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.     

Optimization of Interplanetary Flights of Spacecraft with Low-Thrust Engines Taking into Account the Ellipticity and Noncoplanarity of Planetary Orbits

The problem of optimization of the interplanetary flight Earth–Mars–Earth is formulated with restrictions on the total duration of this mission and with taking the ellipticity and noncoplanarity of planetary orbits into account. An iteration scheme for solving the problem is developed, which is based on applying a sequence of flight models with increasing complexity. An approach to choosing the points of mating the planetocentric and heliocentric trajectory segments is suggested. The influence of the errors of method of the model on the results of optimization is estimated. Software tools are developed, and full computer start-to-finish simulation of the flight is carried out with graphic representation of the trajectory segments.     

Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method

The problem of optimization of interplanetary trajectories is considered for spacecraft with a small-thrust ideally regulated engine. When the maximum principle is used, determination of the optimal trajectory is reduced to solution of a two-point boundary value problem for a system of ordinary differential equations. In order to solve this boundary value problem, the method of continuation in parameter is used, and with the help of it the formal reduction of the boundary value problem to a Cauchy problem is performed. Different variants of the continuation method are considered, including the method of continuation in the gravitational parameter which allows one to find extreme trajectories with a preset angular distance. The issues of numerical realization of the continuation method are discussed, and numerical examples of its use for solving the problems of optimization of interplanetary trajectories are presented.     

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.     

行星际Halo轨道转移的多目标优化设计

研究了星历约束下不同太阳—行星系统Halo轨道间转移的多目标优化设计问题。分析了直接和间接两种转移方式的特点,并引入伪流形技术加快了Halo轨道的逃逸和捕获速度。构建了两种转移机制的多目标优化模型。对于直接转移方式,采用伪流形双向拼接策略实现了转移轨道的构建;对于间接转移方式,通过近拱点庞加莱映射与双曲超速匹配完成了转移轨道的拼接。进一步,采用多项式样条函数对伪流形进行逼近,提高了伪流形的计算效率。两种转移机制的轨道优化设计都可以归结为简单的多变量无约束优化问题,采用非支配快速排序遗传算法NSGA-II求解。对地球—火星Halo轨道间的转移进行了多目标优化设计,校验了本文方法的有效性。     

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。     

Possibilities of Combining High- and Low-Thrust Engines in Flights to Mars

The use of combinations of chemical and electric jet engines in the spacecraft designs results in a multistage vehicle configuration and in related problems of the optimum distribution of masses between the stages, the problems of flight trajectory optimization, and the problems of choosing the design parameters of a spacecraft. The appropriate issues are considered using flights to Mars as an example. The conditions for the optimum matching of high and low thrust trajectory segments are presented. The model of the simultaneous optimization of the geocentric and heliocentric legs of the trajectory is proposed. One- and two-orbit optimum trajectories of flight are investigated and analyzed.     

Optimization of Flight Trajectories of a Spacecraft with Electric Propulsion Using the Gravitational Maneuver

Necessary conditions of optimality of the use of a gravitational maneuver during a flight are obtained, and a mathematical model for its study is proposed. With the help of the developed method of optimization of a trajectory of an interplanetary flight using a favorable gravitational maneuver, estimations of a spacecraft's transport capabilities are made for flights to Mercury and for the delivery of a solar probe into the near vicinity of the Sun.     

地球-火星的燃料最省小推力转移轨道的设计与优化

小推力转移轨道的设计与优化一直是深空探测轨道设计方面的难点。针对这些问题，提出了一种基于等高线图的初始发射机会搜索方法，该方法通过绘制探测器一火星距离的等高线图寻找满足任务约束的小推力转移轨道发射机会；同时，本文还给出了一种小推力轨道的直接优化算法，该算法通过将连续的控制变量参数化，把轨道优化问题转化为参数优化问题，然后基于所提搜索方法，采用逐次二次规划方法进行求解。数值计算验证了该发射机会初值猜测方法和优化算法的有效性。     

How we will go to Mars

This article studies the efficiency of ejecting waste generated by the life support system (LSS) of a manned spacecraft to reduce initial mass on low earth orbit. The spacecraft is used for a long-duration interplanetary mission and is equipped with either a chemical or a nuclear-thermal propulsion system. For this study we simulate an optimal control problem for a given spacecraft maneuver. An impulsive approximation of the optimal interplanetary spacecraft trajectory is assumed, which allows us to reduce the general optimal control problem to hierarchic structure of 'outer' and 'inner' subproblems. This structure is analyzed using the Pontryagin's Maximum principle. Numerical results, illustrating the efficiency of waste ejection are shown for typical Earth-Mars transfer trajectories. This results confirm in theory that using a waste ejection system makes an early manned Mars mission possible without having to design and build new, advanced biological LSS.     

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。     

Trajectory of spacecraft with photonic laser propulsion in the two-body problem

The photonic laser propulsion (PLP) system can produce continuous and constant thrust. This paper reviews its basics and then studies its application in the two-body interplanetary trajectory. This study also derives the equations of motion (EOM) for a spacecraft in an inertial frame and rotational frame for the two-body problem, and uses the Jacobi integral to investigate the spatial restrictions on trajectory. This study proposes a constraint on the smallest thrust at the launching stage, and finds the in-plane and out-of-plane equilibria. Numerical simulations confirm the validity of the derivations. The results of this paper are directly applicable to future PLP thrust missions, and particularly interplanetary travel.     

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。     

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.     

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.     

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.     

大型挠性航天器的鲁棒模型预测姿态控制

针对大型挠性航天器的三轴姿态控制问题,考虑了控制输入约束,设计了鲁棒模型预测姿态控制器。首先,将模型预测控制应用到不考虑扰动的标称挠性航天器系统中,通过求解优化问题推导预测控制律,从而得到三轴姿态的标称轨迹。然后,为有效处理大型挠性附件振动对中心刚体姿态造成的扰动,针对带有扰动的挠性航天器实际姿态控制系统,设计由最优状态与实际系统状态的误差构成的辅助反馈控制器,使实际系统状态维持在以标称轨迹为中心的“管道”(Tube)不变集内,并驱使实际系统状态到达标称轨迹上,最终沿着标称轨迹到达平衡点。仿真结果表明,在鲁棒模型预测控制的作用下,实现了姿态角的快速精确跟踪,有效地处理了由大挠性附件振动对中心刚体姿态产生的扰动,增强了系统的鲁棒性。     

吸气式超声速导弹爬升段多约束轨迹优化

针对吸气式超声速导弹飞行过程多约束及强耦合的特性,研究了超声速导弹爬升段的轨迹优化设计问题。考虑吸气式推进系统与气动力、飞行轨迹的耦合,对超声速导弹冲压发动机的性能进行分析,揭示了吸气式发动机推力、静压裕度以及余气系数随飞行状态的变化规律;在考虑过载、动压、终端弹道参数及发动机参数等约束的条件下,建立多约束条件下的轨迹优化模型,提出一种适用于此类飞行器飞行轨迹与推力规律的优化设计方法,并对最小油耗的爬升弹道进行优化设计分析。仿真结果表明,该方法能有效解决吸气式超声速导弹多约束轨迹优化问题,可为吸气式超声速导弹的弹道规划与制导律设计提供参考。     

On solving the problems of optimization of trajectories of many-revolution orbit transfers of spacecraft

The problem of optimal control over many-revolution spacecraft orbit transfers between circular coplanar orbits of satellites is considered. The spacecraft flight is controlled by a thrust vector of a jet engine with restricted thrust (JERT). The mass expenditure is minimized at a limited time of flight. The optimal control problem is solved based on the maximum principle. The boundary value problem of the maximum principle is solved numerically using the shooting method. A modified computation scheme of the shooting method is suggested (multi-point shooting), as well as a method (correlated with the scheme) of choosing the initial approximation with the use of a solution to the optimization problem in the impulse formulation. The scheme and method allow one to construct many-revolution spacecraft orbit transfers.     

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.