A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near...A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near aster- oids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an as- teroid can be classified into 9 categories： （1） surrounding- to-surrounding, （2） surrounding-to-surface, （3） surrounding- to-infinity, （4） infinity-to-infinity, （5） infinity-to-surface, （6） infinity-to-surrounding, （7） surface-to-surface, （8） surface- to-surrounding, and （9） surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.展开更多
Asteroid exploration is currently one of the most concerned topics among international space agencies. Or- bital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief ...Asteroid exploration is currently one of the most concerned topics among international space agencies. Or- bital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near as- teroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospec- tive of future studies with emphasis on the key techniques of these issues in the asteroid exploration missions.展开更多
This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orb...This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.展开更多
Asteroid exploration trajectories which start from a lunar orbit are investigated in this work.It is assumed that the probe departs from lunar orbit and returns to the vicinity of Earth,then escapes from the Earth by ...Asteroid exploration trajectories which start from a lunar orbit are investigated in this work.It is assumed that the probe departs from lunar orbit and returns to the vicinity of Earth,then escapes from the Earth by performing a perigee maneuver.A low-energy transfer in Sun-EarthMoon system is adopted.First,the feasible region of lowenergy transfer from lunar orbit to perigee within 5 000 km height above the Earth surface in Sun-Earth-Moon system is calculated and analyzed.Three transfer types are found,i.e.,large maneuver and fast transfers,small maneuver and fast transfers,and disordered and slow transfers.Most of feasibility trajectories belong to the first two types.Then,the lowenergy trajectory leg from lunar orbit to perigee and a heliocentric trajectory leg from perigee to asteroid are patched by a perigee maneuver.The optimal full-transfer trajectory is obtained by exploiting the differential evolution algorithm.Finally,taking 4179 Toutatis asteroid as the target,some low-energy transfer trajectories are obtained and analyzed.展开更多
Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stabil...Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates.展开更多
In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi...In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.展开更多
Driven by curiosity about possible flight options for the Chang＇e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroi...Driven by curiosity about possible flight options for the Chang＇e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories. The approaches include the use of modified unstable manifolds, grid search of the manifolds＇ parameters, and a two-impulse maneuver for orbital phase matching and z-axis bias change, and are demonstrated to be effective in asteroid target screening and trajectory optimization. Asteroid flybys are expected to be within a distance of 2 × 10^7 km from the Earth owing to the constrained Earth-spacecraft communication range. In this case, the spacecraft＇s orbital motion is significantly affected by the gravities of both the Sun and the Earth, and therefore, the concept of the ＂he- liocentric oscillating-Kepler orbit＂ is proposed, because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time. The analysis and results presented in this study show that, among the asteroids whose orbits are the most accurately predicted, ＂Toutatis＂, ＂2005 NZ6＂, or ＂2010 CL19＂ might be encountered by Chang＇e-2 in late 2012 or 2013 with total impulses less than 100 rn/s.展开更多
In this paper we calculate the volume, mass, gravitational attraction to the Earth, angular momentum the orbit of the Trojan asteroid (TK7) [1]. In this paper, we use classical Newtonian mechanics to analyse some of t...In this paper we calculate the volume, mass, gravitational attraction to the Earth, angular momentum the orbit of the Trojan asteroid (TK7) [1]. In this paper, we use classical Newtonian mechanics to analyse some of the physical and orbital properties of the Trojan asteroid, which are still experimentally unknown. The asteroid should remain in Earth’s orbit for the next 100 years. We conclude by providing informed estimates of 2010 TK7’s yet unknown physical properties: i.e. mass, volume, gravitational attraction to Earth and angular momentum.展开更多
Lyapunov-based model predictive control(LMPC)is an effective approach for trajectory tracking because of its wellguaranteed and easy-to-implement stability.However,traditional LMPC utilizes pre-designed auxiliary cont...Lyapunov-based model predictive control(LMPC)is an effective approach for trajectory tracking because of its wellguaranteed and easy-to-implement stability.However,traditional LMPC utilizes pre-designed auxiliary controllers to estimate the domain of attraction(DOA)and construct stability constraints,which inevitably reduces its stable domain and degrades tracking performance.For this problem,this paper proposes a relaxed LMPC(RLMPC)which is designed independently of auxiliary controllers.The control Lyapunov function(CLF)is firstly introduced to decouple the DOA and auxiliary control,alleviating the conservatism in traditional LMPC.Subsequently,a multi-resolution sampling-based search algorithm is developed to estimate the DOA,where the state space is partitioned into hyper-rectangles.A verification condition is derived to extend the verification validity of sampling points to all states within hyper-rectangles,thereby reducing DOA estimation error.Based on the auxiliary-controller-independent DOA(ACI-DOA)and CLF,stability constraints are formulated to ensure stability for RLMPC,while relaxing the stable domain of RLMPC to the entire ACI-DOA.Furthermore,a convergence rate adaptive adjustment technology is developed to enhance the convergence rate while balancing it with control effort.Through numerical simulations involving asteroid orbiting missions,the proposed method is found to significantly expand the stable domain and improve tracking performance.展开更多
近地小行星的巡天项目不断涌现,得到了海量的观测数据.而巡天观测方式使获得的数据弧段过短,传统方法在定轨和识别上存在极大困难,加之短弧定轨问题本身的病态性,如何有效利用这些短弧数据对于发现、监测和评估小行星的威胁具有重要意义...近地小行星的巡天项目不断涌现,得到了海量的观测数据.而巡天观测方式使获得的数据弧段过短,传统方法在定轨和识别上存在极大困难,加之短弧定轨问题本身的病态性,如何有效利用这些短弧数据对于发现、监测和评估小行星的威胁具有重要意义.在进化算法下构建极短弧定轨的计算框架,选用三变量的(a, e, M)优选法,保持维数较低的同时,使优化结果不再依赖观测量.采用参数较少、操作简便的差分进化算法,利用不同偏心率小行星的轨道模拟数据进行试验,对获得的最优解及其分布聚集区域进行分析,大偏心率轨道由于其本身的复杂性,会对算法搜索的灵敏度产生影响,需缩小搜索空间以提高搜索能力.结果表明算法在小偏心率问题中表现较好,可以得到有效结果为后续工作提供参考信息,大偏心率问题在传统方法失效的情况下,虽然最优解在整体分布中并不明显,但分布仍包含真实解,可结合分布密度和适值大小进行分析.未来需要对大偏心率问题作进一步研究,考虑其观测位置和观测时刻对算法产生的影响,分类计算.展开更多
文摘A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near aster- oids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an as- teroid can be classified into 9 categories： （1） surrounding- to-surrounding, （2） surrounding-to-surface, （3） surrounding- to-infinity, （4） infinity-to-infinity, （5） infinity-to-surface, （6） infinity-to-surrounding, （7） surface-to-surface, （8） surface- to-surrounding, and （9） surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.
基金supported by the National Basic Research Program of China(973 Program)(2012CB720000)the National Natural Science Foundation of China(11372150)
文摘Asteroid exploration is currently one of the most concerned topics among international space agencies. Or- bital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near as- teroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospec- tive of future studies with emphasis on the key techniques of these issues in the asteroid exploration missions.
基金partially supported by an innovation fund from Chinese academy of space technology and a grant from the Jet Propulsion Laboratory
文摘This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.
基金supported by the National Basic Research Programof China(973 Program)(2012CB720000)the National Natural Science Foundation of China(11102020)+1 种基金Program for New Century Excellent Talents in UniversityBeijing Higher Education Young Elite Teacher Project and China Scholarship Council
文摘Asteroid exploration trajectories which start from a lunar orbit are investigated in this work.It is assumed that the probe departs from lunar orbit and returns to the vicinity of Earth,then escapes from the Earth by performing a perigee maneuver.A low-energy transfer in Sun-EarthMoon system is adopted.First,the feasible region of lowenergy transfer from lunar orbit to perigee within 5 000 km height above the Earth surface in Sun-Earth-Moon system is calculated and analyzed.Three transfer types are found,i.e.,large maneuver and fast transfers,small maneuver and fast transfers,and disordered and slow transfers.Most of feasibility trajectories belong to the first two types.Then,the lowenergy trajectory leg from lunar orbit to perigee and a heliocentric trajectory leg from perigee to asteroid are patched by a perigee maneuver.The optimal full-transfer trajectory is obtained by exploiting the differential evolution algorithm.Finally,taking 4179 Toutatis asteroid as the target,some low-energy transfer trajectories are obtained and analyzed.
文摘Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates.
基金supported by the National Natural Science Foundation of China(Grant11372311)the grant from the State key Laboratory of Astronautic Dynamics(2014-ADL-DW0201)
文摘In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.
基金supported by the State Key Laboratory of Astronautic Dynamics(2011ADL-DW0202)
文摘Driven by curiosity about possible flight options for the Chang＇e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories. The approaches include the use of modified unstable manifolds, grid search of the manifolds＇ parameters, and a two-impulse maneuver for orbital phase matching and z-axis bias change, and are demonstrated to be effective in asteroid target screening and trajectory optimization. Asteroid flybys are expected to be within a distance of 2 × 10^7 km from the Earth owing to the constrained Earth-spacecraft communication range. In this case, the spacecraft＇s orbital motion is significantly affected by the gravities of both the Sun and the Earth, and therefore, the concept of the ＂he- liocentric oscillating-Kepler orbit＂ is proposed, because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time. The analysis and results presented in this study show that, among the asteroids whose orbits are the most accurately predicted, ＂Toutatis＂, ＂2005 NZ6＂, or ＂2010 CL19＂ might be encountered by Chang＇e-2 in late 2012 or 2013 with total impulses less than 100 rn/s.
文摘In this paper we calculate the volume, mass, gravitational attraction to the Earth, angular momentum the orbit of the Trojan asteroid (TK7) [1]. In this paper, we use classical Newtonian mechanics to analyse some of the physical and orbital properties of the Trojan asteroid, which are still experimentally unknown. The asteroid should remain in Earth’s orbit for the next 100 years. We conclude by providing informed estimates of 2010 TK7’s yet unknown physical properties: i.e. mass, volume, gravitational attraction to Earth and angular momentum.
基金supported by the National Natural Science Foundation of China(12472354)the National Key Research and Development Program of China(2020YFC2200902)the Key Technology Research Project of TW-3(TW3005).
文摘Lyapunov-based model predictive control(LMPC)is an effective approach for trajectory tracking because of its wellguaranteed and easy-to-implement stability.However,traditional LMPC utilizes pre-designed auxiliary controllers to estimate the domain of attraction(DOA)and construct stability constraints,which inevitably reduces its stable domain and degrades tracking performance.For this problem,this paper proposes a relaxed LMPC(RLMPC)which is designed independently of auxiliary controllers.The control Lyapunov function(CLF)is firstly introduced to decouple the DOA and auxiliary control,alleviating the conservatism in traditional LMPC.Subsequently,a multi-resolution sampling-based search algorithm is developed to estimate the DOA,where the state space is partitioned into hyper-rectangles.A verification condition is derived to extend the verification validity of sampling points to all states within hyper-rectangles,thereby reducing DOA estimation error.Based on the auxiliary-controller-independent DOA(ACI-DOA)and CLF,stability constraints are formulated to ensure stability for RLMPC,while relaxing the stable domain of RLMPC to the entire ACI-DOA.Furthermore,a convergence rate adaptive adjustment technology is developed to enhance the convergence rate while balancing it with control effort.Through numerical simulations involving asteroid orbiting missions,the proposed method is found to significantly expand the stable domain and improve tracking performance.
文摘近地小行星的巡天项目不断涌现,得到了海量的观测数据.而巡天观测方式使获得的数据弧段过短,传统方法在定轨和识别上存在极大困难,加之短弧定轨问题本身的病态性,如何有效利用这些短弧数据对于发现、监测和评估小行星的威胁具有重要意义.在进化算法下构建极短弧定轨的计算框架,选用三变量的(a, e, M)优选法,保持维数较低的同时,使优化结果不再依赖观测量.采用参数较少、操作简便的差分进化算法,利用不同偏心率小行星的轨道模拟数据进行试验,对获得的最优解及其分布聚集区域进行分析,大偏心率轨道由于其本身的复杂性,会对算法搜索的灵敏度产生影响,需缩小搜索空间以提高搜索能力.结果表明算法在小偏心率问题中表现较好,可以得到有效结果为后续工作提供参考信息,大偏心率问题在传统方法失效的情况下,虽然最优解在整体分布中并不明显,但分布仍包含真实解,可结合分布密度和适值大小进行分析.未来需要对大偏心率问题作进一步研究,考虑其观测位置和观测时刻对算法产生的影响,分类计算.
