Optimal reconfigurations of two-craft Coulomb formations along manifolds

Coulomb formations refer to swarms of closely flying spacecraft, in which the net electric charge of each vehicle is controlled. Active charge control is central to this concept and enables a propulsion system with highly desirable characteristics, albeit with limited controllability. Numerous Coulomb formation equilibria have been derived, but to maintain and maneuver these configurations, some inertial thrust is required to supplement the nearly propellant-less charge control. In this work, invariant manifold theory is applied to two-craft Coulomb equilibria, which are admitted in a linearized two-body gravity model. The manifolds associated with these systems are analyzed for the first time, and are then utilized as part of a general procedure for formulating optimal reconfigurations. Specifically, uncontrolled flows along the manifolds are sought which provide near continuous transfers from one equilibrium to another. Control is then introduced to match continuity, while minimizing inertial thrusting. This methodology aims to exploit uncontrolled motions and charge control to realize the shape-changing ability of these formations, without large inertial control efforts. Some variations in formulating and parameterizing the optimal transfers are discussed, and analytical expressions are derived to aid in establishing control parameter limits, under certain assumptions. Numerical results are provided, as demonstrative examples of the optimization procedure, using relatively simple control approximations. Finally, Particle Swarm Optimization, a novel stochastic method, is used with considerable success to solve the numerically difficult parameter optimization problems.     

Out-of-plane stability analysis of collinear spinning three-craft Coulomb formations

The results of a stability analysis focusing on the out-of-plane motion of collinear three-craft Coulomb formations with set charges are discussed. Such a formation is assumed to be spinning in deep space without relevant gravitational forces present. Assuming in-plane motion only with circular relative trajectories and initial position and velocity perturbations confined to the orbital plane, the previous work analytically proves marginal stability in the linear sense and numerically shows marginal stability in the short term. In this paper, the equations of motion are presented in the cylindrical coordinate frame in order to analyze the out-of-plane motion in more detail. The out-of-plane motion is shown to decouple to first order from the marginally stable in-plane motion. A simple control law is developed and applied, which directly controls the out-of-plane motion only within specified deadbands. For a wide variety of out-of-plane perturbations, the control law succeeds in preserving the in-plane variant shape despite some out-of-plane motion. A trend between the settling time and deadband, which defines the largest out-of-plane errors allowed before the controller is turned on, is determined, which illustrates how large the deadband may be before the in-plane motion is affected.     

Stability and shape analysis of relative equilibrium for three-spacecraft electromagnetic formation

The invariant shapes for close formation flying with inter-craft electromagnetic force ensure several potential space applications. However, the 6-DOF relative equilibrium problem has not been systematically investigated. This paper mainly analyzes the invariant shapes of relative equilibrium for the three-spacecraft electromagnetic formation, and studies the families of invariant shape solutions with real and constant magnetic moments as well as their linear stability. The problem is examined based on the full nonlinear coupled dynamic models for collinear and general triangular configurations. The relative equilibrium conditions are analyzed to determine whether an invariant shape do exist, and the corresponding families of invariant shape solutions are identified for static and spinning configurations respectively. Finally, the linear stability of such invariant shapes is numerically discussed, which have shown that most invariant shapes are unstable and controllable.     

Self-stabilising attitude control for spinning tethered formations

The paper analyses the dynamics of a spinning tethered formation where the tethered units are modelled as extended rigid bodies. The system, composed by two platforms linked by a flexible tether a few hundreds of meters long, constitutes the building block of more complex tethered architectures utilised in proposed space interferometry missions. The issue investigated herein is the transfer of a collimated beam from one platform to another in the presence of environmental perturbations and structural vibrations affecting the position and attitude of the two tethered units. We propose to damp residual oscillations and limit the effect of environmental torques with the aid of two passive dampers placed at the tether attachment point. When the damping system is properly tuned, this approach has the considerable advantage of rapidly bringing the system to a minimum energy configuration (zero residual vibrations) without any external control force. Numerical results show the effectiveness of the proposed control strategy and provide an important element towards the implementation of future space-based observatories and formation-flying demonstration mission based on tether-connected architectures.     

一种新的共线平动点拟周期轨道稳定保持策略

限制性三体问题下共线平动点附近的拟周期轨道在深空探测中具有重要的实际应用价值,得到了各航天大国的广泛重视。通过将动力学中心流形结构引入轨道控制方法的设计之中,得到了基于投影到中心流形的共线平动点拟周期轨道稳定保持策略。首先推导了会合坐标到中心流形坐标的正则变换方法,在此基础上设法通过引入轨道机动,将偏差状态点投影到中心流形上,从而达到消除不稳定分量的目的。该方法充分整合了平动点的动力学特性,并且也适用于周期轨道的稳定保持。通过对Lissajous轨道和晕轨道的数值仿真表明,该方法较以往方法具有更强的稳定性,能在显著降低轨控燃料消耗的基础上达到较好的稳定保持效果。     

一种恒电长度干涉仪分析的新方法

对数周期天线的相位中心随频率呈线性变化,用2个对数周期天线可以构成具有恒电特性的干涉仪天线阵,在工程应用中,天线相位中心较大的测试误差会导致天线阵调试困难.通过对恒电长度干涉仪的分析,提出了利用相位扫频测试对天线阵进行调试分析的方法,避免了繁杂的相位中心测试,简化了天线阵的调试过程,测试数据可直接用于系统校正.     

利用库仑力实现悬停轨道的新方法研究

研究了利用库仑力控制实现近距离悬停轨道的问题。针对常规推力器对悬停任务可能产生的羽流污染,提出了一种使用航天器间库仑力实现悬停轨道的新方法,并研究了使用该方法实现悬停轨道的开环与闭环控制问题。基于所建立的库仑力悬停轨道动力学模型,给出了目标为一般椭圆轨道时的开环控制律。基于线性化的悬停轨道动力学模型,给出了目标轨道为圆轨道时的闭环控制律,并进行了数值仿真,结果表明所建立的动力学模型及所设计的控制律是有效的和可行的。文章提出的方法也可以用于其他类型的航天器近距离相对运动控制问题。     

Robust stationkeeping and reconfiguration of underactuated spacecraft formations

Feasibility of achieving reliable control for spacecraft formation keeping and reconfiguration without the need for thrust in either the radial or along-track direction is explored in this paper. Analysis of the linearized dynamics without along-track input indicates the presence of an uncontrollable eigenvalue at the origin. A nonlinear controller is designed to indirectly stabilize the uncontrollable modes to a stable manifold around the equilibrium. Conditions for robustness against unmatched uncertainties and disturbances are derived to establish the regions of asymptotic stabilization. The benefits of the proposed control method are also validated via numerical simulations to show that precise formation maintenance can be achieved by dealing with the issues of system nonlinearities, variations in initial conditions, and external disturbances, concurrently.     

共线平动点的动力学特征及其在深空探测中的应用

首先系统地阐述了限制性三体问题中共线平动点的动力学特征,给出了这类平动点附近的中心流形（周期轨道和拟周期轨道）及双曲流形（稳定与不稳定流形）的计算方法,并在限制性三体问题模型下给出了相应的数值算例。在此基础上,进一步探讨了将探测器定点在共线平动点附近的条件和相应的轨道控制问题以及如何利用共线平动点的不稳定性实现节能过渡问题,并在太阳系多天体引力模型下给出了一些算例。     

Optimization of entry-vehicle shapes during conceptual design

During the conceptual design of a re-entry vehicle, the vehicle shape and geometry can be varied and its impact on performance can be evaluated. In this study, the shape optimization of two classes of vehicles has been studied: a capsule and a winged vehicle. Their aerodynamic characteristics were analyzed using local-inclination methods, automatically selected per vehicle segment. Entry trajectories down to Mach 3 were calculated assuming trimmed conditions. For the winged vehicle, which has both a body flap and elevons, a guidance algorithm to track a reference heat-rate was used. Multi-objective particle swarm optimization was used to optimize the shape using objectives related to mass, volume and range. The optimizations show a large variation in vehicle performance over the explored parameter space. Areas of very strong non-linearity are observed in the direct neighborhood of the two-dimensional Pareto fronts. This indicates the need for robust exploration of the influence of vehicle shapes on system performance during engineering trade-offs, which are performed during conceptual design. A number of important aspects of the influence of vehicle behavior on the Pareto fronts are observed and discussed. There is a nearly complete convergence to narrow-wing solutions for the winged vehicle. Also, it is found that imposing pitch-stability for the winged vehicle at all angles of attack results in vehicle shapes which require upward control surface deflections during the majority of the entry.     

考虑状态约束的二体旋转库仑卫星系统重构控制

研究考虑控制输入饱和与状态约束的深空旋转二体库仑卫星构型控制问题,只采用卫星之间的库仑力作为控制力,提出一种基于反步法的非线性控制方法。首先推导了二体库仑卫星在地-月系平动点附近的相对运动方程,利用旋转二体库仑卫星的特性,对方程进行了简化。为了完成禁止相对运动区域的回避,设计了新的状态限制辅助函数,结合抗饱和方法与反步法得到了二体库仑卫星的构型控制器。接着证明了由于状态限制辅助函数的加入,所设计的控制器可以保证卫星相对运动不超出限制范围。进一步应用Lyapunov稳定性定理证明了其闭环系统的一致最终有界性。最后在Matlab/Simulink平台上进行了仿真校验,结果表明了方法的有效性。     

Fuel consumption and collision avoidance strategy in multi-static orbit formations

This paper analyses the fuel consumption of interferometric radar missions employing small satellite formations like, e.g., Cross-track Pendulum, Cartwheel, CarPe, or Trinodal Pendulum. Individual analytic expressions are provided for each of the following contributions: separation from a simultaneously injected master satellite, formation set-up, orbit maintenance, formation maintenance, and distance maintenance. For this, a general system of equations is derived describing the relative motion of the small satellites in a co-rotating reference frame. The transformation into Keplerian elements is carried out. To evaluate fuel consumption, three master satellites are assumed in different orbital heights, which are typical for Earth observation missions. The size of the exemplarily analysed formations is defined by remote sensing aspects and their respective fuel requirements are estimated. Furthermore, a collision avoidance concept is introduced, which includes a formation separation and formation set-up after a desired time period.     

等质量立体五星库仑编队飞行的分析与控制

分析了立体五星编队在静电力和万有引力作用下的静态构型。分别讨论了五星编队在共线和平面情况下的静态构型,着重研究了五星构成立体双直角六棱锥构型时各个卫星所带的静电荷量。由于地球同步轨道的卫星所受到的作用力不仅是万有引力与静电库仑力,还有空气阻力等摄动力,因此只有对其施加控制,卫星才能在静态平衡点保持编队构型的稳定性。本文采用线性二次型最优控制方法来保持编队的静态构型稳定,并通过Matlab实现了五星立体库伦编队飞行控制仿真。     

库仑力卫星编队动力学建模及基本稳定条件分析

分析了空间德拜屏蔽效应对库伦力编队应用范围的影响,根据库伦力编队静止轨道最佳应用前提,建立了基于拉格朗日方程的地球同步轨道库仑力卫星编队动力学模型并对其进行简化,讨论了沿地心和沿轨道面法线方向存在两星库伦力编队稳定构形的基本平衡条件。仿真结果表明:为提高库伦力编队效率以节约能源,应减小编队距离,减轻卫星质(重)量,同时尽可能增大卫星外表面体积。     

Effects of eccentricity of the reference orbit on multi-tethered satellite formations

The paper discusses the relevance of eccentric reference orbits on the dynamics of a tethered formation, when a massive cable model is included in the analysis of a multi-tethered satellite formation. The formations examined in this study are hub-and-spoke (HAS) and closed-hub-and-spoke (CHAS) configurations for in-plane and Earth-facing spin planes. Stability of the formations is studied by means of numerical simulation, together with the evaluation of the effects of eccentricity on tether elongation, agents relative position, and formation orientation and shape.     

基于RCS序列的空间目标形状估计

将空间目标等效为椭球体,在分析椭球体RCS方向图的基础上,提出了利用空间目标RCS序列极大值与极小值比值来估计空间目标长短轴比值的方法。实测数据处理结果表明,该方法能有效估计出目标长短轴比值。目标长短轴比值反映了目标的形状信息,具有明显的物理意义,有利于后续的空间目标分类与识别。     

Spatial approaches to moons from resonance relative to invariant manifolds

In this study, the final approach to a moon or other body from resonance is explored and compared to the invariant manifolds of unstable periodic orbits. It is shown that the stable manifolds of planar Lyapunov orbits can act as a guide for the periods or resonances that are required for the final approach in both the planar and spatial problems. Previously developed techniques for the planar problem are expanded for use with resonances and used for comparison with trajectories approaching a moon from these resonances. A similar technique is then used for exploring the relationship of invariant manifolds to approach trajectories in the spatial problem. It is shown that the invariant manifolds of unstable periodic orbits provide insight into the trajectory design, and they can be used as a guide to the more direct approach trajectories.