Study of highly perturbed spacecraft formation dynamics via approximation

This paper explores methods for approximating and analyzing the dynamics of highly perturbed spacecraft formations with an emphasis on computationally efficient approaches. This facilitates on-board computation or rapid preliminary mission design analysis. Perturbed formation dynamics are often approximated as linear time-varying (LTV) systems, for which Floquet theory can be used to analyze the degree of system instability. Furthermore, the angular momentum of the relative orbital state can be computed with the approximate dynamics to provide additional insight. A general methodology is developed first and then applied to the problem of unstable formation dynamics in asteroid orbits. Here the dominant perturbative effects due to low-order gravitational harmonics and solar radiation pressure are modeled. Numerical simulations validate the approach and illustrate the approximation accuracy achieved.     

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。     

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.     

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.     

Decentralized formation pose estimation for spacecraft swarms

For spacecraft swarms, the multi-agent localization algorithm must scale well with the number of spacecraft and adapt to time-varying communication and relative sensing networks. In this paper, we present a decentralized, scalable algorithm for swarm localization, called the Decentralized Pose Estimation (DPE) algorithm. The DPE considers both communication and relative sensing graphs and defines an observable local formation. Each spacecraft jointly localizes its local subset of spacecraft using direct and communicated measurements. Since the algorithm is local, the algorithm complexity does not grow with the number of spacecraft in the swarm. As part of the DPE, we present the Swarm Reference Frame Estimation (SRFE) algorithm, a distributed consensus algorithm to co-estimate a common Local-Vertical, Local-Horizontal (LVLH) frame. The DPE combined with the SRFE provides a scalable, fully-decentralized navigation solution that can be used for swarm control and motion planning. Numerical simulations and experiments using Caltech’s robotic spacecraft simulators are presented to validate the effectiveness and scalability of the DPE algorithm.     

Automated design architectures for co-orbiting spacecraft swarms for planetary moon mapping

This work describes the design and optimization of spacecraft swarm missions to meet spatial and temporal visual mapping requirements of missions to planetary moons, using resonant co-orbits. The algorithms described here are a part of Integrated Design Engineering and Automation of Swarms (IDEAS), a spacecraft swarm mission design software that automates the design trajectories, swarm, and spacecraft behaviors in the mission. In the current work, we focus on the swarm design and optimization features of IDEAS, while showing the interaction between the different design modules. In the design segment, we consider the coverage requirements of two general planetary moon mapping missions: global surface mapping and region of interest observation. The configuration of the swarm co-orbits for the two missions is described, where the participating spacecraft have resonant encounters with the moon on their orbital apoapsis. We relate the swarm design to trajectory design through the orbit insertion maneuver performed on the interplanetary trajectory using aero-braking. We then present algorithms to model visual coverage, and collision avoidance in the swarm. To demonstrate the interaction between different design modules, we relate the trajectory and swarm to spacecraft design through fuel mass, and mission cost estimations using preliminary models. In the optimization segment, we formulate the trajectory and swarm design optimizations for the two missions as Mixed Integer Nonlinear Programming (MINLP) problems. In the current work, we use Genetic Algorithm as the primary optimization solver. However, we also use the Particle Swarm Optimizer to compare the optimizer performance. Finally, the algorithms described here are demonstrated through numerical case studies, where the two visual mapping missions are designed to explore the Martian moon Deimos.     

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。     

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.     

The new ESA meteoroid model

The orbital distributions of meteoroids in interplanetary space are revised in the ESA meteoroid model to account for recently obtained observational data and to comply with the constraints due to the orbital evolution under planetary gravity and Poynting–Robertson effects. Infrared observations of the zodiacal cloud by the COBE DIRBE instrument, in situ flux measurements by the dust detectors on board Galileo and Ulysses spacecraft, and the crater size distributions on lunar rock samples retrieved by the Apollo missions are synthesized into a single model. Within the model, the orbital distributions are expanded into a sum of contributions due to a number of known sources, including the asteroid belt with the emphasis on the prominent families Themis, Koronis, Eos and Veritas, as well as comets on Jupiter-encountering orbits. An attempt to incorporate the meteor orbit database acquired by the AMOR radar is also discussed.     

Dynamics and control of spacecraft hovering using the geomagnetic Lorentz force

To achieve hovering, a spacecraft thrusts continuously to induce an equilibrium state at a desired position. Due to the constraints on the quantity of propellant onboard, long-time hovering around low-Earth orbits (LEO) is hardly achievable using traditional chemical propulsion. The Lorentz force, acting on an electrostatically charged spacecraft as it moves through a planetary magnetic field, provides a new propellantless method for orbital maneuvers. This paper investigates the feasibility of using the induced Lorentz force as an auxiliary means of propulsion for spacecraft hovering. Assuming that the Earth’s magnetic field is a dipole that rotates with the Earth, a dynamical model that characterizes the relative motion of Lorentz spacecraft is derived to analyze the required open-loop control acceleration for hovering. Based on this dynamical model, we first present the hovering configurations that could achieve propellantless hovering and the corresponding required specific charge of a Lorentz spacecraft. For other configurations, optimal open-loop control laws that minimize the control energy consumption are designed. Likewise, the optimal trajectories of required specific charge and control acceleration are both presented. The effect of orbital inclination on the expenditure of control energy is also analyzed. Further, we also develop a closed-loop control approach for propellantless hovering. Numerical results prove the validity of proposed control methods for hovering and show that hovering around low-Earth orbits would be achievable if the required specific charge of a Lorentz spacecraft becomes feasible in the future. Typically, hovering radially several kilometers above a target in LEO requires specific charges on the order of 0.1 C/kg.     

Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

The Lorentz force acting on an electrostatically charged spacecraft as it moves through the planetary magnetic field could be utilized as propellantless electromagnetic propulsion for orbital maneuvering, such as spacecraft formation establishment and formation reconfiguration. By assuming that the Earth’s magnetic field could be modeled as a tilted dipole located at the center of Earth that corotates with Earth, a dynamical model that describes the relative orbital motion of Lorentz spacecraft is developed. Based on the proposed dynamical model, the energy-optimal open-loop trajectories of control inputs, namely, the required specific charges of Lorentz spacecraft, for Lorentz-propelled spacecraft formation establishment or reconfiguration problems with both fixed and free final conditions constraints are derived via Gauss pseudospectral method. The effect of the magnetic dipole tilt angle on the optimal control inputs and the relative transfer trajectories for formation establishment or reconfiguration is also investigated by comparisons with the results derived from a nontilted dipole model. Furthermore, a closed-loop integral sliding mode controller is designed to guarantee the trajectory tracking in the presence of external disturbances and modeling errors. The stability of the closed-loop system is proved by a Lyapunov-based approach. Numerical simulations are presented to verify the validity of the proposed open-loop control methods and demonstrate the performance of the closed-loop controller. Also, the results indicate the dipole tilt angle should be considered when designing control strategies for Lorentz-propelled spacecraft formation establishment or reconfiguration.     

深空探测航天器巡航段自主导航方法研究

对深空探测航天器自主导航方法进行了研究。为了应对深空探测中航天器轨道动力学模型的误差，在分光计测量航天器相对于太阳径向速度基础上，引入了小行星的视线矢量测量。通过最小二乘法计算出由小行星视线矢量所得到的位置信息，采用改进的信息融合方法修正扩展卡尔曼滤波中不精确的动力学模型造成的状态估计误差。同时计算了模型的能观度，对模型的可观性进行了分析。最后对算法进行了仿真分析，仿真结果表明，该算法对动力学模型的依赖性明显低于其他算法，在相同模型精度下，可获得更好的滤波精度。     

集群航天器球形边界控制

集群航天器由于其独特的优势,在未来航天任务中将举足轻重,其边界控制也随即成为研究热点.针对近距离伴飞的圆轨道集群航天器,以集群航天器蜂拥控制模型为基础,通过集群航天器球形边界的定义,运用粒子群优化算法,实现了稳定状态下集群航天器的边界参数寻优.采用球形空腔势函数的控制方法,结合集群航天器边界参数反馈信息,实现了对集群航天器球形边界控制,并仿真验证了算法的可行性.     

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.     

Mapping orbits around the asteroid 2001SN263

The present paper has the goal of mapping orbits, with respect to the perturbations, for a spacecraft traveling around the asteroid 2001SN₂₆₃. This asteroid is a triple system, which center of mass is in an elliptic orbit around the Sun. The perturbations considered in the present model are the ones due to the oblateness of the central body, the gravity field of the two satellite bodies (Beta and Gamma), the Sun, the Moon, the asteroids Vesta, Pallas and Ceres and all the planets of the Solar System. This mapping is important, because it shows the relative importance of each force for a given orbit for the spacecraft, helping to make a decision about which forces need to be included in the model for a given accuracy and nominal orbit. Another important application of this type of mapping is to find orbits that are less perturbed, since it is expected that those orbits have good potential to require a smaller number of station-keeping maneuvers. Simulations under different conditions are made to find those orbits. The main reason to study those trajectories is that, currently, there are several institutions in Brazil studying the possibility to make a mission to send a spacecraft to this asteroid (the so-called ASTER mission), because there are many important scientific studies that can be performed in that system. The results showed that Gamma is the main perturbing body, followed by Beta (10 times smaller) and the group Sun–Mars-oblateness of Alpha, with perturbations 1000 times weaker than the effects of Gamma. The other bodies have perturbations 10⁷ times smaller. The results also showed that circular and polar orbits are less perturbed, when compared to elliptical and equatorial orbits. Regarding the semi-major axis, an internal orbit is the best choice, followed by a larger external orbit. The inclination of the orbit plays an important role, and there are values for the inclination where the perturbations show minimum and maximum values, so it is important to make a good decision on those values.     

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.     

Practical method to identify orbital anomaly as spacecraft breakup in the geostationary region

Identifying spacecraft breakup events is an essential issue for better understanding of the current orbital debris environment. This paper proposes an observation planning approach to identify an orbital anomaly, which appears as a significant discontinuity in archived orbital history, as a spacecraft breakup. The proposed approach is applicable to orbital anomalies in the geostationary region. The proposed approach selects a spacecraft that experienced an orbital anomaly, and then predicts trajectories of possible fragments of the spacecraft at an observation epoch. This paper theoretically demonstrates that observation planning for the possible fragments can be conducted. To do this, long-term behaviors of the possible fragments are evaluated. It is concluded that intersections of their trajectories will converge into several corresponding regions in the celestial sphere even if the breakup epoch is not specified and it has uncertainty of the order of several weeks.     

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。     

A guidance approach to satellite formation reconfiguration based on convex optimization and genetic algorithms

This paper presents a new approach for autonomous reconfiguration of distributed space systems, which ensures safe guidance of spacecraft formations towards the desired patterns while optimizing the total propellant consumption. The orbital transfer is reduced to the form of a convex optimization problem to guarantee rapid computation of control laws. Hence, tasks are iteratively assigned to the component platforms to detect the best reconfiguration strategy. The path-planning is entrusted to a reference satellite of the cluster, that coordinates the remaining ones by means of a procedure based on genetic algorithms. Two methods are proposed, depending on the organizational architecture of the spacecraft formation. In the first one, the maneuver is completely planned by the reference satellite, that determines final tasks and control actions for the whole cluster. As an alternative to such a fully-centralized approach, a distributed version of the algorithm is proposed: tasks are sorted by the reference satellite and transfer orbits are computed by exploiting the computational resources of the whole cluster. Whatever the considered framework, both the planners ensure a safe transition of the formation towards the target geometry. Simulation results show that, when relative distances are of the order of hundreds of meters, a mean delta-v per satellite of the order of 0.1 m/s is required to reconfigure LEO clusters within one orbital period.     

主带小行星采样返回任务中的离子电推进应用方案

由于离子电推进的高比冲特性,采用它执行小行星探测器巡航阶段轨道机动任务时,将使探测器在同样的有效载荷下的发射重量大大减轻。针对我国规划中的主带小行星采样返回任务,调研了国外离子电推进在深空探测任务中的应用情况,在借鉴国外成功经验和任务需求分析的基础上,设计了主带小行星探测器离子电推进系统方案和应用策略,计算了在目前离子推力器寿命水平下,既定探测任务对离子电推进推力、比冲、推进剂量以及功耗需求。研究表明,目前研制的离子推力器可以满足规划中的主带小行星探测任务需求。研究成果对探测器的方案设计有参考价值。