The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

In this first part of our paper, it is suggested to use solutions to boundary value problems in the optimization problems (in impulse formulation) for spacecraft trajectories in order to obtain the initial approximation, when boundary value problems of the maximum principle are solved numerically by the shooting method. The technique suggested is applied to the problems of optimal control over motion of the center of mass of a spacecraft controlled by the thrust vector of jet engine with limited thrust in an arbitrary gravitational field in a vacuum. The method is based on a modified (in comparison to the classic scheme) shooting method computation together with the method of continuation along a parameter (maximum reactive acceleration, initial thrust-to-weight ratio, or any other parameter equivalent to them). This technique allows one to obtain the initial approximation with a high precision, and it is applicable to a wide range of optimal control problems solved using the maximum principle, if the impulse formulation makes sense for these problems.     

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.     

Optimal impulse point-to-elliptical orbit transfers of a spacecraft

The paper deals with energetically optimal multi-impulse transfer of a spacecraft in the central Newtonian gravity field near a planet. At the initial state of the transfer the distance from the spacecraft to the center of attraction, its radial and transversal velocity projections are known. At the end of the transfer the spacecraft must be located in the elliptical orbit with the given area and energy constants. The distance from the spacecraft to the center of attraction is bounded above and below, the transfer time being unspecified. The initial orbit intersects the inner boundary of the given ring.All the optimal solutions have been obtained by analytical way. A number of new solutions has been found for the given problem in comparison with the case of the transfer from the orbit at the free initial point.Up to five impulses can be applied on the optimal trajectories. The numerical simulation of the problem is carried out. It shows that all obtained solutions give not only local but global optimal energetic input on the corresponding conditions.     

Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.     

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.     

基于FE-SEA方法的航天器含支架组件噪声分析

安装在支架上的航天器设备的随机环境条件的制定一般是以经验为基础,并通过试验结果修正,而对于全新构型的航天器,其设备的随机环境条件的制定则只能依靠试验。鉴于目前没有一种成熟的分析方法能在航天器研制初期得出设备安装界面处的噪声响应,文章提出采用FE-SEA 方法,将含支架组件和航天器结构本体看成互相独立的两部分,分别采用不同子系统建模,并以“嫦娥三号”某推力器组件噪声试验数据进行了验证。分析结果表明,含支架组件和航天器结构本体分别采用FE 和SEA 子系统建模,可准确地获得设备安装界面处高频噪声响应,结合低频噪声分析,可作为制定设备随机环境条件的参考。     

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.     

Algorithms for the transport spacecraft descending stage lateral motion control

This report deals with the problems of synthesizing algorithms for controlling the attitude manoeuver of a transport spacecraft aimed at injecting the spacecraft into a closed terminal domain of “heading-range” phase coordinates which makes it possible to descend to the landing aerodrome region in accordance with a spiral trajectory tracking pattern. The descent trajectory is controlled by changing the roll angle. The principal distinguishing feature of the suggested method of transport spacecraft lateral motion control resides in guiding the spacecraft to a terminal curve and in providing an automatic transfer from roll control to interacting control of roll angle and angle of attack. The performance of the control algorithm under transient conditions are considered in detail.Algorithms controlling the longitudinal range by varing the magnitude of the roll angle and lateral range by selecting the respective sign of the roll control angle are thereafter synthesized separately. The major problem in designing the angular motion control system of transport spacecraft is the development of a high-rate roll axis turn control algorithm. To ensure high accuracy of lateral manoeuvering of the spacecraft it is expedient to accomplish the spacecraft reorientation in roll in a minimum time. It is therewith necessary to take into account with the sideslip angle limitation associated with the need of complying the design conditions of the spacecraft flowaround and with the spacecraft skin selected temperature conditions. It is expected that the total side slip angle is acceptable for measurement. Within the greater portion of the descent trajectory constant-thrust jet-reaction control engines are employed as actuators. Therefore, together with the high speed of response developed control algorithm provides an adequate efficiency of the system from the viewpoint of fuel consumption. The possibilities offered by the suggested algorithms controlling the lateral motions of the center of masses and around the center of masses during the descent stage and in the course of landing approach manoeuvering are illustrated by an example considering a hypothetical transport spacecraft featuring variable aerodynamics and a low frequency of natural oscillations of the angular motion loop. The suggested algorithms make it possible to fully employ the transport spacecraft maneuverability and to meet the terminal heading and velocity requirements within a wide class of disturbances.     

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.     

Optimal flights to near-Earth asteroid

The spacecraft flights to the Near-Earth asteroid in order to give an impact influence on the asteroid, correct its orbit and prevent the asteroid’s collision with the Earth are analyzed.In the first part, the impulse flights are analyzed in the Lambert approach. There are determined the optimal trajectories maximizing the asteroid deviation from the Earth.In the second part, the flights with the chemical and electric-jet engines are analyzed. The high thrust is used to launch the spacecraft from the geocentric orbit, and the low thrust is applied for the heliocentric motion. On the base of optimal impulse transfer, the optimal low thrust trajectories are determined using Pontryagin maximum principle.The numerical results are given for the flight to the asteroid Toutatis. Parameters of the spacecraft impact on the asteroid are determined. The asteroid deviation from the Earth caused by the spacecraft influence is presented.     

Adaptive attitude control of spacecraft using neural networks

An adaptive control technique can be applicable to reorient spacecraft with uncertain properties such as mass, inertial and various misalignments. A nonlinear quaternion feedback controller is chosen as a baseline attitude controller. A linearly added adaptive input supported by neural networks to the baseline controller can estimate and eliminate the uncertain spacecraft property adaptively. The normalized input neural networks (NINNs) are examined for reliable computation of the adaptive input. The newly defined learning rules of the neural networks are established appropriately for a spacecraft. To prove the stability of the closed-loop dynamics with the control law, Lyapunov stability theory is considered. As a result, the proposed approach results in the uniform ultimate boundedness in tracking error and robustness of the chattering and the singularity problems.     

航天器真空热试验用加热板的数值仿真

文章针对加热板在航天器热试验中的传热特点,利用Thermal Desktop软件建立了加热板和空间模拟器热沉的热数学模型,分析了电热丝数量、加热板材料和液氮管路布置方式对加热板升、降温时间和温度分布的影响;建立了模拟星、加热板和热沉的热模型,分析了加热板和星表间距对模拟星表面温度的影响。根据分析研究结果,提出了加热板设计及其在航天器热试验中的应用方法建议。     

航天器结构用材料应用现状与未来需求

航天器结构是所有航天器的重要组成部分和基础,影响航天器结构性能的最主要的因素是结构用材料。文章着重对航天器结构中广泛使用的复合材料、金属材料、防热材料的应用现状进行了分析,同时提出了未来发展需求。     

基于感应耦合式无线能量传输的 微纳聚合体航天器电源系统设计与验证

微纳聚合体航天器是一种以机械或电磁锁紧机构实现各模块化基本单元航天器连接的新型航天器架构,可以灵活实现在轨组装与自重构以满足不同任务需求。但是,基于传统电连接器的电气互联方式无法适应模块化航天器间灵活交汇对接与快速分离需求。针对上述问题,文章建立了基于感应耦合式双向无线能量传输的微纳聚合体航天器电源系统架构,根据地面演示验证需求分别设计了能源核航天器和载荷任务航天器电源系统参数,然后根据各模块化航天器间非接触供电需求,设计了双向无线能量传输单元参数,最后通过地面演示试验验证了基于双向无线能量传输的微纳聚合体航天器电源系统架构可行性,单级无线能量传输功率在20W~30W时传输效率稳定在75.8%以上,通过效率优化提升至95%以上,将可实现四个基本单元航天器的多级功率传输。     

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.     

航天器展开机构阻尼器技术概述

航天器上的一些展开机构采用了弹性元件为动力源。当其展开到位时,通常会对与之相连的部件产生冲击。加装阻尼器是抑制这种冲击的有效措施之一。文章介绍了航天器展开机构常用转动型阻尼器的类型、工作原理及特点,并对相关技术的发展和应用作了分析和评述,提出了开展黏滞阻尼器研究的建议,并指出了研究中应考虑的问题。     

Trajectories for missions of low-thrust spacecraft aimed at delivery of soil samples from main belt asteroids and Phobos

Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft.     

利用航天器分舱段振动试验数据获取整器响应的方法

未来大型组合体航天器振动试验可能难以在现有设备上进行,需要进行分舱考核。文章针对此问题开展了利用分舱段振动试验获取整器响应的方法研究。提出的方法为:根据不同界面下模态的映射关系,利用单舱段的振动试验数据辨识出舱段的两端固支模态;采用模态综合技术计算出整器组合体模态参数,拟合出结构的加速度响应传递函数;结合整器的加速度试验条件可以给出整器的试验响应曲线。仿真验证结果表明该方法合理可行,具有工程应用价值。     

“天宫一号”目标飞行器结构模态试验方法

“天宫一号”目标飞行器结构初样模态试验的激励方式、模态参数的识别方法及试验结果的评估等都有其独到的地方。多点激励模态试验的关键在于激励位置的选择及考核输入激励力的相关性,识别耦合紧密的模态结果重点在于参数识别算法。文章从模态试验原理出发,对多点激励在“天宫一号”目标飞行器结构初样模态试验中的应用及耦合紧密的模态试验结果的识别方法进行了探讨和分析。