Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

The Lorentz force acting on an electrostatically charged spacecraft as it moves through the planetary magnetic field could be utilized as propellantless electromagnetic propulsion for orbital maneuvering, such as spacecraft formation establishment and formation reconfiguration. By assuming that the Earth’s magnetic field could be modeled as a tilted dipole located at the center of Earth that corotates with Earth, a dynamical model that describes the relative orbital motion of Lorentz spacecraft is developed. Based on the proposed dynamical model, the energy-optimal open-loop trajectories of control inputs, namely, the required specific charges of Lorentz spacecraft, for Lorentz-propelled spacecraft formation establishment or reconfiguration problems with both fixed and free final conditions constraints are derived via Gauss pseudospectral method. The effect of the magnetic dipole tilt angle on the optimal control inputs and the relative transfer trajectories for formation establishment or reconfiguration is also investigated by comparisons with the results derived from a nontilted dipole model. Furthermore, a closed-loop integral sliding mode controller is designed to guarantee the trajectory tracking in the presence of external disturbances and modeling errors. The stability of the closed-loop system is proved by a Lyapunov-based approach. Numerical simulations are presented to verify the validity of the proposed open-loop control methods and demonstrate the performance of the closed-loop controller. Also, the results indicate the dipole tilt angle should be considered when designing control strategies for Lorentz-propelled spacecraft formation establishment or reconfiguration.     

Optimal spacecraft rendezvous using the combination of aerodynamic force and Lorentz force

This paper presents a propellantless spacecraft rendezvous method by using the optimal combination of aerodynamic force and Lorentz force. Aerodynamic force is provided by the rotations of the plates attached to the spacecraft, and Lorentz force is achieved by modulating spacecraft's electrostatic charge. Considering the limitation of the charging level of the spacecraft and physical constraints of the plates system, an optimal open-loop rendezvous trajectory is designed, which aims to minimize the energy consumed to actuate the hybrid system. The rotation rates of the plates and the electrostatic charge are constrained in the optimization problem, which is solved via the Gauss pseudospectral method. To track the open-loop trajectory in the presence of external perturbations, a novel adaptive nonsingular terminal sliding mode controller is designed. The stability of the closed-loop system is proved by the Lyapunov-based method. Several numerical examples are conducted to verify the validity of both the open-loop and closed-loop control strategy.     

基于混杂系统的空间飞行器悬停控制

基于空间飞行器的轨道动力学原理,利用混杂系统模型研究了悬停轨道问题,建立了悬停轨道的混杂系统模型;借此模型,针对目标星轨道为椭圆的情况,提出了等距离悬停轨道控制和椭圆悬停轨道控制两种方案,分别推导出在这两种方案下对悬停星所施加的控制力。数值仿真结果表明,分别对悬停星施加相应的控制力,能够实现对目标星的悬停。     

Formation flying for magnetic sails around artificial equilibrium points

This paper investigates the problem of magnetic sail-based spacecraft formation control around the artificial equilibrium points (AEPs), which can eliminate the requirement of the propellant. The thrusts are achieved by utilizing the interaction between the solar wind and the artificial magnetosphere generated by superconducting current coil onboard. The circular restricted three-body problem (CRTBP) of magnetic sail is discussed including the allowed regions and linear stability of AEPs, the locations of collinear AEPs and the possibility of existence of periodic orbits around the collinear AEPs. Next, the dynamical models of magnetic sail formation around the collinear AEPs are established. A novel fast fixed-time nonsingular terminal sliding mode controller (FFNTSM) based on fixed-time disturbance observer (FTDO) is developed to account for external disturbances. Several numerical simulations are conducted to substantiate that spacecraft formation can be precisely controlled by the proposed propellantless propulsion method in the presence of external disturbances.     

Methods of spacecraft impulsive relative hovering and trajectory safety analysis

Based on the analytical solutions of T-H equations and its state transition matrix form,the open-loop control method of spacecraft impulsive relative hovering was studied,which is promising for practical engineering use.The true anomaly intervals of the hovering impulse were optimized by the nonlinear mathematical programming.Based on the calculation of collision probability,the method of safety analysis and risk management was proposed.The numerical simulations show that the introduced relative hovering method can be used for circular and elliptical reference orbits hovering.Furthermore,the local optimal solution can be obtained by applying the true anomaly intervals optimization method.The maximum collision probability and the minimum relative distance nearly appear at the same time.And,the smaller the relative distance is,the larger the collision probability.     

相对空间目标任意位置悬停闭环控制方法研究

研究了相对空间目标任意位置悬停的控制方法,针对现有的开环控制方法对外部干扰和初始误差敏感的问题,基于Hill方程提出了悬停闭环控制方法。进行了仿真计算,证明了方法的有效性。仿真结果表明:该文方法的燃料消耗与开环控制接近而控制性能更好,可以在具有初始速度误差的情况下实现相对于空间目标的任意位置悬停。     

Formation flying reconfiguration manoeuvres via environmental forces in highly elliptical orbits

A study on reconfiguration manoevres applied to a tetrahedral formation in highly elliptical orbits is proposed, by using a propellantless solution. The manoeuvring strategy consists in exploiting certain environmental forces, specifically those provided by solar radiation pressure and atmospheric drag, by actively controlling the satellites’ attitudes. Through inverse dynamics particle swarm optimization the optimal attitudes required for the manoeuvres are evaluated, whereas the configuration’s evolution is simulated by a high-fidelity orbital simulator. The goal of the reconfiguration problem is to find an optimal control in order for the four spacecraft to reach a desired configuration in a specified portion of orbit, where the desired configuration is evaluated by a shape and size geometric parameter. By increasing the manoeuvring time and the satellites’ area to mass ratio, all the case studies considered are successfully verified.     

Feasibility analysis of LEO and GEO large space debris de/re-orbiting taking into account launch mass of spacecraft-collector and its configuration layout

Analysis of the efficiency of two basic strategies for de/re-orbiting large space debris objects to disposal orbits (DO) is given. Large objects in LEO are classified into groups with similar orbital inclinations and comprise primarily last stages of launch vehicles, in GEO vicinity the paper studies upper stages. Under the first de/re-orbiting variant, it is assumed a spacecraft-collector is equipped with several thruster de/re-orbiting kits (TDKs); one of them can be fixed on an object and is capable of de/re-orbiting an object to a DO independently of the collector. In the second variant, a collector operates as a space tug: transfers objects to a DO and then returns to the next objects in line. The authors study possible configuration layouts of collectors in LEO and near GEO. The available analogous projects are analyzed. The efficiency of both de/re-orbiting variants can be properly compared using the estimations of collector's dry mass and having at one's disposal the parameters of the maneuvers required for transfers between all objects in the group. As reasonable criteria of effectiveness, one can consider (separately or jointly) the launch mass of an equipped collector, its ΔV budget, and the required number of such active spacecraft. Two de/re-orbiting variants are compared in terms of these criteria via mass-energy diagrams constructed for each group of objects in both altitude regions. Analysis of these diagrams shows that low Earth orbits can be more efficiently cleaned under the first de-orbiting variant by using a two-stage space system consisting of an active spacecraft carrying TDKs. For GEO, it is expedient to choose the second re-orbiting variant using a single-stage spacecraft. Our analysis shows that LEO cleaning is an order of magnitude more expensive than that for GEO, hence the problem of LEO population should be given increased attention.     

椭圆轨道卫星空间任意位置悬停的方法

对任务星施加持续的控制加速度,使其在飞行过程中相对于目标卫星的空间位置保持不变,即实现任意位置悬停飞行。通过对任务星与目标星的相对运行分析和重力差异补偿分析,给出了在飞行过程中任务星相对于运行在椭圆轨道上的目标星实现任意位置悬停所需的径向、切向和法向控制加速度公式。最后对典型悬停飞行过程进行了动力学仿真,并对不同悬停飞行任务的能量消耗进行了对比分析,表明在一段时间内对任务星进行轨道悬停是可行的。     

High precision dynamic model and control considering J2 perturbation for spacecraft hovering in low orbit

For spacecraft hovering in low orbit, a high precision spacecraft relative dynamics model without any simplification and considering J₂ perturbation is established in this paper. Using the derived model, open-loop control and closed-loop control are proposed respectively. Gauss's variation equations and the coordinate transformation method are combined to deal with the relative J₂ perturbation between the two spacecraft. The sliding mode controller is adopted as the closed-loop controller for spacecraft hovering. To improve the control accuracy, the relative J₂ perturbation is regarded as a known parameter term in the closed-loop controller. The external uncertainty perturbations except J₂ perturbation are estimated by numerical difference method, and the boundary layer method is used to weaken the impact of chattering on the sliding mode controller. The open-loop control of spacecraft hovering with the relative J₂ perturbation and without the relative J₂ perturbation are simulated and compared, and the results prove that the accuracy of open-loop control with relative J₂ perturbation has been significantly improved. Similarly, the simulation of the closed-loop control are presented to validate the effectiveness of the designed sliding mode controller, and the results demonstrate that the designed sliding mode controller including the derived relative J₂ perturbation can guarantee the high accuracy and robustness of spacecraft hovering in long-term mission.     

A guidance approach to satellite formation reconfiguration based on convex optimization and genetic algorithms

This paper presents a new approach for autonomous reconfiguration of distributed space systems, which ensures safe guidance of spacecraft formations towards the desired patterns while optimizing the total propellant consumption. The orbital transfer is reduced to the form of a convex optimization problem to guarantee rapid computation of control laws. Hence, tasks are iteratively assigned to the component platforms to detect the best reconfiguration strategy. The path-planning is entrusted to a reference satellite of the cluster, that coordinates the remaining ones by means of a procedure based on genetic algorithms. Two methods are proposed, depending on the organizational architecture of the spacecraft formation. In the first one, the maneuver is completely planned by the reference satellite, that determines final tasks and control actions for the whole cluster. As an alternative to such a fully-centralized approach, a distributed version of the algorithm is proposed: tasks are sorted by the reference satellite and transfer orbits are computed by exploiting the computational resources of the whole cluster. Whatever the considered framework, both the planners ensure a safe transition of the formation towards the target geometry. Simulation results show that, when relative distances are of the order of hundreds of meters, a mean delta-v per satellite of the order of 0.1 m/s is required to reconfigure LEO clusters within one orbital period.     

星间洛仑兹力编队飞行的平衡点及零速度曲面

提出了一种新的利用星间洛仑兹力控制卫星相对运动的方法:使主星产生自旋磁场,副星带电,通过控制副星所受的星间洛仑兹力进行编队。假设主星产生的人造磁场表现为偶极子并且运动在一条开普勒圆形轨道上,副星恒定带电并在主星附近运动,同时假设星间洛仑兹力只影响副星的运动而不影响主星的运动。推导了副星在主星HCW(当地垂直当地地平坐标系)坐标系下的相对运动动力学方程。针对偶极子与HCW坐标轴X轴重合的情况下,推导了动力系统下的平衡点(并采用稳定性分析方法分析其线性化意义下的稳定性)、积分常数和零速度曲面,证明了有界相对运动的存在。最后用数值仿真验证了上述结论。     

电磁航天器编队悬停鲁棒协同控制方法

针对电磁航天器编队近地轨道悬停问题,提出一种在缺少参考轨道准确信息时的协同控制方法。用TH方程描述航天器间的相对运动,选择与参考轨道同周期的圆轨道为标称轨道。将参考轨道相对于标称圆轨道的偏差、地球非球形引力、大气阻力及其他天体引力等参数单独归类,视其为不确定量,构成不确定系统。通过引入一致性理论,在电磁作用模型和动力学方程均存在不确定性的条件下,针对航天器编队悬停的目标设计了鲁棒协同控制律。考虑能量消耗最优和均衡以及轨道姿态解耦,给出了通过优化进行磁矩配置的方案。仿真结果表明,所设计的鲁棒协同控制律能够实现编队电磁航天器高精度悬停,所给出的磁矩配置方案能够实现磁矩的合理分配。      

Dynamics in the Phobos environment

The dynamical environment on and about the Martian moon Phobos is explored. This planetary moon provides a unique dynamical environment in the solar system, being subject to extreme tidal forces and having a characteristically non-spherical shape. Further, it is not in a fully circular orbit, meaning that it has librations that arise from its eccentricity, contributing to a periodic forcing environment. Thus, to plan and implement missions in the vicinity of and on Phobos will require these considerations be taken into account. In this paper the latest published models of the Phobos shape and dynamics are used to characterize its dynamical environment in close proximity orbit about the body, for motion across its surface and for controlled hovering motion in its vicinity. It is found that surface motion is subject to a number of “speed limits” that can cause a moving vehicle to leave the surface and to possibly escape the moon and enter orbit about Mars. In terms of orbital stability, the existence of libration orbit families are characterized down to the surface using an exact potential, and the known stable QSO orbits are shown to be associated with families of stable quasi-periodic orbits.     

基于状态转移矩阵的航天器多脉冲悬停方法

基于航天器相对运动的状态转移矩阵描述,研究了空间相对悬停的多脉冲控制方法,解决了工程实践中连续推力悬停轨道控制技术对航天器控制推进系统要求较高的难题。给出了两航天器在圆、椭圆和双曲线等圆锥曲线参考轨道上相对运动的状态转移矩阵描述。在此基础上,定性分析了椭圆参考轨道偏心率对悬停精度的影响,推导了航天器多脉冲悬停速度脉冲控制量的计算方法。数值仿真算例显示,该方法可有效实现一定悬停精度要求下的空间相对悬停控制,且随着一个轨道周期内脉冲数的增加,相对悬停的效果得到提升。     

连续小推力非开普勒悬浮轨道研究综述

连续小推力非开普勒悬浮轨道在深空探测与地球极地观测任务中有着重要的应用前景。归纳了电推进、太阳帆推进等连续小推力技术的发展历程与现状；阐述了日心、行星悬浮轨道的动力学特性、稳定性、轨道保持策略；分析了三体问题下人工拉格朗日点的优势及其在深空探测方面的应用；讨论了悬浮轨道编队飞行的研究方法与控制策略。最后针对小推力悬浮轨道研究发展面临的难题，提出了研究新思路和应用新方向。     

椭圆轨道编队的构形变化控制方法

推导了椭圆轨道编队的一些典型构形模态,指出椭圆轨道卫星编队的模态不同于圆轨道的构形模态,是极为丰富的。基于T-H方程的解析解,推导了副星在沿航向常值推力作用下的椭圆轨道编队的构形变化控制方法。推导的构形变化控制方法,通过合理的选择控制量的作用时刻,可达到大量节约燃料的目的。最后,给出仿真算例。     

气动辅助异面变轨在多碎片清除中的应用分析

碎片清除飞行器异面变轨需要消耗大量燃料.从气动辅助异面变轨优化设计及被清除碎片轨道高度差值、倾角差值等参数对变轨性能的影响出发,比较分析了优化气动辅助异面变轨与双脉冲霍曼轨道转移的燃料节约量,研究了不同轨道高度差对于实施气动辅助变轨燃料节约量的影响.当地球静止轨道（GEO）与低地轨道（LEO）间气动辅助变轨优化速度增量约为1.55km·s-1、质量面积比172kg·m-2、比冲310s、轨道倾角变化16°时,燃料节约率约为45%.对比研究了不同轨道高度差LEO轨道间实施气动辅助变轨的燃料节约情况.结果表明:随着轨道高度的增加,气动辅助优化效率逐渐降低;在相同高度轨道间实施异面变轨,随着轨道倾角的增加,气动辅助变轨燃料节约率先增大后减小,倾角改变量约为20°时,燃料节约率最大;当轨道倾角为5°时,采用气动辅助变轨和双脉冲变轨的燃料消耗量相同.      

Dynamical evolution of high area-to-mass ratio objects in Molniya orbits

For special demands, some notable orbit types have been developed by human, including the Molniya orbits, which have a relatively high eccentricity up to about 0.7, and a period of 12 h. Considering that space debris with high area-to-mass ratio (A/M) has been discovered, such objects may also exist in Molniya orbits due to spacecraft and upper stages fragmentation events. However, there are not sufficient studies of the complex dynamical phenomena of such orbits. These studies can enrich the knowledge about the long-term evolution of these orbits, be helpful to propose uncatalogued objects observation and identification, and also set the protected region as well as active debris removal. In this paper, the characteristics of 2:1 resonance of Molniya satellite orbits are studied. A large set of numerical simulations, including all the relevant perturbations, is carried out to further investigate the main characteristics, and special attention is payed to the dynamical evolution of objects with high A/M, particularly affected by the direct solar radiation pressure. The long-term dynamical evolution of orbital elements, as well as the dependency of lifetime on the A/M value, is discussed.     

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.