行星际小推力轨道Lambert解及应用

 为提高行星际小推力转移轨道初始设计精度,提出了基于N次逆多项式逼近的半解析Lambert算法,并基于该算法发展了一种转移轨道初始设计方法。首先,采用N次逆多项式近似小推力轨道形状,应用推力方向假设和位置速度边界条件推导出部分系数及推力大小解析式。接着,分析了飞行时间约束和轨道动力学约束下解的存在性,并给出了关键系数的可行域。然后,利用探测器质量消耗方程建立了Lambert问题求解模型并加以解决。最后,基于所提Lambert算法,通过对连续推力约束进行降维,提出一种求解多圈非固定时间的行星际小推力转移轨道初始设计方法。分别以固定和非固定时间转移任务为例对所提Lambert算法和初始轨道设计方法进行了数学仿真,数值结果表明：相比传统6阶方法,所提Lambert算法在目标轨道半长轴为5 AU时可减少速度增量需求36.63%;所提初始设计方法与最优化方法设计结果接近,可为转移轨道的精确设计提供可行的设计初值。     

小推力航天器的地月低能转移轨道

 在限制性四体模型下研究基于小推力方式的地月低能转移问题,通过借助于平动点轨道的相空间结构来揭示小推力转移的机理。重点研究了小推力转移自由飞行段的构造：经由LL₁点穿越获得最小能量的低能转移;而经由LL₁点Halo轨道穿越,得到(M,N)圈穿越轨道;由于Halo轨道相对于平动点增加了一维度的选择,根据(2,2)圈穿越轨道构造该转移的自由飞行段。在地球势阱逃逸和月球势阱捕获段,分别设计了合适的小推力的控制律及发动机开/关机时间,成功实施近地球段的小推力加速和近月球段的减速。尽管未对所得到的结果进行优化,所得转移轨道的燃料消耗也与类似边界条件的SMART-1轨道基本一致。     

三体模型下二维平面地月转移轨道设计与特性分析

为提高地月转移轨道搜索速度和提供精确的初值猜测,在三体模型下研究了双脉冲地月转移轨道的快速设计方法及其轨道特性。首先基于三体模型建立了地心旋转系下地月转移轨道系统模型,选择物理意义明显的地月转移加速速度增量和地心旋转系对准角作为控制变量;其次在二体模型假设下给出控制变量的初值估计方法,提出了不同运行方向地月转移轨道的搜索策略,并采用序列二次规划算法对4种类型地月转移轨道进行求解,分析其控制变量差异;最后分析了转移时间、近地点高度和近月点高度对地月转移轨道的影响,以及月球引力对二体模型下初值估计的修正量。仿真结果表明,本文提出的设计方法能快速准确地搜索出指定类型的地月转移轨道,同时其轨道特性分析结论可为后续月球探测任务地月转移轨道选择提供依据。     

月地转移轨道精确轨道设计

以基于Lambert算法的快速轨道设计结果为初值,开展精确轨道设计研究.通过对月地返回飞行阶段的摄动项和量级分析,建立了月地转移轨道的动力学方程,提出了一种双向嵌套循环搜索算法,采用该算法求解同时满足两端约束条件的精确月地转移轨道.该算法以出月球影响球的时刻和位置、速度为中间变量,一方面采用前向数值积分和微分改正法搜索满足地球再入端的轨道,另一方面采用后向数值积分并进行倾角和近月距修正得到满足月球端的轨道,通过这种双向嵌套循环,使得两段轨道在月球影响球边界处的位置和速度连续,从而获得一条完整的满足两端约束条件的月地转移精确轨道.最后以2017年1月26日出月球影响球作为返回窗口,给出了具体的设计算例,并通过STK软件仿真验证了程序的设计结果.     

载人登月着陆器奔月窗口搜索方法

对环月轨道共面交会的载人登月任务中,着陆器(LM)奔月零窗口与轨道参数精确快速设计方法进行了研究。任务采用人货分离奔月模式,着陆器于载人飞船到达环月轨道前抵达环月共面交会轨道,着陆器近月点一次共面减速完成近月制动。提出一种三层快速精确奔月窗口搜索方法:第一层采用地心二体轨道理论解析计算月窗口及奔月轨道参数初值,作为正确性基本参考;第二层采用改进的双二体解析动力学模型求解月窗口内奔月轨道参数变化规律;第三层采用高精度轨道动力学模型和SQP_Snopt优化求解奔月零窗口及轨道参数精确解。仿真结果表明,本文提出的三层逐级奔月窗口搜索方法能快速精确求解载人登月任务中着陆器奔月窗口及精确轨道参数,也揭示了影响着陆器奔月窗口的主次因素和规律,为中国未来载人登月工程提供参考。     

定常幅值小推力登月飞行器轨道研究

 进行了基于平面三体模型的登月飞行器轨道控制方法的研究;研究了从近地低轨道到近月低轨道的飞行轨道;给出了在地球逃逸段、惯性漂移段和月球捕获段的运动轨迹和关键点的参数。提出使用“远地点可达”概念完成了地球逃逸段发动机推力终点的选择和使用飞行器相对月心能量完成了在月球捕获段止推发动机工作初始点的选择。     

地月系L1点的月球借力间接转移轨道设计

针对地月系L1点（LL1）的轨道转移问题,在平面圆型限制性三体问题模型下,提出了利用月球借力的间接转移设计方法.转移设计分为地月转移轨道段和月球至LL1流形段.首先,通过改变LL1点初始机动速度,逆向积分LL1点的拟流形,以寻找初始速度、月心会合坐标系下的轨道高度和相位角这三者之间的关系,确定月球—LL1流形段微分改正的初始条件.然后,借助地月系不同转移时间的霍曼转移轨道所对应的近月点高度和相位角的关系,获得使2段转移在近月点相拼接的地月转移轨道段.这种设计方法给出了一系列LL1点间接转移轨道,将此设计结果与其他文献中的转移设计方法进行比较,此间接转移轨道比低能量转移轨道节省时间,比直接转移轨道节约能量.     

利用重复使用地月转移级往返近地轨道空间站的载人月球探测飞行模式

为提高中国月球探测的安全性和效费比,提出了一种利用重复使用地月转移级往返近地轨道空间站进行载人月球探测的任务模式,分析了任务往返的轨道和窗口,通过多方案对比分析给出2种构型重复使用地月转移级方案建议,估算对比了重复使用地月转移级效益,得出对于长期多次载人月球探测任务,采用重复使用地月转移级方案将具有更低的任务成本.     

火星探测器飞行轨道设计

在一些基本假设的基础上,初步设计了从地球停泊轨道发射探测器到达火星的飞行轨道。运用圆锥曲线拼接法,设计了采用双共切和单共切两种不同的日心段转移方式时,探测器日心段、地心段和火星中心段的飞行轨道,并分析比较了这两种设计方法的特点。根据限制性二体问题动力学模型,仿真计算了探测器在不同轨道段的飞行轨迹,结果表明,探测器可以按照所设计的轨道飞行到达火星,并被其捕获,成为环绕火星飞行的卫星。     

一种基于轨道根数约束的最优制导方法

针对航天器空间变轨的制导问题,研究了一种基于轨道根数约束的最优制导方法。在地心惯性坐标系下直接建立航天器的最优控制模型,给出了位置速度表达式和协态变量初值之间的关系;进一步,在不约束真近点角的前提下,推导了5个轨道根数的约束方程,并通过对轨道根数和最优控制理论中协态方程的特性分析,获得了另外两个约束方程。协态变量初值可直接通过求解7个完整约束方程组获得,进而得到最优推力方向。仿真验证了所提制导方法的有效性。     

Earth-moon Trajectory Optimization Using Solar Electric Propulsion

The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit (500 km altitude) to a low lunar circular orbit (200 km altitude). Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending (from low Earth orbit to high Earth orbit) and lunar descending (from high lunar orbit to low lunar orbit) trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.     

Scheme design of the CHANG’E-5T1 extended mission

Flight schemes for the CHANG’E-5T1 extended mission are investigated in this paper. In the flight scheme and trajectory design, the remaining propellant of the CHANG’E-5T1 mission is utilized. The CHANG’E-5T1 mission is firstly introduced with feasible flight goals derived based on the terminal trajectory and satellite status. The flight schemes are designed to include a lunar return and the libration points in the Sun-Earth/Moon and Earth-Moon systems, with an emphasis on the Earth-Moon triangle libration point thus far unexplored. Secondly, three schemes are proposed for the CHANG’E-5T1 extended mission with different flight goals. The direct libration point orbit transfer and injection method is adopted to solve the issue in the transfer trajectory design. Furthermore, an innovative concept is proposed to transfer from the Earth-Moon collinear libration point to the triangle point using the Sun-Earth/Moon libration point. Finally, the merits and drawbacks of the three schemes are discussed in terms of flight time, control energy and frequency, flight distance, and goal value. As a result, the scheme including a lunar return and the Earth-Moon L2 libration point is selected for the CHANG’E-5T1 extended mission. A flight to the Earth-Moon libration point is achieved, replicating the achievement of the ARTEMIS mission.     

基于大幅值Lyapunov轨道的地月转移轨道设计研究

基于平面圆形限制性三体问题模型,利用与绕月轨道相切的大幅值Lyapunov周期轨道,提出了一种新的地月转移轨道设计方法。根据Poincaré截面与限制性三体问题动力学系统对称性计算得到的大幅值Lyapunov轨道,通过与绕月轨道拼接,将地月转移问题转化为地球到大幅值Lyapunov轨道的转移问题。为保证探测器能够从近地轨道（LEO）切向逃逸到达大幅值Lyapunov轨道,通过计算其稳定流形,采用最近点作为Poincaré截面的终止条件求解探测器的初始状态,并根据初始状态完成地月轨道的设计。仿真结果表明,该地月转移策略相比于Hohmann转移,在同样只需要两次速度增量的前提下,约节约100 m/s的速度增量,该研究为地月转移轨道的设计提供了一种新思路。     

High-precision shape approximation low-thrust trajectory optimization method satisfying bi-objective index

The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory; however, it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints. In this paper, a modified shape approximation low-thrust model is presented, and a novel constrained optimization algorithm is developed to solve this problem. The proposed method aims at settling the bi-objective optimization o...     

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

The two-body orbital transfer problem from an elliptic parking orbit to an excess veloc-ity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. First, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse trajectory.     

星际小推力转移轨道快速设计方法

 针对星际探测任务中燃料最省小推力转移轨道问题,提出一种基于标称轨道的快速设计方法。首先以具有相同端点时刻的无摄动标称轨道为参考,对传统的非线性轨道优化模型进行合理变换,将复杂的优化问题简化为可解的两点边值问题;然后基于标称轨道3个独立积分推导出解析的状态转移矩阵,并以此为基础导出了两点边值问题的最优解析解。该方法无需数值迭代,有效地克服了数值优化方法收敛性差、计算效率低的缺点。最后,以探测火星的小推力转移轨道为例对该方法进行了验证,与精确的数值结果相比,该方法计算的燃料消耗误差小于1%。     

ARTEMIS Mission Design

The ARTEMIS mission takes two of the five THEMIS spacecraft beyond their prime mission objectives and reuses them to study the Moon and the lunar space environment. Although the spacecraft and fuel resources were tailored to space observations from Earth orbit, sufficient fuel margins, spacecraft capability, and operational flexibility were present that with a circuitous, ballistic, constrained-thrust trajectory, new scientific information could be gleaned from the instruments near the Moon and in lunar orbit. We discuss the challenges of ARTEMIS trajectory design and describe its current implementation to address both heliophysics and planetary science objectives. In particular, we explain the challenges imposed by the constraints of the orbiting hardware and describe the trajectory solutions found in prolonged ballistic flight paths that include multiple lunar approaches, lunar flybys, low-energy trajectory segments, lunar Lissajous orbits, and low-lunar-periapse orbits. We conclude with a discussion of the risks that we took to enable the development and implementation of ARTEMIS.     

基于解析梯度的微推进转移轨道优化方法

 研究基于离散脉冲策略的行星际微推进转移轨道优化问题,为改善收敛性和计算效率,提出了一种解析的梯度矩阵计算方法。首先,基于离散脉冲思想建立了行星际微推进转移轨道优化模型,通过对速度脉冲矢量进行参数变换,避免了传统优化模型初值猜测和搜索域难以界定的缺点;然后,基于变分原理分析了离散脉冲模型中轨道状态转移矩阵与状态变分之间的关系,并给出了多种轨道特征条件下状态变分的计算方法,该方法可扩展到多次状态不连续情况;在此基础上,推导了离散脉冲轨道优化模型中性能指标与轨道约束对寻优参数梯度矩阵的解析表达式。以地球-火星的燃料最省微推进转移为例对所提解析梯度方法进行了仿真验证。数值结果表明：本文推导的解析梯度矩阵是正确的,与传统数值梯度计算方法相比,解析梯度矩阵可有效改善寻优算法的收敛特性,并能够提高计算效率约47%。