A lunar cargo mission design strategy using variable low thrust

A design technique for a near optimal, Earth–Moon transfer trajectory using continuous variable low thrust is proposed. For the Earth–Moon transfer trajectory, analytical and numerical methods are combined to formulate the trajectory optimization problem. The basic concept of the proposed technique is to utilize analytically optimized solutions when the spacecraft is flying near a central body where the transfer trajectories are nearly circular shaped, and to use a numerical optimization method to match the spacecraft’s states to establish a final near optimal trajectory. The plasma thruster is considered as the main propulsion system which is currently being developed for crewed/cargo missions for interplanetary flight. The gravitational effects of the 3rd body and geopotential effects are included during the trajectory optimization process. With the proposed design technique, Earth–Moon transfer trajectory is successfully designed with the plasma thruster having a thrust direction sequence of “fixed-varied-fixed” and a thrust acceleration sequence of “constant-variable-constant”. As this strategy has the characteristics of a lesser computational load, little sensitivity to initial conditions, and obtaining solutions quickly, this method can be utilized in the initial scoping studies for mission design and analysis. Additionally, derived near optimal trajectory solution can be used as for initial trajectory solution for further detailed optimization problem. The demonstrated results will give various insights into future lunar cargo trajectories using plasma thrusters with continuous variable low thrust, establishing approximate costs as well as trajectory characteristics.     

A new class of intermediate thrust arcs in the restricted three-body problem

The Mayer’s variational problem of determining spacecraft optimal trajectories in the context of a classical restricted three-body problem is considered. Integrability of differential equations of a controllable motion in the non-central gravitational field represents well known and challenging task. It is shown that in the absence of sufficient number of first integrals, an explicit dependability of unknown integrals on certain variables can be used to explore the existence of previously unknown particular integrals and solutions of these equations utilizing Dokshevich’s method of analytical dynamics. A new class of extremal analytical solutions of the problem for intermediate thrust arcs is presented. An illustrative example of utilizing these solutions in minimizing the spacecraft characteristic velocity of a transfer from a specified initial position to some final position in the Earth-Moon system is discussed.     

升力体飞行器能量近似最优倾斜转弯飞行策略

升力体飞行器返回地球大气层内时受到热流、动压及过载等约束条件,为使得飞行器在倾斜转弯飞行过程中能量损失最小,需要研究一种能量最优的倾斜转弯机动飞行策略。本文的主要研究内容包括:从再入动力学模型出发,分析了升力体飞行器倾斜转弯的弹道特性,推导了终端速度与倾斜转弯幅度相关的解析解,提出了一种多约束条件下能量近似最优的倾斜转弯飞行策略;为进一步验证飞行策略的能量近似最优性,建立了能量最优的非线性轨迹优化模型,通过高斯伪谱法进行求解,获得能量最优的飞行轨迹。仿真结果表明,该飞行策略与优化方法获得的结果高度一致,并且该方法求解效率更高,工程应用性更强。      

基于有限Fourier级数的航天器转移轨迹设计

针对航天器小推力转移轨迹的初始设计问题，利用基于三阶Fourier级数的设计方法实现了航天器小推力的多圈转移。同时，基于有限Fourier级数的形状法，对具有多个约束条件的小推力多圈转移轨迹进行了优化设计。选取了共面同轴同偏心率的初始和末端轨道位置，对所提出的方法进行了仿真验证。结果表明：与改进逆五阶多项式形状法相比，所提出的方法虽然增加了转移时间，但当转移圈数为5圈、有限Fourier级数的项数为10时，可减少将近75%的转移速度增量，同时大大减小了所需的最大推力加速度的值。     

常推力作用下飞行器固定时间最优交会

研究了在常推力作用下,两个空间飞行器的固定时间最省燃料交会问题。通过对飞行器交会过程中最优推力弧段的研究,给出了关于飞行器的最优推力弧段的几个性质。这些结果为空间飞行器交会对接的工程设计提供了理论依据。     

基于星下点机动的再入飞行器离轨规划

针对约束再入点地理位置的再入飞行器离轨问题,提出了一种基于星下点机动的离轨规划方法。再入飞行器的离轨轨道设计受到飞行器当前轨道状态和再入点参数的约束。首先,基于轨道飞行原理,建立了一般椭圆轨道冲量模型下离轨制动参数和再入点参数的关系,分析了最优离轨的推力施加原则;其次,在考虑地球自转的前提下,提出了直接离轨必要条件,针对约束再入点经纬度的问题,完善了利用非线性规划优化方法确定有限推力模型下离轨点位置的策略,同时给出了符合燃料最优目标的离轨制动参数;最后,探讨了一般情况下初始轨道不满足直接离轨必要条件时,为满足星下点约束而进行的轨道机动施加策略。      

最优气动力辅助空间拦截和交会

航天器从高轨道向位于低地球圆轨道的靶目标实施拦截或进行交会 ,并用间接求解的直接伴随方法 ,即用D型拉格朗日方法求解其优化问题。拦截条件是指在最终时刻两者的位置相同 ,而交会条件是指不仅位置相同且最终的速度矢量亦相等。文章讨论了最小时间与最小脱靶量 ,或最小时间与最小燃料消耗的复合性能指标 ,以及推力协同机动的优化解。推力协同下 ,对于特定情况 ,如在热流约束边界部分推力弧是奇异的 ,气动力控制是正常的。这种复杂性和奇异问题的求解在拦截和交会问题中都是值得慎重处理的。     

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.     

一种小推力借力飞行转移轨道初始设计方法

提出一种基于正弦指数函数的小推力借力飞行转移轨道初始设计方法。建立极坐标形式的正弦指数函数表达式,用于模拟小推力转移轨道,并用绕圈参数和飞行路径角对转移轨道的参数进行表征;在约束条件下对转移轨道参数进行离散化处理,求解转移轨道与目标星投射轨道在参考面内的交点,计算到达目标轨道时刻的极角,进而得出小推力转移轨道的初始设计参数;设计了地球—木星的火星借力小推力转移轨道,仿真结果验证了该方法在小推力转移轨道初始设计中的快速性与准确性。     

基于高斯伪谱法的空天飞机上升段最优轨迹设计

针对复杂多约束条件下空天飞机上升段燃料最优轨迹优化问题,提出一种基于高斯伪谱法的上升段轨迹优化策略.依据发动机的推力特性将上升轨迹合理分段,使原最优控制问题转化为多段最优控制问题后,采用高斯伪谱法进行并行优化计算.数值仿真结果表明采用这种轨迹优化策略能够满足组合动力系统工作模态转换时对飞行状态的约束条件,可以在较短的时间内完成高精度的上升段轨迹优化任务,从而验证了该方法的有效性.     

Navigating BepiColombo during the weak-stability capture at Mercury

BepiColombo is scheduled for launch in August 2013 and to arrive after a nearly six-year long transfer at Mercury in June 2019. The trajectory has a number of challenging elements: a launch with Soyuz/Fregat into a geostationary transfer orbit, followed by a lunar flyby, long low-thrust arcs and five more planetary flybys (one at the Earth, two at Venus and two at Mercury). At arrival the low thrust arcs reduce the approach velocity so much that BepiColombo passes by the Sun–Mercury Lagrange points L₁ and L₂ and gets weakly captured in a highly eccentric orbit around Mercury in case the orbit insertion manoeuvre would fail.This paper describes the navigation strategy during the final phase. Five trajectory correction manouevres during the last 65 days requiring up to 20 m/s (3σ) are proposed. With this strategy it is possible to navigate BepiColombo safely through the weak-stability boundary of Mercury and to reach the target periherm with a precision of 11 km.     

月面上升的轨迹优化与参数分析

面向月球采样返回任务分析需求,对月面上升段的轨迹优化及燃料消耗影响因素进行了研究。基于上升器运动模型,建立以燃料消耗最优为目标考虑入轨约束的轨迹优化模型,通过Gauss伪谱法和序列二次规划求解上升过程最优推力方向。改变运动模型中的初始推重比、入轨约束中的目标轨道参数,根据轨迹优化结果得到对应的燃料消耗,分析了这些因素对上升器燃料消耗的影响。针对上升器非共面起飞的问题,提出了上升偏航、升交点调整、倾角调整3种方案,从燃料消耗的角度分析了各方案的适用情况,为未来工程应用提供参考。     

全电推进卫星轨道优化的推力同伦解法

全电推进卫星的入轨过程是一个典型的多圈小推力轨道优化问题,由于其推力器加速度小,变轨圈数多,造成其最优理论解的求解较困难。为解决该问题,利用最优控制理论建立了全电推进卫星变轨优化的间接法模型,将变轨优化问题转化为协态变量初值猜测的两点边值问题。从大推力问题开始,通过遗传算法获得大范围猜测值并结合系列二次规划方法获得大推力的精确解。采用推力同伦思想,使用逐渐缩小推力的方式完成小推力问题的求解。仿真算例表明,采用推力同伦的方法,通过数十次的推力缩减即可有效解决多达上百圈变轨的静止轨道全电推进卫星入轨优化问题。     

战术飞行任务的水平航迹快速生成算法

由于军机的水平航迹规划必须考虑飞机作战生存性和执行任务的有效性，并且借鉴 实时性，所以成为较特殊的优化问题，应用多重尺度奇异摄动法简化了水平航迹规划问题，构成了战术飞行任务的水平航迹快速生成算法，仿真优化计算结果表明，算法能够快速生成水平航迹，优化结果也是有效的。     

一种用于SGCMG奇异规避的CVP轨迹规划

采用单框架控制力矩陀螺(SGCMG)作为执行机构的小型敏捷卫星在姿态机动过程中存在着奇异问题.本文从SGCMG姿态控制系统整体出发，将奇异问题转化为状态约束的动态控制问题，基于控制变量参数化(CVP)方法，设计了一种用于SGCMG奇异规避的轨迹规划.该算法在实现小型敏捷卫星大角度姿态机动过程无奇异的基础上，将SGCMG框架角转速的最优轨迹通过CVP方法进行分段线性规划.这种规划策略对框架伺服系统的算法设计无复杂要求，仅需要简单的加减速控制，从而节约了星上资源.在轨迹规划实现过程中，考虑了工程实际中的约束条件，可以按照姿态机动任务要求规划出一条综合考虑能量资源和目标精度的最优轨迹.仿真结果表明：该算法实现了姿态参数轨迹和星体角速度轨迹的平缓变化，目标误差在1×10-3量级，星体在机动过程中运行稳定，SGCMG不会出现奇异现象.     

基于分段常值的全电推进GEO卫星制导策略

电推进技术因其比冲高的技术特点在GEO轨道转移中应用可大大减少燃料质量,提高有效载荷质量比,延长任务寿命等。针对全电推进GEO卫星入轨的轨迹优化和制导问题,首先利用间接法获得小推力燃料最优GEO轨道转移的数值解,提出一种多项式曲线拟合最优轨迹的方法,多项式曲线形式简单,可作为参考轨道在星上存储和使用。在多项式参考轨道的基础上,建立了一种分段常值推力跟踪参考轨道的闭环制导策略,在常值推力条件下,轨道要素控制量与控制力有解析关系,简化了制导律设计;将多圈轨道转移问题分解为多个单圈轨道优化问题。结果显示,本文提出的分段常值跟踪制导策略跟踪精度高,和最优轨道相比多消耗7%的燃料。本制导策略控制结构简单,易于工程实施。     

地球同步卫星远地点最省燃料小推力多次变轨

在推力较小时，通信卫星在远地点变轨的弧段很长，从而导致较大的速度损失。文章采用极大值原理，研究了在远地点采用多次变轨的最优变轨过程。给出了推力方向的最优变化规律及中间轨道的最优值，并对计算结果进行了讨论。     

常值推力下面内轨道优化的一种改进间接法

针对常值推力下航天器面内轨道转移燃耗最省的轨道优化问题,利用极大值原理导出了最优轨迹下推力方向角应满足的控制方程,结合动力学方程建立了一种求解航天器面内最优转移轨道的改进间接法,及其在推力方向角调节能力受限条件下的应用方法。由于避免了协态变量微分方程组的求解,改进间接法相对于传统间接法降低了初值猜测的难度和计算量;与采用Gauss伪谱法求解相比,所建立的改进间接法求解结果精度更高,数值光滑性更好。仿真算例表明:推力方向角调节能力受限会改善推力方向角变化规律,降低推力方向角变化范围;就燃耗而言,推力越大燃耗越多,优化轨道节省燃耗更加显著。     

有限推力轨迹优化问题的直接打靶法研究

研究了求解有限推力轨迹优化问题的直接打靶方法。说明了利用直接打靶法将最优轨迹问题转化为参数优化问题的基本转换方法 ;给出了状态和控制变量的等式 (或不等式 )约束的转化方法 ;从插值和数值积分两个方面对转换过程中产生的误差进行了深入分析。最后 ,以最优交会问题为例 ,说明了不同节点数目和积分步数对计算结果的影响     

Solar sail optimal control with solar irradiance fluctuations

The optimization of a solar sail-based orbital transfer amounts to searching for the control law that minimizes the flight time. In this context, the optimal trajectory is usually determined assuming constant solar properties. However, the total solar irradiance undergoes both long-term (solar cycles) and short-term variations, and recent analyses have shown that this may have an impact on solar sailing for missions requiring an accurate thrust modulation. In this regard, the paper discusses a strategy to overcome such an issue by suitably adjusting the thrust vector in order to track a reference, optimal, transfer trajectory. In particular, the sail propulsive acceleration magnitude is modified by means of a set of electrochromic material panels, which change their optical properties on application of a suitable electric voltage. The proposed control law is validated with a set of numerical simulations that involve a classical Earth-Mars, orbit-to-orbit, heliocentric transfer.