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orbit optimization and time delay interferometry for inclined ASTROD-GW formation with half-year precession-period

Chinese Physics B 2015年第5期24卷 671-681页

作者：王刚倪维斗 Shenzhen National Climate Observatory Center for Gravitation and Cosmology (CGC) Department of Physics Tsing Hua University

ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirais （EMRIs） and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The 3 space, crafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD- GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry （TDI） for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precessionperiod. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° （no inclination）, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.

关键词： orbit optimization ASTROD-GW gravitational wave detector time delay interferometry

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orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris

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Chinese Physics B 2013年第4期22卷 571-579页

作者：王刚倪维斗 Shenzhen National Climate Observatory Shanghai United Center for Astrophysics (SUCA) Shanghai Normal University Center for Gravitation and Cosmology (CGC) Department of Physics National Tsing Hua University

Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna （LISA）. The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry （TDI） to match the two different optical paths （times of travel）. Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 （here, CGC stands for center for gravitation and cosmology） ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.

关键词： orbit optimization ASTROD-GW gravitational wave detector time delay interferometry

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Design and optimization of low-energy transfer orbit to Mars with multi-body environment

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Science China(Technological Sciences) 2015年第10期58卷 1660-1671页

作者： LU Yi LI HengNian LI JiSheng CHE Zheng YANG YiKang YANG Yuan SUN Yang School of Electronic and Information Engineering Xi’an Jiaotong University State Key Laboratory of Astronautic Dynamics (ADL) Affiliated to Xi’an Satellite Control Center College of Aeronautics and Astronautics University of Electronic Science and Technology of China School of Aerospace Xi’an Jiaotong University

This paper discusses the problem of design and optimization of low-energy transfer orbit with multi-body environment. A new integrative method is proposed to effectively solve the problem, in which the parameterized patched manifolds in CR3BP(circular restricted three-body problems), the shape-based method with multi-body environment, the homotopic method with multi-body environment, and the low-thrust capturing and descending algorithm with multi-body environment are all included. Firstly, the parameters describing the patched manifolds in CR3 BP are optimized until the least total absolute velocity increment has been got, including the employment of the shape-based method with multi-body environment. Secondly, the low-thrust control laws of the transfer orbit are optimized employing the homotopic method with multi-body environment that transfers the fuel optimization problem to an easier energy optimization problem. Thirdly, the low-thrust descending orbit around Mars is computed using the laws proposed in this paper. As a typical example, the Earth-Mars transfer orbit design is discussed. The results showed that the parameters describing the patched manifolds could be optimized by the DE(differential evolution) algorithm effectively; the homotopic method with multi-body environment could get the optimal value that meets the first order optimality conditions; and the low-thrust descending orbit could effectively be captured by Mars and finally become a circular parking orbit around it by the hypothesis control laws proposed in this paper. It shows that the final fuel cost is much less than the optimal transfer in the patched two-body problems. In conclusion, the method proposed in this paper could effectively solve the low-energy low-thrust optimal control problem in multi-body environment for the future deep space explorations.

关键词： orbit optimization multi-body patched manifolds low-energy low-thrust

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LEO navigation augmentation constellation design with the multi-objective optimization approaches

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Chinese Journal of Aeronautics 2021年第4期34卷 265-278页

作者： Yi HAN Lei WANG Wenju FU Haitao ZHOU Tao LI Beizhen XU Ruizhi CHEN State Key Laboratory of Information Engineering in Surveying Mapping and Remote SensingWuhan UniversityWuhan 430079China Collaborative Innovation Center for Geospatial Technology Wuhan 430079China

Low Earth orbit(LEO)satellite for navigation augmentation applications can significantly reduce the precise positioning convergence time and attract increasing attention recently.A few LEO Navigation Augmentation(LEO-NA)constellations have been proposed,while corresponding constellation design methodologies have not been systematically *** LEO-NA constellation generally consists of a huge number of LEO satellites and it strives for multiple optimization *** is essentially different from the communication constellation or earth observing constellation design *** this study,we modeled the LEO-NA constellation design problem as a multi-objective optimization problem and solve this problem with the MultiObjective Particle Swarm optimization(MOPSO)*** objectives are used to strive for the best tradeoff between the augmentation performance and deployment efficiency,namely the Position Dilution of Precision(PDOP),visible LEO satellites and the orbit altitude.A fuzzy set approach is used to select the final constellation from a set of Pareto optimal solutions given by the MOPSO *** evaluate the performance of the optimized constellation,we tested two constellations with 144 and 288 satellites and each constellation has three optimization schemes:the polar constellation,the single-layer constellation and the two-layer *** results indicate that the optimized two-layer constellation achieves the best global coverage and is followed by the single-layer *** MOPSO algorithm can help to improve the constellation design and is suitable for solving the LEO-NA constellation design problem.

关键词： LEO-augmented multi-GNSS LEO constellation design MOPSO Multi-objective optimization orbit optimization

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Interplanetary transfer optimization using cost function with variable coecients

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Astrodynamics 2019年第2期3卷 173-188页

作者： Xiangyu Li Dong Qiao Hongbo Chen School of Aerospace Engineering Beijing Institute of TechnologyBeijing 100081China Key Laboratory of Dynamics and Control of Flight Vehicle Ministry of EducationBeijing 100081China China Academy of Launch Vchicle T'echnology Beijing 100076China

In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric *** on primer vector theory,a modi ed cost function with variable coecients is developed to re ect the gravitational e ect more *** necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in *** introducing the initial and nal coasts,the optimal interplanetary transfer is extended to the time-free ***,the proposed method is applied to the Earth-Mars and Earth-Asteroid *** with existing methods show that the proposed method can provide better transfer performances with high e*** proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.

关键词： orbit optimization primer vector interplanetary transfer time-free

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Concept of the Solar Ring mission: Preliminary design and mission profile

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Science China(Technological Sciences) 2021年第1期64卷 131-138页

作者： WANG YaMin CHEN Xin WANG PengCheng QIU ChengBo WANG YuMing ZHANG YongHe Innovation Academy for Microsatellites Chinese Academy of Sciences(CAS)Shanghai 201203China Key Lab of Microsatellite Chinese Academy of SciencesShanghai 201203China Shanghai Engineering Center for Microsatellites Shanghai 201203China CAS Key Laboratory of Geospace Environment School of Earth and Space SciencesUniversity of Science and Technology of ChinaHefei 230026China CAS Center for Excellence in Comparative Planetology University of Science and Technology of ChinaHefei 230026China

The Solar Ring mission, a concept to monitor the Sun and inner heliosphere from multiple perspectives, has been funded for prephase study by the Strategic Priority Program of Chinese Academy of Sciences in space sciences. The Solar Ring is comprised of 6 spacecraft, grouped in three pairs, moving around the Sun in an elliptical orbit in the ecliptic plane. The mission costs,including launch fee, deep-space maneuvers, and deployment time of the ring, are highly relevant to the working orbit, deepspace transfer, and phase angle within a group. The preliminary mission profile is analyzed and designed in this paper. The launch way, two spacecraft with one rocket, is adopted. The deployment time, phasing maneuvers, and C_(3) of launch energy are evaluated for the elliptical orbits with the perihelion between 0.7 and 0.9 AU using the rockets of Long March(LM) 3A and *** simulations show two candidate trajectories: fast deployment within 4 years by LM-3B, medium deployment more than 6 years by cheaper rocket of LM-3A. In order to obtain both fast deployment and low launch cost, another orbit profile is proposed by shortening the phase angle within a group. The suggested working orbits and the corresponding costs of launch,deployment time, and phasing maneuvers will strongly support the science objectives.

关键词： solar and heliospheric observations deep-space transfer orbit optimization

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Solution set calculation of the Sun-perturbed optimal two-impulse trans-lunar orbits using continuation theory

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Astrodynamics 2020年第1期4卷 75-86页

作者： Bo-yong He Hong-xin Shen State Key Laboratory of Astronautic Dynamics Xi’an Satellite Control CenterXi’an710043China

The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission.A model for computing the two-impulse trans-lunar orbit,which strictly satisfies the boundary constraints,is *** solution set is computed first with a circular restricted three-body model using a generalized local gradient optimization algorithm and the strategy of design variable initial *** taking the solution set of a circular restricted three-body model as the initial values of the design variables,the Sun-perturbed solution set is calculated based on the dynamic model continuation theory and traversal search methodology.A comparative analysis shows that the fuel cost may be reduced to some extent by considering the Sun’s perturbation and choosing an appropriate transfer ***,there are several optimal two-impulse trans-lunar methods for supporting a lunar mission to select a scenario with a certain ground measurement and to control the time cost.A fitted linear dependence relationship between the Sun’s befitting phase and the trans-lunar duration could thus provide a reference to select a low-fuel-cost trans-lunar injection window in an engineering project.

关键词： trans-lunar orbit optimization optimal solution set continuation theory Sun-perturbed

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