Optimal mission planning of the reconfiguration process of satellite constellations through orbital maneuvers: A novel technical framework

In this paper, a general new methodology is presented for the orbital reconfiguration of satellite constellations on the basis of Lambert targeting theorem. In view of the cost and risk reduction, it is very important to consider the problem of satellite constellation reconfiguration with the two constraints of overall mission cost minimization and the desired final configuration. Hence, the dependent non-simultaneous deployment approach is proposed to minimize overall fuel cost. Despite the fact that the satellites deploy in a non-simultaneous manner, supplementary phasing maneuvers on the target orbital pattern to achieve the desired orbital configuration are avoided. Moreover, a novel idea is presented to optimize the flight of satellites, which plays an important role in complying with the constraint of overall fuel cost minimization as much as possible. In order to achieve the global optimal solution of the satellite constellation reconfiguration problem, the efficient hybrid Particle Swarm Optimization/Genetic Algorithm (PSO/GA) technique, is implemented. Finally, to indicate the superiority of the presented method, a comparison to the simultaneous maneuver viewpoint is made on a number of representative cases. The obtained results imply significant reduction of reconfiguration costs by employing the proposed method.     

多星近距离绕飞观测任务姿轨耦合控制研究

针对多星近距离绕飞观测任务,建立了相对姿态轨道动力学模型,分别考虑了在椭圆、空间圆绕飞轨道上观测卫星的两种期望三角形编队构型,以观测卫星视线始终指向目标为期望姿态,采用基于四元数和角速度误差反馈的比例 微分控制律以及一种改进的基于人工势场法的制导方法相结合,对相对姿态及轨道进行控制。仿真结果表明：在控制律的作用下,绕飞过程中各观测卫星均能够有效地跟踪期望相对姿态和期望相对轨道;在空间圆绕飞轨道构型中,各观测卫星从初始同一位置出发后,在任意时刻3颗观测卫星构成的编队构型始终为正三角形,且正三角形的边长从零逐渐增大,最终等于期望正三角形构型的边长。     

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.     

不规则区域成像覆盖星座构型优化设计

近年来卫星对地观测需要呈现逐年上升趋势.从单个目标点的对地观测卫星星座构型设计方法入手,推广为设计满足不规则大范围成像区域重访时间需求的卫星星座.以卫星数目最少及满足重访时间要求为优化目标,采用改进的模拟退火算法,结合改进的等面积网格点覆盖法,提出了一种针对不规则区域成像全覆盖的卫星星座构型优化设计方法.分析了光照因素对重访时间、所需卫星数目以及星座构型的影响,并通过仿真分析验证了算法的可行性.     

Dynamics and operation optimization of partial space elevator with multiple climbers

This work studies the dynamics and optimal stabilization method of a partial space elevator (PSE) system with multiple climbers. All satellites and climbers are assumed as lumped masses that are connected by straight, massless, and inextensible tethers. A general dynamic model is derived for the PSE with multiple climbers. It is found different climber moving patterns of climbers have major influence of dynamic behavior of PSE. Optimal control is used to develop optimal operation modes to suppress the libration of PSE with multiple climbers. Moreover, a new operation mode is proposed to approach the desired mission objectives. It is found that all libration angles can be suppressed to zero by the end of the transfer period if two climbers can be kept at a constant speed. At the same time, the magnitudes of libration angles can be kept bounded by regulating the speed of the middle climber relative to other two climbers.     

Optimization of fault-tolerant thruster configurations for satellite control

The fault tolerance of spacecraft actuators significantly affects the reliability of satellites and the likelihood of successful missions. To enhance the fault tolerance of the actuators, this study derives optimal fault-tolerant configurations of fixed thrusters that maximize the controllability of a fully-actuated or underactuated satellite. The proposed method optimizes thrust and torque directions generated by the thrusters. Thus a cost function in terms of the thruster locations and directions is defined as the summation of the generated control forces and torques with respect to the body-fixed frame. The optimal configuration is obtained by the successive use of an energy potential method that is motivated by Thomson’s problem. Some numerical examples are provided that show the effectiveness of the proposed formulation and optimization method.     

航天器与空间碎片的混合编队重构控制与应用

针对空间碎片清理问题,提出了一种利用航天器与空间碎片混合编队队形重构控制技术捕获碎片的方法。首先,分析了地/月—日系L2拉格朗日平动点附近的限制性三体环境,并建立了编队卫星相对运动动力学模型;其次,提出了以太阳光压力作为航天器与空间碎片编队队形重构的控制力,实现各从星接近空间碎片的目的;最后,设计了基于线性二次型的最优控制器,并在Matlab/Simulink环境下进行仿真实验。仿真结果表明该方法可控制从星到达期望的位置(空间碎片的位置),且太阳帆板的姿态变化在可控范围内,进而证明了该方案可以应用于复杂空间环境下的碎片清理任务。     

一类卫星推力器布局的多目标优化设计方法

针对一类卫星平台的推力器布局进行优化方法建模,给出推力器布局设计原则和优化指标,将推力器布局问题转化为一个多约束多目标寻优问题．最后对IntelSat—VII／VIIA推力器布局进行优化设计,优化结果达到了预期效果,验证了本文方法和指标的有效性．     

星载InSAR辅星编队优化设计与分析

以“主星—辅星编队”InSAR系统干涉测高为应用背景,研究辅星编队的优化设计问题。首先,定义优化指标———“有效观测时间比”来描述全轨道周期观测性能,以共绕飞轨道、相位均匀分布的卫星编队(构形类似于CartWheel)作为研究的重点。选取描述编队卫星相对运动的振幅比和相位差作为寻优变量,通过仿真实例用搜索法得出了寻优变量与优化指标的三维关系图,并给出了优化构形的参数区域,得到了最优的编队卫星轨道根数。进一步研究了在主要摄动因素影响下卫星编队构形保持与轨道保持的燃料预算方法,并计算了上述优化构形一年的燃料预算。最后得出有益的结论,为全InSAR系统优化设计提供依据。     

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.     

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.     

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.     

一种基于FPGA位流回读与重配置的空间硬件容错方法

分析FPGA的配置数据帧格式以及整个器件中配置数据帧的类型和分布,在此基础上给出具体的位流回读故障检测方法和重配置容错方法,最后给出了实现该容错方法的一个实例.论文研究可为星上拟采用基于SRAM的FPGA的各分系统电路容错设计所借鉴.     

基于最小PDOP准则的星间链路拓扑方案

星间链路是卫星导航系统实现自主运行的一项关键技术.研究了一种 Walker(24/3/2) 星座,通过对卫星间可见性以及星间链路相关约束条件的分析,计算并确定了同轨卫星的A,B类排列方案,探索了建立位置精度因子(PDOP,Position Dilution Of Precision)值最小,即测距精度最高的星间链路拓扑结构的方法,并在此基础上利用Dijkstra算法计算出卫星之间以及卫星与地面站之间的最优路径.通过对星间数据传输时间延迟和星座网络卫星节点数据流量的统计,表明这种链路生成方案切实可行,能够满足预先设定的技术指标要求.同时对最短路径、最小跳数和网络流量均衡3种不同的计算策略进行了仿真,验证了这3种策略所造成的结果差异.      

Energy-optimal reconfiguration of satellite formation flying in the presence of uncertainties

In this study, a two-step control methodology is developed for energy-optimal reconfiguration of satellites in formation in the presence of uncertainties or external disturbances. First, based on a linear deterministic system model, an optimal control law is analytically determined such that a satellite maneuvers from an initial state to a final state relative to another satellite. The structure of this optimal solution is predetermined and simply given by a linear combination of the fundamental matrix solutions associated with the original equations of relative motion. Only the coefficients are to be determined to satisfy given initial and final conditions. In the second step, an uncertain nonlinear formation system is considered and a robust adaptive controller is designed to compensate for the effects of uncertainties or disturbances that the formation system may encounter. Although the control strategy is inspired by sliding mode control, it produces smooth control signals, thereby avoiding chattering. Also, an adaptation law is added such that the uncertainty or disturbance effects are effectively and quickly eliminated without a priori information about them. The combination of these two controllers guarantees that the satellite accurately tracks the optimal path in the unknown environment. Numerical simulations demonstrate the effectiveness and accuracy of the proposed two-step control methodology, in which a satellite formation is optimally reconfigured under unknown environmental disturbances.     

基于卫星编队的空间碎片视觉高精度导航方法

视觉方法被广泛应用于空间碎片这类和卫星之间没有任何通信的非合作目标导航。针对观测过程中视觉传感器的像差偏差引起位置不确定的问题,提出了利用卫星编队的立体视觉导航方法。首先,利用卫星编队构造了长基线的视觉传感器,通过Fisher矩阵对系统的可观测性进行了分析,验证了系统是可观的;其次,对视觉传感器进行了误差分析,通过安排最优视差角,使多颗卫星的观测信息融合达到最优;最后,应用卫星编队的视觉导航方法对空间碎片进行了导航仿真验证。结果表明,基于卫星编队的视觉导航方法可以显著减小观测误差,精度能达到01m量级,而且编队构形简单,易于工程实现。     

系绳卫星控制系统可重构性评价指标

针对系绳卫星控制系统,展开系绳卫星控制系统可重构性评价指标的研究。首先建立了由三个子卫星组成的系绳卫星控制系统;然后针对该模型进行可重构性评价,给出可重构性评价指标,该指标不仅描述了系统的重构能力,同时还强化了可重构性评价对重构策略指导的作用,体现了重构设计对可重构性评价方法的依赖性。最后通过数值算例,分析了系绳卫星的可重构性指标,并对故障后的系统重新设计重构控制律使其保持稳定。     

多变量全局寻优与智能优化在星座组网中的应用

顶层任务规划通常与星座组网紧密结合,小卫星分散灵活的特性尤其适用于星群规模化在轨运行。针对热点区域覆盖和全球覆盖的不同任务需求,提出了对构型多变量进行全局寻优和利用智能优化技术进行星座构型优化的方法,两种优化方法可分别获得小规模星群最优效能与超大型星群的较优效能。优化方法不受轨道类型和任务目标分布的约束,具有良好的鲁棒性。     

Multi-objective optimal formation reconfiguration with scalarization and stochastic boundaries

A new method is proposed for multi-objective optimal control of satellite formation reconfiguration. First, necessary optimality conditions of single-objective fuel-optimal reconfiguration are studied. Problem of initial guess of the costate and control discontinuity are addressed by using a new developed stochastic based method. Terminal conditions of Two Point Boundary Value Problem (TPBVP) of the optimal control equations are relaxed using augmented Gaussian. Variances or bandwidths of the terminal conditions are set to decision variables to be optimized. Responses of varied initial costate are modeled and propagated using Riccati equation. Using quadratic convolution of relaxed terminal conditions, objective function of the fuel-optimal problem is reformulated into a quadratic equation, and a gradient based optimizer is used to search the optimal initial guess. In the second part of the paper, optimal control of format flying reconfiguration with two competitive objectives:fuel and time of flight (ToF) is studied. With Pascoletti-Serafini scalarization, the Multi-objective Optimal Control Problem (MOCP) is scalarized into a set of weighted Single-objective Optimal Control Problems (SOCP). Hamiltonian and switch function for the weighted SOCP are developed and constructed. New developed stochastic based approach is then used to search the optimal Pareto solutions. Verification and performances of proposed algorithms are demonstrated through numerical simulations of single-objective and multi-objective optimal control of low-thrust elliptical orbit formation reconfiguration. Potential applications of the algorithms to some other preliminary space mission designs are also discussed.     

异构多星编队的脉冲构型保持控制方法

近地轨道的双星编队通常设计具有自稳定性的编队构型参数初值,通过保持编队构型参数形成长期稳定的相对周期运动。针对编队中卫星数量增多产生的相对运动耦合问题,提出了基于Hill坐标和三角函数公式的多星相对运动分析方法。基于SAR载荷测量基线定义,结合多星编队构型参数的相对运动特性,提出了编队构型参数的设计方法,能够实现多星编队的最大有效基线组合。通过分析J2项摄动和大气阻力摄动的长期影响,研究了异构多星编队的相对运动衍化规律,提出了主从形式的脉冲偏置控制,能够有效保持针对异构多星编队设计的编队构型。通过面质比异构的四星编队控制仿真,验证了脉冲偏置控制形式下异构多星编队构型保持控制方法的有效性。