Fuel-optimal and Energy-optimal guidance schemes for lunar soft landing at a desired location

Two guidance schemes (i) fuel-optimal (ii) energy-optimal to realize soft landing at a desired location on the moon are developed using the optimal control laws. The optimal control laws are obtained by solving a two-point boundary value problem formulated based on Pontryagin’s principle. The guidance laws, adapted from the optimal control laws, are obtained as a function of unknown co-state variables. Differential Transformation (DT) technique is employed to determine the unknown co-states at each time instant of landing trajectory using the information on the current vehicle state, target landing site (loaded on-board apriori) and the time-to-go. The numerical integration of co-state dynamics is avoided due to the DT based approach. The time-to-go, a critical parameter for any guidance scheme, is computed and updated real time using a simple strategy which uses the current and end states. The simple strategy for time-to-go works well even when the shape of the trajectory is nonlinear. Extensive analysis is carried out to evaluate and compare the proposed guidance schemes. Further, the proposed schemes are compared with other popular guidance schemes. The DT based proposed schemes help quantify the landing masses for fuel-optimal and energy-optimal objectives. Other features of the proposed schemes are that they do not assume constant gravity field and independent of reference trajectory.     

Depth dependency of neutron density produced by cosmic rays in the lunar subsurface

Depth dependency of neutrons produced by cosmic rays (CRs) in the lunar subsurface was estimated using the three-dimensional Monte Carlo particle and heavy ion transport simulation code, PHITS, incorporating the latest high energy nuclear data, JENDL/HE-2007. The PHITS simulations of equilibrium neutron density profiles in the lunar subsurface were compared with the measurement by Apollo 17 Lunar Neutron Probe Experiment (LNPE). Our calculations reproduced the LNPE data except for the 350–400 mg/cm² region under the improved condition using the CR spectra model based on the latest observations, well-tested nuclear interaction models with systematic cross section data, and JENDL/HE-2007.     

怀念恩师钱学森

作者从初见钱学森的印象、在工程力学研究班学习、从事早期卫星准备工作、合作进行远程星际航行后续研究、航天名词规范及航天科普宣传等多方面,回忆了钱学森对自己的引导、指导和教导。     

月面着陆动力下降段最优轨迹序列凸优化方法

针对月面着陆器动力下降制导过程中,时变惯性加速度和重力加速度难以估计与补偿等问题,提出一种基于序列凸优化的在线制导算法。在考虑月面曲率及月球自转的着陆器动力学建模基础上,首先对模型及约束条件进行凸化,得到一个二阶锥规划(SOCP)问题;然后对经典序列凸优化进行了改进,对时变加速度剖面予以实时估计和补偿,提升了现有优化算法的性能,使着陆器在尽可能节约燃料的前提下实现高精度着陆。仿真结果表明,与经典的显式制导律相比,所提出的算法在动力下降段燃料消耗更少。由多种位置偏差下的打靶分析结果可知,所提出的算法均能满足性能指标要求;即使起始位置存在±2500 m的较大波动时,仍能以高精度的速度、位置完成动力下降制导。     

Plume aerodynamic effects of cushion engine in lunar landing

 During the second period of China "Tanyue" Project, the explorer will softland on the moon. The cushion engines are used to decelerate the explorer and reduce the impact on the lunar ground. It is necessary to study its plume effects on the explorer component. The self-developed PWS (Plume WorkStation) software based on direct simulation Monte Carlo (DSMC) method is used to simulate the plume effects of two 150 N engines. Due to the complex structure of the explorer, PWS uses a decoupling method to treat the boundary mesh, which mainly interacts with simulation particles, and has no relation with the computational grids. After the analytical expressions of plane surfaces and curved surfaces of each boundary block are given, the particle position within or without the boundary blocks can be easily determined. Finally the 3D plume field of two 150 N engines is simulated. The pressure, temperature and velocity distributions of plume field are clearly presented by three characteristic slices. The aerodynamic effects on the explorer bottom, the landfall legs and antenna are separately shown. The compression influence on the plume flow of four landfall legs can be observed.     

Issues in planetary protection: policy, protocol and implementation

Planetary protection is NASA's term for the practice of protecting solar system bodies from Earth life while protecting Earth from life that may be brought back from other solar system bodies. Spacefaring nations will soon begin retrieving samples from Mars and other solar system bodies. For these samples, planetary protection is in order, and measures are already in place to prevent the forward contamination of Mars and other bodies by Earth microbes and the backward contamination of Earth by possible extraterrestrial life. A major goal of planetary protection controls on forward contamination is to preserve the planetary record of natural processes by preventing human-caused microbial introductions.     

Journey to the Moon: Recent results,science, future robotic and human exploration

The upcoming fleet of lunar missions, and the announcement of new lunar exploration initiatives, show an exciting “Journey to the Moon”, covering recent results, science, future robotic and human exploration. We review some of the questions, findings and perspectives given in the papers included in this issue of Advances in Space Research.     

企业职能管理工作的定量方法研究

本文是以企业科室职能工作为对象,提出了对以脑力劳动为主体的作业的工作量的量度理论、量度原则、时间分类、工作特点,并介绍了10种量度方法,以解决当前企业管理上的一大难题。量化管理属于现代管理方法的一个分支,是企业管理基础工作的重要组成部分。本文所提的论点和模式,为开展全面量化管理创造了条件。     

Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem

Motivated by the near-future re-exploration of the cislunar space, this paper investigates dynamical substitutes of the Earth-Moon’s resonant Near-Rectilinear Halo Orbits (NRHOs) under the Elliptic-Circular Restricted Four-Body Problem formulation of the Earth-Moon-Sun system. This model considers that the Earth and Moon move in elliptical orbits about each other and that a third body, the Sun, moves in a circular orbit about the Earth-Moon barycenter. By making use of this higher-fidelity dynamical model, we are able to incorporate the Sun’s influence and the Moon’s eccentricity, two of the most significant perturbations of the cislunar environment. As a result of these perturbations, resonant periodic NRHOs of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) are hereby replaced by two-dimensional quasi-periodic tori that better represent the dynamical evolution of satellites near the vicinity of the Moon. We present the steps and algorithms needed to compute these dynamical structures in the Elliptic-Circular model and subsequently assess their utility for spacecraft missions. We focus on the planned orbit for the NASA-led Lunar Gateway mission, a 9:2 synodic resonant L₂ southern NRHO, as well as on the 4:1 synodic and 4:1 sidereal resonances, due to the proximity to the nominal orbit and their advantageous dynamical properties. We verify that the dynamical equivalents of these orbits preserve key dynamical attributes such as eclipse avoidance and near-linear stability. Furthermore, we find that the higher dimensionality of quasi-periodic solutions offers interesting alternatives to mission designers in terms of phasing maneuvers and low-altitude scientific observations.     

Lunar laser topography by LALT on board the KAGUYA lunar explorer – Operational history,new topographic data,peak height analysis of laser echo pulses

In this paper we review the lunar laser ranging conducted by the laser altimeter (LALT) on board the KAGUYA lunar explorer (2007–2009). Five aspects of LALT measurements are described: (1) General operational history, (2) Laser shot and data statistics, (3) Revisions to LALT topographic data, (4) Variations in laser output energy, and (5) Peak height analysis of laser echo pulses. LALT was able to range to the lunar surface despite some troubles with respect to laser output energy in the middle of the KAGUYA mission. The time series topographic data set was revised (Ver. 2) by incorporating new lunar gravity model based on KAGUYA and other historical lunar satellite’s orbit data, along with other improvements, for example by incorporating the accurate position of the laser collimator on board the KAGUYA; however, more than half of the acquired range data could not be converted properly due to problems with orbit accuracy during the extended phase of the mission. The spherical harmonic coefficients and the basic lunar figure parameters derived from LALT_LGT_TS agree very well with LRO-LOLA and the Chang’E-1 LAM model. It is possible that partial failure to the laser diode was responsible for the gradual degradation of laser power (0.835 mJ per million shots) and the rapid decrease that occurred over April 9–14, 2008. The laser power also proved to be extremely sensitive to the temperature of the laser oscillator. The peak height ratio – that is peak height telemetry data divided by calculated ratio – is about 19% on average using the mean slope and albedo data from LALT and Spectral Profiler on KAGUYA space craft, respectively, which suggests the performance of peak height measurement is more than 1/5 for more than 70 km altitude, if compared with calculated one. The peak height ratio may be better if we take the effect of small scale topography within a footprint into account.