Finite-time asteroid hovering via multiple-overlapping-horizon multiple-model predictive control

This paper investigates the asteroid hovering problem using the Multiple-Overlapping-Horizon Multiple-Model Predictive Control method. The effectiveness of the predictive controllers in satisfying control constraints and minimizing the required control effort is making Model Predictive Control a desirable control method for asteroid exploration missions which consist of the asteroid hovering phase. However, the computational burden of Model Predictive Control is an obstacle to employing the asteroid’s complex gravitational field model. As an alternative option, the Multiple Horizon Multiple-Model Predictive Control method has been introduced previously, which could provide a solution with the less computational burden with respect to the nonlinear Model Predictive Control. It was shown that it is not necessary to deduce the exact dynamics model to predict the system’s behavior during a long period using this approach. However, the calculated control acceleration was not smooth enough because of the crisp borders of consecutive horizons, which may cause an image motion and degrades the geometric accuracy of high-resolution images in asteroid hovering missions. In this paper, the Multiple-Overlapping-Horizon Multiple-Model Predictive Control method is introduced instead to solve the problem of controlling acceleration fluctuations by overlapping consecutive horizons. Numerical simulation results are presented to validate the effectiveness of the proposed control method, and its advantage is demonstrated accordingly for the asteroid hovering problem in achieving the hovering position and velocity.     

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。     

Landing of hopping rovers on Irregularly-shaped small bodies using attitude control

A hopping rover that is driven only by internal or external attitude actuators is an ideal mobility approach for surface exploration of small solar system bodies. Without thrust control and grasping mechanisms, a hopping rover is mechanically simple to design and less prone to mechanical failures, but faces challenges during soft landing. It may rebound from the surface, causing deviations from its original landing site. In this paper, landing of a hopping rover on the surface of an asteroid is investigated, and a strategy using only attitude control to shorten the landing distance is proposed. Based on rigid body impact dynamics, the edge impact configuration is investigated in detail. The factors that affect the impact states of a cube-shaped hopping rover are studied. Then, controlled edge landing is analyzed, in which the post-impact velocity of the hopping rover is changed by controlling its attitude prior to impact. Three guidance schemes are developed, followed by attitude profile generation and finite time stable attitude control. Finally, simulations are performed on an ideal flat surface and uneven terrain. The results show that controlled edge landing can effectively reduce the landing distance and settling time, compared with uncontrolled landing. This study on hopping motion on the surface of an irregular-shaped asteroid with attitude control, can provide a reference for hopper trajectory plan in future asteroid surface explorations.     

Excavation of artificial caverns inside asteroids by leveraging rotational self-energy

Future space ventures will likely require exploitation of near-Earth asteroid resources. Moreover, it can be envisaged that asteroids may host habitats in their interiors. In fact, a cavern inside an asteroid would be a natural radiation shield against cosmic radiation and may also serve as a confined environment for storage of mined material such as water ice or other processed volatiles such as propellants. To this end, this paper proposes to leverage the asteroid rotational self-energy to remove material from the asteroid interiors and create a spherical cavern, by means of the orbital siphon concept. The siphon is a chain of tether-connected payload masses (the asteroid material), which exploits the rotation of the asteroid for the delivery of mass from the asteroid to escape. Under certain conditions the siphon can be initiated to ensure self-sustained flow of mass from the asteroid to escape. A net orbital siphon effect is generated by connecting new payloads at the bottom of the chain while releasing the upper payloads. Key parameters are discussed, such as the required siphon dimension and the maximum size of the internal cavity that can be excavated, as a function of the asteroid rotational period. Moreover, assuming elastic material behaviour, a closed-form expression for the stress tensor is found and a failure criterion is used to identify regions in the asteroid interiors subjected to the larger stresses. It is shown that the conditions for failure are relaxed as the radius of the internal void increases.     

小行星防御动能撞击效果评估

以动能撞击防御潜在威胁小行星概念为背景,采用物质点法(Material Point Method,MPM)模拟了铝弹高速撞击S型小行星的过程,将撞击结果导入引力N体–离散元动力学模型中,对其后续演化过程进行仿真,并分析了撞击后碎片对地球的威胁指数。结果显示小行星在高速撞击的作用下部分破碎,大量碎片以与撞击方向相反的速度向外喷射,从而提升了小行星的撞击偏移效果。研究采用了两种不同结构的小行星模型:完整结构(monolithic structure)的小行星在遭受撞击后会喷射出比原小行星小得多的碎片,而碎石堆结构(rubble-pile structure)的小行星在撞击作用下可分裂成大小和速度分布较为均匀的碎片。威胁指数的分析表明动能撞击方式确实有效减小了小行星的威胁程度,撞击后的最大剩余碎片可被成功偏移至安全轨道,但仍有部分碎片会与地球相撞。与完整结构相比,针对碎石堆结构小行星的撞击防御的总体效果更好,次生灾害主要为大质量碎片的撞击。研究方法可用于未来开展防御小行星的动能撞击任务的撞击条件选择和撞击结果预估。     

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.     

利用绳系太阳帆减缓小行星自转的技术研究

提出一种利用太阳帆绳系系统逐渐减小小行星自转速率的方法。在系绳长度不变的情况下,利用太阳帆受到的太阳光压力使其始终保持与小行星同步,避免了由于小行星自转而引起的系绳缠绕问题。通过控制太阳帆使系绳始终拉紧,系绳中的拉力便可以持续提供一个与小行星自转方向相反的力矩,从而减小其自转速率。仿真结果表明,面积10⁶ m²的太阳帆,经过约86天可将小行星的自转消除,验证了该方法的有效性。     

Space debris observations with the Slovak AGO70 telescope: Astrometry and light curves

The Faculty of Mathematics, Physics and Informatics of Comenius University in Bratislava, Slovakia (FMPI) operates its own 0.7-m Newtonian telescope (AGO70) dedicated to the space surveillance tracking and research, with an emphasis on space debris. The observation planning focuses on objects on geosynchronous (GEO), eccentric (GTO and Molniya) and global navigation satellite system (GNSS) orbits. To verify the system’s capabilities, we conducted an observation campaign in 2017, 2018 and 2019 focused on astrometric and photometric measurements. In last two years we have built up a light curve catalogue of space debris which is now freely available for the scientific community. We report periodic signals extracted from more than 285 light curves of 226 individual objects. We constructed phase diagrams for 153 light curves for which we obtained apparent amplitudes.     

Sq(H) field variations at Sonmiani geomagnetic observatory,Pakistan for solar cycle 24

In this study, Sq(H) field results for Sonmiani geomagnetic observatory (SON), Pakistan are presented first time for solar cycle i.e., Solar Cycle 24. Sonmiani observatory was established in 2008 and was included in the list of INTERMAGNET Magnetic Observatory (IMO) in 2012. The analysis of Sq(H) field is performed to examine diurnal, annual and seasonal behaviour of Sq(H) field at Sonmiani along with Honolulu which is used as reference observatory. Both the observatories lie at the Equatorial Ionisation Anomaly (EIA) crest. In general strong dependency of Sq(H) field on solar cycle has been observed. First peak of SC24 was visible in Sq(H) field at both observatories. However, at HON maximum Sq(H) was observed in 2015 instead of 2014, a year later than the year of solar maximum. Prominent longitudinal difference has been noted between both observatories. At HON, maximum Sq(H) was observed during equinox while at SON it was noted during equinox and summer as a consequence of shift in latitude of Sq focus. Phase shift of Sq(H) at SON followed a general trend, that is maximum Sq(H) shifted to later hours in solar maximum as compared to solar minimum. Whereas, an opposite trend was noted at HON which might be due to coastal effect. In case of seasonal phase shift, at both observatories maximum Sq(H) occurred at later hours in summer than in winter which is opposite to the results obtained by many workers. These points need further investigation and geomagnetic as well as wind, and electric field data of other observatories situated at the EIA crest region is required to interpret the Sq(H) phase shift extensively.     

Martian Buildings: Design loading

Multiplanetary life has been studied by scientists as a way to supply energy or sustain human life in the future. Mars is likely to be man’s first destination, colonization using onsite structural construction would be one of the main options. The first step to designing a reliable building is to know the applied structural loads and to have an accurate design load combination. Due to lack of complete knowledge, short span of recorded data, Martian environment, and hazardous environment that Martian structures face, constructed Martian structures should behave appropriately under the highest likely live, dead and environmental loads either simultaneously or as a worst-case scenario. The present study evaluated and calculated probable Martian structural loads, including live, internal pressure, snow, gravity (dead), dust accumulation, thermal stress, wind, marsquake, asteroid, and meteoroid impact loads and their effects. Information was gathered from previous studies and valid data from Martian landers, rovers and orbiters. Wind loads were calculated based on the over 6.5 years of data recorded by Vikings 1 and 2, temperature and winds for InSight (TWINS) sensor. A wind shear exponent and wind profile have been proposed for a Martian flat terrain construction site. Marsquake lateral loads, frequency content and seismicity were assessed using data from the seismic experiment for interior structure (SEIS) and the Viking 2 seismometer. Considering the high influx of micrometeoroids, their penetration distance, impact loads and their effects on structures were calculated. The annual probability of an asteroid impact on a settlement was assessed for a 30-year mission. A load map for Martian residential buildings that considers the worst-case scenario in which a Martian structure should be designed based on them has been proposed.     

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.     

Encounter trajectories for deep space mission ASTER to the triple near Earth asteroid 2001-SN263. The laser altimeter (ALR) point of view

In cooperation with Russia, the Brazilian deep space mission ASTER plans to send a small spacecraft to investigate the triple asteroid 2001-SN263. The nearest launch opportunities for this project include June 2022 and June 2025. One main exploration campaign is being planned with focus on the largest asteroid (Alpha). Among the instruments under development, a laser altimeter (named ALR) was preliminarily designed and presented in 2010–2011. Many studies to define mission and instruments requirements were performed aiming at the characterization of important issues for the successful realization of the mission. Among them, the identification of a suitable trajectory that could be followed by the ASTER spacecraft in the encounter phase, when the main campaign will take place. This paper describes the effort undertaken with focus on the laser altimeter operation. Possible encounter trajectories were modelled and simulated to identify suitable approach parameters and conditions allowing the accomplishment of the intended investigation. The simulation also involves the instrument operation, considering approach geometry, attitude, relative motion, time/date, and the dynamics of the main asteroid. From the laser altimeter point of view, keeping in mind the desired coverage results (50% minimum surface coverage of asteroid Alpha, complying with horizontal and vertical resolution requirements), results point out crucial features for the encounter trajectory, like the need for a small inclination (10^-6 degrees; with respect to the asteroid's orbit), the most favourable spacecraft positioning (between the Sun and the asteroid) and pointing condition (back to the Sun), the minimum amount of achievable surface coverage (58%, focused on central areas), and the most proper time to conduct the main campaign (January 2025). Concerning the instrument, results offer refined values for divergence angle (500 to 650 μrad, half-cone), pulse repetition frequencies (from 1/20 to 1 Hz), and consequent data generation rates. A simulation tool that can use any 3D generated trajectories as input data was created for the analyses presented here. Although created for the ALR in this mission, this simple analysis tool can be adapted to other instruments in this or other missions.     

小行星探测电推进系统方案研究

小行星探测以及资源开发与利用对国家抢占深空探测主动权和制高点有着不可估量的战略意义。电推进具有高比冲、长寿命和高度自主巡航等特点,小行星探测器采用电推进执行巡航阶段轨道机动任务,将大幅减少推进剂重量和提高载重比。调研了国外小行星探测的电推进系统方案,针对我国小行星探测对电推进系统的任务需求及现有电推力器的技术基础,提出了5种电推进系统方案,并进行多维度对比,对最优方案进行了设计和关键技术梳理。     

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。     

近地小行星采矿与防御计划发展现状

近地小行星交会、绕飞、着陆与采样返回技术经过数10年的发展日趋成熟。美国的OSIRIS-Rex对C类小行星进行特征分析与采样,日本宇宙航空研究开发机构的“隼鸟-2号”任务目的是小行星深层采样。美国国家航空航天局（NASA）和欧洲空间局（ESA）的小行星探测任务开始转向行星防御领域。NASA的ARM（Asteroid Redirect Mission）计划是开展小行星抓捕与轨道重定向,ESA联合NASA提出了小行星撞击与偏转评估计划,拟对双星系统开展撞击实验,为行星防御提供技术积累。此外,行星资源公司和深空工业公司分别规划了小行星商业采矿的蓝图,并已开展相关的在轨技术验证。对近地小行星的探测历程进行了回顾,重点介绍了OSIRIS-Rex、“隼鸟-2号”、NASA和ESA的行星防御计划及小行星采矿公司的商业采矿战略规划,总结了未来开展行星防御与采矿的关键技术。     

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。     

The northern and southern mid-latitude ionospheric trough using global IGS vTEC maps

The aim of this work is the analysis of the mid-latitude ionospheric trough (MIT) using the Global Ionospheric Maps from IGS (GIMs) during the solar minimum, year 2008. This study was performed for different local times, 22, 00, 02 and 04 LT on the Northern and Southern hemisphere simultaneously. In the two hemispheres the MIT show asymmetric pattern. The high-latitude troughs are clearly distinguished in autumn and winter. Another feature is the longitudinal development towards the west of the geomagnetic pole covering a wider area in the Northern Hemisphere. Five empirical reference models were tested and compared with the MIT minimum position obtained from GIMs at different local times for both hemisphere. The results show a better agreement with the observations for the Northern Hemisphere specially with the Köehnlein & Raitt model. Fluctuations of 9 days and 27 days of the MIT minimum position are found, which could be related with the solar wind oscillations, especially for 00 and 02 LT in both hemisphere, suggesting a link between them.     

On tethered sample and mooring systems near irregular asteroids

A tethered asteroid sample and mooring system is investigated in this paper. In this system the spacecraft is moored to the surface of an irregular asteroid such as 216 Kleopatra by using a rocket-propelled anchor with a cable. The rocket-propelled anchor is a kind of space penetrator, which can inject into asteroids at high speeds generated by its own rocket engine. It can be used to explore the interior structure of asteroids, and it can also be used as a sample collector. When the sampling mission is done, the sample can be pulled back to the spacecraft with the anchor. Using this method, the spacecraft can be kept in a safe region in which it cannot be trapped by the gravitational field of the asteroid. This work is concerned with the dynamics of the tethered system near irregular asteroids. First, a shape model and gravitational field model of irregular asteroids are built. Then, the configuration and the stability of the tethered system are investigated, and the quasi-periodic motion near the equilibrium point of the tethered system is analyzed. Finally, the non-uniform density distribution of the asteroids is considered. The deployment process and the oscillation of the tethered system in the uncertain asteroid gravity field are simulated using the Monte Carlo method. The feasibility of the tethered asteroid sample and mooring system is proved.     

A small mission for in situ exploration of a primitive binary near-Earth asteroid

We present a concept for a challenging in situ science mission to a primitive, binary near-Earth asteroid. A sub-400-kg spacecraft would use solar electric propulsion to rendezvous with the C-class binary asteroid (175706) 1996 FG3. A campaign of remote observations of both worlds would be followed by landing on the ∼1 km diameter primary to perform in situ measurements. The total available payload mass would be around 34 kg, allowing a wide range of measurement objectives to be addressed. This mission arose during 2004 from the activities of the ad-hoc Small Bodies Group of the DLR-led Planetary Lander Initiative. Although the particular mission scenario proposed here was not studied further per se, the experience was carried over to subsequent European asteroid mission studies, including first LEONARD and now the Marco Polo near-Earth asteroid sample return proposal for ESA’s Cosmic Vision programme. This paper may thus be of interest as much for insight into the life cycle of mission proposals as for the concept itself.     

Two-phase framework for near-optimal multi-target Lambert rendezvous

This paper proposes a two-phase framework to obtain a near-optimal solution of multi-target Lambert rendezvous problem. The objective of the problem is to determine the minimum-cost rendezvous sequence and trajectories to visit a given set of targets within a maximum mission duration. The first phase solves a series of single-target rendezvous problems for all departure-arrival object pairs to generate the elementary solutions, which provides candidate rendezvous trajectories. The second phase formulates a variant of traveling salesman problem (TSP) using the elementary solutions prepared in the first phase and determines the final rendezvous sequence and trajectories of the multi-target rendezvous problem. The validity of the proposed optimization framework is demonstrated through an asteroid exploration case study.