Two classes of extreme motion trajectories of a point with varying specific impulse

The variational problem to determine the optimal trajectories of the center of mass of a spacecraft moving in the central Newtonian field with limited power and specific momentum was considered. The extremal trajectory was shown to contain elements of zero, intermediate, and maximal power with a constant or variable specific momentum. For the circular and spiral trajectories, extremal analytical solutions were established. These elements can find use in the problems of departure and transfer to the parking orbit, as well as in the problems of orbital transfers. The problem of transfer to the given elliptical orbit was considered as an example.     

航天器任意椭圆轨道最优转移问题研究

目前航天器最优转移轨道研究中,常忽略摄动力影响,仅考虑能量最优,且采用常值推力控制量,得到的转移轨道精度低,转移时间长,非理论最优。本文考虑地球非球形摄动力J2的影响,建立时间-能量综合最优性能指标,基于变推力控制量,研究了任意椭圆轨道最优转移问题。建立高斯拉格朗日状态方程,应用Pontryagin极小值原理和共轭梯度法求解最优转移问题;研究了J2摄动力对转移轨道根数、推力加速度和最优转移轨道的影响。结果表明:J2摄动力对转移轨道根数和推力加速度都有影响,不能忽略;时间-能量综合最优转移同时考虑轨道转移时间和能量消耗,优化结果更利于工程应用;最优推力加速度不是常值,即采用常值推力控制量得到的并非理论最优转移轨道。     

一类磁性刚体航天器的混沌控制研究

采用基于误差线性系统稳定性准则的混沌控制方法,控制具有结构内阻尼的磁性刚体航天器在重力场与磁场共同作用下在圆形轨道的混沌姿态运动.讨论了航天器姿态运动方程中部分参数的取值对于运动姿态的影响,给出了这些参数通过倍周期分岔或逆倍周期分岔通往混沌的途径.当参数使系统做混沌姿态运动时,采用上述方法将混沌运动控制至周期-4轨道,并实现周期-1、2、4轨道之间转换的灵活控制.此外,分析了控制参数的变化对于控制效果的影响,并分别给出了控制至不同轨道时的输入扰动范围及控制参数范围.仿真结果表明,该方法能够实现混沌姿态运动在预定周期轨道间的灵活控制,且输入扰动量小、控制速度快、具有高精度,从而验证了该方法在航天器混沌姿态运动控制方面的有效性.     

Optimizing Flight Trajectories for Space Vehicles with an Additional Fuel Tank. II

We solve the optimization problem for space trajectories of spacecraft flights with an auxiliary fuel tank from a low round orbit of a man-made Earth satellite to a geotransitional orbit. Control over the spacecraft motion is performed with a jet engine of bounded thrust. To discard the auxiliary tank, one has to turn off the engine, which takes some known time. The mass of the discarded tank is assumed to be proportional to the mass of fuel spent, and the mass of the engine and additional constructions is proportional to the thrust-to-weight ratio. We minimize the value of injection impulse needed to transfer to the geostationary orbit for a given useful mass.In the second part of the paper the problem at hand is formalized as an optimal control problem for a collection of dynamical systems and is solved based on the corresponding maximum principle. In this work we solve boundary problems of the maximum principle numerically with the shooting method. As a result of solving the problem, we construct one- and two-revolution Pontryagin extremals. We perform a series of parametric computations that are used to determine optimal parameters of the spacecraft construction: the best thrust-to-weight ratio and the best distribution of fuel among the tanks.     

Estimates of near-circular orbits after a single correction: a geometrical method

Estimates of the maneuvers of active space objects are considered. We propose analytical and numerical-analytical algorithms to estimate short-term and long-term one-impulse maneuvers for the case where the initial and final orbits are determined with errors. Both coplanar and noncoplanar maneuvers are considered. Special attention is given to the velocity and reliability of the solution of the problem. The process to find the solution has a geometrical interpretation. We provide examples of estimates for maneuvers of spacecraft located at geosynchronous orbits. The results obtained by the proposed method are compared with the results obtained by the traditional approach, excluding errors of orbit determination.     

The problem of optimal control of the orientation of an orbit of a spacecraft as a deformable figure

The problem of optimal control of the orbit orientation of a spacecraft regarded as a deformable figure is studied. The problem of optimal re-orientation of an orbit is formulated as a problem of optimal control of the motion of the center of mass of a spacecraft with a movable right end of the trajectory and is solved based on the Pontryagin maximum principle. To describe the orientation of an instantaneous orbit, a new quaternion osculating element that replaces three classical angular elements of the orbit is applied. Necessary optimality conditions are obtained; several first integrals of the system of equations of the boundary-value problem of the maximum principle are found; transformations that reduce the dimension of the system of differential equations of the boundary-value problem (without their complication) are proposed; the proposed approach is analyzed, and an example of numerical solution of the problem is presented     

在轨释放伴随卫星方法与仿真分析

伴随卫星的轨道动力学分析与仿真是航天器伴随领域的一个重要研究方向。为飞行器执行警卫任务,以动力学方法为基础,建立了卫星的绝对轨道模型和伴飞轨道维持模型,推导了简化的相对运动方程解析解,并作为对伴星进行轨道维持的依据。仿真分析不同释放方案形成的共面椭圆伴飞轨道,伴星的燃料消耗,轨道维持措施对伴飞的影响。仿真结果表明,伴星活动范围越大,轨道维持所耗燃料越多;增加轨道维持措施可延长伴飞圈数;在满足应用任务要求的前提下,选定合适的伴星释放方案,能够实现燃料消耗最少。     

Unloading angular momentum for inertial actuators of a spacecraft in the pitch channel

The problem of gravitational unloading of the angular momentum of inertial actuators of a spacecraft in the pitch channel for circular and elliptic orbits is considered using the band theory of modal control. Control laws for gravitational unloading and stabilization of a given spacecraft position unambiguously determined by the object parameters and given coefficients of characteristic equation are obtained.     

Necessary and sufficient conditions of the rendezvous between a single spacecraft and three non-coplanar Walker constellation satellites

The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied,and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduced.The rendezvous orbit design can be transformed into the patching of two spacecraft orbits,either of which can achieve the rendezvous with two satellites.Firstly,due to the precious quality of spherical geometry,the unique existence of the rendezvous orbit for two constellation satellites is ...     

Near real-time geocoding of SAR imagery with orbit error removal

When utilizing knowledge of the spacecraft trajectory for near real-time geocoding of Synthetic Aperture Radar (SAR) images, the main problem is that predicted satellite orbits have to be used, which may be in error by several kilometres. As part of the development of a Dutch autonomous mobile ground station to receive and process satellite SAR data, a method has been developed that removes the effects of orbit errors from the computed azimuth and slant-range coordinates, whilst maintaining the real-time character. Results show that predicted orbits can be used to geocode SAR imagery in near real time with the same accuracy as when using precise orbits, i.e. 30–40m.     

Fast and accurate analyses of spacecraft dynamics using implicit time integration techniques

This paper deals with the implementation techniques of an implicit integrator to achieve fast and accurate analyses of spacecraft dynamics. For this purpose, the pseudospectral method is adopted to directly integrate the second-order system of equations for both the spacecraft dynamics and corresponding state transition matrix. Various implementation techniques are proposed to enhance the numerical efficiency and integration accuracy, which include a moving horizon approach, the decoupled integration of the second-order dynamics for the state transition matrix, and the grid adaptation method. The numerical features of the proposed techniques are investigated through their applications to a spacecraft’s motion around highly eccentric elliptic orbits, and the resultant numerical errors and computing times are compared with those from the Runge-Kutta method to show the relative efficiency and accuracy of the presented methods. In addition, an optimal two-impulse orbit transfer from the Earth to the Moon is analyzed by implementing the proposed methods using a multiple-shooting framework. The results show that the proposed techniques are extremely effective for dynamical problems requiring intensive and accurate time integrations, and can provide much better accuracy and efficiency than the explicit Runge-Kutta integrator.     

高精度航天器轨道预报仿真软件的研制

在航天器的设计过程中,必须要对轨道飞行状态进行预报,以确保航天器的正常运行.高精度轨道预报仿真软件是对航天器轨道进行预报的重要工具.首先简要介绍了航天器轨道预报的理论基础,详细阐述了航天器轨道动力学模型的建立方法,接着研究了高精度航天器轨道预报仿真软件的设计思路,提出了软件的实现方法,最后介绍了利用C 语言开发的适合航天器轨道预报仿真的航天器轨道计算工具软件包"Spacecraft Orbit Calculation Tool(SOCT)",并利用STK软件对SOCT进行测试验证,结果表明SOCT达到了高精度航天器轨道预报仿真的要求.     

Formation of high inclined orbits to the ecliptic by multiple gravity assist maneuvers

Methods for designing trajectories of spacecraft (SC) for missions that need to increase the inclination of their orbits to the ecliptic using energy-efficient gravity assist maneuvers (GAMs) around planets, their moons, and small Solar system bodies are developed. The focus is on the development of algorithms (taking into account accurate ephemerides) for designing chains of multiple GAMs that significantly raise the orbit of a SC above the plane of the ecliptic. Complete analytical formulas for the change of inclination as a result of a GAM in the general case of elliptic orbits of the SC and the partner planet are obtained.     

日心悬浮轨道航天器编队飞行控制

针对日心悬浮轨道航天器编队飞行控制问题,应用线性自抗扰控制（LADRC）技术设计了编队飞行控制器．首先,考虑外部扰动,基于圆形限制性三体问题（CRTBP）模型推导了航天器编队日心悬浮轨道非线性动力学方程．其次,提出了一种基于扰动估计和补偿的编队飞行控制方法,避免了通过航天器局部线性化动力学方程或精确非线性动力学方程设计编队飞行控制器时存在的模型精确性过度依赖等缺陷．最后,数值仿真表明存在系统模型不确定性、初始入轨误差及地球轨道偏心率扰动的情况下,所设计的控制器实现了高精度的编队飞行控制,并优于NASA制定的5 mm编队飞行精度标准．     

航天器自主高精度时间管理系统设计

为满足航天器长期在轨飞行期间高精度的时间同步需求,提出了一种航天器自主高精度时间管理系统,将北斗导航定位授时设备和频率综合器两种时钟源系统进行融合使用,两种时钟源系统可根据导航定位状态自主切换,在消除了频率源系统误差累积效应问题的同时,解决了导航非定位情况下时间精度急剧下降的问题.通过建立系统的误差模型,以航天器应用设计实例进行计算分析,结果表明:系统时间同步精度优于37.8μs.研究结果可以为后续航天器高精度时间管理系统设计提供参考.     

Modification of the exact pole placement method and its application for the control of spacecraft motion

For linear stationary models of the spacecraft motion, a modification of the exact pole placement method is developed that makes it possible to design a modal control for any class of linear stationary systems. In the case of circular orbits, the modified method is used to obtain an analytical solution of the problem of gravitational angular momentum unload problem for inertial actuators of a spacecraft in the gyroscopically coupled roll-yaw channels.     

基于MATLAB的航天器二次点火非共面轨道最优转移策略研究

航天器的非共面轨道转移对于航天器拦截、交汇、对接有着非常重要的意义。运用MATLAB仿真,主要研究基于二次点火的非共面轨道最优转移策略,结果表明该方法能有效减少轨道转移过程中所需的速度增量,降低航天器的燃料消耗。     

Autonomous navigation system of near-Earth spacecraft

An autonomous navigation system for near-Earth spacecraft is described; this system allows determination of the satellite orbit and prediction of its motion parameters. Radio navigation measurements of GLONASS and GPS satellite systems are used for this purpose. The autonomous navigation system is designated for operation on near-Earth orbits which do not go beyond the navigation areas of GLONASS and/or GPS and on orbits with large eccentricity whose apocenter is at a distance of 50–70 thousand km from the Earth’s surface. The developed methods and algorithms for orbit determination are based on the application of laws of motion dynamics of a spacecraft directly at processing primary phase measurements of the carrier frequency and code pseudo-range using an extended measurement base. Algorithms for determination of motion parameters of the spacecraft and results of simulation and operation of a model system are presented. The possibility of creation of an onboard autonomous navigation system with precision and reliability higher than those of the ground measuring complex is demonstrated.     

On optimal spacecraft damping

The problem of spacecraft damping (damping of initial angular velocity to zero) for a minimal time is studied. Two variants of formulation of the optimization problem are considered; these variants differ in the form of constraints on the control torque. Analytical solution to the formulated problem is obtained in the closed form and numerical expressions for synthesis of optimal angular velocity control program are given. Similar problem of time-optimal angular acceleration of the spacecraft to the given value is also solved. Procedure for determination of the control torque at the initial time instant for the problem of acceleration of the spacecraft to the required angular velocity is presented. Numerical example of solution of the problems of buildup and damping of spacecraft rotation velocity for a minimal time is given.     

Autonomous implementation of dynamic operations in a geostationary orbit. II. Synthesis of control algorithms

This study continues the series of papers devoted to the problems of autonomous operation of spacecraft in a geostationary orbit. The solution of the problem considered here assumes the formation of a set of algorithms for control processes in a closed autonomous spacecraft control and navigation system in a geostationary orbit. The paper is aimed at the formalization and solution of the new technical task of autonomous control during the spacecraft’s ascent to the given orbital position and remaining in this position. An important requirement is to provide the safe separation of several spacecraft in one orbital position. The control problem is solved using the combined optimization method developed by us; in this method, the control vector is divided into the synthesized and the programmed components taking into account the principle of the separation of the navigation and control problem in the stochastic approach. The motion’s models proposed in the previous paper are used to develop the control algorithms for a spacecraft’s ascent to the working position in a geostationary orbit and remaining in this position. The results of the algorithms simulating the ascent and maintaining for the exactly known state vector taking into account the random spread of the initial conditions and thrust are presented.