Halo orbit long-term control keeping method based on attraction domain

Abstract

The invention discloses a Halo orbit long-term control maintaining method based on an attraction domain, and belongs to the field of aerospace. The realization method comprises the following steps: based on three-body dynamics, obtaining a nominal Halo orbit through a differential correction technology; on the basis of controlling a Lyapunov function, an attraction domain discrimination condition is constructed, an attraction domain corresponding to nominal Halo is solved on the basis of a sampling method, a spacecraft is constrained in the attraction domain, and the stability and controllability of a controller can be ensured. On the basis, a dead zone located in an attraction domain is selected, the outer boundary of the dead zone is taken as an outer ring, the inner boundary of the dead zone is taken as an inner ring, the thruster is started when the spacecraft touches the outer boundary, the thruster stops working when the spacecraft is controlled to the inner boundary, and a double-ring control strategy is constructed. And based on a double-loop control strategy, taking control of Lyapunov function decline and control amplitude as constraints, taking burnup as a performance index, obtaining a corresponding feedback control law by solving the optimization problem, and performing control and maintenance on the spacecraft located on the Halo orbit.

Description

Technical Field

[0001] The invention relates to a method for long-term control and maintenance of a Halo orbit near a balance point of a sun-earth three-body system, and belongs to the field of aerospace. Background Art

[0002] The libration point is not only an excellent location for scientific exploration of the space environment, but also an important transit station for human deep space exploration. It has important research significance and has become a hot target for deep space exploration missions of major space powers. The Halo orbit near the Sun-Earth L1 / L2 point is a special type of three-dimensional periodic orbit near the collinear libration point in the three-body dynamic system. This orbit can be used as a deployment orbit for missions such as near-Earth asteroid observation and cosmic observation, and has important application value. However, due to the unstable characteristics of the collinear libration point orbit and the chaotic characteristics of the three-body system, the spacecraft running on it will quickly deviate from the original orbit. Therefore, in actual missions, it is necessary to maintain its orbit. For the control and maintenance of the Halo orbit, compared with the pulse control maintenance, the small thrust control method has high precision and large specific impulse. However, the small thrust control method usually requires the thruster to work all the time. Limited by the working life of the thruster, the small thrust control maintenance method is difficult to apply to the long-term maintenance mission of the Halo orbit.

[0003] Among the developed Halo orbit control and maintenance methods, the prior art [1] (Nazari M, Anthony W, and Butcher EA Continuous Thrust Station-keeping in Earth-Moon L1 Halo Orbits Based on LQR control and Floquet Theory [c]. AIAA / AAS Astrodynamics Specialist Conference, 2014, 4140) proposed an orbit maintenance strategy based on time-varying LQR for the Halo orbit maintenance problem at the Earth-Moon L1 point, and combined it with dead zone control to reduce the thruster working time. The advantage of this method is that compared with the continuous controller with constant control gain, the time-varying LQR requires lower fuel consumption, and the dead zone control takes into account the working life limit of the thruster. The disadvantage is that the dead zone range is not designed, so the spacecraft may deviate too much from the nominal orbit, and the spacecraft flies away from the nominal Halo orbit under the thrust constraint.

[0004] Prior art [2] (Yi Q, Ruiter AdStation-keeping strategy for real translunar libration point orbits using continuous thrust [J]. Aerospace Science and Technology, 2019, 94: 105376) proposed an orbit-keeping strategy based on backstepping and dead zone control for periodic orbits near the Earth-Moon libration point, and discussed the impact of different dead zone range settings on orbit control and maintenance. The advantage of this method is that the dead zone control is used in the low-thrust maintenance control strategy to consider the working life limit of the thruster, and the impact of the area range setting in the dead zone scheme on fuel consumption is analyzed. The disadvantage is that this method cannot consider the control constraints when designing the controller and the dead zone range, and cannot guarantee the stability and controllability of the controller. Summary of the invention

[0005] In order to solve the problem that the existing Halo orbit long-term maintenance method based on dead zone control cannot consider the control constraints when designing the dead zone range, which makes the spacecraft uncontrollable in the dead zone and causes the spacecraft to become unstable, the main purpose of the present invention is to provide a Halo orbit long-term control maintenance method based on the attraction domain, which calculates the attraction domain of the Halo orbit by sampling method to ensure the stability and controllability of the spacecraft control. Based on the Halo orbit attraction domain, a dual-loop control strategy is designed to reduce the working time of the thruster while ensuring stability and controllability, solving the problem of limited working life of the thruster.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] The invention discloses a long-term control and maintenance method of Halo orbit based on attraction domain. The nominal Halo orbit is obtained by differential correction technology based on three-body dynamics. Based on the control of Lyapunov function, the judgment condition of attraction domain is constructed, and the attraction domain corresponding to the nominal Halo is solved based on the sampling method. The spacecraft is constrained in the attraction domain, which can ensure the stability and controllability of the controller. On this basis, a dead zone located in the attraction domain is selected, and the outer boundary of the dead zone is used as the outer ring, and the inner boundary of the dead zone is used as the inner ring. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working, and the dual-loop control strategy is constructed. Based on the dual-loop control strategy, the control of the Lyapunov function decreases and the control amplitude is constrained, and the fuel consumption is used as a performance indicator. The corresponding feedback control law is obtained by solving the optimization problem, and the spacecraft on the Halo orbit is controlled and maintained. The control method can ensure the stability and controllability of the spacecraft, reduce the working time of the thruster, and achieve long-term stable maintenance of the spacecraft on the Halo orbit.

[0008] The present invention discloses a method for long-term control and maintenance of a Halo orbit based on an attraction domain, comprising the following steps:

[0009] Step 1: Construct the natural motion equation of the spacecraft. Based on the circular restricted three-body model, calculate the third-order analytical solution of the periodic orbit near the libration point in the circular restricted three-body system of the Sun and the Earth. Use the differential correction technique to correct the third-order analytical solution to obtain a high-precision nominal Halo orbit. For the Halo orbit keeping problem, construct the controlled motion equation of the spacecraft. Combine the controlled motion equation of the spacecraft with the natural motion equation to obtain the tracking error dynamics.

[0010] The specific implementation method of step one is:

[0011] The natural motion equation of the spacecraft is expressed as:

[0012]

[0013] Among them, x, y, z are the positions of the spacecraft, μ is the three-body gravitational coefficient, and r1 and r2 represent the distances between the spacecraft and the sun and the earth respectively:

[0014]

[0015] Based on the circular restricted three-body model, the third-order analytical solution of the periodic orbit near the libration point in the Sun-Earth circular restricted three-body system is calculated. The third-order analytical solution is corrected using the differential correction technique to obtain a high-precision nominal Halo orbit.

[0016] The natural motion equation (1) of the spacecraft is simplified as:

[0017]

[0018] Where the subscript r represents the dynamics of the nominal Halo orbit,

[0019] For the Halo orbit keeping problem, the controlled motion equation of the spacecraft is constructed as:

[0020]

[0021] in, is the position and velocity state vector of the controlled spacecraft, B=[0 3×3 I 3×3 ] T , u=[u1,u2,u3] T is the control input and satisfies u∈U={u|u T Pu≤U max}, P is a symmetric positive definite matrix.

[0022] Combining the controlled motion equation (3) and the natural motion equation (1) of the spacecraft, the tracking error dynamics is obtained as:

[0023]

[0024] Where Δx = xx r ,

[0025] Step 2: Discretize the Halo orbit to obtain discrete points. Each discrete point can be regarded as an equilibrium point. The problem of solving the attraction domain of the Halo orbit is transformed into the problem of solving the attraction domain of the error dynamics equilibrium point. Based on the control Lyapunov function, the judgment condition of the attraction domain and the optimization problem of maximizing the attraction domain are constructed. The set of all sampling points that meet the judgment condition is solved based on the sampling method to obtain the attraction domain of the nominal Halo orbit in step 1. The stability and controllability of the controller are guaranteed based on the attraction domain.

[0026] The specific implementation method of step 2 is:

[0027] For error dynamics, the uncontrolled equilibrium point is Δx = 0, that is, when u(t)≡0, The Halo orbit is discretized to obtain discrete points, each of which can be regarded as an equilibrium point. Therefore, the problem of solving the attraction domain of the Halo orbit is transformed into solving the attraction domain of the equilibrium point Δx = 0 of the error dynamics (4). Based on the method of controlling the Lyapunov function, under the control constraint u T Pu≤U max Next, solve the attraction domain corresponding to the nominal Halo orbit obtained in step 1. If the state of the spacecraft is in the attraction domain at the initial time, it is determined that there is a control law that satisfies the control constraints, so that the spacecraft can converge to the nominal trajectory.

[0028] Based on the method of controlling the Lyapunov function, under the control constraint u T Pu≤U max Next, solve the attraction domain corresponding to the nominal Halo orbit obtained in step 1. The specific implementation method is as follows:

[0029] In a finite state space Select candidate control Lyapunov function V is selected as a star function, and in Shang Zheng Ding, that is For each point in the attraction domain The following criteria are met:

[0030]

[0031] in, is the gradient of V, and:

[0032]

[0033] The judgment condition (5) is used as a necessary but not sufficient condition to determine whether the point Δx belongs to the attraction domain. Based on this necessary but not sufficient condition, the attraction domain is estimated by sampling method.

[0034] For a finite state space Perform uniform sampling to obtain N sampling points, denoted as Δx i , i = 1, 2, ... N. Verify whether the judgment condition (5) is true for each sampling point. The set of all sampling points that meet the judgment condition (5) is X.

[0035] Then the estimated equation of the attraction domain is:

[0036]

[0037] Among them, γ is a parameter related to the size of the attraction domain, which is obtained by solving the following attraction domain optimization problem:

[0038]

[0039] Based on the sampling method, the discrimination condition (5), the estimation equation of the attraction domain (6) and the characteristic attraction domain optimization problem (7) are solved to obtain the attraction domain of the Halo orbit near the L2 point of the Sun-Earth three-body system. The spacecraft is constrained in this attraction domain to ensure the stability and controllability of the controller.

[0040] Step three, divide the control strategy design into two parts: dead zone design and control law design. Select the dead zone contained in the attraction domain obtained in step two; on this basis, in order to consider the life limit of the thruster and avoid the continuous operation of the thruster, construct a dual-loop control strategy: the outer boundary of the dead zone is the outer loop, and the inner boundary of the dead zone is the inner loop. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working. Combined with this dual-loop control strategy, with the control of the Lyapunov function decreasing and the control amplitude as constraints, and fuel consumption as a performance indicator, the long-term control optimization problem of the Halo orbit is constructed. By solving the long-term control optimization problem of the Halo orbit, the corresponding feedback control law is obtained. The feedback control law is used to maintain the control of the spacecraft to ensure the stability and controllability of the controller and achieve long-term stable maintenance of the Halo orbit.

[0041] The specific implementation method of step three is:

[0042] The control strategy design is divided into two parts: dead zone design and control law design. The dead zone is selected to be included in the attraction domain obtained in step 2, that is, the dead zone is α1 and α2 are the correlation coefficients of the outer and inner boundaries of the dead zone. The dual-loop control strategy based on the attraction domain is: the outer boundary is the outer loop, and the inner boundary is the inner loop. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working. Based on this dual-loop control strategy, the life limit of the thruster is considered to avoid continuous operation of the thruster. When the spacecraft is in the attraction domain, according to the judgment condition (5) in step 2, there is a control law u∈U , so that the derivative of the control Lyapunov function is less than zero. This ensures that the spacecraft is controllable. The control logic is:

[0043]

[0044] Measure the spacecraft state x at each moment and get the error state Δx Taking the decreasing Lyapunov function and the amplitude as constraints and the fuel consumption as the performance index, the long-term control optimization problem of Halo orbit is constructed as shown in formula (9):

[0045]

[0046] By solving the Halo orbit long-term control optimization problem (9), the corresponding feedback control law is obtained. The spacecraft is controlled according to the feedback control law to ensure the stability and controllability of the controller, reduce the thruster working time, and achieve long-term stable maintenance of the Halo orbit.

[0047] Beneficial effects:

[0048] 1. The present invention discloses a method for long-term control and maintenance of Halo orbit based on attraction domain. Based on the Halo orbit attraction domain, a dead zone located in the attraction domain is selected, with the outer boundary of the dead zone as the outer ring and the inner boundary of the dead zone as the inner ring. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working. Using this dual-loop control strategy, the Halo orbit can be controlled and maintained for a long time, which can solve the problem of continuous operation of the thruster and increase the on-orbit operation time of the spacecraft.

[0049] 2. The long-term control and maintenance method of Halo orbit based on attraction domain disclosed in the present invention uses the control Lyapunov function to construct the attraction domain discrimination condition, and solves the attraction domain corresponding to the nominal Halo that meets the thrust constraint based on the sampling method. Constraining the spacecraft within the attraction domain can solve the problem of uncontrollability or controller instability during the control and maintenance of Halo orbit, and ensure the stability and controllability of the spacecraft when running on the Halo orbit. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of the long-term control and maintenance method of the Halo orbit based on the attraction domain of the present invention.

[0051] Figure 2 In the specific implementation plan, the amplitude A near the L2 point of the Sun-Earth circular restricted three-body z =Halo simulation diagram of 200000km.

[0052] Figure 3 This is a simulation diagram of the Halo attraction domain near the L2 point of the Sun-Earth circular restricted three-body system solved under thrust constraints in a specific implementation plan.

[0053] Figure 4 It is a schematic diagram of the retention control strategy based on the attraction domain in a specific implementation scheme.

[0054] Figure 5 It is a simulation diagram of the thrust curve of the Halo long-term control near the L2 point in the attraction domain in a specific implementation scheme.

[0055] Figure 6 This is a simulation diagram of the Lyapunov function change curve based on the Halo long-term maintenance control near the L2 point of the attraction domain in a specific implementation scheme. DETAILED DESCRIPTION

[0056] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0057] In order to verify the feasibility of the method, the control and maintenance simulation of the base attraction domain is carried out for the Halo orbit mission at the L2 point of the Sun-Earth three-body system. Figure 1 As shown, the method for long-term control and maintenance of Halo orbit based on attraction domain disclosed in this example has the following specific implementation steps:

[0058] Step 1: Construct the natural motion equation of the spacecraft. Based on the circular restricted three-body model, calculate the third-order analytical solution of the periodic orbit near the libration point in the circular restricted three-body system of the Sun and the Earth. Use the differential correction technique to correct the third-order analytical solution to obtain a high-precision nominal Halo orbit. For the Halo orbit keeping problem, construct the controlled motion equation of the spacecraft. Combine the controlled motion equation of the spacecraft with the natural motion equation to obtain the tracking error dynamics.

[0059] The specific implementation method of step one is:

[0060] This example selects the Sun-Earth three-body system and constructs the natural motion equation of the spacecraft as:

[0061]

[0062] Where x, y, and z are the positions of the spacecraft, μ = 3.0035 × 10 -6 is the gravitational coefficient of the Sun-Earth system, r1 and r2 represent the distances between the spacecraft and the Sun and the Earth respectively:

[0063]

[0064] Based on the circular restricted three-body model, the third-order analytical solution of the periodic orbit near the libration point in the circular restricted three-body system of the Sun and the Earth is calculated, and the third-order analytical solution is corrected by differential correction technology to obtain a high-precision nominal Halo orbit. z = 200000km Halo orbit, the obtained Halo orbit is as follows Figure 2 shown.

[0065] The natural motion equation (1) of the spacecraft is simplified as:

[0066]

[0067] Where the subscript r represents the dynamics of the nominal Halo orbit,

[0068] For the Halo orbit keeping problem, the controlled motion equation of the spacecraft is constructed as:

[0069]

[0070] in, is the position and velocity state vector of the controlled spacecraft, B=[0 3×3 I 3×3 ] T , u=[u1,u2,u3] T is the control input and satisfies u∈U={u|u T Pu≤U max}, in this case U max =250mN, P is a symmetric positive definite matrix, which in this case is a 3×3 unit matrix.

[0071]

[0072] Combining the controlled motion equation (3) and the natural motion equation (1) of the spacecraft, the tracking error dynamics is obtained as:

[0073]

[0074] Where Δx = xx r ,

[0075] Step 2: Discretize the Halo orbit to obtain discrete points. Each discrete point can be regarded as an equilibrium point. The problem of solving the attraction domain of the Halo orbit is transformed into the problem of solving the attraction domain of the error dynamics equilibrium point. Based on the control Lyapunov function, the judgment condition of the attraction domain and the optimization problem of maximizing the attraction domain are constructed. The set of all sampling points that meet the judgment condition is solved based on the sampling method to obtain the attraction domain of the nominal Halo orbit in step 1. This attraction domain can ensure the stability and controllability of the controller.

[0076] The specific implementation method of step 2 is:

[0077] For error dynamics, the uncontrolled equilibrium point is Δx = 0, that is, when u(t)≡0, The Halo orbit is discretized to obtain discrete points, each of which can be regarded as an equilibrium point. Therefore, the problem of solving the attraction domain of the Halo orbit is transformed into solving the attraction domain of the equilibrium point Δx = 0 of the error dynamics (4). Based on the method of controlling the Lyapunov function, under the control constraint u T Pu≤U max Next, solve the attraction domain corresponding to the nominal Halo orbit obtained in step 1. If the state of the spacecraft is in the attraction domain at the initial time, it is determined that there is a control law that satisfies the control constraints, so that the spacecraft can converge to the nominal trajectory.

[0078] Based on the method of controlling the Lyapunov function, under the control constraint u T Pu≤U max Next, solve the attraction domain corresponding to the nominal Halo orbit obtained in step 1. The specific implementation method is as follows:

[0079] In a finite state space Select candidate control Lyapunov function V is selected as a star function, and in Shang Zheng Ding, that is For each point in the attraction domain The following criteria are met:

[0080]

[0081] in, is the gradient of V, and:

[0082]

[0083] The judgment condition (5) is used as a necessary but not sufficient condition to determine whether the point Δx belongs to the attraction domain. Based on this necessary but not sufficient condition, the attraction domain is estimated by sampling method.

[0084] For a finite state space Perform uniform sampling to obtain N sampling points, denoted as Δx i , i = 1, 2, ... N. Verify whether the judgment condition (5) is true for each sampling point. The set of all sampling points that meet the judgment condition (5) is X.

[0085] Then the estimated equation of the attraction domain is:

[0086]

[0087] Among them, γ is a parameter related to the size of the attraction domain, which is obtained by solving the following attraction domain optimization problem:

[0088]

[0089] Based on the sampling method, the discrimination condition (5), the estimation equation of the attraction domain (6) and the characteristic attraction domain optimization problem (7) are solved to obtain the attraction domain of the Halo orbit near the L2 point of the Sun-Earth three-body system. Constraining the spacecraft within this attraction domain can ensure the stability and controllability of the controller. In this case, for the amplitude A near the Sun-Earth L2 point z = 200000km Halo orbit, using the above algorithm calculator corresponding to the attraction domain, finally get γ = 0.5, the attraction domain of the Halo orbit is as follows Figure 3 shown.

[0090] Step three, divide the control strategy design into two parts: dead zone design and control law design. Select the dead zone contained in the attraction domain obtained in step two; on this basis, in order to consider the life limit of the thruster and avoid the continuous operation of the thruster, construct a dual-loop control strategy: the outer boundary of the dead zone is the outer loop, and the inner boundary of the dead zone is the inner loop. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working. Combined with this dual-loop control strategy, with the control of the Lyapunov function decreasing and the control amplitude as constraints, and fuel consumption as a performance indicator, the long-term control optimization problem of the Halo orbit is constructed. By solving the long-term control optimization problem of the Halo orbit, the corresponding feedback control law is obtained. The feedback control law is used to maintain the control of the spacecraft to ensure the stability and controllability of the controller and achieve long-term stable maintenance of the Halo orbit.

[0091] The specific implementation method of step three is:

[0092] The control strategy design is divided into two parts: dead zone design and control law design. The dead zone is selected to be included in the attraction domain obtained in step 2. In this case, the area with a size of 0.1 to 0.5 times the attraction domain is selected as the dead zone, that is, the dead zone is The dual-loop control strategy based on the attraction domain is: the outer boundary is the outer loop, and the inner boundary is the inner loop. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working. Figure 4 As shown. Based on this dual-loop control strategy, the life limit of the thruster is considered to avoid the thruster from working continuously. When the spacecraft is in the attraction domain, according to the judgment condition (5) in step 2, there is a control law u∈U , so that the derivative of the control Lyapunov function is less than zero. This ensures that the spacecraft is controllable. The control logic is:

[0093]

[0094] Measure the spacecraft state x at each moment and get the error state Δx Taking the decreasing Lyapunov function and the amplitude as constraints and the fuel consumption as the performance index, the long-term control optimization problem of Halo orbit is constructed as shown in formula (9):

[0095]

[0096] By solving the Halo orbit long-term control optimization problem (9), the corresponding feedback control law is obtained. The spacecraft is controlled according to the feedback control law to ensure the stability and controllability of the controller, reduce the thruster working time, and achieve long-term stable maintenance of the Halo orbit.

[0097] The spacecraft in the Halo orbit is controlled and maintained using a double-loop control strategy based on the attraction domain. Figure 5 The control change curve is given, and it can be seen that the dual-loop control strategy provided by the present invention can effectively reduce the working time of the thruster, thereby increasing the on-orbit operation time of the spacecraft. In addition, the change curve of the Lyapunov function of the Halo long-term maintenance control near the L2 point based on the attraction domain is as follows Figure 6 As shown, it can be seen that the Lyapunov function shows a decreasing trend, and the corresponding controller is stable.

[0098] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for long-term control and maintenance of Halo orbit based on attraction domain, characterized by: The steps include: Step 1: Construct the natural motion equation of the spacecraft. Based on the circular restricted three-body model, calculate the third-order analytical solution of the periodic orbit near the libration point in the Sun-Earth circular restricted three-body system. Use the differential correction technique to correct the third-order analytical solution to obtain a high-precision nominal Halo orbit. For the Halo orbit keeping problem, construct the controlled motion equation of the spacecraft. Combine the controlled motion equation of the spacecraft with the natural motion equation to obtain the tracking error dynamics. Step 2: Discretize the Halo orbit to obtain discrete points. Each discrete point can be regarded as an equilibrium point. The problem of solving the attraction domain of the Halo orbit is transformed into the problem of solving the attraction domain of the error dynamics equilibrium point. Based on the control Lyapunov function, the attraction domain discrimination condition and the optimization problem of maximizing the attraction domain are constructed, and the set of all sampling points that meet the discrimination condition is solved based on the sampling method to obtain the attraction domain of the nominal Halo orbit in step 1; Step 3: Divide the control strategy design into two parts: dead zone design and control law design; The dead zone contained in the attraction domain obtained in step 2 is selected; on this basis, in order to consider the life limit of the thruster and avoid continuous operation of the thruster, a dual-loop control strategy is constructed: the outer boundary of the dead zone is the outer loop, and the inner boundary of the dead zone is the inner loop. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working; combined with the dual-loop control strategy, the control of the Lyapunov function decreases and the control amplitude is constrained, and the fuel consumption is used as a performance indicator to construct the Halo orbit long-term control optimization problem. By solving the Halo orbit long-term control optimization problem, the corresponding feedback control law is obtained, and the feedback control law is used to maintain control of the spacecraft to ensure the stability and controllability of the controller and achieve long-term stable maintenance of the Halo orbit.

2. A method for long-term control and maintenance of Halo orbit based on attraction domain as claimed in claim 1, characterized in that: The specific implementation method of step one is: The natural motion equation of the spacecraft is expressed as: Among them, x, y, z are the positions of the spacecraft, μ is the three-body gravitational coefficient, and r1 and r2 represent the distances between the spacecraft and the sun and the earth respectively: Based on the circular restricted three-body model, the third-order analytical solution of the periodic orbit near the libration point in the circular restricted three-body system of the Sun and the Earth is calculated, and the third-order analytical solution is corrected by differential correction technology to obtain a high-precision nominal Halo orbit. The natural motion equation (1) of the spacecraft is simplified as: Where the subscript r represents the dynamics of the nominal Halo orbit, For the Halo orbit keeping problem, the controlled motion equation of the spacecraft is constructed as: in, is the position and velocity state vector of the controlled spacecraft, B=[0 3×3 I 3×3 ] T , u=[u1,u2,u3] T is the control input and satisfies u∈U={u|u T Pu≤U max }, P is a symmetric positive definite matrix; Combining the controlled motion equation (3) and the natural motion equation (1) of the spacecraft, the tracking error dynamics is obtained as: Where Δx = xx r , 3. A method for long-term control and maintenance of Halo orbit based on attraction domain as claimed in claim 2, characterized in that: The specific implementation method of step 2 is: For error dynamics, the uncontrolled equilibrium point is Δx = 0, that is, when u(t)≡0, The Halo orbit is discretized to obtain discrete points, each of which can be regarded as an equilibrium point. Therefore, the problem of solving the attraction domain of the Halo orbit is transformed into solving the attraction domain of the equilibrium point Δx = 0 of the error dynamics (4). Based on the method of controlling the Lyapunov function, under the control constraint u T Pu≤U max Next, solve the attraction domain corresponding to the nominal Halo orbit obtained in step 1; if the state of the spacecraft is in the attraction domain at the initial time, it is determined that there is a control law that satisfies the control constraints, so that the spacecraft can converge to the nominal trajectory; Based on the method of controlling the Lyapunov function, under the control constraint u T Pu≤U max Next, solve the attraction domain corresponding to the nominal Halo orbit obtained in step 1. The specific implementation method is as follows: In a finite state space Select candidate control Lyapunov function V is selected as a star function, and in Shang Zheng Ding, that is For each point in the attraction domain The following criteria are met: in, is the gradient of V, and: The discriminant condition (5) is used as a necessary but not sufficient condition to determine whether the point Δx belongs to the attraction domain. Based on the necessary but not sufficient condition, the attraction domain is estimated by sampling method. For a finite state space Perform uniform sampling to obtain N sampling points, denoted as Δx i , i=1,2,...N; verify whether the judgment condition (5) is established for each sampling point; the set of all sampling points that meet the judgment condition (5) is X; Then the estimated equation of the attraction domain is: Among them, γ is a parameter related to the size of the attraction domain, which is obtained by solving the following attraction domain optimization problem: Based on the sampling method, the discrimination condition (5), the estimation equation of the attraction domain (6) and the characteristic attraction domain optimization problem (7) are jointly solved to obtain the attraction domain of the Halo orbit near the L2 point of the Sun-Earth three-body system; the spacecraft is constrained in this attraction domain to ensure the stability and controllability of the controller.

4. A method for long-term control and maintenance of Halo orbit based on attraction domain as claimed in claim 3, characterized in that: The specific implementation method of step three is: The control strategy design is divided into two parts: dead zone design and control law design; the dead zone is selected to be included in the attraction domain obtained in step 2, that is, the dead zone is α1 and α2 are the correlation coefficients of the outer and inner boundaries of the dead zone; the dual-loop control strategy based on the attraction domain is: the outer boundary is the outer loop, and the inner boundary is the inner loop. When the spacecraft touches the outer boundary, the thruster is turned on, and when the spacecraft is controlled to the inner boundary, the thruster stops working; based on this dual-loop control strategy, the life limit of the thruster is considered to avoid continuous operation of the thruster; When the spacecraft is in the attraction domain, according to the judgment condition (5) in step 2, there exists a control law u∈U , so that the derivative of the control Lyapunov function is less than zero; that is, the spacecraft can be controlled; the control logic is: Measure the spacecraft state x at each moment and get the error state Δx ; Taking the control of the Lyapunov function decrease and the control amplitude as constraints, and the fuel consumption as the performance index, the long-term control optimization problem of the Halo orbit is constructed as shown in formula (9): By solving the Halo orbit long-term control optimization problem (9), the corresponding feedback control law is obtained. The spacecraft is controlled according to the feedback control law to ensure the stability and controllability of the controller, reduce the thruster working time, and achieve long-term stable maintenance of the Halo orbit.

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