Modeling irregular small bodies gravity field via extreme learning machines and Bayesian optimization

Close proximity operations around small bodies are extremely challenging due to their uncertain dynamical environment. Autonomous guidance and navigation around small bodies require fast and accurate modeling of the gravitational field for potential on-board computation. In this paper, we investigate a model-based, data-driven approach to compute and predict the gravitational acceleration around irregular small bodies. More specifically, we employ Extreme Learning Machine (ELM) theories to design, train and validate Single-Layer Feedforward Networks (SLFN) capable of learning the relationship between the spacecraft position and the gravitational acceleration. ELM-base neural networks are trained without iterative tuning therefore dramatically reducing the training time. Analysis of performance in constant density models for asteroid 25143 Itokawa and comet 67/P Churyumov-Gerasimenko show that ELM-based SLFN are able learn the desired functional relationship both globally and in selected localized areas near the surface. The latter results in a robust neural algorithm for on-board, real-time calculation of the gravity field needed for guidance and control in close-proximity operations near the asteroid surface.     

三小行星系统216 Kleopatra引力场中的动力学

主带三小行星系统216 Kleopatra是由主星216 Kleopatra及两个小月亮(moonlet)Alexhelios[S/2008(216)1]和Cleoselene[S/2008(216)2]组成。其中主星216Kleopatra是一个具有强不规则形状如哑铃的连接双星,大小为217km×94km×81km,外小月亮Alexhelios大小约为8.9km,内小月亮大小约为6.9km。其动力学行为具有非常丰富的科学内涵。研究了三小行星系统216Kleopatra自身的动力学机制及其引力场中探测器的运动规律,分析了主星质心固连系中探测器的动力学方程,给出了三小行星引力全多体问题的动力学方程及Jacobi积分,方程考虑了三个小行星的不规则外形、轨道与姿态。发现三小行星系统216Kleopatra主星引力场中一种新的周期轨道族的倍周期分岔。考虑主星的不规则精确外形与引力、两个小月亮的相互作用,研究了该三小行星系统的动力学构形。发现Kleopatra的强不规则几何外形及两个小月亮Alexhelios和Cleoselene的相互作用引起两个小月亮的轨道参数的显著变化。     

双小行星系统引力场建模方法研究

针对弱引力双小行星系统的引力场建模问题,本文采用复杂度和精度依次递增的球体–球体模型、椭球体–球体模型和改进的限制性椭球体–椭球体模型来进行引力场建模,并分别采用椭圆积分以及无积分环节、计算效率高的二阶二次球谐函数来表征引力势,从而比较精确地刻画双小行星系统和探测器构成的限制性全三体问题的动力学模型;针对双小行星系统1999KW4,对其不同的引力场模型进行了仿真研究,分别给出了不同模型下的等效势能函数曲面及零速度曲线,比较了不同模型下的平动点位置坐标偏差。结果表明,二阶二次球谐函数计算引力势的椭球体-椭球体模型计算精度高,复杂程度低,计算量更少,计算速度更快,能够较精确的对双小行星系统进行引力场建模。     

附着小天体的动态面鲁棒制导与控制方法

以精确附着小天体表面的任务为背景,提出一种基于扰动观测器(DOB)和动态面控制的附着小天体的制导与控制方法。根据探测器的初始条件与终端着陆条件规划了标称轨迹,并将引力场建模误差、参数摄动和外部干扰等视为总扰动,结合动态面控制和DOB设计了标称轨迹跟踪控制器。分析总扰动估计误差的渐进收敛性以及闭环标称轨迹跟踪控制系统的稳定性,并确定控制器参数选取条件。数值仿真结果表明,所设计的DOB可以有效地估计并抑制总扰动且闭环标称轨迹跟踪控制系统具有良好的稳定性和控制精度。     

潜在威胁小行星碰撞防御的计算与分析

研究了采用碰撞的方式进行小行星防御的动力学问题。采用多面体模型来建立小行星的外形模型,以碎石堆模型来建立小行星的结构模型,计算了小行星受到与其密度和材质相同的球体高速碰撞过程和碰撞后的碎石分布。计算过程在考虑了小行星与碰撞球体的接触形变以及小行星内部组成碎石堆的接触形变条件下,计算了碎石堆内部的相互引力、法向接触力、切向静摩擦力、切向动摩擦力和滚动摩擦力矩。以小行星101955 Bennu(中文名贝努)为对象计算了潜在威胁小行星的碰撞防御过程的动力学行为。结果显示:采用高速碰撞的方法进行小行星防御可以有效地将小行星撞成大量碎小的石块,且该方法具有核爆的方法不可比拟的优势,即对空间环境无污染。     

Design of a formation of solar pumped lasers for asteroid deflection

This paper presents the design of a multi-spacecraft system for the deflection of asteroids. Each spacecraft is equipped with a fibre laser and a solar concentrator. The laser induces the sublimation of a portion of the surface of the asteroid, and the resultant jet of gas and debris thrusts the asteroid off its natural course. The main idea is to have a formation of spacecraft flying in the proximity of the asteroid with all the spacecraft beaming to the same location to achieve the required deflection thrust. The paper presents the design of the formation orbits and the multi-objective optimisation of the formation in order to minimise the total mass in space and maximise the deflection of the asteroid. The paper demonstrates how significant deflections can be obtained with relatively small sized, easy-to-control spacecraft.     

A fast Chebyshev polynomial method for calculating asteroid gravitational fields using space partitioning and cosine sampling

This paper presents a computationally fast method for solving gravitational accelerations near irregularly-shaped asteroids. This method is based on analytical three-dimensional Chebyshev polynomial approximation of the polyhedral gravity. For the purpose of improving the approximation accuracy, space partitioning schemes based on practical flight zones is used to avoid interpolation the whole space around the target asteroid. Specifically, a minimum ellipsoid close to the asteroid surface is defined to select the space for surrounding trajectories with safe distance and a cone connected to the surface is defined to select the space for descent trajectories. Moreover, interpolation points are sampled in a cosine sampling fashion according to the Chebyshev-Gauss-Lobatto nodes and a radial adaption technique. The performance of different space partitioning schemes is analyzed. The effectiveness of the proposed method is validated through simulations of solving gravitational accelerations at the test points near different shaped asteroids 1996 HW1, 433 Eros, 25143 Itokawa and 101955 Bennu.     

Spacecraft swarm dynamics and control about asteroids

This paper presents a novel methodology to control spacecraft swarms about single asteroids. This approach enables the use of small, autonomous swarm spacecraft in conjunction with a mothership, reducing the need for the Deep Space Network and improving performance in future asteroid missions. The methodology is informed by a semi-analytical model for the spacecraft relative motion that includes relevant gravitational effects without assuming J2-dominance as well as solar radiation pressure. The dynamics model is exploited in an Extended Kalman Filter (EKF) to produce an osculating-to-mean relative orbital element (ROE) conversion that relies on minimum knowledge of the asteroid gravity. The resulting real-time relative mean state estimate is utilized in a new formation-keeping control algorithm. The control problem is cast in mean relative orbital elements to leverage the geometric insight of secular and long-period effects in the definition of control windows for swarm maintenance. Analytical constraints that ensure collision avoidance and enforce swarm geometry are derived and enforced in ROE space. The proposed swarm-keeping algorithms are tested and validated in high-fidelity simulations for a reference asteroid mission.     

Solar-photon sail hovering orbits about single and binary asteroids

Solar-photon sails can be useful for missions towards and about asteroids. Indeed, for the interplanetary transfer phase, missions to asteroids often require a large variation in inclination and solar-photon sails perform very well for such high energy missions. In the same way, solar-photon sails are also expected to perform well in the phase about the asteroid. This paper studies single and binary asteroids’ hovering regions by using a sailcraft. In order to consider a sailcraft with its own mass and shape, the mutual polyhedral method (usually used to study asteroid dynamics) is used; therefore, the sailcraft is designed by means of tetrahedra. The procedure to obtain the hovering regions about a single asteroid is presented and an accurate analysis of the control variables is carried out. Moreover, control torques required to maintain hovering orbits are obtained by considering the gravitational torques acting on the sailcraft due to the asteroid. In the end, the theory for hovering orbits is extended to binary-asteroid systems and applied to the binary system 1999 KW4.     

小行星远距离抵近轨道

讨论了小行星引力一阶项可被忽略情况下的小行星远距离轨道设计及动力学。此时,航天器的运动受太阳引力和太阳光压的影响。航天器和小行星的加速度之差在这两者之间形成的独特的相对动力学,为航天器在小行星附近停驻与观测提供特定轨道。完整解决了小行星处于圆形日心轨道这一较简单情况,也考虑和阐述了椭圆轨道情况,并取得了一些初步结果。     

双星系统L1点悬停探测控制器设计与仿真

双小行星系统探测具有重要的科学意义,受其复杂动力学环境影响,探测任务极具挑战。利用球谐函数法对双星系统进行引力场建模,求解双星系统平动点,并选取其内部共线平动点L_1点作为双星系统悬停探测目标位置。采用航天探测实际任务中常用的脉冲推力式发动机,设计了一种原理简单、便于工程实现的常值切换bang-bang控制器。以69230Hermes双星系统为例,将Hermes近似为双椭球系统,仿真分析航天器在Hermes双星系统L_1点悬停飞行的控制效果,验证所提控制策略有效性。     

航天器内部磁场环境主动补偿方法

为解决空间引力波探测任务中航天器磁场对惯性传感器干扰的问题,研究在航天器复杂磁环境下利用主动测控方式获取小尺度均匀磁场环境的方法.在惯性传感器周围进行分布式磁场探测,并采用球谐函数法或多磁偶极子法实现对惯性传感器外部磁源的估计,计算惯性传感器所处位置的空间磁场及其梯度分布.利用线圈技术,对磁场及其梯度进行线性补偿.讨论分析传感器数量以及磁源布局方式等因素对最终补偿效果的影响.仿真试验结果表明,通过这一方法可将惯性传感器所在区域的磁场及其梯度降低1～2个数量级,降低引力波航天器平台的剩磁控制压力,为引力波探测提供满足要求的磁场环境.      

近地小行星防御策略分析

近年来,各国针对近地小行星的威胁及相应防御策略的研究越来越多。调研了国内外近地天体观测发展现状和多种近地小行星撞击地球的防御策略,通过比较分析防御策略的实现原理、关键技术和存在的问题,对各种策略的适用性、可行性和有效性进行了评估。通过对各种策略的分析和总结,结合我国近地小行星防御策略的研究现状,尝试性提出了采用多种策略组合的方式对有潜在威胁的小行星采取相关有效方案,为航天器的研制和防御策略的实施争取更多的时间。     

强不规则天体引力场中的动力学研究进展

小行星探测与彗星探测是深空探测的重要方面。一般来说,小行星和彗星因质量都不足以使得万有引力克服应力达到流体静力学平衡,而具有强不规则的外形。研究强不规则天体引力场中的动力学行为及其内在机制,是探测器被不规则天体捕获并对其形成近距离探测轨道的基础。从引力场模型和动力学行为两个方面综述了强不规则天体引力场中动力学的研究进展,在引力场模型的研究方面介绍了强不规则天体引力场建模的球谐函数摄动展开模型、简单特殊体模型及多面体模型的研究现状,在动力学机制的研究方面介绍了强不规则天体引力场中的周期轨道和拟周期轨道、平衡点、流形、分岔与共振以及混沌运动的研究现状,指出了这些方面研究的重点与难点。分析了强不规则体引力场中动力学的研究趋势。     

Solar sails for perturbation relief: Application to asteroids

A major cause of spacecraft orbital variation comes from natural perturbations, which, in close proximity of a body, are dominated by its non-spherical nature. For small bodies, such as asteroids, these effects can be considerable, given their uneven (and uncertain) mass distribution. Solar sail technology is proposed to reduce or eliminate the net secular effects of the irregular gravity field on the orbit. Initially, a sensitivity analysis will be carried out on the system which will show high sensitivity to changes in initial conditions. This presents a challenge for optimisation methods which require an initial guess of the solution. As such, the Genetic Algorithm (GA) is proposed as the preferred optimisation method as this requires no initial guess from the user. A multi-objective optimisation is performed which aims to achieve a periodic orbit whilst also minimising the effort required by the sail to do so. Given the system sensitivity, the control law for one orbit is not necessarily applicable for any subsequent orbit. Therefore, a new method of updating the control law for subsequent orbits is presented, based on linearisation and use of a Control Transition Matrix (CTM). The techniques will later find application in a multiple asteroid rendezvous mission with a solar sail as the primary propulsion system.     

Stability of relative equilibria of the full spacecraft dynamics around an asteroid with orbit–attitude coupling

The full dynamics of spacecraft around an asteroid, in which the spacecraft is considered as a rigid body and the gravitational orbit–attitude coupling is taken into account, is of great value and interest in the precise theories of the motion. The spectral stability of the classical relative equilibria of the full spacecraft dynamics around an asteroid is studied with the method of geometric mechanics. The stability conditions are given explicitly based on the characteristic equation of the linear system matrix. It is found that the linearized system decouples into two entirely independent subsystems, which correspond to the motions within and outside the equatorial plane of the asteroid respectively. The system parameters are divided into three groups that describe the traditional stationary orbit stability, the significance of the orbit–attitude coupling and the mass distribution of the spacecraft respectively. The spectral stability of the relative equilibria is investigated numerically with respect to the three groups of system parameters. The relations between the full spacecraft dynamics and the traditional spacecraft dynamics, as well as the effect of the orbit–attitude coupling, are assessed. We find that when the orbit–attitude coupling is strong, the mass distribution of the spacecraft dominates the stability of the relative equilibria; whereas when the orbit–attitude coupling is weak, both the mass distribution and the traditional stationary orbit stability have significant effects on the stability. We also give a criterion to determine whether the orbit–attitude coupling needs to be considered.     

A multiple-rendezvous,sample-return mission to two near-Earth asteroids

We propose a dual-rendezvous mission, targeting near-Earth asteroids, including sample-return. The mission, Asteroid Sampling Mission (ASM), consists of two parts: (i) flyby and remote sensing of a Q-type asteroid, and (ii) sampling of a V-type asteroid. The targeted undifferentiated Q-type are found mainly in the near-Earth space, and to this date have not been the target of a space mission. We have chosen, for our sampling target, an asteroid from the basaltic class (V-type), as asteroids in this class exhibit spectral signatures that resemble those of the well-studied Howardite–Eucrite–Diogenite (HED) meteorite suite. With this mission, we expect to answer specific questions about the links between differentiated meteorites and asteroids, as well as gain further insight into the broader issues of early Solar System (SS) evolution and the formation of terrestrial planets. To achieve the mission, we designed a spacecraft with a dry mass of less than 3 tonnes that uses electric propulsion with a solar-electric power supply of 15 kW at 1 Astronomical Unit (AU). The mission includes a series of remote sensing instruments, envisages landing of the whole spacecraft on the sampling target, and employs an innovative sampling mechanism. Launch is foreseen to occur in 2018, as the designed timetable, and the mission would last about 10 years, bringing back a 150 g subsurface sample within a small re-entry capsule. This paper is a work presented at the 2008 Summer School Alpbach,“Sample return from the Moon, asteroids and comets” organized by the Aeronautics and Space Agency of the Austrian Research Promotion Agency. It is co-sponsored by ESA and the national space authorities of its Member and Co-operating States, with the support of the International Space Science Institute and Austrospace.     

Synergistic approach of asteroid exploitation and planetary protection

The asteroid and cometary impact hazard has long been recognised as an important issue requiring risk assessment and contingency planning. At the same time asteroids have also been acknowledged as possible sources of raw materials for future large-scale space engineering ventures. This paper explores possible synergies between these two apparently opposed views; planetary protection and space resource exploitation. In particular, the paper assumes a 5 tonne low-thrust spacecraft as a baseline for asteroid deflection and capture (or resource transport) missions. The system is assumed to land on the asteroid and provide a continuous thrust able to modify the orbit of the asteroid according to the mission objective. The paper analyses the capability of such a near-term system to provide both planetary protection and asteroid resources to Earth. Results show that a 5 tonne spacecraft could provide a high level of protection for modest impact hazards: airburst and local damage events (caused by 15–170 m diameter objects). At the same time, the same spacecraft could also be used to transport to bound Earth orbits significant quantities of material through judicious use of orbital dynamics and passively safe aero-capture manoeuvres or low energy ballistic capture. As will be shown, a 5 tonne low-thrust spacecraft could potentially transport between 12 and 350 times its own mass of asteroid resources by means of ballistic capture or aero-capture trajectories that pose very low dynamical pressures on the object.     

基于引力场不对称性的三体系统轨道自主导航

以月球背面的中继通信为背景,提出了基于三体系统引力场不对称特性的星–星测距自主定轨方案。该方案以环月极轨卫星和地–月L2点Halo轨道卫星组成中继通信网,以实现对月球两极和背面的覆盖。通过采集极轨卫星与Halo轨道卫星的测距信息,结合卡尔曼滤波在日–地–月动力学模型下获得两颗卫星的绝对轨道。数值仿真结果表明:本文方法能将导航的位置精度和速度精度分别提高到百米和厘米/秒量级。该自主导航方法还可以扩展到不规则引力场小天体附近星群运动的自主导航。     

Proposal for a multiple-asteroid-flyby mission with sample return

Asteroid exploration provides a new approach to study the formation of the solar system and the planetary evolution. Choosing a suitable target and designing of feasible profile for asteroid mission are challenging due to constraints such as scientific value and technical feasibility. This paper investigates a feasible mission scenario among the potential candidates of multiple flybys and sample return missions. First, a group of potential candidates are selected by considering the physical properties and accessibility of asteroids, for the sample return missions. Second, the feasible mission scenarios for multiple flybys and sample return missions to various spectral-type asteroids are investigated. We present the optimized design of preliminary interplanetary transfer trajectory for two kinds of missions. One is the single sample return mission to asteroids with various spectral types. The other is the multiple flybys and sample return mission to several asteroids. In order to find the optimal profiles, the planetary swing-by technique and Differential Evolution algorithm are used.