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.     

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.     

基于多学科设计优化算法的再入轨迹优化设计

传统的再入轨迹优化问题通常是在气动外形和质量等总体参数给定的情况下建立起来的。所设计的最优轨迹从飞行力学的角度来看是最优的，但从系统角度来看未必是最优的。在总体初步设计阶段，考虑气动外形和质量等其他学科影响的再入轨迹优化对于提高RLV的系统性能无疑具有重要意义。此时再入轨迹优化将是一个静态，动态多学科混合优化问题。以球头双锥的升力体构型RLV为例，以最小化热防护系统质量和最大横向机动距离为指标，采用两种典型的多学科优化算法来研究考虑气动外形、轨迹和热防护系统三个学科的再入轨迹优化设计问题。仿真结果表明多学科优化算法能够用来求解静态，动态多学科混合优化的再入轨迹优化设计问题，是RLV初步外形设计和任务轨迹规划的重要工具。     

An Improved United Trajectory Optimization Approach in Boost-phase Considering Attitude Control Ability

This paper covers the trajectory optimization design problem of a class of demonstration flight test vehicles. Different from the traditional "once downward" movement principle of negative attack angle, the "twice downward" lower trajectory is proposed based on a SQP algorithm to meet the requirement for validating thermal protection materials. Furthermore, an important advantage of this presented method, compared to the traditional method, is that both trajectory constraints and attitude control constraints are considered. An engineering example is also given to show the advantage and effectiveness of this method.     

复杂禁飞区高超声速飞行器路径-轨迹双层规划

针对高超声速飞行器在复杂禁飞区的规避场景,为解决现有轨迹规划方法对任务初值依赖性强的问题,提出一种基于双层规划建模的路径-轨迹规划方法。其中,上层为路径规划,为轨迹提供路径点引导信息,避免轨迹陷入局部解;下层为轨迹规划,利用上层输出的路径点信息,将轨迹分割成多个横向机动小的子段,解析求解横纵向飞行剖面,减小运动模型简化误差。数值仿真表明,与现有轨迹优化方法相比,本方法能够选择指标更优的路径,提高了轨迹规划的全局性能;解析飞行剖面制导误差不超过0.03%,解决了大范围横向机动的剖面解析难题。     

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。     

Ares I–X Flight Test Vehicle similitude to the Ares I Crew Launch Vehicle

The Ares I–X Flight Test Vehicle is the first in a series of flight test vehicles that will take the Ares I Crew Launch Vehicle design from development to operational capability. Ares I–X is scheduled for a 2009 flight date, early enough in the Ares I design and development process so that data obtained from the flight can impact the design of Ares I before its Critical Design Review. Decisions on Ares I–X scope, flight test objectives, and FTV fidelity were made prior to the Ares I systems requirements being baselined. This was necessary in order to achieve a development flight test to impact the Ares I design. Differences between the Ares I–X and the Ares I configurations are artifacts of formulating this experimental project at an early stage and the natural maturation of the Ares I design process. This paper describes the similarities and differences between the Ares I–X Flight Test Vehicle and the Ares I Crew Launch Vehicle. Areas of comparison include the outer mold line geometry, aerosciences, trajectory, structural modes, flight control architecture, separation sequence, and relevant element differences. Most of the outer mold line differences present between Ares I and Ares I–X are minor and will not have a significant effect on overall vehicle performance. The most significant impacts are related to the geometric differences in Orion Crew Exploration Vehicle at the forward end of the stack. These physical differences will cause differences in the flow physics in these areas. Even with these differences, the Ares I–X flight test is poised to meet all five primary objectives and six secondary objectives. Knowledge of what the Ares I–X flight test will provide in similitude to Ares I—as well as what the test will not provide—is important in the continued execution of the Ares I–X mission leading to its flight and the continued design and development of Ares I.     

高超声速滑翔飞行器引入段弹道优化

高超声速飞行器弹道优化设计的目的足得到高超声速飞行的控制指令，从而得到方案弹道，针对其数学模型，寻找一个作为输入的攻角规律使得弹道最优。我们将此弹道问题转化成最优控制问题，通过极大值原理得到最优弹道的一阶必要条件。我们采用遗传算法求解了此两点边值问题。首先从次优化弹道得到攻角的变化规律，然后由从次优化弹道估计出的攻角范围推导出初始伴随变量的变化范围，再用遗传算法在此范崮内优化初始伴随变量得到了伞局最优弹道和相应的初始伴随变量。通过一个实例求得了满足热流约束的最大终端速度弹道，通过比较可知优于次优化弹道，从数值计算例子还可以看到遗传算法是求解两点边值问题的一种比较好的方法。     

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。     

RLV再入轨迹机载快速优化

为了可重复使用飞行器再入轨迹机载快速优化的需求,开发一种再入轨迹快速优化算法。根据RLV再入三维轨迹的特点,引入了新的假设,对RLV再入轨迹状态方程进行简化处理,使优化迭代计算量大大减少,在此基础上,使用乘子法对再入终端约束进行处理,然后用共轭梯度法求解优化再入轨迹,最后以美国航天飞机为例计算再入最优轨迹。结果验证该算法在满足约束条件的情况下,具有很快的收敛速度,在不同初始再入条件和终端约束条件下,计算机时一般小于一分钟。该算法具有很好的工程应用前景。     

A new treatment of Lambertian mechanics

Lambert's formulas for the time of orbital flight between two points in space are rederived by first establishing a universal differential equation governing the time function, independent of the conic type of the trajectory, the focal characteristics of the trajectory sector, and the range angle. A unified form of Lambert's formulas is then obtained as the general solution of the differential equation, and the various forms of the classical Lambert's formulas are obtained as its particular solutions under different boundary conditions. Following this basic treatment, various hypergeometric expansions for Lambert's time function and its derivatives are developed, and the behavior of the function and its implications in the solution of Lambert's problem and the isochronous trajectories are briefly reviewed. Finally, a short comparison of the present treatment with those found in current literature on Lambertian Mechanics is made and briefly discussed.     

基于Gauss伪谱法的临近空间飞行器上升段轨迹优化

综合考虑密度变化、声速变化、发动机推力变化及地球引力等因素对飞行轨迹的影响,研究了与实际飞行环境更加相符的临近空间飞行器燃料最优爬升轨迹。针对该问题在气动数据处理和优化求解上存在的困难,提出一种基于Gauss伪谱法(Gauss Pseudospectral Method,GPM)的求解策略。首先,依据气动数据特点,设计拟合模型对气动参数进行高精度拟合;其次,为避免间接法和传统直接法的缺点,将Gauss伪谱法和序贯二次规划(Sequential Quadratic Programming,SQP)相结合,对存在边值及加速度约束的轨迹优化问题进行求解,获得最优飞行轨迹。仿真结果表明,在更为真实的飞行环境下,利用GPM和SQP相结合的方法可在5.83s获得一条精度为10-4～10-6左右的飞行轨迹。     

高超声速飞行器多约束再入轨迹快速优化

针对高超声速飞行器再入过程中面临测控区和绕飞区的再入轨迹设计问题,提出了一种基于Gauss伪谱法(GPM)的分段轨迹优化策略。将轨迹优化的一般最优控制问题转换为多段最优控制问题,进而将各段轨迹按Gauss伪谱方法进行离散化,将连续多段最优控制问题转换为非线性规划问题(NLP)进行求解。所得再入轨迹能够使得飞行器在满足各种约束条件的情况下成功进入测控区并且有效规避绕飞区,最终到达指定点。此外,本文综合考虑飞行器再入飞行的快速性和工程实用性,并提出了再入时间、弹道倾角以及航向角相关指标的加权性能指标,同时保证了轨迹规划快速、再入轨迹平滑以及控制量变化平缓等实际需求,提高了计算效率。仿真结果表明,本文所提出的分段优化方案能够快速规划出适应不同飞行任务的再入轨迹。     

基于组合优化算法的临近空间飞行器轨迹优化

提出一种临近空间飞行器轨迹优化方法,利用基于支持向量机与遗传算法的组合优化算法,解决多约束条件下的高效轨迹优化问题。首先,建立临近空间飞行器轨迹优化数学模型。然后,通过参数化方法和惩罚函数法将轨迹优化问题转化为约束参数优化问题。在此基础上,提出一种求解无约束参数优化问题的组合优化算法,通过支持向量机对遗传过程中产生的种群进行分类,提高基本遗传算法的计算效率,结合轨迹优化数学模型,给出轨迹优化算法。最后,以临近空间飞行器航程最远轨迹优化问题为例,进行数学仿真分析。仿真结果表明,针对给定的算例,文中提出的方法与基于基本遗传算法的轨迹优化方法相比,计算效率显著提高。     

基于序列凸规划的运载火箭轨迹在线规划方法

针对大气层内气动力对轨迹规划求解实时性与收敛性的影响,提出一种基于模型补偿序列凸规划的大气层内火箭轨迹规划方法.该方法的核心思想是通过设计一种序列补偿的方式,将火箭动力学中非线性项(气动力加速度与重力加速度)与过程约束项(动压、过载约束等)进行凸化,从而将轨迹规划问题转化为序列凸规划问题而得到快速求解.在此基础上,本文...     

配点法和网格细化技术用于非光滑轨迹优化

针对非光滑轨迹优化问题,采用局部配点法开发出通用的轨迹优化方法（考虑NLP的规范化处理、稀疏特性和数值微分算法等）,从细化效率、易用性和适应性等角度对基于数据压缩原理的网格细化技术进行改进,发展出通用的非光滑轨迹优化方法。采用典型的非光滑轨迹优化算例对方法进行了验证,结果表明：(1) 所述方法能够以较少的离散节点高精度、快速求解非光滑轨迹优化问题,在轨迹变化平坦区域采用较稀的网格,在轨迹变化剧烈区域加密网格;(2) 采用控制变量作为网格细化函数能够捕捉到状态变量的剧烈变化特性;(3) 采用局部配点法优化轨迹时,在非光滑区域应该加密网格而不宜分段优化。     

基于能量约束的翼伞系统分段归航设计与仿真

针对翼伞系统的基本飞行特性和良好的可操纵性,采用分段设计的思想对翼伞系统的归航轨迹进行规划.根据各分段轨迹之间的几何关系,将航迹规划问题转变为对设计参数的寻优问题.实际系统所能提供的能量是有限的.因此,在目标函数中加入控制能量的约束.运用改进的粒子群算法对目标函数进行求解计算,得到整个归航轨迹的设计参数.仿真结果表明:...     

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.     

TBCC飞行器发动机尺寸选型及爬升策略设计

针对临近空间高速飞行器爬升航迹问题,提出了一种涡轮冲压组合发动机尺寸选型的依据和一种固体火箭助推器辅助加速的爬升策略。以本文设计的一型临近空间高速飞行器为原型,基于hp自适应Radau伪谱法开展爬升航迹优化研究,将最优控制问题转化为非线性规划问题,以爬升消耗燃料质量最小为目标,利用序列二次规划算法求解最优航迹。在此基础上,分析了涡轮冲压组合发动机尺寸选型和采用固体火箭助推器加速爬升策略对爬升航迹和巡航航程的影响。结果表明,选取合理的发动机尺寸和助推器辅助爬升策略,均可有效减少飞行器爬升消耗燃料质量,提升巡航航程。     

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.