Target sequence optimization for multiple debris rendezvous using low thrust based on characteristics of SSO

A method is proposed to select the target sequence for a J 2-perturbed multiple debris rendezvous mission aimed at removing dozens of debris from several thousand debris candidates running on sun-synchronous orbits(SSO).The solving methodology proceeds in two steps:Firstly,the variance of the right ascension of ascending node(RAAN)of the debris group is used for narrowing down the potential debris candidate;secondly,the debris of the candidate group that has closest RAAN to the current debris is chosen as the next debris.The low thrust near-minimum-fuel trajectories of each rendezvous leg are obtained by the indirect optimization method.The proposed approach is demonstrated for the problem of the 8th China Trajectory Optimization Competition(CTOC).The radar cross section(RCS)of the debris is also considered in the first step since the primary performance index of the competition is to maximize the total RCS of the debris visited.The results show that the proposed approach achieves better performance within a competition period.Of the many rendezvous sequences found,the best one submitted for the competition obtained a total RCS of 184 by accomplishing rendezvous with 70 debris within a transfer duration of one year.

Practical Optimization of Low-Thrust Minimum-Time Orbital Rendezvous in Sun-Synchronous Orbits

High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.

Fuel optimal low thrust rendezvous with outer planets via gravity assist

Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.

Low-thrust trajectory optimization in a full ephemeris model

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

Optimization of multi-revolution low-thrust transfer based on modified direct method

A modified direct optimization method is proposed to solve the optimal multi-revolution transfer with low-thrust between Earth-orbits.First,through parameterizing the control steering angles by costate variables,the search space of free parameters has been decreased.Then,in order to obtain the global optimal solution effectively and robustly,the simulated annealing and penalty function strategies were used to handle the constraints,and a GA/SQP hybrid optimization algorithm was utilized to solve the parameter optimization problem,in which,a feasible suboptimal solution obtained by GA was submitted as an initial parameter set to SQP for refinement.Comparing to the classical direct method,this novel method has fewer free parameters,needs not initial guesses,and has higher computation precision.An optimal-fuel transfer problem from LEO to GEO was taken as an example to validate the proposed approach.The results of simulation indicate that our approach is available to solve the problem of optimal multi-revolution transfer between Earth-orbits.

Low-thrust trajectory optimization for multiple target bodies tour mission

Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission.The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission.For the problem of global trajectory optimization,even with recent advances in low-thrust trajectory optimization,a full enumeration of this problem is not possible.This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions.The flight sequence is determined in ballistic scenario,and a differential evolution method is used with constructing a three-impulse transfer problem,then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories.The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.

Perturbed low-thrust geostationary orbit transfer guidance via polynomial costate estimation

This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit.The Earth’s oblateness perturbation and shadow are taken into account.It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time,including high guidance optimality,robustness,and onboard computational efficiency.In this work,a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified,which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation.Based on this relationship,the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged trajectory.Five polynomial regression models are trained on the training dataset and are regarded as the costate estimators.In the transfer,the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any time.Moreover,all these computations onboard are analytical.The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality,robustness,and onboard computational efficiency.

基于调相机制的航天器碰撞规避策略设计

针对携带电推进等小推力推进系统工作的航天器,提出一种利用连续推力调相机制的在轨碰撞规避机动策略。首先,采用混沌多项式展开方法对初始状态不确定性的航天器碰撞概率进行分析,并以此作为碰撞规避策略的评价指标;进而推导了一种适用于小推力的轨道机动的解析解。利用这一解析结果可以提出一种新的避碰方法,即通过航天器轨道相位的微调减小航天器碰撞概率,并且在机动后能够迅速恢复原轨道相位。数值仿真表明:基于所提出的避碰机动策略,可以在较短时间内减小碰撞概率。数值仿真还揭示了避碰时间、燃耗和推力加速度之间的关系。

基于EKF/PI滤波的小推力轨控期间自主导航算法

研究了以电推小推力作为主要的轨控推力来源的高轨卫星在轨控期间的自主导航算法。针对GNSS接收机在高轨的测速精度相对较差,以及轨控期间电推产生的推力较小,常规加速度计无法准确测量,从而导致在轨控期间自主导航精度下降的问题,提出了基于EKF+PI滤波的一体化自主导航算法。通过结合EKF滤波和PI滤波算法,经EKF滤波抑制GNSS接收机定位数据的测量白噪声,然后通过PI滤波估计电推加速度并反馈给EKF滤波算法,提高电推工作期间EKF算法的导航精度。仿真结果表明,基于EKF+PI滤波的一体化自主导航算法可以准确估计出电推加速度大小,同时可有效提高连续小推力轨控期间的自主导航精度。

相继增压系统切换过程对增压器辅推轴承轴向力影响与轴承优化研究

采用数值仿真方法研究基本增压器在系统切换过程中的轴向力变化规律,并提出了辅助推力轴承的改进设计方法。首先数值仿真研究了基本增压器的转子系统在切换时的压气机/涡轮关键典型截面气动参数分布情况,分析了在柴油机增压模式切换过程中基本增压器转子轴向力大小和方向变化规律,然后提出了增加轴承承力面及改变承力面材料的优化方案。结果表明:基本增压器辅助推力轴承在切换的5 s时间内轴向力发生翻转,最大约承受2273 N的反向轴向力,是造成切换过程辅助推力轴承磨损的关键原因;优化方案最大承载能力为优化前的4.8倍,显著提升了辅助推力轴承承载力。经增压器平台可靠性验证,改进后的增压器辅助推力轴承在相同时间内未出现碰磨现象。

Effect of Spanwise Flexibility on Propulsion Performance of a Flapping Hydrofoil at Low Reynolds Number

Spanwise flexibility is a key factor influencing propulsion performance of pectoral foils. Performances of bionic fish with oscillating pectoral foils can be enhanced by properly selecting the spanwise flexibility. The influence law of spanwise flexibility on thrust generation and propulsion efficiency of a rectangular hydro-foil is discussed. Series foils constructed by the two-component silicon rubber are developed. NACA0015 shape of chordwise cross-section is employed. The foils are strengthened by fin rays of different rigidity to realize variant spanwise rigidity and almost the same chordwise flexibility. Experiments on a towing platform developed are carried out at low Reynolds numbers of 10 000, 15 000, and 20 000 and Strouhal numbers from 0.1 to 1. The following experimental results are achieved: (1) The average forward thrust increases with the St number increased; (2) Certain degree of spanwise flexibility is beneficial to the forward thrust generation, but the thrust gap is not large for the fins of different spanwise rigidity; (3) The fin of the maximal spanwise flexibility owns the highest propulsion efficiency; (4) Effect of the Reynolds number on the propulsion efficiency is significant. The experimental results can be utilized as a reference in deciding the spanwise flexibility of bionic pectoral fins in designing of robotic fish prototype propelled by flapping-wing.

一种利用卫星星历计算机动加速度的方法

对于近地轨道卫星,由于受大气影响较大,轨道机动比较频繁,…轨道机动的快速检测以及推力的计算,对保障空间目标运行安全及故障分析意义重大。本文基于公开发布的卫星星历数据,提出了基于卫星星历识别轨道机动的方法,并通过轨道预报迭代反演和能量转化两种方式,实现了小推力条件下卫星轨道机动加速度的计算,两种计算方法计算结果有很好的一致性。应用该方法基于星历文件对多个星座目标进行机动识别与加速度解算,以解算结果对卫星轨道进行星历仿真,仿真结果与发布的星历基本一致。

组合动力飞行器模态转换段推阻匹配与控制律设计

针对组合动力飞行器在进行模态转换时,发动机推力的损失以及进气道进气时对飞行器周围气流的影响,导致飞行器本体动力学特性呈现出强烈的非线性、耦合性和模型不匹配性等问题。文中根据涡喷发动机和冲压发动机输出推力随流量变化的关系,提出一种流量分配方案补偿了发动机动力切换时的推力损失。考虑到组合动力飞行器模态转换段动力学的复杂性,采用L1鲁棒自适应控制实现飞行器的内环增稳,采用蒙特卡洛打靶方式验证控制律的鲁棒性。仿真实验证明,设计的控制律具有一定鲁棒性。

新型永磁辅助同步磁阻直线电机设计

同步磁阻直线电机是一种通过次级侧在不同位置引起磁阻变化、产生磁阻推力的交流电机,具有成本低、耗能小、推力易于控制等优点,但存在凸极比低、推力小等不足。针对传统直线电机推力小、推力波动大、成本高等问题,采用磁路法建立磁路模型、有限元分析等方法,设计了一种新型永磁同步直线电机,相对传统电机性能有了很大提升,尤其对推力精度要求高的场景,该新型永磁同步直线电机应用范围会更加广阔。

低压涡轮导向器开度对变循环发动机的影响

建立了变循环发动机整机模型并对可变几何低压涡轮特性进行修正,研究了低压涡轮导叶开度从-6°~6°时对各部件以及发动机整体性能的影响。结果表明:随低压涡轮导向器角度变大,低压涡轮进口折合流量增大,不论低压涡轮导向器开大或关小,高、低涡轮效率均下降;随导叶开度增大,高压涡轮膨胀比增大,高压轴功率增大,高压压气机(High pressure compressor,HPC)与核心机驱动风扇级(Core driven fan stage,CDFS)压比增大;双外涵模式下涡轮导叶角度为0°时单位推力最大,单外涵模式下涡轮角度为-1°时单位推力最大。

基于高斯伪光谱的星际小推力转移轨道快速优化

针对星际小推力转移轨道优化问题,给出了一种基于高斯伪光谱配点的快速优化算法。首先,基于归一化的改进春分点根数建立了星际小推力转移轨道的优化模型;然后,采用高斯伪光谱配点策略对优化模型进行离散化处理,推力方向限制和天体星历分别作为路径约束和事件约束,将轨道优化问题转化为一个大规模多约束参数优化问题;在此基础上,基于高斯伪光谱的配点特性,推导出性能指标和约束方程的解析雅可比矩阵,保证了雅可比矩阵计算的准确性和效率;最后,以利用太阳能电推进探测火星和水星为例,对所给算法进行了数值验证。数值结果表明:高斯伪光谱方法可有效用于星际小推力轨道的优化问题,并且与数值差分相比,解析的雅可比矩阵算法可提高计算效率67.78%。

快速绕飞卫星空间圆编队设计方法

连续小推力条件下,针对圆参考轨道卫星,推导了满足快速绕飞条件的空间圆编队动力学模型。分析了一个绕飞周期内的燃耗情况。在绕飞周期确定的条件下,给出了最小燃耗的计算方法,并利用数值方法验证了所推导公式的正确性。计算结果表明,在高度为500km的圆轨参考道卫星实现周期为10分钟、半径100m的空间圆绕飞,一个绕飞周期所需最小速度增量约为4.77m/s。文章提出的基本设计原理并不局限于空间圆编队,也可用于其它快速绕飞编队的设计工作。

结合行星借力飞行技术的小推力转移轨道初始设计

针对结合行星借力和小推力技术的行星际转移轨道设计问题,提出一种基于形状逼近策略的初始设计方法。采用改进的逆六次多项式策略计算小推力弧段,通过引入B平面参数和推进器开关点时间系数实现行星借力和推滑混合轨道的拼接,将初始设计问题转化为求解混合整数非线性规划问题。为降低规划模型求解难度,通过参数变换对模型进行简化处理,并采用具有全局大范围搜索能力的改进微分进化算法求解最优设计参数。数值结果表明:相比正弦指数曲线设计方法,本文方法可以有效对交会型转移轨道进行设计,并且可以提供更少燃料消耗的探测机会。

面向小推力变轨的天文组合自主导航方法

针对小行星探测任务对导航系统自主性强、实时性高的需求,研究了一种面向小推力变轨的天文组合自主导航方法。根据工程实践分析并建立了电推进变轨过程中的动力学模型,给出了天文测角测速组合的小行星探测自主导航方案。为克服小行星探测器推力的不确定性,提出了采用自适应交互式多模型无迹卡尔曼滤波(AIMM-UKF)算法,以较少的模型个数实现对导航系统状态的覆盖,克服了模型集合先验信息不准确对导航精度的影响,提高了组合导航系统的鲁棒性和抗干扰能力。最后,通过数学仿真对组合导航算法的性能进行了验证,结果表明本文提出的组合导航方法估计精度更高、计算消耗更小,可满足小行星探测工程任务对导航系统自主性、实时性和高精度的需求。