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Design and optimization of a trajectory for Moon departure Near Earth Asteroid exploration

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Science China(Physics,Mechanics & Astronomy) 2011年第4期54卷 748-755页

作者： CHEN Yang baoyin hexi li junfeng School of Aerospace Tsinghua University Beijing 100084 China

The lunar probe often has some remaining fuel on completing the predefined Moon exploration mission and may carry out some additional tasks from the Moon orbit using the *** possibility for the lunar probe to escape from the Moon and the Earth is *** and optimization of the trajectory from the Moon orbit to the Near Earth Asteroids (NEAs) using the spacecraft's residual fuel is *** first,the semi-major axis,inclinations and the phase relations with the Earth of all the numbered NEAs are investigated to preliminarily select the possible *** on the Sun-centered two-body problem,the launch window and the asteroid candidates are determined by calculating the minimum delta-v for two-impulse rendezvous mission and one-impulse flyby mission,*** a precise designed trajectory,a full ephemeris dynamical model,which includes gravities of the Sun,the planets and the Moon,is adopted by reading the JPL *** departure time,arrival time,burning time duration and thrust angles are set as variables to be designed and *** optimization problem is solved via the Particle Swarm Optimization (PSO) ***,two feasible NEA flyby missions are presented.

关键词： trajectory design full ephemeris model Near Earth Asteroid exploration Particle Swarm Optimization

Formation reconfiguration in restricted three body problem

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Acta Mechanica Sinica 2007年第3期23卷 321-328页

作者： Shengping Gong junfeng li hexi baoyin Yunfeng Gao School of Aerospace Tsinghua UniversityBeijing 100084 China

Reconfiguration of formation flying around a halo orbit of the Sun-Earth restricted three body system is investigated with impulse maneuvers. For a short time reconfiguration, the two-impulse maneuver is investigated with both analytical and numerical methods and the Beginning-Ending （BE） method is proven to be an energy-optimal one of all two-impulse （TI） reconfigurations, and the energy consumption of BE is independent of the position of the chief spacecraft, and decreases with the reconfiguration time. Then, genetic algorithm is adopted to optimize the energy consumption. The results show that the optimal energy increases with radius difference between the initial and final orbits, and decreases with the reconfiguration time.

关键词： Three body problem Halo orbit Formation reconfiguration Formation flying

Entropy method of measuring and evaluating periodicity of quasi-periodic trajectories

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Science China(Physics,Mechanics & Astronomy) 2018年第6期61卷 30-49页

作者： Yanshuo Ni Konstantin Turitsyn hexi baoyin junfeng li School of Aerospace Engineering Tsinghua University Department of Mechanical Engineering Massachusetts Institute of Technology

This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform （DFT） to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem （CRTBP） are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator （OFli）. The results show that entropy is a better tool for discriminating periodicity in quasiperiodie trajectories than OFli and can detect periodicity while excluding the spirals that are judged as periodic cases by OFli. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.

关键词： quasi-periodic trajectories entropy quality evaluating

Trajectory design for the Moon departure libration point mission in full ephemeris model

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Science China(Technological Sciences) 2011年第11期54卷 2924-2934页

作者： CHEN Yang baoyin hexi li junfeng School of Aerospace Tsinghua University Beijing 100084 China

The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon *** Moon departure mission for the lunar probe is the focus of this *** possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is *** trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard *** applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are *** the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.

关键词： Moon exploration trajectory design full ephemeris model libration point halo orbit

Dynamic modelling and analysis of space webs

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Science China(Physics,Mechanics & Astronomy) 2011年第4期54卷 783-791页

作者： YU Yang baoyin hexi li junfeng School of Aerospace Tsinghua University Beijing 100084 China

Future space missions demand operations on large flexible structures,for example,space webs,the lightweight cable nets deployable in space,which can serve as platforms for very large structures or be used to capture orbital *** interest in research on space webs is likely to increase in the future with the development of promising applications such as Furoshiki sat-ellite of JAXA,Robotic Geostationary Orbit Restorer (ROGER) of ESA and Grapple,Retrieve And Secure Payload (GRASP) of *** high-tensioned nets in civil engineering,space webs may be low-tensioned or tensionless,and extremely flexible,owing to the microgravity in the orbit and the lack of support components,which may cause computational *** models are necessary in the analysis of space webs,especially in the conceptual design and evaluation for prototypes.A full three-dimensional finite element (FE) model was developed in this *** truss elements were adopted to reduce the computational *** cable is a compression-free material and its tensile stiffness is also variable,we introduced the cable material constitutive relationship to work out an accurate and feasible model for prototype analysis and *** the static analysis,the stress distribution and global deformation of the webs were discussed to get access to the knowledge of strength of webs with different types of *** the dynamic analysis,special attention was paid to the impact *** max stress and global deformation were *** simulation results indicate the interesting phenomenon which may be worth further research.

关键词： space webs finite element method cable material nonlinear constitutive relationship

A new solar sail orbit

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Science China(Technological Sciences) 2012年第3期55卷 848-855页

作者： GONG ShengPing li junfeng baoyin hexi SIMO Jules School ofAerospace Tsinghua UniversityBeijing 100084China State Key Laboratory of Astronautical Dynamics Xi'an Satellite Control CenterXi'an 710043China Advanced Space Concepts Laboratory Department of Mechanical EngineeringUniversity of StrathclydeGlasgow G11X JUnited Kingdom

Solar sail is used to achieve a geocentric sun-synchronous frozen *** kind of orbit combines the characteristics of both sun-synchronous orbits and frozen ***,the impossible orbits for a typical spacecraft such as sun-synchronous orbits whose inclination is less than 90° are also possible for solar *** achieve a sun-synchronous frozen orbit,the characteristic acceleration of the sail is chosen *** addition,the attitude of the sail is adjusted to keep the sun-synchronous and frozen *** perturbations including atmosphere drag,third-body gravitational forces and shaded regions are discussed,where the atmosphere drag is cancelled by solar radiation pressure force,third-body gravitational forces have negligible effects on the orbit and the shaded region can be avoided by choosing the classical orbit elements of the *** last,a numerical example is employed to validate the sun-synchronous frozen characteristics of the sail.

关键词： solar sail sun-synchronous orbit frozen orbit

Optimal four-impulse rendezvous between coplanar elliptical orbits

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Science China(Physics,Mechanics & Astronomy) 2011年第4期54卷 792-802页

作者： WANG JianXia baoyin hexi li junfeng SUN FuChun School of Aerospace Tsinghua University Beijing 100084 China Department of Computer Science and Technology Tsinghua University Beijing 100084 China

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively w

关键词： If the initial values are taken randomly it is difficult to converge to the optimal solution. elliptical orbit rendezvous primer vector fuel optimal

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

Feasibility analysis of the angular momentum reversal trajectory via hodograph method for high performance solar sails

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Science China(Technological Sciences) 2011年第11期54卷 2951-2957页

作者： ZENG XiangYuan baoyin hexi li junfeng GONG ShengPing School of Aerospace Tsinghua University Beijing 100084 China

In this paper a new phase space of hodograph method is adopted to investigate and better understand the two-dimensional angular momentum reversal(H-reversal) trajectories for high performance solar sails within a fixed cone *** the hodograph method and the H-reversal trajectory are not very common,both of them are briefly *** relationship between them are constructed and addressed with a sample *** the phase space varies according to the sail quality and the fixed sail cone angle is also *** variation of the phase space,the minimum sail lightness number can be obtained by solving a set of algebraic equations instead of a parameter optimization *** a given sail lightness number,there are three types of the two-dimensional possible heliocentric motion,including the spiral inward trajectories towards the Sun,the H-reversal trajectories and the directly outward escape *** boundaries that separate these different groups are easily determined by using the phase ***,the method and procedures to achieve the feasible region of the H-reversal trajectory with required perihelion distance are presented in detail.

关键词： solar sail angular momentum reversal (H-reversal) hodograph method