Optimization of Flights between the Orbits of Artificial Satellites of Two Planets Using a Combination of High and Low Thrusts

The problem of optimization of the trajectory of an interplanetary flight of a multistaged spacecraft using jet engines with high and low thrust is considered. The issues concerning the problem of choosing the main design parameters of a multistage spacecraft are touched upon. A mathematical model of start-to-finish optimization of all segments of the interplanetary flight trajectory is proposed. Using this model the specific features of flights to the orbits of satellites of Jupiter and Mars are studied.     

全太阳系深空探测轨迹全局优化(英文)

针对太阳系中全部的248997颗行星的探测问题,给出了一种关于探测飞行器的深空探测全局四维轨迹(t,x,y,z)优化方案,即飞行器从地球发射进入太阳系并采用小推力控制,优化方案的性能指标为飞行器与太阳系中全部行星中相遇和交会的星的数量最多并且燃料消耗最少。本方案给出了四维飞行轨迹进行全局优化的一套算法,该算法由搜索算法和四维轨迹优化算法组成。此搜索算法从太阳系的248997颗行星中寻找获得尽可能多的经过近地球3维走廊内的行星;而四维轨迹优化算法由改进的动态规划算法、基于最优控制理论的共轭梯度算法和静态参数优化算法组成,其中静态参数优化算法用于搜索最优发射时间窗口。基于该组合算法,通过长时间的大规模的飞行数字仿真,最终计算出探测器的四维最优飞行轨迹,在一年内路过了太阳系中全部行星中的12颗行星。     

The Use of a Solar Electrojet Propulsion System for Jupiter Satellite Injection

The problem of optimization of the interplanetary trajectory of flight for a multistage spacecraft with high- and low-thrust engines into the Jupiter satellite orbit is considered. Low-thrust engines (stationary plasma engines) are used on a heliocentric flight segment. Their operation is maintained with electric power supply from solar batteries. The principal feasibility of the realization of such a project is shown, and estimations of the mass of a spacecraft placed into Jupiter's satellite orbit are presented.     

面向木星卫星交会任务的探测器飞行路径规划

针对探测器在木星系统内多次借力的飞行路径和轨道优化设计问题,提出了一种基于三层优化思想的飞行路径规划方法,该方法可根据给定的任务约束和交会目标,自动搜索探测器在木星系统内的借力飞行序列,同时完成标称飞行轨道的优化设计。首先,文章在给定轨道动力学模型和木卫借力模型基础上,建立了面向木卫交会任务的两次借力飞行轨道优化设计模型和求解方法;然后,采用结合遗传算法、全局遍历和贪婪算法的三层优化设计思路,给出了一种环木飞行路径规划方法;最后,以木星四颗卫星的交会任务为例进行了仿真分析。仿真结果表明：针对木卫的交会任务,探测器速度增量需求随木卫借力次数的增多,呈现先显著减小后逐渐增大的现象;探测器采用多次木卫借力的策略,可显著降低探测器的速度增量需求;探测器速度增量达到最优之后,借力目标收敛于交会目标,且速度增量随借力次数的进一步增多而逐渐增大。     

One optimization problem for trajectories of spacecraft rendezvous mission to a group of asteroids

The optimization problem is considered for the trajectory of a spacecraft mission to a group of asteroids. The ratio of the final spacecraft mass to the flight time is maximized. The spacecraft is controlled by changing the value and direction of the jet engine thrust (small thrust). The motion of the Earth, asteroids, and the spacecraft proceeds in the central Newtonian gravitational field of the Sun. The Earth and asteroids are considered as point objects moving in preset elliptical orbits. The spacecraft departure from the Earth is considered in the context of the method of a point-like sphere of action, and the excess of hyperbolic velocity is limited. It is required sequentially to have a rendezvous with asteroids from four various groups, one from each group; it is necessary to be on the first three asteroids for no less than 90 days. The trajectory is finished by arrival at the last asteroid. Constraints on the time of departure from the Earth, flight duration, and final mass are taken into account in this problem.     

飞行器固体火箭助推器设计优化方法比较

综合考虑飞行器总体设计约束、轨道设计、气动特性与固体火箭助推器设计间相互影响的情况下,建立了飞行器固体火箭助推器总体/气动/轨道/动力多学科的系统分析模型和设计优化模型。采用传统设计优化方法和多学科设计优化(MDO)方法进行了固体火箭助推器设计优化。结果表明,固体推进单学科的最优设计不等价于飞行器总体多学科的最优设计;与传统设计优化方法相比,MDO方法一次设计优化就可得到满足飞行器总体设计指标的最优设计,得到内外弹道相匹配的助推器最优推力-时间曲线。传统设计优化方法需要飞行器总体和固体推进学科两个设计优化过程不断迭代协调,容易漏掉满足飞行器总体设计指标的最优设计。采用MDO方法,可提高固体火箭助推器的设计质量,大大减少设计迭代次数,从而缩短设计周期。     

Solving Optimization Problems for the Flight Trajectories of a Spacecraft with a High-Thrust Jet Engine in Pulse Formulation for an Arbitrary Gravitational Field in a Vacuum

A mathematically well-posed technique is suggested to obtain first-order necessary conditions of local optimality for the problems of optimization to be solved in a pulse formulation for flight trajectories of a spacecraft with a high-thrust jet engine (HTJE) in an arbitrary gravitational field in vacuum. The technique is based on the Lagrange principle of derestriction for conditional extremum problems in a function space. It allows one to formalize an algorithm of change from the problems of optimization to a boundary-value problem for a system of ordinary differential equations in the case of any optimization problem for which the pulse formulation makes sense. In this work, such a change is made for the case of optimizing the flight trajectories of a spacecraft with a HTJE when terminal and intermediate conditions (like equalities, inequalities, and the terminal functional of minimization) are taken in a general form. As an example of the application of the suggested technique, we consider in this work, within the framework of a bounded circular three-point problem in pulse formulation, the problem of constructing the flight trajectories of a spacecraft with a HTJE through one or several libration points (including the case of going through all libration points) of the Earth–Moon system. The spacecraft is launched from a circular orbit of an Earth's artificial satellite and, upon passing through a point (or points) of libration, returns to the initial orbit. The expenditure of mass (characteristic velocity) is minimized at a restricted time of transfer.     

空间快速响应航天器轨道/弹道一体化规划

以空间应急响应任务为背景,采用轨道/弹道一体化规划设计方法,实现空间快速响应航天器全程飞行轨迹规划。在分析弹道设计参数对轨道参数影响性的基础上,将弹道规划分为程序角参数设计和发射诸元参数设计,采用改进的粒子群算法和牛顿迭代法进行混合优化求解。算例表明,使用混合优化求解方法收敛速度快,迭代次数少,易于工程实现,能满足一体化任务规划的快速性要求,可为空间快速响应航天器设计提供理论参考。     

返回舱弹道重建与黑障区弹道再现研究

对于飞船返回舱，黑障区弹道再现是再人飞行试验气动分析工作的重要环节。利用舱上测量数据和有限的雷达测量数据重构飞行弹道，是黑障区弹道再现的有效方法。本文建立了返回舱弹道重建的数学模型，包括运动学模型、观测模型、测量误差模型，从而将返回舱弹道重建问题转化为一个非线性动态系统的参数辨识问题。给出了基于极大似然判据和Newton-Raphson迭代的弹道重建算法。对某飞船返回舱的飞行试验数据进行了计算和分析，结果证实了弹道重建数学模型的正确性和算法的可行性。通过弹道重建，不仅再现了黑障区的弹道，而且提供了可靠的、完整的弹道数据。     

Guidance of a spacecraft with low lift-to-drag ratio to a landing point

The problem of terminal control over a deorbiting spacecraft at the stage of its flight after leaving plasma (altitude of ∼40 km) is considered, the aim being to guide it to a preset landing point. The algorithm is based on a modification of the well-known method of proportional navigation, when a fixed point is the target. It is suggested to use satellite navigation systems (of the GLONASS or GPS types) and/or radio beacons, which should allow one to determine the spacecraft trajectory parameters with high precision. Single-channel control is performed by changing the roll angle according to current parameters of the trajectory, which ensures adaptability of the method. Examples of three-dimensional trajectories of flight are presented for a manned spacecraft with low lift-to-drag ratio (∼0.5), currently under design in Russia. The results of statistical modeling taking into account initial deviations of the trajectory parameters and wind disturbances are presented. A method of statistical choice of a reference trajectory for the guidance stage is suggested. A theoretical possibility of using the algorithm of spacecraft guidance (in case of in-light accident with a carrier launcher) to preset regions in the vicinity of launching route is demonstrated. A qualitative analysis of proportional navigation with a fixed target is presented.     

The Motion of a Material Point in a Newtonian Field under the Action of Equiangular Thrust

The problems of investigation and optimization of the motion of spacecraft are extensively discussed in the literature. Nevertheless, in many cases a large variety of qualitative characteristics of their motion and of the form of their trajectories are still unclear. In this paper we consider a plane equiangular acceleration of a spacecraft both in a Newtonian field and in its absence (at a large distance from the center of attraction). The general equation of a trajectory of plane acceleration is presented with the introduction of a new variable, an index of an exponent, which allows one to obtain convenient solutions at different values of the time-independent angle of inclination of the vector of thrust to the spacecraft's radius vector (i.e., when equiangular acceleration takes place). Asymptotic solutions are constructed and an interesting fact is revealed. Namely, it is shown that when the center of attraction exists or is absent, for all initial conditions the trajectories appearing at the above equiangular acceleration of a material point tend to the standard logarithmic spirals at a large distance from the center. Specifically, when the value of transverse (perpendicular to the radius vector) thrust is constant, there appears a logarithmic spiral with an angle of inclination to the radius vector equal to 35.264°. Different forms of the trajectory of equiangular acceleration of spacecraft at a low thrust are also studied. The results obtained can be useful for the investigation and choice of optimum space trajectories.     

航天器热设计中的系统性和鲁棒性

从航天器系统设计最优的角度,讨论了热设计应关注的几个问题:系统最优而非分系统指标最优的热设计原则,合理并充分利用航天器资源的热管理思路,解决航天器研制问题的热设计最小重构手段,适应航天器在轨意外故障的鲁棒性热设计方法。提出了现阶段航天器热设计应适当增加主动热控比例的设计原则;结合卫星应用实例,给出了充分利用电加热这种简单可靠的主动热控手段,来提高热设计鲁棒性,从而提升热设计系统性的方案和流程。     

Influence of anisotropic fluctuations of the ionosphere plasma density on deep radio sounding by a ultra wide band radar with synthesized aperture

The problem of deep sounding of planet interior using ultra wide band radar with synthesized aperture is considered for the case when anisotropic fluctuations of the ionosphere plasma density take place. Modeling is performed for a number of values of the medium and radar characteristic parameters. The degree of influence of mutual orientation of the anisotropy direction of ionospheric fluctuations and of the spacecraft flight trajectory is estimated. It is demonstrated that widening of radar pulses is determined by characteristic spatial scale of ionosphere plasma disturbances in the transverse direction relative to the spacecraft flight trajectory. On the other hand, attenuation of the peak power of the pulses is shown to be determined basically by the longitudinal scale of disturbance correlations.     

Analysis of the Accuracy of Ballistic Descent from a Circular Circumterrestrial Orbit

The problem of the transportation of the results of experiments and observations to Earth every so often appears in space research. Its simplest and low-cost solution is the employment of a small ballistic reentry spacecraft. Such a spacecraft has no system of control of the descent trajectory in the atmosphere. This can result in a large spread of landing points, which make it difficult to search for the spacecraft and very often a safe landing. In this work, a choice of a compromise scheme of the flight is considered, which includes the optimum braking maneuver, adequate conditions of the entry into the atmosphere with limited heating and overload, and also the possibility of landing within the limits of a circle with a radius of 12.5 km. The following disturbing factors were taken into account in the analysis of the accuracy of landing: the errors of the braking impulse execution, the variations of the atmosphere density and the wind, the error of the specification of the ballistic coefficient of the reentry spacecraft, and a displacement of its center of mass from the symmetry axis. It is demonstrated that the optimum maneuver assures the maximum absolute value of the reentry angle and the insensitivity of the trajectory of descent with respect to small errors of orientation of the braking engine in the plane of the orbit. It is also demonstrated that the possible error of the landing point due to the error of specification of the ballistic coefficient does not depend (in the linear approximation) upon its value and depends only upon the reentry angle and the accuracy of specification of this coefficient. A guided parachute with an aerodynamic efficiency of about two should be used at the last leg of the reentry trajectory. This will allow one to land in a prescribed range and to produce adequate conditions for the interception of the reentry spacecraft by a helicopter in order to prevent a rough landing.     

Features of RadioAstron Mission Control

Support means of the Spektr-R spacecraft flight and features of the Mission Control Center operation and spacecraft control are considered. Software for scheduling and preparing sessions of controlling and simulating for the spacecraft operation are considered. The problems of ballistic navigation support of the spacecraft flight are presented. Ground spacecraft control segment and software for analyzing and imaging telemetric information are considered.     

小行星探测器轨迹优化方法

对小行星探测器轨迹优化方法进行了综述。介绍了直接法中的直接打靶法、直接配点法、伪谱法、微分包含法,以及间接法两种典型的轨迹优化方法,分析了其优缺点,以及在小行星轨迹优化中的应用。介绍了智能优化算法中的遗传算法、模拟退火算法、粒子群算法和多目标进化算法,分析了其相对传统优化方法的优缺点,以及相应的改进方法。     

基于气动辅助变轨的变气动外形飞行器概念研究--最优控制律问题

从一个天地往返飞行器的上升轨道和再入返回轨道的优化，以及适用不同飞行任务的变轨要求的气动外形问题，提出一项基于气动力辅助变轨的变气动外形飞行器的新概念研究。对于一个固定气动外形飞行器要同时满足上升轨道有效载荷最大和再入轨道热流峰值、过载峰值及机动性能约束下的成本最低往往是困难的。若同时满足不同飞行任务：飞往太空站的运输任务，空间拦截和交会机动巡航任务及星际探测任务，则更为困难，实际上是不可能的。文章研究基于气动力辅助变轨，在热流约束下，气动外形参数变化对最优控制的影响。其结论为：热流约束下的最优控制解，包括考虑推力协同变轨，除了在非约束弧的滚转角不直接受气动外形影响外，其余的控制律，升力系数和滚转角都是气动外形参数和攻角的函数。因而变气动外形可作为一项新技术，即通过气动外形参数变化和相应的变轨策略而获得性能和成本都最佳的用途很广的一种新型飞行器。     

General solution for the optimal trajectory of an AFE-type spacecraft

The aeroassisted flight experiment (AFE) refers to an experimental spacecraft to be launched and then recovered by the Space Shuttle. It simulates a transfer from a geosynchronous Earth orbit (GEO) to a low Earth orbit (LEO). In this paper, with reference to an AFE-type spacecraft, an actual GEO-to-LEO transfer is considered under the following assumptions: the GEO and LEO orbital planes are identical; both the initial and final orbits are circular; the initial phase angle is given, while the final phase angle is free. The aeroassisted orbital transfer trajectory involves three branches: a preatmospheric branch, GEO-to-entry; an atmospheric branch, entry-to-exit; a post-atmospheric branch, exit-to-LEO. The optimal trajectory is determined by minimizing the total characteristic velocity. The optimization is performed with respect to the velocity impulses at GEO, LEO, and the time history of the angle of bank during the atmospheric pass. It is assumed that the entry path inclination is free and that the angle of attack is constant, = 17.0 deg. The sequential gradient-restoration algorithm is used to compute the optimal trajectory and it is shown that the best atmospheric pass is to be performed with constant angle of bank. The resulting optimal trajectory constitutes an ideal nominal trajectory for the generation of guidance trajectories for two reasons: the fact that the low value of the characteristic velocity is accompanied by relatively low values of the peak heating rate and the peak dynamic pressure; and the simplicity of the control distribution, requiring constant angle of bank.     

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.     

吸气式高超声速飞行器助推-巡航轨迹优化

针对吸气式高超声速巡航飞行器建立了纵向平面内的二维轨迹优化模型(包括火箭助推段和吸气式飞行段),其中大气模型、气动力模型和发动机模型均建立了比较详细的模型,能够比较全面、准确地描述吸气式高超声速巡航飞行器的特征;基于配点法建立了适用于高超声速巡航飞行器助推-巡航轨迹优化的方法,在求解非线性规划时引入了规范化处理、稀疏分析和偏导数计算方法等,以提高优化效率;对吸气式高超声速飞行器助推-巡航轨迹进行了优化研究,分析了典型设计参数变化对最优轨迹的影响。仿真结果表明:所建立的方法能够快速、高精度求解吸气式高超声速巡航飞行器轨迹优化问题,并且能够方便地分析设计参数变化对最优轨迹的影响,可用于吸气式高超声速飞行器飞行剖面设计与优化。