial state of flying-around approach process. The analytical expression of optimal energy guidance is obtained based on the Pontryagin minimum principle which can be used in real time. A couple of solar panels on the target spacecraft are considered as obstacles during proximity maneuvers, so secure docking region is discussed. A two-phase optimal guidance method is adopted for collision avoidance with solar panels. Simulation demonstrates that the closed-loop optimal energy guidance satisfies the ending docking constraints, avoids collision with time-varying rotating target, and provides the initial velocity conditions of flying-around approach maneuver. Flying-around approach maneuver can maintain fixed relative position and attitude for docking.     

PDE model-based boundary control of a spacecraft with double flexible appendages under prescribed performance

This paper investigates a boundary control scheme of a spacecraft with double flexible appendages under prescribed performance. The flexible spacecraft system comprises a rigid central hub and two flexible appendages regarded as continuum models, so that the motion of the system can be portrayed by using partial differential equations (PDEs). In this paper, only one control torque and two control forces are applied to guarantee the desired attitude angle of the spacecraft and simultaneously suppress the vibration of the two flexible appendages. Moreover, the angle tracking error of the spacecraft can be restricted in a small residual set under a minimum convergence rate by adopting the prescribed performance technique (PPT). The stability of the boundary control is analyzed by employing LaSalle’s invariance principle. Finally, the feasibility of the proposed controller is verified through numerical results.     

Robust fault-tolerant saturated control for spacecraft proximity operations with actuator saturation and faults

In this paper, the motion control problem of autonomous spacecraft rendezvous and docking with a tumbling target in the presence of unknown model parameters, external disturbances, actuator saturation and faults is investigated. Firstly, a nonlinear six degree-of-freedom dynamics model is established to describe the relative motion of the chaser spacecraft with respect to the tumbling target. Subsequently, a robust fault-tolerant saturated control strategy with no precise knowledge of model parameters and external disturbances is proposed by combining the sliding mode control technique with an adaptive methodology. Then, within the Lyapunov framework, it is proved that the designed robust fault-tolerant controller can guarantee the relative position and attitude errors converge into small regions containing the origin. Finally, numerical simulations are performed to demonstrate the effectiveness and robustness of the proposed control strategy.     

Optimal station-keeping near Earth–Moon collinear libration points using continuous and impulsive maneuvers

In this study the gravitational perturbations of the Sun and other planets are modeled on the dynamics near the Earth–Moon Lagrange points and optimal continuous and discrete station-keeping maneuvers are found to maintain spacecraft about these points. The most critical perturbation effect near the L₁ and L₂ Lagrange points of the Earth–Moon is the ellipticity of the Moon’s orbit and the Sun’s gravity, respectively. These perturbations deviate the spacecraft from its nominal orbit and have been modeled through a restricted five-body problem (R5BP) formulation compatible with circular restricted three-body problem (CR3BP). The continuous control or impulsive maneuvers can compensate the deviation and keep the spacecraft on the closed orbit about the Lagrange point. The continuous control has been computed using linear quadratic regulator (LQR) and is compared with nonlinear programming (NP). The multiple shooting (MS) has been used for the computation of impulsive maneuvers to keep the trajectory closed and subsequently an optimized MS (OMS) method and multiple impulses optimization (MIO) method have been introduced, which minimize the summation of multiple impulses. In these two methods the spacecraft is allowed to deviate from the nominal orbit; however, the spacecraft trajectory should close itself. In this manner, some closed or nearly closed trajectories around the Earth–Moon Lagrange points are found that need almost zero station-keeping maneuver.     

三维充液航天器的位置和姿态联合控制

考虑充液月球着陆器悬停避障阶段的控制问题,采用三维球摆作为液体晃动部分的等效模型.针对球摆与刚体耦合的三维动力学模型,给出动力学模型的矢量方程及各矢量在本体系的投影坐标,设计位置和姿态联合控制器.所设计的控制器可以稳定航天器刚体的位置和姿态,且只依赖刚体的位置和姿态,不依赖晃动角或者动力学方程,利于工程应用.利用LaSalle不变原理分析闭环系统的稳定性,给出期望姿态为竖直时系统渐近稳定的控制器参数选择依据.最后数值仿真验证控制方法的有效性.     

小天体着陆动力学参数不确定性影响分析

针对小天体不规则程度高、引力场复杂,且物理参数存在较高不确定性的问题,基于小天体着陆动力学方程线性化近似解析解,对各动力学参数不确定性的影响进行了分析。考虑动力学方程线性化带来的误差,引入线性化误差补偿校正方法,建立了探测器轨迹对动力学参数不确定性的敏感度方程。以小行星Eros 433为例,重点分析了目标小天体质量、自转角速度、引力势函数系数,以及探测器初始状态、推力加速度等动力学参数不确定性对探测器着陆轨迹的影响。数学仿真分析表明,针对本文选取的目标小天体,推力加速度扰动为主要影响因素,探测器初始状态的不确定性为次要影响因素,其他参数扰动的影响较小。