This paper investigates a novel quasi fixed-time orbit tracking control method for spacecraft around an asteroid in the presence of uncertain dynamics and unknown uncertainties.To quantitatively characterize the trans...This paper investigates a novel quasi fixed-time orbit tracking control method for spacecraft around an asteroid in the presence of uncertain dynamics and unknown uncertainties.To quantitatively characterize the transient and steady-state responses of orbit tracking error system,a continuous performance function is devised via using a quartic polynomial.Then,integrating backstepping control technique and barrier Lyapunov function leads to a quasi fixed-time convergent orbit tracking controller without using any fractional state information and symbolic functions.Finally,two groups of illustrative examples are employed to test the effectiveness of the proposed orbit control method.展开更多
Digital micro-thruster arrays can be used for special missions of micro/nano-satellites with the requirements of high precision and small impulse.This paper presents a novel control allocation algorithm for the digita...Digital micro-thruster arrays can be used for special missions of micro/nano-satellites with the requirements of high precision and small impulse.This paper presents a novel control allocation algorithm for the digital micro-thruster array,namely status graph based control allocation(SGBCA)algorithm,which aims at finding the optimal micro thrusters combination scheme to realize the sequential control synthesis for micro/nano-satellite during real-time orbit control tasks.A mathematical model is set up for the control allocation of this multivariate over-actuated system.Through dividing thrusters into disjoint segments by offline calculation and combining segments dynamically online to provide a sequence of the required impulse for the micro/nano-satellite,the time complexity of the control allocation algorithm decreases significantly.All levels of impulse can be generated by the digital micro thruster arrays and the service life of the arrays can be extended using the segment converting strategy proposed in this paper.The simulation indicates that the algorithm can satisfy the requirements of real-time orbit control for micro/nano-satellites.展开更多
To accomplish high-resolution imaging of the preselected landing area, it was necessary for the Chang＇E-2 mission to perform orbital maneuvering on the far side of the moon to meet the conditional height requirement ...To accomplish high-resolution imaging of the preselected landing area, it was necessary for the Chang＇E-2 mission to perform orbital maneuvering on the far side of the moon to meet the conditional height requirement of the imaging area. Engine shutdown would be executed invisibly on the back side of the moon if the descent maneuver mode opposite to the target perilune or the fuel optimal maneuver mode was used. To ensure the satellite safety, the project collectivety required that the engine shutdown should be designed to be executed in the domestic segmental arcs and meet the requirement of satellite emergency treatment simultaneously. Accordingly, the asymmetric-descent orbit control technology was adopted by offsetting the ma- neuver point, which obtained the orbit control parameters of finite-thrust mode with an iteration algorithm and modified the results with target perilune drift estimation. The Chang＇E-2 satellite declined to the target of 100 km×l5 km orbit successfully on 26 October 2010, and has been flying for 32 circles in the experimental orbit to accomplish the preselected landing area imaging. This paper describes the mechanism and realization method of the asymmetric-descent orbit control technology and evaluates the maneuver effect with the actual mission data.展开更多
A new attitude control method for solar sails is proposed using a single-axis gimbal mechanism and three-axis reaction wheels.The gimbal angle is varied to change the geometrical relationship between the force due to ...A new attitude control method for solar sails is proposed using a single-axis gimbal mechanism and three-axis reaction wheels.The gimbal angle is varied to change the geometrical relationship between the force due to solar radiation pressure(SRP)and the center of mass of the spacecraft,such that the disturbance torque is minimized during attitude maintenance for orbit control.Attitude maneuver and maintenance are performed by the reaction wheels based on the quaternion feedback control method.Even if angular momentum accumulates on the reaction wheels due to modelling error,it can also be unloaded by using the gimbal to produce suitable torque due to SRP.In this study,we analyzed the attitude motion under the reaction wheel control by linearizing the equations of motion around the equilibrium point.Further,we newly derived the propellent-free unloading method based on the analytical formulation.Finally,we constructed the integrated attitude–orbit control method,and its validity was verified in integrated attitude–orbit control simulations.展开更多
The problem of control of orbit for the dynamic system x ¨+x(1-x)(x-a)=0 is discussed. Any unbounded orbit of the dynamic system can be controlled to become a bounded periodic orbit by adding a periodic step ex...The problem of control of orbit for the dynamic system x ¨+x(1-x)(x-a)=0 is discussed. Any unbounded orbit of the dynamic system can be controlled to become a bounded periodic orbit by adding a periodic step excitation to the system. By using a nonlinear feedback control law presented in this paper the chaos of the dynamic system with excitation and damping is stabilized. This method is more effectual than the linear feedback control.展开更多
This paper proposes an intelligent low-thrust orbit phasing control method for multiple spacecraft by simultaneously considering fuel optimization and collision avoidance. Firstly,the minimum-fuel orbit phasing contro...This paper proposes an intelligent low-thrust orbit phasing control method for multiple spacecraft by simultaneously considering fuel optimization and collision avoidance. Firstly,the minimum-fuel orbit phasing control database is generated by the indirect method associated with the homotopy technique. Then,a deep network representing the minimum-fuel solution is trained. To avoid collision for multiple spacecraft,an artificial potential function is introduced in the collision-avoidance controller. Finally,an intelligent orbit phasing control method by combining the minimum-fuel neural network controller and the collision-avoidance controller is proposed. Numerical results show that the proposed intelligent orbit phasing control is valid for the multi-satellite constellation initialization without collision.展开更多
A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse...A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.展开更多
Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keeps re...Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keeps relative position and attitude to observe a specific surface of another satellite among the cluster. Specially, the target space vehicle is malfunctioning. The present paper focuses on the problem that how to control a chaser satellite to fly around an out-of-work target satellite closely in earth orbit and to track a specific surface. Relative attitude and first approximate relative orbital dynamics equations are presented. Control strategy is derived based on feedback linearization and Lyapunov theory of stability. Further, considering the uncertainty of inertia, an adaptive control method is developed to obtain the correct inertial ratio. The numerical simulation is given to verify the validity of proposed control scheme.展开更多
The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated.The directed information communication topology between followers is taken into ...The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated.The directed information communication topology between followers is taken into account in the overall paper.When the satellite mass is assumed to be constant,a distributed prescribed-time orbit containment controller is,firstly,presented to drive the followers into the dynamic convex hull produced by multiple leaders.Then,the parameter uncertainty is considered,and a prescribed-time sliding mode estimator is introduced to estimate the desired velocity of each follower.Based on the estimated state,a novel distributed adaptive prescribed-time orbit containment control scheme is proposed.The Lyapunov stability theory is utilized to prove the prescribed-time stability of the closed-loop system.Finally,several numerical simulations and comparison of different control methods are provided to verify the effectiveness and superiority of the proposed control method.展开更多
Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the mode...Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the modeling of dynamics environment and the orbital dynamics mechanism. This paper introduced state-ofthe-art researches, major challenges, and future trends in this field. Three topics are mainly discussed： the gravitational field modeling of irregular-shaped small celestial bodies, natural orbital dynamics and control, and controlled orbital dynamics. Finally, constructive suggestions are made for China’s future space exploration missions.展开更多
The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along hal...The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along halo orbits, a nonlinear output tracking control scheme based on the θ- D technique is proposed. Compared with the popular time-variant linear quadratic regulator （LQR） controller, this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation. Besides, the obtained nonlinear suboptimal controller is in a closed form and easy to implement. Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors. The axis of rotation can keep pointing to an inertial specific object to fulfill an observation mission. In addition, the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.展开更多
This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the...This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.展开更多
This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm ar...This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm arising from the disturbance from orbit control force. The effects of orbit control force on the fault diagnosis system for satellite attitude control systems, including the disturbing torque caused by the misalignments and the model uncertainty caused by the fuel consumed, are discussed, where standard Lu- enberger observer cannot work well. Then the nonlinear unknown input observer is proposed to decouple faults from disturbance, Besides, a linear matrix inequality approach is adopted to reduce the effect of nonlinear part and model uncertainties on the observer. The numerical and semi-physical simulation demonstrates the effectiveness of the proposed observer for the fault diagnosis system of the satellite during orbit maneuver.展开更多
This paper investigates an analytical optimal pose tracking control problem for chaser spacecraft during the close-range proximity operations with a non-cooperative space target subject to attitude tumbling and unknow...This paper investigates an analytical optimal pose tracking control problem for chaser spacecraft during the close-range proximity operations with a non-cooperative space target subject to attitude tumbling and unknown orbital maneuvering.Firstly,the relative translational motion between the orbital target and the chaser spacecraft is described in the Line-of-Sight(LOS)coordinate frame along with attitude quaternion dynamics.Then,based on the coupled 6-Degree of Freedom(DOF)pose dynamic model,an analytical optimal control action consisting of constrained optimal control value,application time and its duration are proposed via exploring the iterative sequential action control algorithm.Meanwhile,the global closed-loop asymptotic stability of the proposed predictive control action is presented and discussed.Compared with traditional proximity control schemes,the highlighting advantages are that the application time and duration of the devised controller is applied discretely in light of the influence of the instantaneous pose configuration on the pose tracking performance with less energy consumptions rather than at each sample time.Finally,three groups of illustrative examples are organized to validate the effectiveness of the proposed analytical optimal pose tracking control scheme.展开更多
This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted thre...This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,展开更多
基金This work was supported in part of the Open Funds from National Key Laboratory of Aerospace Flight Dynamics and Key Laboratory of Space Intelligent Control Technology.
文摘This paper investigates a novel quasi fixed-time orbit tracking control method for spacecraft around an asteroid in the presence of uncertain dynamics and unknown uncertainties.To quantitatively characterize the transient and steady-state responses of orbit tracking error system,a continuous performance function is devised via using a quartic polynomial.Then,integrating backstepping control technique and barrier Lyapunov function leads to a quasi fixed-time convergent orbit tracking controller without using any fractional state information and symbolic functions.Finally,two groups of illustrative examples are employed to test the effectiveness of the proposed orbit control method.
文摘Digital micro-thruster arrays can be used for special missions of micro/nano-satellites with the requirements of high precision and small impulse.This paper presents a novel control allocation algorithm for the digital micro-thruster array,namely status graph based control allocation(SGBCA)algorithm,which aims at finding the optimal micro thrusters combination scheme to realize the sequential control synthesis for micro/nano-satellite during real-time orbit control tasks.A mathematical model is set up for the control allocation of this multivariate over-actuated system.Through dividing thrusters into disjoint segments by offline calculation and combining segments dynamically online to provide a sequence of the required impulse for the micro/nano-satellite,the time complexity of the control allocation algorithm decreases significantly.All levels of impulse can be generated by the digital micro thruster arrays and the service life of the arrays can be extended using the segment converting strategy proposed in this paper.The simulation indicates that the algorithm can satisfy the requirements of real-time orbit control for micro/nano-satellites.
文摘To accomplish high-resolution imaging of the preselected landing area, it was necessary for the Chang＇E-2 mission to perform orbital maneuvering on the far side of the moon to meet the conditional height requirement of the imaging area. Engine shutdown would be executed invisibly on the back side of the moon if the descent maneuver mode opposite to the target perilune or the fuel optimal maneuver mode was used. To ensure the satellite safety, the project collectivety required that the engine shutdown should be designed to be executed in the domestic segmental arcs and meet the requirement of satellite emergency treatment simultaneously. Accordingly, the asymmetric-descent orbit control technology was adopted by offsetting the ma- neuver point, which obtained the orbit control parameters of finite-thrust mode with an iteration algorithm and modified the results with target perilune drift estimation. The Chang＇E-2 satellite declined to the target of 100 km×l5 km orbit successfully on 26 October 2010, and has been flying for 32 circles in the experimental orbit to accomplish the preselected landing area imaging. This paper describes the mechanism and realization method of the asymmetric-descent orbit control technology and evaluates the maneuver effect with the actual mission data.
基金supported by the Japan Society for the Promotion of Science,KAKENHI Grant Numbers JP21K14345 and JP21H04588.
文摘A new attitude control method for solar sails is proposed using a single-axis gimbal mechanism and three-axis reaction wheels.The gimbal angle is varied to change the geometrical relationship between the force due to solar radiation pressure(SRP)and the center of mass of the spacecraft,such that the disturbance torque is minimized during attitude maintenance for orbit control.Attitude maneuver and maintenance are performed by the reaction wheels based on the quaternion feedback control method.Even if angular momentum accumulates on the reaction wheels due to modelling error,it can also be unloaded by using the gimbal to produce suitable torque due to SRP.In this study,we analyzed the attitude motion under the reaction wheel control by linearizing the equations of motion around the equilibrium point.Further,we newly derived the propellent-free unloading method based on the analytical formulation.Finally,we constructed the integrated attitude–orbit control method,and its validity was verified in integrated attitude–orbit control simulations.
文摘The problem of control of orbit for the dynamic system x ¨+x(1-x)(x-a)=0 is discussed. Any unbounded orbit of the dynamic system can be controlled to become a bounded periodic orbit by adding a periodic step excitation to the system. By using a nonlinear feedback control law presented in this paper the chaos of the dynamic system with excitation and damping is stabilized. This method is more effectual than the linear feedback control.
基金supported in part by the National Natural Science Foundation of China (No. 11772104)in part by the Key Research and Development Plan of Heilongjiang Province(No. GZ20210120)in part by the Fundamental Research Funds for the Central Universities。
文摘This paper proposes an intelligent low-thrust orbit phasing control method for multiple spacecraft by simultaneously considering fuel optimization and collision avoidance. Firstly,the minimum-fuel orbit phasing control database is generated by the indirect method associated with the homotopy technique. Then,a deep network representing the minimum-fuel solution is trained. To avoid collision for multiple spacecraft,an artificial potential function is introduced in the collision-avoidance controller. Finally,an intelligent orbit phasing control method by combining the minimum-fuel neural network controller and the collision-avoidance controller is proposed. Numerical results show that the proposed intelligent orbit phasing control is valid for the multi-satellite constellation initialization without collision.
基金supported by the Innovation Foundation of BUAA for PhD Graduates (No.YWF-12-RBYJ-024)the National Natural Science Foundation of China (No.11002008)National Basic Research Program of China (No.2009CB723906)
文摘A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.
基金Project supported by the National Natural Science Foundation of China(No.10672084)the Specialized Research Fund for Doctoral Program of Higher Education(No.20060003097)
文摘Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keeps relative position and attitude to observe a specific surface of another satellite among the cluster. Specially, the target space vehicle is malfunctioning. The present paper focuses on the problem that how to control a chaser satellite to fly around an out-of-work target satellite closely in earth orbit and to track a specific surface. Relative attitude and first approximate relative orbital dynamics equations are presented. Control strategy is derived based on feedback linearization and Lyapunov theory of stability. Further, considering the uncertainty of inertia, an adaptive control method is developed to obtain the correct inertial ratio. The numerical simulation is given to verify the validity of proposed control scheme.
文摘The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated.The directed information communication topology between followers is taken into account in the overall paper.When the satellite mass is assumed to be constant,a distributed prescribed-time orbit containment controller is,firstly,presented to drive the followers into the dynamic convex hull produced by multiple leaders.Then,the parameter uncertainty is considered,and a prescribed-time sliding mode estimator is introduced to estimate the desired velocity of each follower.Based on the estimated state,a novel distributed adaptive prescribed-time orbit containment control scheme is proposed.The Lyapunov stability theory is utilized to prove the prescribed-time stability of the closed-loop system.Finally,several numerical simulations and comparison of different control methods are provided to verify the effectiveness and superiority of the proposed control method.
文摘Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the modeling of dynamics environment and the orbital dynamics mechanism. This paper introduced state-ofthe-art researches, major challenges, and future trends in this field. Three topics are mainly discussed： the gravitational field modeling of irregular-shaped small celestial bodies, natural orbital dynamics and control, and controlled orbital dynamics. Finally, constructive suggestions are made for China’s future space exploration missions.
基金supported by the National Natural Science Foundation of China (No.61174200)
文摘The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along halo orbits, a nonlinear output tracking control scheme based on the θ- D technique is proposed. Compared with the popular time-variant linear quadratic regulator （LQR） controller, this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation. Besides, the obtained nonlinear suboptimal controller is in a closed form and easy to implement. Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors. The axis of rotation can keep pointing to an inertial specific object to fulfill an observation mission. In addition, the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.
基金supported by the China Postdotoral Science Foundation(20060401004)
文摘This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.
基金supported by the National Natural Science Foundation of China (61034005)the Natural Science Foundation of Jiangsu Province (BK2010072)
文摘This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm arising from the disturbance from orbit control force. The effects of orbit control force on the fault diagnosis system for satellite attitude control systems, including the disturbing torque caused by the misalignments and the model uncertainty caused by the fuel consumed, are discussed, where standard Lu- enberger observer cannot work well. Then the nonlinear unknown input observer is proposed to decouple faults from disturbance, Besides, a linear matrix inequality approach is adopted to reduce the effect of nonlinear part and model uncertainties on the observer. The numerical and semi-physical simulation demonstrates the effectiveness of the proposed observer for the fault diagnosis system of the satellite during orbit maneuver.
基金This study was co-supported by the National Natural Science Foundation of China(Nos.62003371,62373379,62103446,61273351,62073343)the Outstanding Youth Fund of Hunan Provincial Natural Science,China(No.2022JJ20081)the Innovation Driven Project of Central South University,China(No.2023CXQD066).
文摘This paper investigates an analytical optimal pose tracking control problem for chaser spacecraft during the close-range proximity operations with a non-cooperative space target subject to attitude tumbling and unknown orbital maneuvering.Firstly,the relative translational motion between the orbital target and the chaser spacecraft is described in the Line-of-Sight(LOS)coordinate frame along with attitude quaternion dynamics.Then,based on the coupled 6-Degree of Freedom(DOF)pose dynamic model,an analytical optimal control action consisting of constrained optimal control value,application time and its duration are proposed via exploring the iterative sequential action control algorithm.Meanwhile,the global closed-loop asymptotic stability of the proposed predictive control action is presented and discussed.Compared with traditional proximity control schemes,the highlighting advantages are that the application time and duration of the devised controller is applied discretely in light of the influence of the instantaneous pose configuration on the pose tracking performance with less energy consumptions rather than at each sample time.Finally,three groups of illustrative examples are organized to validate the effectiveness of the proposed analytical optimal pose tracking control scheme.
基金National Natural Science Foundation of China (10702003)Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D. Graduates
文摘This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,
