Deep reinforcement learning for six degree-of-freedom planetary landing

This work develops a deep reinforcement learning based approach for Six Degree-of-Freedom (DOF) planetary powered descent and landing. Future Mars missions will require advanced guidance, navigation, and control algorithms for the powered descent phase to target specific surface locations and achieve pinpoint accuracy (landing error ellipse <5 m radius). This requires both a navigation system capable of estimating the lander’s state in real-time and a guidance and control system that can map the estimated lander state to a commanded thrust for each lander engine. In this paper, we present a novel integrated guidance and control algorithm designed by applying the principles of reinforcement learning theory. The latter is used to learn a policy mapping the lander’s estimated state directly to a commanded thrust for each engine, resulting in accurate and almost fuel-optimal trajectories over a realistic deployment ellipse. Specifically, we use proximal policy optimization, a policy gradient method, to learn the policy. Another contribution of this paper is the use of different discount rates for terminal and shaping rewards, which significantly enhances optimization performance. We present simulation results demonstrating the guidance and control system’s performance in a 6-DOF simulation environment and demonstrate robustness to noise and system parameter uncertainty.     

考虑相互碰撞影响的月壤颗粒运动轨迹计算方法研究

针对登月着陆器下降过程扬起月壤颗粒的运动轨迹及空间分布问题, 提出了考虑月壤颗粒发生完全弹性碰撞和非完全弹性碰撞两种情况的月壤颗粒运动轨迹计算方法. 根据质量守恒和能量守恒定律确定月壤颗粒相互碰撞后的速度, 通过羽流场与月壤颗粒的流固耦合相互迭代计算方法, 获得被扬起的月壤颗粒在羽流场和相互碰撞共同作用下随时间的运动轨迹和空间分布. 基于美国Apollo 11登月过程实测数据, 采用数值模拟对该方法进行验证. 结果表明, 考虑月壤颗粒相互碰撞的影响后, 其运动规律出现较明显的扩散趋势. 进一步考虑月壤颗粒相互碰撞引起能量损失的影响后, 月壤颗粒的扩散趋势有所减弱, 并且扬起的高度随着恢复系数的减小而降低.      

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.     

嫦娥四号着陆器月面工作遮挡应对方案研究

嫦娥四号着陆于月球背面南极 艾特肯盆地内,着陆区周围复杂地形导致测控和通信遮挡风险。针对这一问题,开展了着陆区的测控、光照遮挡分析,提出利用轨道控制策略的精细化设计来提高着陆点精度、优化月面工作程序和增加自主控制功能的设计方法,全方面降低嫦娥四号着陆器在月球背面着陆区的生存风险。该方法已通过嫦娥四号着陆器在轨验证,可以为其他深空探测任务提供参考和借鉴。     

柔性系绳平衡状态临界绳长研究

为了确定柔性系绳系统在平衡状态下的临界绳长,在考虑大气阻力、系绳伸展性、系绳质量等因素的情况下,基于系绳系统轨道运动建立了系绳平衡状态方程.为确定求解系绳平衡方程所需初值条件,分析了载荷受力情况并建立其平衡状态方程,进而分析给出了系绳长度达到临界值的条件以及临界绳长的计算方法.仿真计算了不同载荷质量、系绳直径和载荷弹道系数这三种情况下系绳的临界绳长,分别拟合得到这三种情况下临界绳长的计算方程,并分析了不同载荷质量、系绳直径和载荷弹道系数对系绳临界绳长的影响.      

Simulation study of motion of charged particles trapped in Earth’s magnetosphere

This article aims to understand the motion of the charged particles trapped in the Earth’s inner magnetosphere. The emphasis is on identifying the numerical scheme, which is appropriate to characterize the trajectories of the charged particles of different energies that enter the Earth’s magnetosphere and get trap along the magnetic field lines. These particles perform three different periodic motions, namely: gyration, bounce, and azimuthal drift. However, often, the gyration of the particle is ignored, and only the guiding center of the particle is traced to reduce the computational time. It is because the simulation of all three motions (gyro, bounce, and drift) together needed a robust numerical scheme, which has less numerical dissipation. We have developed a three-dimensional test particle simulation model in which the relativistic equation of motion is solved numerically using the fourth and sixth-order Runge-Kutta methods. The stability of the simulation model is verified by checking the conservation of total kinetic energy and adiabatic invariants linked with each type of motion. We found that the sixth-order Runge-Kutta method is suitable to trace the complete trajectories of both proton and electron of a wide energy range, 5 keV to 250 MeV for L = 2 – 6. We have estimated the bounce and drift periods from the simulations, and they are found to be in good agreement with the theory. The study implies that a simulation model with sixth-order Runge-Kutta method can be applied to the time-vary, non-analytical form of magnetic configuration in future studies to understand the dynamics of charged particles trapped in Earth’s magnetosphere.     

磁层高能粒子运动的Fokker Planck方程位置项扩散系数研究

利用准线性理论计算了磁层高能粒子运动的Fokker Planck方程在可观测相空间的位置项扩散系数,并与绝热不变量径向扩散系数进行对比分析.研究发现:位置项扩散系数随径向距离呈现R6的比例关系快速增大.相同径向距离条件下,由于空间位置项z分量的作用,高纬度地区的位置项扩散系数小于低纬度地区.通过与径向扩散系数对比发现,两者具有相同的量级,但两者的相对大小需要根据具体的扰动形态进行分析.此研究对使用测试粒子模拟磁层高能粒子运动,尤其是根据引导中心理论,利用蒙特卡洛方法求解磁层高能粒子运动的Fokker Planck方程,建立磁层空间高能粒子运动的精细化模型具有重要意义.      

基于随机森林的月球表面软着陆实时最优控制

针对传统月球表面软着陆在处理入轨偏差或降落过程轨迹偏离实时性差,文章提出一种通过监督学习离线训练随机森林结构,使得着陆器在降落过程中根据其状态,通过训练的随机森林结构在线计算其控制量,从而达到实时控制的目的。文章还提出一种基于随机森林的模型对月球着陆过程轨迹重规划技术,通过动力学建模将月球着陆过程分成制动段、接近段和着陆段共3个阶段,利用离线训练好的模型根据航天器状态在线计算其控制量,并通过三段下降过程逐渐降低航天器位置速度误差。仿真结果表明,针对入轨偏离500m的情况,通过第一阶段将位置误差缩短至50m,保证了航天器状态位于第二阶段训练集内,经过接近段后再将位置误差缩小至10m范围内,速度误差降至0.01m/s量级,满足着陆误差要求,且控制量计算时间短,达到了轨迹实时重规划的目的。     

The effect of a rocky terrain for CubeSat landing on asteroid surfaces

The paper describes a general modelling procedure to build a simulation tool to investigate contact motion of a CubeSat on an asteroid surface. We investigate landing performance and landing success for the case of elastic rocky terrain and flat surfaces. As a case study, we focus on the disposal of ESA’s Hera Milani CubeSat by landing on the moon of Didymos binary asteroid system. The simulation environment includes the modelling of real shape and 6-DOF motion of the lander, the shape-based gravity models of Didymos and Dimorphos and rocks on surface, that are generated as physical obstacles. Trends and estimates on the performance of the landing phase and the most relevant effects on the outcome of the soil interaction process, are inferred. The statistical results on settling time, dispersion area and motion characteristics, such as number of bounces, show and quantify the effect of rocks on a successful passive and permanent landing.     

月球着陆器软着陆冲击仿真

为提高分析月球着陆器软着陆有效载荷着陆冲击响应的准确性,提出一种基于瞬态动力学的着陆器有效载荷软着陆冲击响应分析方法.根据着陆器全机结构柔性和月壤柔性对有效载荷着陆冲击响应的影响,参照某型着陆器,于MSC.PATRAN环境中建立着陆器全机柔性体模型及月壤柔性体模型,运用瞬态动力学仿真软件MSC.DYTRAN对着陆器软着陆有效载荷着陆冲击响应特性进行了仿真研究.仿真结果与试验结果具有一定的一致性.研究结果表明:使用该方法分析着陆器软着陆有效载荷的着陆冲击响应是准确有效的,能够比较逼真地模拟月球着陆器实际着陆工况.     

基于多工况的新型着陆器软着陆性能优化

以新型腿式着陆器为研究对象,建立其刚柔耦合动力学分析模型,实现着陆器软着陆过程的仿真。通过仿真计算,确定着陆器最易翻倒、底面最易与星球表面岩石碰撞、主体承受最大碰撞力的3组恶劣着陆工况。分析着陆器缓冲机构构型选取设计变量,基于仿真得到的3组恶劣工况,应用第二代非劣排序遗传算法(NSGA-Ⅱ)实现着陆器软着陆性能的优化,优化目标为增强着陆器抗翻倒能力、降低着陆器底面与星球表面岩石碰撞的可能性、降低着陆器主体最大受力值。将优化所得参数代入模型重新进行仿真,着陆器不再发生翻倒,着陆平台底面与星球表面最小距离提高4.2%,主体最大受力值降低12.1%。     

Evaluating the robustness of the enantioselective stationary phases on the Rosetta mission against space vacuum vaporization

The European Space Agency’s Rosetta mission was launched in March 2004 in order to reach comet 67P/Churyumov–Gerasimenko by August 2014. The Cometary Sampling and Composition experiment (COSAC) onboard the Rosetta mission’s lander “Philae” has been designed for the cometary in situ detection and quantification of organic molecules using gas chromatography coupled to mass spectrometry (GC–MS). The GC unit of COSAC is equipped with eight capillary columns that will each provide a specific stationary phase for molecular separation. Three of these stationary phases will be used to chromatographically resolve enantiomers, as they are composed of liquid polymers of polydimethylsiloxane (PDMS) to which chiral valine or cyclodextrin units are attached. Throughout the ten years of Rosetta’s journey through space to reach comet 67P, these liquid stationary phases have been exposed to space vacuum, as the capillary columns within the COSAC unit were not sealed or filled with carrier gas. Long term exposures to space vacuum can cause damage to such liquid stationary phases as key monomers, volatiles, and chiral selectors can be vaporized and lost in transit. We have therefore exposed identical spare units of COSAC’s chiral stationary phases over eight years to vacuum conditions mimicking those experienced in space and we have now investigated their resolution capabilities towards different enantiomers both before and after exposure to space vacuum environments. We have observed that enantiomeric resolution capabilities of these chiral liquid enantioselective stationary phases has not been affected by exposure to space vacuum conditions. Thus we conclude that the three chiral stationary phases of the COSAC experiment onboard the Rosetta mission lander “Philae” can be considered to have maintained their resolution capacities throughout their journey prior to cometary landing in November 2014.     

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.     

一种基于陨石坑拟合椭圆的着陆器位姿估计算法

针对星际着陆自主导航问题,提出一种利用陨石坑边缘曲线估计着陆器位姿的简便算法。该算法首先利用至少3条陨石坑边缘曲线及其对应的像曲线,建立关于着陆器位姿的几何约束方程;然后由克罗内克积和最小二乘算法,求取着陆器位置、姿态的解析解。该方法的优点在于,计算过程简单、快速。仿真结果表明,该算法可以较精确的估计着陆器位姿,鲁棒性好。     

Estimation of ballistic coefficients of low altitude debris objects from historical two line elements

This paper presents a new method for estimating ballistic coefficients (BCs) of low perigee debris objects from their historical two line elements (TLEs). The method uses the drag perturbation equation of the semi-major axis of the orbit. For an object with perigee altitude below 700 km, the variation in the mean semi-major axis derived from the TLE is mainly caused by the atmospheric drag effect, and therefore is used as the source in the estimation of the ballistic coefficient. The method is tested using the GRACE satellites, and a number of debris objects with external ballistic coefficient values, and agreements of about 10% are achieved.     

Model of energetic populations at Ganymede,implications for an orbiter

A model is developed to study the energetic particle populations in Ganymede’s magnetosphere. The main objective is to estimate to what extent the moon could protect an orbiter from radiations. Using Liouville’s theorem, the phase space density of particles coming from Jupiter’s magnetosphere is calculated at any point of Ganymede’s environment. Up to energies of ∼50–100 keV for ions and ∼10–20 MeV for electrons, Ganymede’s magnetic field appears to be able to form distinctive populations as loss-cones over the polar caps and radiation belts. At larger energies, these features are blurred by Larmor radius effects; the moon absorption simply creates a quasi-isotropic layer of ∼500 km thickness where the flux is reduced by ∼40–50%. The predictions are compared to Galileo measurements. In particular, we demonstrate the importance of the moon sweeping in reducing the flux over the polar caps. Interestingly, this can be accounted for by assuming that the particles bouncing between Jupiter and Ganymede are ideally scattered in pitch angle and permanently re-fill the loss-cone, which increases the precipitation on Ganymede’s polar cap. In overall, it is estimated that the radiation dose received by an orbiter of Ganymede will be reduced by more than 50–60% compared to the expected dose at Jupiter/Ganymede distance. This should have a positive impact on the design of a future orbiter of Ganymede.     

Statistical study of energetic electrons in Jupiter’s inner magnetosphere by Juno/JEDI

The Juno spacecraft made the first in-situ observations of energetic particles in the polar region of Jupiter’s magnetosphere. After Jupiter Orbit Insertion (JOI) in July 2016, data from ~20 Juno perijoves (PJs) obtained by Juno/JEDI are accumulated, providing an excellent opportunity to study the long term spatio-temporal distribution of energetic particles in Jupiter’s radiation belt. We transform Juno’s position from a Cartesian to a magnetic coordinate system by tracing magnetic field lines based on a fourth order Runge-Kutta method. Then the fluxes of energetic electrons from PJ1 to PJ14 sorted by different locations in magnetic coordinate space and the data are well organized by the L-shell parameter. The variation of electron flux increases with L-shell. The deviation (the ratio of the 75th percentile to the 25th percentile) of 0.51 MeV electron flux varies from a factor of 1.23 near L = 9.5 to 27.57 near L = 15.5. However, the mean flux decreases by about one order of magnitude in the same region. The electron spectra at larger L-shells are softer than that at smaller L-shells. On the other hand, the electron flux decreases more rapidly with increased L-shell when the location is off the equator. Along an L-shell, the electron flux decrease at first and then increase again from equator to mid-latitude region. In addition, we compare the statistical results with the widely used GIRE2 model. JEDI data correspond well with the GIRE2 model when the L-shell is > 14.75. GIRE2 underestimate the electron flux for L-shell smaller than 13.25. These results of this analysis are applicable to estimate the effects of the radiation environment in Jupiter’s magnetosphere.     

不确定条件下高超声速俯冲弹道鲁棒优化

针对俯冲段不确定性因素所导致的弹道偏差和落点精度问题,研究了一种增强弹道抗干扰能力的高超声速滑翔飞行器俯冲攻击鲁棒弹道优化方法。首先建立了考虑模型偏差、阵风干扰等不确定性因素的滑翔飞行器俯冲段运动数学模型;其次,推导了不确定条件下滑翔飞行器运动模型的雅各比矩阵解析表达式,得到了基于线性协方差分析法的系统误差传播方程;最后,建立了不确定性条件下的俯冲段弹道优化模型,并应用高斯伪谱法对该弹道优化问题进行求解。仿真结果表明,与不考虑不确定性因素影响的弹道优化方法相比,本文方法可有效提高高超滑翔飞行器俯冲弹道抗干扰能力,且抗干扰能力随着权重系数值的增大而增强。