Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.     

基于模型预测控制的多约束火星精确着陆制导律研究

主要研究了火星着陆动力下降段考虑燃料消耗和实际任务约束条件的制导律设计问题。选取可变推力发动机作为执行机构,首先建立了着陆器在动力下降段的运动方程及质量变化方程;其次对实际任务中需要考虑的斜坡、推力幅值和方向等约束条件建立了约束模型;接下来通过构造由控制量和状态量构成的性能指标,提出一种基于模型预测控制的多约束火星精确着陆制导算法。可实现多种约束条件下的指标最优精确着陆任务。最后,通过数值仿真对比了本文与已有典型着陆策略,验证了所提算法可以在满足约束条件的前提下有效地完成既定火星精确着陆任务。     

Time-optimal trajectories to circumsolar space using solar electric propulsion

The aim of this paper is to explore the capabilities of a solar electric propelled spacecraft on a mission towards circumsolar space. Using an indirect approach, the paper investigates minimum time of transfer (direct) trajectories from an initial heliocentric parking orbit to a desired final heliocentric target orbit, with a low perihelion radius and a high orbital inclination. The simulation results are then collected into graphs and tables for a trade-off analysis of the main mission parameters. Finally, a comparison of the performance between a solar electric and a (photonic) solar sail based spacecraft is discussed.     

Multiobjective genetic optimization of Earth–Moon trajectories in the restricted four-body problem

In this paper, optimal trajectories of a spacecraft traveling from Earth to Moon using impulsive maneuvers (ΔV maneuvers) are investigated. The total flight time and the summation of impulsive maneuvers ΔV are the objective functions to be minimized. The main celestial bodies influencing the motion of the spacecraft in this journey are Sun, Earth and Moon. Therefore, a three-dimensional restricted four-body problem (R4BP) model is utilized to represent the motion of the spacecraft in the gravitational field of these celestial bodies. The total ΔV of the maneuvers is minimized by eliminating the ΔV required for capturing the spacecraft by Moon. In this regard, only a mid-course impulsive maneuver is utilized for Moon ballistic capture. To achieve such trajectories, the optimization problem is parameterized with respect to the orbital elements of the ballistic capture orbits around Moon, the arrival date and a mid-course maneuver time. The equations of motion are solved backward in time with three impulsive maneuvers up to a specified low Earth parking orbit. The results show high potential and capability of this type of parameterization in finding several Pareto-optimal trajectories. Using the non-dominated sorting genetic algorithm with crowding distance sorting (NSGA-II) for the resulting multiobjective optimization problem, several trajectories are discovered. The resulting trajectories of the presented scheme permit alternative trade-off studies by designers incorporating higher level information and mission priorities.     

Enhancing the kinematic precise orbit determination of low earth orbiters using GPS receiver clock modelling

Clock error estimation has been the focus of a great deal of research because of the extensive usage of clocks in GPS positioning applications. The receiver clock error in the spacecraft orbit determination is commonly estimated on an epoch-by-epoch basis, along with the spacecraft’s position. However, due to the high correlation between the spacecraft orbit altitude and the receiver clock parameters, estimates of the radial component are degraded in the kinematic approach. Using clocks with high stability, the predictable behaviour of the receiver oscillator can be exploited to improve the positioning accuracy, especially for the radial component. This paper introduces two GPS receiver clock models to describe the deterministic and stochastic property of the receiver clock, both of which can improve the accuracy of kinematic orbit determination for spacecraft in low earth orbit. In particular, the clock parameters are estimated as time offset and frequency offset in the two-state model. The frequency drift is also estimated as an unknown parameter in the three-state model. Additionally, residual non-deterministic random errors such as frequency white noise, frequency random walk noise and frequency random run noise are modelled. Test results indicate that the positioning accuracy could be improved significantly using one day of GRACE flight data. In particular, the error of the radial component was reduced by over 40.0% in the real-time scenario.     

共面圆轨道航天器在轨服务任务规划

为了降低"一对多"在轨服务的成本,以共面圆轨道卫星群为研究对象,开展了在轨服务任务规划问题的研究。首先,对"一对多"在轨服务任务场景进行了分析,建立了任务规划数学模型,将其简化为包含内层Lambert问题、外层最优时间分配问题的双层优化模型。然后,给出了任务规划求解方法及流程,提出采用工程图解法的思想求解内层多圈Lambert问题,采用遗传算法求解外层最优时间分配问题。最后,以三个目标航天器为例,针对限制和不限制在轨服务任务完成总时间这两种情况,采用上述方法进行求解,计算结果验证了方法的有效性。     

Optimal guidance and collision avoidance for docking with the rotating target spacecraft

The guidance and control strategy for spacecraft rendezvous and docking are of vital importance, especially for a chaser spacecraft docking with a rotating target spacecraft. Approach guidance for docking maneuver in planar is studied in this paper. Approach maneuver includes two processes: optimal energy approach and the following flying-around approach. Flying-around approach method is presented to maintain a fixed relative distance and attitude for chaser spacecraft docking with target spacecraft. Due to the disadvantage of energy consumption and initial velocity condition, optimal energy guidance is presented and can be used for providing an initial state of flying-around approach process. The analytical expression of optimal energy guidance is obtained based on the Pontryagin minimum principle which can be used in real time. A couple of solar panels on the target spacecraft are considered as obstacles during proximity maneuvers, so secure docking region is discussed. A two-phase optimal guidance method is adopted for collision avoidance with solar panels. Simulation demonstrates that the closed-loop optimal energy guidance satisfies the ending docking constraints, avoids collision with time-varying rotating target, and provides the initial velocity conditions of flying-around approach maneuver. Flying-around approach maneuver can maintain fixed relative position and attitude for docking.     

Spacecraft formation flying control around L2 sun-earth libration point using on–off SDRE approach

In this paper, on–off SDRE control approach is presented for spacecraft formation flying control around sun-earth L2 libration point. Orbits around libration points are significant targets for many space missions mainly because of efficient fuel consumption. Furthermore, less propellant usage can be achieved by considering optimal control approaches in spacecraft formation flying control design. Among various nonlinear and optimal control methods, SDRE has shown to be a popular controller in various missions due to the privileges including efficiency, accuracy and robustness. The spacecraft are assumed to have on–off thrusters as actuators. It requires them to be fed with a sequence of on–off pulses which is regarded as a challenge for spacecraft designers. Hence, the main contribution of this paper is designing an on–off SDRE approach for the formation flight around sun-earth L2 point with uncertainty with energy and accuracy considerations. Including on–off input as a constraint is not feasible for SDRE implementation because it makes the system non-affine. An alternative is utilizing an integral action technique and an auxiliary control to make the system affine which leads to on–off SDRE approach. It has also been shown that the proposed method is robust against parametric uncertainties of the states. Present study aims to design an energy-beneficial, simple and attractive controller for a complex nonlinear system with on–off inputs and uncertainty in CRTBP. Simulation results show that the on–off SDRE control could provide the formation flight around L2 point with high accuracy using less energy consumption.     

脉冲推力轨道拦截可达性描述及求解方法

针对航天器单脉冲轨道拦截可达性分析问题,基于共面变轨、逆轨拦截假设,考虑能量、时间和交会角约束,提出了拦截航天器可拦截区和可发射区的概念。在航天器单脉冲空间可达范围的基础上,进一步考虑了目标轨道的约束,建立了目标轨道命中区的计算策略,对异面轨道交叉点为燃料最省点做出了解释。把拦截可达性相关的问题归纳为8个基本拦截问题,通过这8个问题的组合,描述了考虑能量、时间和交会角约束下拦截问题的可拦截区和可发射区的计算方法。采用圆轨道共面变轨、逆轨拦截场景进行了仿真验证,结果表明该方法能够快速有效地计算出约束条件下航天器的拦截可达范围,能够用于分析特定任务情况下的拦截可达性。     

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.     

Small satellite survey mission to the second Earth moon

This paper presents an innovative space mission devoted to the survey of the small Earth companion asteroid by means of nano platforms. Also known as the second Earth moon, Cruithne, is the target identified for the mission. Both the trajectory to reach the target and a preliminary spacecraft budget are here detailed. The idea is to exploit high efficient ion thrusters to reduce the propellant mass fraction in such a high total impulse mission (of the order of 1e6 Ns). This approach allows for a 100 kg class spacecraft with a very small Earth escape energy (5 km²/s²) to reach the destination in about 320 days. The 31% propellant mass fraction allows for a payload mass fraction of the order of 8% and this is sufficient to embark on such a small spacecraft a couple of nano-satellites deployed once at the target to carry out a complete survey of the asteroid. Two 2U Cubesats are here considered as representative payload, but also other scientific payloads or different platforms might be considered according with the specific mission needs. The small spacecraft used to transfer these to the target guarantees the manoeuvre capabilities during the interplanetary journey, the protection against radiations along the path and the telecommunication relay functions for the data transmission with Earth stations. The approach outlined in the paper offers reliable solutions to the main issues associated with a deep space nano-satellite mission thus allowing the exploitation of distant targets by means of these tiny spacecraft. The study presents an innovative general strategy for the NEO observation and Cruithne is chosen as test bench. This target, however, mainly for its relevant inclination, requires a relatively large propellant mass fraction that can be reduced if low inclination asteroids are of interest. This might increase the payload mass fraction (e.g. additional Cubesats and/or additional scientific payloads on the main bus) for the same 100 kg class mission.     

Generic procedure for designing and implementing plan management systems for space science missions operations

This paper is one of the components of a larger framework of activities whose purpose is to improve the performance and productivity of space mission systems, i.e. to increase both what can be achieved and the cost effectiveness of this achievement. Some of these activities introduced the concept of Functional Architecture Module (FAM); FAMs are basic blocks used to build the functional architecture of Plan Management Systems (PMS). They also highlighted the need to involve Science Operations Planning Expertise (SOPE) during the Mission Design Phase (MDP) in order to design and implement efficiently operation planning systems. We define SOPE as the expertise held by people who have both theoretical and practical experience in operations planning, in general, and in space science operations planning in particular. Using ESA’s methodology for studying and selecting science missions we also define the MDP as the combination of the Mission Assessment and Mission Definition Phases. However, there is no generic procedure on how to use FAMs efficiently and systematically, for each new mission, in order to analyse the cost and feasibility of new missions as well as to optimise the functional design of new PMS; the purpose of such a procedure is to build more rapidly and cheaply such PMS as well as to make the latter more reliable and cheaper to run. This is why the purpose of this paper is to provide an embryo of such a generic procedure and to show that the latter needs to be applied by people with SOPE during the MDP. The procedure described here proposes some initial guidelines to identify both the various possible high level functional scenarii, for a given set of possible requirements, and the information that needs to be associated with each scenario. It also introduces the concept of catalogue of generic functional scenarii of PMS for space science missions. The information associated with each catalogued scenarii will have been identified by the above procedure and will be relevant only for some specific mission requirements. In other words, each mission that shares the same type of requirements that lead to a list of specific catalogued scenarii can use this latter list of scenarii (regardless of whether the mission is a plasma, planetary, astronomy, etc. mission). The main advantages of such a catalogue are that it speeds-up the execution of the procedure and makes the latter more reliable. Ultimately, the information associated to each relevant scenario (from the catalogue or freshly generated by the procedure) will then be used by mission designers to make informed decisions, including the modification of the mission requirements, for any missions. In addition, to illustrate the use of such a procedure, the latter is applied to a case study, i.e. the Cross-Scale mission. One of the outcomes of this study is an initial set of generic functional scenarii. Finally, although border line with the above purpose of this paper, we also discuss multi-spacecraft specific issues and issues related to the on-board execution of the plan update system (PUS). In particular, we show that the operation planning cost of N spacecraft is not equal to N times the cost of 1 spacecraft and that on-board non-synchronised operation will not require inter-spacecraft communication. We also believe that on-board PUS should be made possible for all missions as a standard.     

木星系探测及行星穿越任务轨迹初步设计

基于我国未来木星系探测任务需求,初步设计了任务轨迹。以目前的发射能力,要实现木星的环绕探测必将利用行星借力,需设计借力轨迹。首先将脉冲变轨的轨迹设计问题转化为参数优化问题,在满足2029—2032年间发射并且飞行时间不超过7年的约束条件下,使用PSO算法对发射时刻、借力时刻、深空机动时刻、到达时刻等参数进行优化,使得探测器需提供的总速度增量最小。探测器进入木星系后,利用木卫3借力捕获至环木大椭圆轨道,又利用木卫4构造共振借力,最终捕获至木卫4的环绕轨道。在此基础上,还考虑了天王星飞越的拓展任务,天王星探测器在到达木星时与木星系探测器分离,利用木星借力可无消耗飞往天王星,并在2043年完成天王星的飞越探测任务。     

Sailing with solar and planetary radiation pressure

Literature on solar sailing has thus far mostly considered solar radiation pressure (SRP) as the only contribution to sail force. However, considering a sail in a planetary mission scenario, a new contribution can be added. Since the planet itself emits radiation, this generates a radial planetary radiation pressure (PRP) that is also exerted on the sail. Hence, this work studies the combined effects of both SRP and PRP on a sail for two case studies, i.e. Earth and Venus. In proximity of the Earth, the effect of PRP can be significant under specific conditions. Around Venus, instead, PRP is by far the dominating contribution. These combined effects have been studied for single- and double-sided reflective coating and including eclipse. Results show potential increase in the net acceleration and a change in the optimal attitude to maximise the acceleration in a given direction. Moreover, an increasing semi-major axis manoeuvre is shown with and without PRP, to quantify the difference on a real-case scenario.     

Mission feasibility analysis on deflecting Earth-crossing objects using a power limited laser ablating spacecraft

This paper analyzes several mission capabilities to deflect Earth-crossing objects (ECOs) using a conceptual future spacecraft with a power limited laser ablating tool. A constrained optimization problem is formulated based on nonlinear programming with a three-dimensional patched conic method. System dynamics are also established, considering the target ECO’s orbit as being continuously perturbed by limited laser power. The required optimal operating duration and operating angle history of the laser ablating tool are computed for various types of ECOs to avoid an Earth impact. The available final warning time is also determined with a given limited laser power. As a result, detailed laser operating behaviors are presented and discussed, which include characteristics of operating duration and angle variation histories in relation to the operation’s start time and target object’s properties. The calculated durations of the optimal laser operation are also compared to those estimated with first-order approximations previous studies. It is discovered that the duration of the laser operation estimated with first-order approximations could result in up to about 50% error if the operation is started at the final warning time. The laser operation should be started as early as possible because an early start requires a short operating duration with a small operating angle variation. The mission feasibility demonstrated in the present study will give various insights into preparing future deflection missions using power limited spacecraft with a laser ablation tool.     

附着小天体的最优制导控制方法

以小天体伴飞附着任务为工程背景,针对探测器在小天体复杂弱引力场条件下附着这一难题,研究了最优制导控制策略。首先,考虑在小天体极区实施附着任务,建立并简化动力学模型,给出约束条件和基于时间-燃耗最优的混合性能指标要求。然后,采用相平面法设计了最优制导律,利用极限环设计最优开关控制律;同时,采用高斯伪谱法把附着小天体的最优制导问题转化成非线性规划问题,利用Matlab/GPOPS优化工具包求取最优数值解。最后,加入已有的基于矢量测量的自主光学导航模块构建GNC仿真回路,对两种最优制导控制策略进行仿真验证。结果表明:两种制导控制策略都能满足任务要求,但基于相平面法得到的最优制导控制具有一定风险,而基于高斯伪谱法得到的最优制导控制精度更高、燃耗更少,适于工程应用。     

连续常值推力机动分析与应用

连续常值推力机动是空间飞行常用的轨道机动方式。其中,小推力适合于地球轨道航天器交会机动,而切向或周向推力以及较大的正径向推力可用于脱离地球引力场的逃逸飞行,执行星际交会使命。应用常推力作用下的质心运动方程,对机动推力的量值没有限制;在航天器交会应用中,对相对距离也无要求。这种方法可直接获得向径、轨道速度等参数随时间或极角(绕地心的转动角)的变化,便于分析轨道转移与逃逸运动,有助于飞行使命与运动轨迹的设计。特别是,若机动转移的初轨为圆轨道,在推力较小、飞行时间不长的情况下,应用量纲1形式的运动方程,可获得具有工程应用价值的近似解。     

Solar sailing in realistic mode,based on a locally-optimal control laws

Ballistic design of solar sailing missions in the solar system is composed of defining the design parameters, the control programs, and the trajectories that provide performance goals of a flight. The use of a solar sail spacecraft imposes specific restrictions on mission parameters that include the degradation limit on the flight duration, the maximum temperature of solar sail's surface, the minimum distance from the Sun, the maximum angular velocity of the spacecraft's rotation and others.Many authors considered the impact of these restrictions on the design of the mission separately, but they used a sophisticated method of finding the exact optimal motion control or applied the most straightforward laws of motion control. This paper uses local-optimal control laws at the complete mathematical models of motion and functioning of solar sail spacecraft to describe a technique of designing interplanetary missions. The described method avoids the need to obtain an accurate optimal solution to the control problem and does not cause significant computational difficulties.     

椭圆轨道卫星空间任意位置悬停的方法

对任务星施加持续的控制加速度,使其在飞行过程中相对于目标卫星的空间位置保持不变,即实现任意位置悬停飞行。通过对任务星与目标星的相对运行分析和重力差异补偿分析,给出了在飞行过程中任务星相对于运行在椭圆轨道上的目标星实现任意位置悬停所需的径向、切向和法向控制加速度公式。最后对典型悬停飞行过程进行了动力学仿真,并对不同悬停飞行任务的能量消耗进行了对比分析,表明在一段时间内对任务星进行轨道悬停是可行的。