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Science China(Physics,Mechanics & Astronomy) 2015年第11期58卷 107-120页

作者： TANG Gao jiang fanghua LI JunFeng School of Aerospace Engineering Tsinghua University

Near-Earth asteroids have gained a lot of interest and the development in low-thrust propulsion technology makes complex deep space exploration missions possible. A mission from low-Earth orbit using low-thrust electric propulsion system to rendezvous with near-Earth asteroid and bring sample back is investigated. By dividing the mission into five segments, the complex mission is solved separately. Then different methods are used to find optimal trajectories for every segment. Multiple revolutions around the Earth and multiple Moon gravity assists are used to decrease the fuel consumption to escape from the Earth. To avoid possible numerical difficulty of indirect methods, a direct method to parameterize the switching moment and direction of thrust vector is proposed. To maximize the mass of sample, optimal control theory and homotopic approach are applied to find the optimal trajectory. Direct methods of finding proper time to brake the spacecraft using Moon gravity assist are also proposed. Practical techniques including both direct and indirect methods are investigated to optimize trajectories for different segments and they can be easily extended to other missions and more precise dynamic model.

关键词： sample return optimization gravity assist

A simple method to design non-collision relative orbits for close spacecraft formation flying

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Science China(Physics,Mechanics & Astronomy) 2018年第5期61卷 20-35页

作者： Wei jiang JunFeng Li fanghua jiang Franco Bernelli-Zazzera School of Aerospace Engineering Tsinghua University Department of Aerospace Science and Technology Politecnico di Milano

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with the same semi-major axis in close formation. Given the initial orbital elements of the leader, this paper presents a simple way to design initial relative orbital elements of close spacecraft with the same semi-major axis, thus preventing collision under non-perturbed conditions. Considering the mean influence of J_2 perturbation, namely secular J_2 perturbation, we derive the mean derivatives of orbital element differences, and then expand them to first order. Thus the first order expansion of orbital element differences can be added to the relative motion equations for further analysis. For a pair of spacecraft that will never collide under non-perturbed situations, we present a simple method to determine whether a collision will occur when J_2 perturbation is considered. Examples are given to prove the validity of the extended relative motion equations and to illustrate how the methods presented can be used. The simple method for designing initial relative orbital elements proposed here could be helpful to the preliminary design of the relative orbital elements between spacecraft in a close formation, when collision avoidance is necessary.

关键词： spacecraft formation relative motion collision avoidance orbit designing

Perturbed low-thrust geostationary orbit transfer guidance via polynomial costate estimation

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Chinese Journal of Aeronautics 2024年第3期37卷 181-193页

作者： Zhao LI Hengnian LI fanghua jiang Junfeng LI State Key Laboratory of Astronautic Dynamics Xi’an Satellite Control CenterXi’an 710043China School of Aerospace Engineering Tsinghua UniversityBeijing 100084China

This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary *** Earth’s oblateness perturbation and shadow are taken into *** is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time,including high guidance optimality,robustness,and onboard computational *** this work,a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified,which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate *** on this relationship,the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged *** polynomial regression models are trained on the training dataset and are regarded as the costate *** the transfer,the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any ***,all these computations onboard are *** simulation results show that the proposed guidance scheme possesses extremely high guidance optimality,robustness,and onboard computational efficiency.

关键词： Low thrust Orbital transfer Trajectory optimization Guidance Indirect method Orbital averaging Machine learning Geostationary satellites

An identifier-actor-optimizer policy learning architecture for optimal control of continuous-time nonlinear systems

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Science China(Physics,Mechanics & Astronomy) 2020年第6期63卷 42-53页

作者： Lin Cheng ZhenBo Wang fanghua jiang JunFeng Li School of Aerospace Engineering Tsinghua UniversityBeijing 100084China Department of Mechanical Aerospaceand Biomedical EngineeringUniversity of TennesseeKnoxville TN 37996USA

An intelligent solution method is proposed to achieve real-time optimal control for continuous-time nonlinear systems using a novel identifier-actor-optimizer(IAO)policy learning *** this IAO-based policy learning approach,a dynamical identifier is developed to approximate the unknown part of system dynamics using deep neural networks(DNNs).Then,an indirect-method-based optimizer is proposed to generate high-quality optimal actions for system control considering both the constraints and performance ***,a DNN-based actor is developed to approximate the obtained optimal actions and return good initial guesses to the *** this way,the traditional optimal control methods and state-of-the-art DNN techniques are combined in the IAO-based optimal policy learning *** to the reinforcement learning algorithms with actor-critic architectures that suffer hard reward design and low computational efficiency,the IAO-based optimal policy learning algorithm enjoys fewer user-defined parameters,higher learning speeds,and steadier convergence properties in solving complex continuous-time optimal control problems(OCPs).Simulation results of three space flight control missions are given to substantiate the effectiveness of this IAO-based policy learning strategy and to illustrate the performance of the developed DNN-based optimal control method for continuous-time OCPs.

关键词： continous-time nonlinear systems identifier-actor-optimizer architecture intelligent optimal control deep neural net-works

Real-time control for fuel-optimal Moon landing based on an interactive deep reinforcement learning algorithm

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Astrodynamics 2019年第4期3卷 375-386页

作者： Lin Cheng Zhenbo Wang fanghua jiang Tsinghua University Beijing 100084China University of Tennessee KnorvilleTN 37996USA

In this study,a real-time optimal control approach is proposed using an interactive deep reinforcement learning algorithm for the Moon fuel-optimal landing *** the remote communication restrictions and environmental uncertainties,advanced landing control techniques are demanded to meet the high requirements of real-time performance and autonomy in the Moon landing *** reinforcement learning(DRL)algorithms have been recently developed for real-time optimal control but suffer the obstacles of slow convergence and difficult reward function *** address these problems,a DRL algorithm is developed using an actor-indirect method architecture to achieve the optimal control of the Moon landing *** this DRL algorithm,an indirect method is employed to generate the optimal control actions for the deep neural network(DNN)learning,while the trained DNNs provide good initial guesses for the indirect method to promote the efficiency of training data *** sufficient learning of the state-action relationship,the trained DNNs can approximate the optimal actions and steer the spacecraft to the target in real ***,a nonlinear feedback controller is developed to improve the terminal landing *** simulations are given to verify the effectiveness of the proposed DRL algorithm and demonstrate the performance of the developed optimal landing controller.

关键词： fuel-optimal landing problem indirect methods deep reinforcement learning interactive network learning real-time optimal control

Fuel optimal low thrust rendezvous with outer planets via gravity assist

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Science China(Physics,Mechanics & Astronomy) 2011年第4期54卷 756-769页

作者： GUO TieDing jiang fanghua BAOYIN HeXi LI JunFeng School of Aerospace Tsinghua University Beijing 100084 China

Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space *** this paper the two techniques are combined and treated comprehensively,both on modeling and numerical *** optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting *** scenarios in the end show the merits of the present approach.

关键词： low thrust fuel optimal trajectory maximum principle homotopic technique gravity assist

Optimization of observing sequence based on nominal trajectories of symmetric observing con guration

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Astrodynamics 2018年第1期2卷 25-37页

作者： Hongwei Yang Gao Tang fanghua jiang School of Aerospace Engineering Tsinghua UniversityBeijing 100084China Department of Mechanical Engineering and Materials Science Duke UniversityDurhamNC 27708USA

This paper presents the crucial method for obtaining our team's results in the 8th Global Trajectory Optimization Competition(GTOC8).Because the positions and velocities of spacecraft cannot be completely determined by one observation on one radio source,the branch and bound method for sequence optimization of multi-asteroid exploration cannot be directly applied *** overcome this diculty,an optimization method for searching the observing sequence based on nominal low-thrust trajectories of the symmetric observing con guration is *** the symmetric observing con guration,the normal vector of the triangle plane formed by the three spacecraft rotates in the ecliptic plane periodically and approximately points to the radio sources which are close to the ecliptic *** possible observing opportunities are selected and ranked according to the nominal trajectories designed by the symmetric observing con ***,the branch and bound method is employed to nd the optimal sequence of the radio source with thrice ***,this method is also used to nd the optimal sequence of the left radio *** nominal trajectories are then corrected for accurate *** performance index of our result is 128,286,317.0 km which ranks the second place in GTOC8.

关键词： branch and bound optimization symmetric observing configuration GTOC low thrust

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近距离航天器间碰撞概率线性模型的解析修正

清华大学学报（自然科学版） 2019年第9期59卷 705-711页

作者：姜薇蒋方华李俊峰清华大学航天航空学院

该文提出一种针对近距离航天器间碰撞概率线性模型的解析修正法。原有碰撞概率线性模型较简单,使用条件严格,适用范围有限,不适用于轨道差别较小的相对运动情况。通过分析碰撞概率线性模型计算结果与Monte Carlo仿真计算结果之间的误差... 详细信息

该文提出一种针对近距离航天器间碰撞概率线性模型的解析修正法。原有碰撞概率线性模型较简单,使用条件严格,适用范围有限,不适用于轨道差别较小的相对运动情况。通过分析碰撞概率线性模型计算结果与Monte Carlo仿真计算结果之间的误差,寻找其与航天器间最大和最小相对运动距离之间的近似解析关系,对原有线性模型进行修正,使其更接近真实碰撞概率。仿真结果表明:该方法拓展了原有线性模型的适用范围,并提高了精度。

关键词：碰撞概率线性模型解析修正

基于在线模型辨识的飞行器多约束复合制导技术

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清华大学学报（自然科学版） 2019年第9期59卷 712-719页

作者：程林张庆振蒋方华清华大学航天航空学院北京100084 北京航空航天大学自动化科学与电气工程学院北京100191

针对飞行器再入制导问题,该文引入控制变量参数化、积分问题转换和在线模型辨识等技术,提出一种跨周期迭代的可行轨迹预测校正算法,并结合标称轨迹跟踪算法形成一套多约束复合制导方案。利用一种复合高度-速度(height velocity,HV)飞行... 详细信息

针对飞行器再入制导问题,该文引入控制变量参数化、积分问题转换和在线模型辨识等技术,提出一种跨周期迭代的可行轨迹预测校正算法,并结合标称轨迹跟踪算法形成一套多约束复合制导方案。利用一种复合高度-速度(height velocity,HV)飞行走廊,将再入轨迹规划问题简化为单调函数寻根问题。为提高射程预测计算效率,引入Gauss-Legendre求积公式,将积分问题转化为函数计算问题。采用递推最小二乘估计方法,收集历史预测信息,实现模型在线辨识功能,并采用跨周期Newton-Raphson方法完成高度权重系数的在线修正。在标称轨迹跟踪器设计的基础上,开展飞行器数值仿真试验,结果表明:基于在线模型辨识的复合制导方法具有显著的速度优势,且具有优异的自主性和自适应能力。

关键词：再入制导复合飞行走廊 Gauss求积法递推最小二乘估计模型辨识跨周期参数校正

悬挂点匀速转动时摆锤圆周运动的存在性与稳定性分析

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应用数学和力学 2018年第2期39卷 183-198页

作者：李舒航蒋方华清华大学附属中学北京100084 清华大学航天航空学院北京100084

悬挂点水平匀速转动时摆锤的圆周运动及其稳定性问题很少被研究,其中蕴含丰富的动力学现象.首先,考虑摆锤在真空和线性阻尼的介质中运动的情况,建立摆锤的动力学方程.其次,将摆锤水平圆周运动的特解的存在性问题转化为四次多项式的求根... 详细信息

悬挂点水平匀速转动时摆锤的圆周运动及其稳定性问题很少被研究,其中蕴含丰富的动力学现象.首先,考虑摆锤在真空和线性阻尼的介质中运动的情况,建立摆锤的动力学方程.其次,将摆锤水平圆周运动的特解的存在性问题转化为四次多项式的求根问题,通过Descartes(笛卡尔)符号规则及多项式函数的单调性分析,得出了摆的物理参数与特解个数的对应关系,真空中的特解可能是0,1,2个,在介质中时,只能是1个或3个.再次,基于Lyapunov(李雅普诺夫)一次近似理论考察非线性稳定性问题.将运动微分方程在特解附近线性化,特解的稳定性问题通过线性微分方程特征根实部的符号来判断.将涉及的四次特征方程巧妙地转化为二次方程,得出真空中特解线性意义下稳定的条件,以及介质中线性意义下渐近稳定的条件.最后,通过数值仿真,验证和明确了理论分析的结论.

关键词：单摆动悬挂点圆周运动稳定性