Multiobjective genetic optimization of Earth–Moon trajectories in the restricted four-body problem

In this paper, optimal trajectories of a spacecraft traveling from Earth to Moon using impulsive maneuvers (ΔV maneuvers) are investigated. The total flight time and the summation of impulsive maneuvers ΔV are the objective functions to be minimized. The main celestial bodies influencing the motion of the spacecraft in this journey are Sun, Earth and Moon. Therefore, a three-dimensional restricted four-body problem (R4BP) model is utilized to represent the motion of the spacecraft in the gravitational field of these celestial bodies. The total ΔV of the maneuvers is minimized by eliminating the ΔV required for capturing the spacecraft by Moon. In this regard, only a mid-course impulsive maneuver is utilized for Moon ballistic capture. To achieve such trajectories, the optimization problem is parameterized with respect to the orbital elements of the ballistic capture orbits around Moon, the arrival date and a mid-course maneuver time. The equations of motion are solved backward in time with three impulsive maneuvers up to a specified low Earth parking orbit. The results show high potential and capability of this type of parameterization in finding several Pareto-optimal trajectories. Using the non-dominated sorting genetic algorithm with crowding distance sorting (NSGA-II) for the resulting multiobjective optimization problem, several trajectories are discovered. The resulting trajectories of the presented scheme permit alternative trade-off studies by designers incorporating higher level information and mission priorities.     

空间小推力轨道最优Bang-Bang控制的两类延拓解法综述

介绍了空间小推力轨道优化问题中的最优Bang-Bang控制问题,对两类延拓解法给出了描述:第一类解法首先求解能量最优解,然后采用能量–燃耗同伦得到最优Bang-Bang控制;第二类解法引入推力开关切换准则,以双脉冲解作为初解,通过参数延拓得到最优Bang-Bang控制。对两类延拓解法进行了比较,指出了各自的优势与特点。对延拓方法应用于求解更加复杂的小推力轨道设计问题进行了展望,提出了包含初解、延拓与拼接三要素的人工智能轨道优化概念。     

Ascent guidance law for a horizontal take-off vehicle with a multi-combined cycle engine

This paper researches the ascent guidance law for the vehicle with a multi-combined cycle propulsion. The guidance law comprises two parts, namely, the off-line optimal trajectories generation and online guidance. With respect to the off-line part, disturbances are discretized and incorporated into the trajectory optimization problem; subsequently, a set of trajectories is calculated to constitute a database. To quickly obtain a database that comprises a large number of trajectories, a novel ascent profile is proposed with respect to height and velocity. Based on this profile, only inequity constraints exist in the optimization model, and the original optimization problem is converted to a parameter searching problem. The optimal trajectories are calculated using a hybrid optimization method that comprises a particle swarm optimization (PSO) method and the Hooke-Jeeves (HJ) method. With respect to online guidance, the profile is updated using a radial basis function neural network (RBFNN) based on the current flight states and the database. Simulation validates the efficiency of the proposed optimization method by comparing the method with the pseudospectral method; the robustness of the guidance law is also validated using Monte Carlo simulation.     

载人小行星探测任务总体方案研究

设计了在近地轨道组装具有分组单元结构的载人深空飞船,包括核热推进单元、燃料储箱与供给单元、主动防辐射单元、人工重力单元、深空居住舱与多任务乘员舱等,给出了各个单元的尺寸与质量参数,并对主要单元的具体组成、功能和技术特点进行了分析。在此基础上,本文以编号4660的Nereus小行星为探测目标,设计了两脉冲转移初始轨道,并进行了轨道优化,得到了发射窗口和最优转移轨道。仿真结果表明,给出的最优两脉冲转移轨道单次施加脉冲在5km/s以内,单程转移时间在160d以内,能够满足未来能量较小的载人小行星探测任务。     

气动力辅助椭圆轨道转移技术研究

研究了两种共面椭圆轨道最优转移方法--基于单纯推力的双脉冲对称转移和基于气动力辅助变轨技术的协同机动方法。推导了双脉冲对称转移问题中转移椭圆轨道的求解公式,采用遗传算法求解最优变轨点位置,给出了变轨脉冲的计算方法。将气动力辅助对称转移过程分为3段：真空飞行段、大气飞行段、真空飞行段。以能量最小为性能指标,将大气飞行段轨迹优化问题转化为标准最优控制问题模型,并利用Gauss伪谱法进行求解,得到“巡航+滑行+巡航+滑行”的大气最优飞行轨迹。最后对两种转移方法进行详细比较,指出初始椭圆轨道近地点越接近大气层,气动力辅助对称转移方法比双脉冲对称转移方法越节省能量。     

基于遗传算法的最优Lambert双脉冲转移

研究了初始位置和转移时间不固定的Lambert双脉冲轨道转移的数值解,用三 维图和截面图直观显示了初始位置、转移时间和速度增量的关系,并说明了其在实际工程任 务中的应用价值.基于数值解,提出了Lambert双脉冲轨道转移的优化问题.目标是找到最 优初始位置和转移时间,使燃料和时间的加权和最小.给出了遗传算法求解该优化问题的设 计步骤.该算法应用于2个算例:①平面圆轨道的燃料最优转移,并将遗传算法和Hohmann 转移的结果进行了比较;②椭圆轨道、初始位置有约束的燃料和时间最优转移.结果说明 了遗传算法寻找最优转移解是准确有效的.      

基于蚁群算法和Powell法的Lambert转移

研究了两次脉冲时刻均不固定的Lambert轨道转移的优化问题,目标是找到施加两次脉冲的最优时刻,使燃料和转移时间的加权和最小.鉴于传统的优化算法难以获得该优化问题的全局最优解,提出了一种蚁群算法和Powell法相结合的优化算法,给出了算法的设计步骤.该算法结合了蚁群算法的全局搜索能力和Powell法的局部寻优能力,在保证全局搜索能力的同时,提高了算法的局部寻优能力和精度,减少了寻优时间.通过两个算例验证了这种结合的有效性和准确性.     

Energy-optimal reconfiguration of satellite formation flying in the presence of uncertainties

In this study, a two-step control methodology is developed for energy-optimal reconfiguration of satellites in formation in the presence of uncertainties or external disturbances. First, based on a linear deterministic system model, an optimal control law is analytically determined such that a satellite maneuvers from an initial state to a final state relative to another satellite. The structure of this optimal solution is predetermined and simply given by a linear combination of the fundamental matrix solutions associated with the original equations of relative motion. Only the coefficients are to be determined to satisfy given initial and final conditions. In the second step, an uncertain nonlinear formation system is considered and a robust adaptive controller is designed to compensate for the effects of uncertainties or disturbances that the formation system may encounter. Although the control strategy is inspired by sliding mode control, it produces smooth control signals, thereby avoiding chattering. Also, an adaptation law is added such that the uncertainty or disturbance effects are effectively and quickly eliminated without a priori information about them. The combination of these two controllers guarantees that the satellite accurately tracks the optimal path in the unknown environment. Numerical simulations demonstrate the effectiveness and accuracy of the proposed two-step control methodology, in which a satellite formation is optimally reconfigured under unknown environmental disturbances.     

星载InSAR辅星编队优化设计与分析

以“主星—辅星编队”InSAR系统干涉测高为应用背景,研究辅星编队的优化设计问题。首先,定义优化指标———“有效观测时间比”来描述全轨道周期观测性能,以共绕飞轨道、相位均匀分布的卫星编队(构形类似于CartWheel)作为研究的重点。选取描述编队卫星相对运动的振幅比和相位差作为寻优变量,通过仿真实例用搜索法得出了寻优变量与优化指标的三维关系图,并给出了优化构形的参数区域,得到了最优的编队卫星轨道根数。进一步研究了在主要摄动因素影响下卫星编队构形保持与轨道保持的燃料预算方法,并计算了上述优化构形一年的燃料预算。最后得出有益的结论,为全InSAR系统优化设计提供依据。     

基于引导型人工免疫算法的最优Lambert变轨

主要研究了燃料最省的Lambert双脉冲变轨问题.首先对普适变量法进行改进以避免奇异,并将其用于Lambert双脉冲变轨问题的求解.然后针对只给定初始时刻追踪航天器和目标航天器的轨道要素及总时间约束的交会问题,引入调相时间的概念,并将其和转移时间作为Lambert变轨的优化变量.最后采用引导型人工免疫算法GAIA(Guiding Artificial Im-mune Algorithm)对该优化问题进行寻优.仿真算例表明,与自适应遗传算法AGA(Adaptive Ge-netic Algorithm)相比,GAIA具有更强的寻优能力和更快的寻优速度,从而验证了GAIA用于最优Lambert变轨的有效性.     

椭圆轨道卫星编队燃料最优机动实时算法

文章针对椭圆轨道编队卫星最优燃料机动的实时计算问题进行研究。利用LGL伪谱法对问题进行快速求解。由于最优燃料控制为非连续控制,如直接采用伪谱法则只有当离散点数目很大时,才能实现较高精度的编队机动控制,而这会影响算法的实时计算效率。为了克服这方面的不足,文章提出了一种时间尺度变换策略,并结合模型预测的滚动优化方法,设计了一种编队实时机动控制算法。该算法在兼顾解的全局最优性的同时改善了解的局部精确性,最后通过数值仿真验证了所设计算法的有效性。     

Optimal mission planning of the reconfiguration process of satellite constellations through orbital maneuvers: A novel technical framework

In this paper, a general new methodology is presented for the orbital reconfiguration of satellite constellations on the basis of Lambert targeting theorem. In view of the cost and risk reduction, it is very important to consider the problem of satellite constellation reconfiguration with the two constraints of overall mission cost minimization and the desired final configuration. Hence, the dependent non-simultaneous deployment approach is proposed to minimize overall fuel cost. Despite the fact that the satellites deploy in a non-simultaneous manner, supplementary phasing maneuvers on the target orbital pattern to achieve the desired orbital configuration are avoided. Moreover, a novel idea is presented to optimize the flight of satellites, which plays an important role in complying with the constraint of overall fuel cost minimization as much as possible. In order to achieve the global optimal solution of the satellite constellation reconfiguration problem, the efficient hybrid Particle Swarm Optimization/Genetic Algorithm (PSO/GA) technique, is implemented. Finally, to indicate the superiority of the presented method, a comparison to the simultaneous maneuver viewpoint is made on a number of representative cases. The obtained results imply significant reduction of reconfiguration costs by employing the proposed method.     

基于自适应模拟退火遗传算法的最优Lambert转移

主要研究了航天器采用Lambert二脉冲变轨的优化问题。对于初始位置、目标位置和转移时间都不固定的Lambert二脉冲转移,由于多变量以及方程本身的复杂性,采用传统的优化方法效率低甚至无法求解.采用了自适应遗传算法(AGA),寻求多变量的最优解.同时结合模拟退火算法,得到了自适应模拟退火遗传算法(ASAGA),该算法既具有全局搜索能力,又改善了一般遗传算法的局部寻优能力.通过仿真,比较了遗传算法和自适应模拟退火遗传算法的寻优结果,表明两者寻求最优转移的有效性,以及自适应模拟退火算法具有更强的寻优能力.      

Formation flying reconfiguration manoeuvres via environmental forces in highly elliptical orbits

A study on reconfiguration manoevres applied to a tetrahedral formation in highly elliptical orbits is proposed, by using a propellantless solution. The manoeuvring strategy consists in exploiting certain environmental forces, specifically those provided by solar radiation pressure and atmospheric drag, by actively controlling the satellites’ attitudes. Through inverse dynamics particle swarm optimization the optimal attitudes required for the manoeuvres are evaluated, whereas the configuration’s evolution is simulated by a high-fidelity orbital simulator. The goal of the reconfiguration problem is to find an optimal control in order for the four spacecraft to reach a desired configuration in a specified portion of orbit, where the desired configuration is evaluated by a shape and size geometric parameter. By increasing the manoeuvring time and the satellites’ area to mass ratio, all the case studies considered are successfully verified.     

临近圆轨道最优脉冲交会中的参考系选择问题研究

利用极坐标下的无量纲化线性方程研究临近圆轨道最优脉冲交会中的参考系选择问题。首先给出了无量纲化线性方程,接着以定理的形式说明参考系的选择对该方程下的最优交会模式的分类和分布没有影响,并以二脉冲最优交会及二脉冲带漂移最优交会、Hohm-ann最优交会三种交会模式为例说明不同参考系的选择对各自模式下的求解过程也没有影响。但是在无量纲化过程中交会时间和轨道半径差受参考系选择的影响,所以参考系的选择会影响最优交会的结果,最后通过三种最优交会模式的仿真对此结论进行了验证。     

A hybrid,self-adjusting search algorithm for optimal space trajectory design

The aim of the present paper is to propose a hybrid, self adjusting, search algorithm for space trajectory optimization. By taking advantage of both direct and indirect methods, the present algorithm allows the finding of the optimal solution through the introduction of some new control parameters, whose number is smaller than that of the Lagrange multipliers, and whose range is bounded. Eventually, the optimal solution is determined by means of an iterative self-adjustment of the search domain occurring at “runtime”, without any correction by an external user. This new set of parameters can be found through a reduction process of the degrees of freedom, obtained through the transversality conditions before entering the search loop. Furthermore, such a process shows that Lagrange multipliers are subject to a deep symmetry mirroring the features of the state vector. The algorithm reliability and efficiency is assessed through some test cases, and by reproducing some optimal transfer trajectories: a full three-dimensional, minimum time Mars mission, an optimal transfer to Jupiter, and finally an injection into a circular Moon orbit.     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

近圆轨道卫星编队捕获技术研究

基于近圆参考轨道的假设,研究处于同一入轨点多颗卫星的编队捕获方法.首先由高斯型拉格朗日轨道摄动运动方程得到轨道坐标系中控制冲量与轨道根数偏差的关系,基于近圆轨道的条件简化并带入相对运动方程,得到控制冲量与相对运动的关系表达式;通过深入分析各个方向(径向、沿迹向与轨道面法向)的控制冲量对相对运动的影响,给出了分别用径向与轨道面法向控制冲量组合和沿迹向与轨道面法向控制冲量组合实现编队捕获的两种控制策略;最后给出了一个空间圆编队捕获实例,并从燃料消耗、施加冲量次数及捕获时间等角度对比研究了两种控制策略的特点.仿真结果表明,这两种控制策略简单、实用,能够较好地解决近圆轨道卫星编队的捕获问题.      

嫦娥一号卫星的地月转移变轨控制

文章阐述了嫦娥一号卫星地月转移阶段(从星箭分离到进入使命轨道)的高可靠、高精度自主变轨控制方案,介绍了飞行轨道、轨控策略及控制参数优化、星上自主变轨控制的系统设计和相关参数的地面标定等,给出了在轨飞行试验的验证结果。     

不规则区域成像覆盖星座构型优化设计

近年来卫星对地观测需要呈现逐年上升趋势.从单个目标点的对地观测卫星星座构型设计方法入手,推广为设计满足不规则大范围成像区域重访时间需求的卫星星座.以卫星数目最少及满足重访时间要求为优化目标,采用改进的模拟退火算法,结合改进的等面积网格点覆盖法,提出了一种针对不规则区域成像全覆盖的卫星星座构型优化设计方法.分析了光照因素对重访时间、所需卫星数目以及星座构型的影响,并通过仿真分析验证了算法的可行性.