基于UKF参数估计的地月自由返回轨道设计

为快速简便地设计地月自由返回轨道,提出了一种基于UKF参数估计算法的地月自由返回轨道设计方法。该算法不仅避免了传统数值方法推导相关梯度矩阵的复杂性,而且只需基于地月系统二体模型给出猜测初值,从而显著降低了自由返回轨道设计的难度,将地月自由返回轨道对应的两点边值问题的求解转化为参数估计问题,该算法可以得到高精度模型下收敛的精确解。数值仿真结果表明:该算法结构简洁,求解效率较高,所得结果精确且具有良好的鲁棒性,可以作为地月自由返回轨道设计的一个有力工具。     

一种地月转移轨道中途修正的制导算法

针对地月转移轨道中途修正问题,提出了一种求解修正速度增量的制导算法。该算法由初值设计和精确解求解两部分组成。首先,利用伪状态理论,通过简单迭代设计中途修正的初值,并通过Vinti预报方法修正了地球扁率的影响。然后,在求解精确解时,提出了一种基于伪状态理论的状态转移矩阵解析算法。该算法通过设计高精度的初值,降低了求解地月转移轨道中途修正问题的难度,而且避免了传统数值方法计算状态转移矩阵的复杂性。数值仿真结果表明,该算法可有效求解中途修正问题。     

Parameterized design of abort trajectories with a lunar flyby for a crewed mission

This article proposes an analytical preliminary design method for abort trajectory with a lunar flyby and the trajectory ergodic representation based on parameterization, as well as their application in studying the abort trajectories’ characteristics. First, by introducing two parameters, the perilune altitude and the perilune transfer time, the preliminary solution is developed parametrically using pseudostate theory to connect two special Lambert processes. The fast convergence of the improved differential correction under the high-fidelity gravity field verifies the accuracy of the proposed preliminary design method. Next, the two parameters are regarded as a set of variables to define an abort trajectory. Based on this, an ergodic representation of the abort trajectory with a certain abort time is yielded using the proposed design method, which offers a global view of the feasible abort trajectories. In addition, the influences of some factors on the performance of these abort trajectories are investigated based on the proposed design method and ergodic representation. The simulation results show that the abort time and the transfer time of the nominal trajectory significantly affect the ergodic representation and characteristics of the abort trajectory.     

包含引力辅助变轨的三体Lambert问题求解算法

对包含引力辅助变轨的三体Lambert问题提出了一种数值求解算法,分为转移轨道初始设计和终值搜索两部分.采用伪状态理论,通过简单迭代求解高精度的转移轨道初始设计结果,在此基础之上,通过数值积分在更复杂的摄动环境中,计算精确的转移轨道和一二阶状态转移矩阵,并利用二阶微分修正算法搜索最终解.经过数值算例检验,这种方法具有较高的效率和鲁棒性,可以有效解决三体系统中引力辅助转移轨道的高敏感性问题.     

直接再入大气的月地转移轨道设计

针对从月球停泊轨道出发直接再入大气的月地转移轨道设计问题,提出了一种数值求解算法。该算法由初值设计和精确解求解两部分组成。首先,根据轨道设计的相应约束,采用伪状态理论,通过简单迭代求解高精度的初值。然后,考虑精确的动力学模型,通过数值积分计算真实轨道和状态转移矩阵,并利用微分修正方法搜索精确解。该算法通过设计高精度的初值,降低了月地转移轨道的设计难度。数值仿真表明:该算法求解效率高,具有良好的鲁棒性。      

面向涡轮叶片方案优化的变保真度设计系统

提出了面向涡轮叶片初始设计的变保真度的多学科设计优化方法,建立了自动化的设计系统以提高设计效率.该系统集成了分析工具和设计团队以及数据管理系统,使得设计过程自动地运行.开始设计阶段使用基于经验公式的低保真度模型;优化中的三维仿真过程使用基于精确的流体分析和结构分析的高保真度模型.过程按照模型保真度的不同分3个阶段,渐近地获得最优解,同时考虑非设计点的优化.通过实验设计搜索并逐渐缩小设计空间,使得高保真度分析所带来的计算成本得以减少.最后以一个2级轴流涡轮的叶片初始方案设计验证了本设计系统.     

翼身组合体的变可信度优化设计

基于信赖域思想,发展了一种变可信度优化设计方法组织和管理不同可信度模型,有效利用低可信度模型建立近似模型,进行优化设计,高可信度模型仅修正优化近似模型,使最终优化结果收敛到高可信度模型上.采用全位势边界层有粘无粘迭代方法作为低可信度模型,多重网格Navier-Stokes方程方法作为高可信度模型,对翼身组合体进行优化设计,优化结果表明:发展的变可信度优化方法优化效率高,且能保证优化精度,具有实际的工程应用价值.     

精确动力学模型中的行星引力辅助轨道设计

轨道设计分为初步设计和精确模型迭代两步,初步设计基于等效脉冲模型,用圆锥曲线拼接法确定时间窗口和引力辅助产生的速度脉冲。精确模型中引力辅助看作是一个连续的过程,将简化模型得到的引力辅助双曲线轨道化为行星心目标B平面参数,以地心逃逸速度作为设计变量,通过微分修正的方法进行求解。通过算例对比分析了简化模型和精确模型设计结果之间的关系,结果表明,引力辅助脉冲等效模型精度较好。     

Design and optimization of stable initial heliocentric formation on the example of LISA

Space-based gravitational wave (GW) detector such as the LISA (Laser Interferometer Space Antenna) mission requires high-precision and stability of the triangular formation. The dynamic environment of the detectors is complex, the science requirements for the formation are tight, and consequently, design and optimization of this high-standard formation with essentially many decision variables are very challenging. This paper studies the design and optimization of the stable initial formation of the heliocentric GW detector by taking the LISA as an example. The linearization method based on relative orbital elements is used for formation design in the two-body system. Three constraints are presented to reduce the number of decision variables to fourteen. The geometric features of the arm length and breathing angle of the triangular formation and the relative position of LISA to the Earth are analyzed and numerically verified in a high-fidelity dynamic model, from which the relationships of multiple requirements of LISA are studied, and a single index is summarized to simplify the optimization. Sobol sensitivity analysis is used to quantitatively evaluate the sensitivities of the decision variables to the cost function, with which a self-adaptive adjustment algorithm of the region of the variables is presented to improve the computational efficiency. The availability of the method to quickly and precisely find a stable initial formation in an extensive neighborhood of the nominal formation is verified by numerical simulation, where the best solution decreases about 47.54% of the arm length change from the requirement. This study shows that the initial formation should be deployed appropriately away from the Earth, and the gravitations of Venus and Jupiter should be utilized to maintain the formation stability.     

A high order method for orbital conjunctions analysis: Sensitivity to initial uncertainties

A high order method to quickly assess the effect that uncertainties produce on orbital conjunctions through a numerical high-fidelity propagator is presented. In particular, the dependency of time and distance of closest approach to initial uncertainties on position and velocity of both objects involved in a conjunction is studied. The approach relies on a numerical integration based on differential algebraic techniques and a high-order algorithm that expands the time and distance of closest approach in Taylor series with respect to relevant uncertainties. The modeled perturbations are atmospheric drag, using NRLMSISE-00 air density model, solar radiation pressure with shadow, third body perturbation using JPL’s DE405 ephemeris, and EGM2008 gravity model. The polynomial approximation of the final position is used as an input to compute analytically the expansion of time and distance of closest approach. As a result, the analysis of a close encounter can be performed through fast, multiple evaluations of Taylor polynomials. Test cases with objects ranging from LEO to GEO regimes are considered to assess the performances and the accuracy of the proposed method.     

Velocity pointing error analysis for symmetric spinning thrusting Cubesat

To solve the problem of thrust vector misalignment from the Cubesat center of mass during orbital maneuver, spin-stabilized method is applied to eliminate velocity pointing error. Spinning thrusting Cubesat model involves the effects of mass variation and jet damping is established. Analytical solutions for the angular velocity, nutation angle, Euler angle, and inertial velocity with nonzero initial conditions are derived. Simulations show that the analytical solutions closely match numerical simulations. Based on the analytical solutions, the velocity pointing error influencing factors is analyzed. The results show that the velocity pointing error caused by initial transverse velocity, nutation angle and transverse disturbance torque can be reduced by raising the spin rate, but the initial Euler angle need to be limited. Also, the spinning thrusting maneuver can allow for a lower spin rate by increasing the axial moment of inertia.     

基于遗传算法的最优Lambert双脉冲转移

研究了初始位置和转移时间不固定的Lambert双脉冲轨道转移的数值解,用三 维图和截面图直观显示了初始位置、转移时间和速度增量的关系,并说明了其在实际工程任 务中的应用价值.基于数值解,提出了Lambert双脉冲轨道转移的优化问题.目标是找到最 优初始位置和转移时间,使燃料和时间的加权和最小.给出了遗传算法求解该优化问题的设 计步骤.该算法应用于2个算例:①平面圆轨道的燃料最优转移,并将遗传算法和Hohmann 转移的结果进行了比较;②椭圆轨道、初始位置有约束的燃料和时间最优转移.结果说明 了遗传算法寻找最优转移解是准确有效的.      

Optimal two-impulse rendezvous with terminal tangent burn considering the trajectory constraints

The two-impulse orbital rendezvous problem with a terminal tangent burn between coplanar elliptical orbits is studied by considering a lower bound on perigee radius and an upper bound on apogee radius for the transfer orbit. This problem requires that two spacecraft arrive at the rendezvous point with the same arrival flight-path angle after the same flight time. The admissible range of the final true anomaly that meets the perigee and apogee constraints is obtained in closed form. The revolution number of the transfer orbit is expressed as a function of the true anomaly and the revolution numbers of the initial and final orbits. All the feasible solutions are obtained with a bound on the revolution number of the final orbit. Then, the minimum-fuel one is determined by comparing their costs. Finally, two numerical examples are provided to obtain all the feasible solutions for given initial impulse points and the optimal solution with the initial coasting arc. Numerical results show that the minimum-fuel solution for the terminal tangent burn rendezvous is close to that for the cotangent rendezvous when the rendezvous time is long enough; however, the cotangent rendezvous may not exist when the rendezvous time is short.     

Four-body cislunar quasi-periodic orbits and their application to ballistic lunar transfer design

Examining the properties of quasi-periodic orbits provides insight into the Sun-perturbed environment in cislunar space. In this investigation, quasi-periodic trajectories and their properties are explored in the Sun-Earth-Moon four-body problem. Computation and the stability characteristics of families of invariant tori are detailed. Furthermore, this investigation offers a framework for construction of ballistic lunar transfer trajectories in the four-body problem. The framework leverages manifold trajectories to supply a set of initial conditions for construction of periapsis Poincaré maps. Periapsis maps reduce the dimensionality of the space and illuminate solutions of interest as a basis to produce feasible families of transfers. Through a continuation process, families of ballistic transfers and families of transfers that include powered lunar flybys are constructed. Ultimately, these solutions supply an initial guess for transition to the Sun-Earth-Moon ephemeris model.     

Cahn-Hilliard方程的行波解

主要利用奇异摄动方法,得到一维Cahn-Hilliard方程行波解形式的内、外解.两者匹配得到整体行波解.这个结果的特点是,它不仅将高阶偏微分方程的解用内外解匹配好,而且完全满足方程的边界条件和初始条件.当长时间变化时, Cahn-Hilliard方程的解以行波结构为极限状态.此结果很好地解释Cahn-Hilliard方程的现有理论及数值结果,实际模型和方程的性质也完全符合.     

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.     

燃料受限的时间最优多脉冲交会问题

主要研究了时间最优多脉冲交会问题中最优交会时间和最优脉冲数随各因素的变化规律.建立了考虑路径约束的数学模型,并利用遗传算法对问题进行了求解.在此基础上通过大量的数值计算研究了共面圆轨道间交会问题中各因素(包括轨道半径比、初始相位差、燃料以及路径约束)对最优交会时间和最优脉冲次数的影响,并总结出了最优交会时间和最优脉冲数随各因素的变化规律.根据最优交会时间随各因素变化的曲线较为"平缓"(均为单调或只有一个极值)的事实,指出可以利用较少的特征点通过插值的方法来快速求解最优交会策略.结论对于空间营救和在轨规避等实际任务的轨道设计具有一定的参考价值.     

Dynamic modeling and multi-stage integrated control method of ultra-quiet spacecraft

Space telescope ultrahigh precision pointing control requires the spacecraft platform to provide an ultra-quiet working environment. Vibration isolator rejection control and the multi-stage integrated control method is believed to be one of the best methods to improve the space telescope attitude control performance. In this paper, the fine dynamics model of multi-stage spacecraft systems is presented and the multi-stage integrated controller design techniques are provided. Effectiveness of the multi-stage integrated control approach is demonstrated by both the numerical simulation and experiment results. An integrated design and demonstrated experimental environment is developed for high-fidelity control performance assessment. The verification experiments for the space telescope attitude control and vibration control are carried out. The results show that the pointing accuracy and stability of the line-of-sight (LOS) for space telescope are improved at least one order by the multi-stage integrated control method.     

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.     

基于LS-DYNA直齿轮动态啮合特性分析

基于接触有限元分析理论和显式计算方法,利用LS-DYNA软件,可以高保真地模拟齿轮动态啮合过程。通过建立某实验研究中齿轮的精确啮合有限元分析模型,利用上述方法,模拟实验齿轮的动态啮合过程,根据数值计算结果分析齿轮动态啮合过程的振动特性。研究表明:齿轮动态啮合过程的数值模拟结果与实验结果具有很好的一致性;薄壁齿轮易产生结构振动,且其轮缘振动明显;降低轮缘及腹板的厚度,会使得轮缘及腹板承担齿轮啮合载荷的比重增大;当腹板位置不在齿宽中心时,会导致直齿轮动态啮合过程产生轴向啮合力。此外,研究还得出齿轮的共振条件以及齿轮共振状态的判定方法。