基于Gauss伪谱法的高超声速飞行器多约束三维再入轨迹优化

高超声速飞行器再入飞行过程中,需要满足多种过程约束和终端状态约束,同时再入初始状态根据飞行任务不同会有较大变化,针对其特点的快速轨迹优化问题已成为当今热点。本文研究了一种基于"初值轨迹生成+Gauss伪谱法+SQP求解NLP"的方法,既利用了Gauss伪谱法收敛快、精度高的特点,又结合初值轨迹生成算法,弥补了Gauss伪谱法对初值敏感的不足。本文在仿真过程中选取再入总吸热量最小为性能指标,求解了满足多种约束的再入轨迹,并将优化的结果与数值积分的结果进行比较,验证了此算法有效性和可行性。     

伪谱法在飞行器轨迹优化中应用分析

伪谱法作为一种在飞行器轨迹优化领域广泛应用的方法,国内外缺乏对其进行综合研究分析的相关文献。介绍了伪谱法在飞行器轨迹优化领域的发展现状,详细分析了已应用于飞行器轨迹优化的4种伪谱法的特点和应用情况,总结了这4种方法优缺点:Legendre伪谱法研究较早、应用最为广泛,Gauss伪谱法和Radau伪谱法精度较高,而Chebyshev伪谱法理论上精度高但研究刚起步。伪谱法具有全局特性,计算精度高,收敛快,但也存在缺乏收敛解判定准则、难以处理非光滑问题等不足。介绍了伪谱法在处理bang-bang控制问题时所遇到的困难,对伪谱法的改进工作做出总结:改进算法,研究与其他算法相结合的优化方法。总体而言,伪谱法在轨迹优化问题上的应用前景很广。     

电动帆航天器谷神星探测任务轨迹优化

针对电动帆航天器谷神星探测任务轨迹优化问题,提出一种基于高斯伪谱法和遗传算法的混合优化算法。为了验证所提出的混合优化算法有效性,并考察任务起始时间和电动帆特征加速度对探测任务的影响,进行了一定数量的数值仿真。仿真结果表明：电动帆航天器自地球至谷神星的飞行时间随着起始时间的变化呈周期性波动,波动周期基本与地球和谷神星的会合周期一致;电动帆航天器的特征加速度越小,完成过渡所需要的飞行时间越长,且一个具有中等特征加速度的电动帆航天器便能在可接受的时间内完成自地球至谷神星的过渡;所提出的混合优化算法是有效的,能够在无任何初值猜测的情况下完成电动帆航天器飞行轨迹的优化。     

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。     

多约束条件下高超声速滑翔飞行器轨迹优化

研究了考虑航路点、禁飞区、热流、动压、过载、控制量以及终端状态等多种约束条件下高超声速滑翔飞行器轨迹优化设计问题。分析了采用一般Gauss伪谱方法进行高超声速滑翔飞行器轨迹优化设计存在的主要问题,为此,提出了轨迹分段优化策略,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进行求解。以多约束条件下最大射程轨迹优化为例进行仿真分析,结果表明分段优化方法能够较快地设计出满足各种约束条件的优化轨迹。     

亚轨道飞行器返回轨迹快速优化

快速、准确、鲁棒的轨迹生成方法可以增加任务的安全性与可靠性,极大地降低成本。针对亚轨道飞行器返回段特点,引入"伪控制量"、"末端进场走廊"等概念,分别采用高斯伪谱法和向前拉道伪谱法进行了返回轨迹快速优化研究,比较了两种伪谱法在处理复杂问题时的能力。仿真结果表明,向前拉道伪谱法不适合处理含控制量约束的问题,而高斯伪谱法在满足各种约束条件下,能够快速准确地生成亚轨道飞行器返回轨迹,同时验证了结果的可行性与最优性。     

基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究

研究Gauss伪谱法在多级固体运载火箭上升段轨迹快速优化设计中的应用。针对多
级固体运载火箭上升段轨迹优化的特点,研究了求解多阶段最优控制问题的Gauss伪谱法,
引入连接点概念处理间断点,设计了边界控制变量计算方法。为进一步提高轨迹优化速度,
设计了含初值生成器的Gauss伪谱法串行轨迹优化策略,实现了固体运载火箭上升段轨迹快
速优化。仿真结果表明,采用提出的优化方法优化一条上升段轨迹所用时间为2~3分钟,终
端约束和路径约束均得到很好满足,算法求解精度高,对初值依赖性小,设计的边界控制变
量计算方法可行。     

基于Gauss伪谱方法的高超声速飞行器再入轨迹快速优化

基于一种求解最优控制问题的新方法—Gauss伪谱法(Gauss Pseudospectral Method\|GPM) ,研究了高超声速飞行器滑翔式再入的快速轨迹优化问题。针对远程多约束条件下滑翔式再 入轨迹优化问题的难点,提出了基于GPM的串行分段优化策略,包括三个方面：(1) 构造了 设计变量初值生成器,获得近似最优解作为优化初值;(2) 提出从可行解到 最优解的串行优化策略;(3) 引入平衡滑翔条件构造动态分段点,将再入轨迹分为初始下降 段和滑翔段分别求解。以某高超声速再入飞行器为对象进行轨迹优化计算,仿真结果验证了 本文的轨迹优化方法具有较高的精度和计算效率。
     

亚轨道飞行器上升段轨迹优化与快速重规划

针对亚轨道飞行器上升段轨迹优化问题,提出了基于Legendre伪谱法的轨迹优化与快速重规划方法.结合亚轨道飞行器上升段运动特点,着重研究气动力的表示方法,建立了矢量形式的动力学方程.应用Legendre伪谱法进行上升段轨迹优化,并分析了优化结果.结合该方法的特点研究了基于Legendre伪谱法的轨迹重规划方法.仿真表明轨迹优化结果具有精度高、满足一阶最优性必要条件等特点,重规划轨迹的入轨精度高,且重规划的时间短,能满足快速性要求.     

Photonic spin control for solar wind electric sail

The electric solar wind sail (E-sail) is a novel, efficient propellantless propulsion concept which utilises the natural solar wind for spacecraft propulsion with the help of long centrifugally stretched charged tethers. The E-sail requires auxiliary propulsion applied to the tips of the main tethers for creating the initial angular momentum and possibly for modifying the spinrate later during flight to counteract the orbital Coriolis effect and possibly for mission specific reasons. We introduce the possibility of implementing the required auxiliary propulsion by small photonic blades (small radiation pressure solar sails). The blades would be stretched centrifugally. We look into two concepts, one with and one without auxiliary tethers. The use of small photonic sails has the benefit of providing sufficient spin modification capability for any E-sail mission while keeping the technology fully propellantless. We conclude that small photonic sails appear to be a feasible and attractive solution to E-sail spinrate control.     

Optimal control laws for heliocentric transfers with a magnetic sail

A magnetic sail is an advanced propellantless propulsion system that uses the interaction between the solar wind and an artificial magnetic field generated by the spacecraft, to produce a propulsive thrust in interplanetary space. The aim of this paper is to collect the available experimental data, and the simulation results, to develop a simplified mathematical model that describes the propulsive acceleration of a magnetic sail, in an analytical form, for mission analysis purposes. Such a mathematical model is then used for estimating the performance of a magnetic sail-based spacecraft in a two-dimensional, minimum time, deep space mission scenario. In particular, optimal and locally optimal steering laws are derived using an indirect approach. The obtained results are then applied to a mission analysis involving both an optimal Earth–Venus (circle-to-circle) interplanetary transfer, and a locally optimal Solar System escape trajectory. For example, assuming a characteristic acceleration of 1 mm/s², an optimal Earth–Venus transfer may be completed within about 380 days.     

Station keeping of a solar sail around a Halo orbit

Solar sails are a concept of spacecraft propulsion that takes advantage of solar radiation pressure to propel a spacecraft. Although the thrust provided by a solar sail is small it is constant and unlimited. This offers the chance to deal with novel mission concept. In this work we want to discuss the controllability of a spacecraft around a Halo orbit by means of a solar sail. We will describe the natural dynamics for a solar sail around a Halo orbit. By natural dynamics we mean the behaviour of the trajectory of a solar sail when no control on the sail orientation is applied. We will then discuss how a sequence of changes on the sail orientation will affects the sail's trajectory, and we will use this information to derive efficient station keeping strategies. Finally we will check the robustness of these strategies including different sources of errors in our simulations.     

Electric sail,photonic sail and deorbiting applications of the freely guided photonic blade

We consider a freely guided photonic blade (FGPB) which is a centrifugally stretched sheet of photonic sail membrane that can be tilted by changing the centre of mass or by other means. The FGPB can be installed at the tip of each main tether of an electric solar wind sail (E-sail) so that one can actively manage the tethers to avoid their mutual collisions and to modify the spin rate of the sail if needed. This enables a more scalable and modular E-sail than the baseline approach where auxiliary tethers are used for collision avoidance. For purely photonic sail applications one can remove the tethers and increase the size of the blades to obtain a novel variant of the heliogyro that can have a significantly higher packing density than the traditional heliogyro. For satellite deorbiting in low Earth orbit (LEO) conditions, analogous designs exist where the E-sail effect is replaced by the negative polarity plasma brake effect and the photonic pressure by atmospheric drag. We conclude that the FGPB appears to be an enabling technique for diverse applications. We also outline a way of demonstrating it on ground and in LEO at low cost.     

太阳帆日心定点悬浮转移轨道设计

研究了太阳帆航天器日心定点悬浮轨道(HFDO)的转移轨道设计问题,以球坐标形式建立了太阳帆的动力学模型,基于该模型给出在日心悬浮轨道基础上实现定点悬浮的条件,提出了一种实现日心定点悬浮的转移轨道设计方法。首先,确定定点悬浮的位置;然后,设计经过该位置的绕日极轨轨道;最后,实施轨道减速实现定点悬浮,并给出了解析形式的轨道控制律。结合太阳极地观测任务,设计了定点悬浮在太阳北极1AU处的太阳帆转移轨道。仿真结果表明:该轨道转移方案总耗时3.5年,太阳帆定点到黄北极距日心1AU处,此后只要保持太阳光垂直照射帆面,即可维持稳定的悬浮状态。     

The Aurora project: Estimation of the optical sail parameters

The thrust model for computing a sailcraft trajectory contains thermo-optical parameters that are averages over the spectrum of the incident photons, namely, with respect to energy, intensity and polarization. These parameters are not observables and could change considerably from a sail to sail for a number of practical reasons. The mission analysis for a sailcraft is a progressive task from a simple trajectory propagator to the orbit determination. Aurora sailcraft mission analysis has advanced another step forward by processing experimental data related to aluminium. Once appropriate fitting functions have been selected, differential specular and diffused reflectance and differential absorptance have been averaged over incident solar spectrum, assumed a Planckian here. The result has been to get incident-angle-dependent optical parameters more reliable than mere literature values. The procedure has entailed the computation of grids of complicated definite integrals. They are particularly important during the trajectory optimization of the Aurora solar flyby, a very sensitive profile that would allow the sailcraft to achieve cruise speeds ranging from 12 to 20 AU/yr.     

基于自适应高斯伪谱法的SGCMG无奇异框架角轨迹规划

针对采用SGCMG作为姿态执行机构的小卫星,在大角度机动过程中SGCMG系统易陷入奇异的问题,提出了一种基于自适应Gauss伪谱法的SGCMG无奇异框架角轨迹快速规划方法。该算法综合考虑到实际工程应用中存在的SGCMG框架角受限、框架角速度受限,奇异量度受限,星体机动角速度受限以及星体初始和终端状态受限等约束条件,将卫星大角度机动问题看成满足上述一系列约束条件和边界条件同时实现某一性能指标最优的最优控制问题。然后,结合自适应高斯伪谱法与非线性规划技术,求解带有边界约束与路径约束的最优化问题,获得实现性能指标最优的无奇异SGCMG系统轨迹。仿真结果表明：该算法能够在25s的时间内给出顺利实现大角度机动并满足所有约束条件,同时近似精度优于10 -3 的高精度平滑轨迹。     

一种高超声速飞行器再入轨迹优化方法

针对高超声速飞行器的再入轨迹优化问题，提出了一种基于动态自适应樽海鞘群算法和高斯伪谱法的混合优化方案。首先，为了使樽海鞘群算法探索和利用之间的平衡更加合理，提出了一种新颖的动态自适应樽海鞘群算法。然后，针对传统高斯伪谱法在轨迹优化过程中对初始猜测值敏感的不足，借助动态自适应樽海鞘群算法强大的全局搜索能力，先利用该算法对控制量进行全局寻优，将求得的近似全局最优解作为高斯伪谱法优化的初始猜测值，接着再利用高斯伪谱法对控制量进行全局寻优。仿真结果表明所提出的动态自适应樽海鞘群算法和混合优化方案的有效性和可行性。