In-orbit tripartite game control method considering sunlight angle constraint

Abstract

The invention discloses an on-orbit tripartite game control method considering sunlight angle constraint. The method comprises the following steps: establishing an optimal control model of each participant in a'chasing-preventing-escaping 'on-orbit tripartite game problem of a chasing spacecraft, a defense spacecraft and a target spacecraft; constructing a'chasing-preventing 'problem and a'chasing-escaping' problem, and respectively solving the optimal control of the two problems based on an optimal control model; weighted combination is carried out on optimal control of the two problems by adopting a weight coefficient, so that the solving dimension of the original problem is reduced from 36 dimensions to 12 dimensions, the calculation efficiency is greatly improved, and the calculation amount is remarkably reduced while the optimality of a control index is ensured; a sunlight angle correction strategy is designed, a sun avoidance vector is added into a control quantity for correction, a final game control quantity of each participant is obtained, and by dynamically adjusting a game control direction, it is ensured that a pursuit approaches a target in a backlight area, optical observation conditions of enemies are weakened, and in-orbit tripartite game control meeting process sunlight angle constraints is achieved.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and particularly to an on-orbit three-party game control method considering solar angle constraints. Background Technique

[0002] In recent years, with the increase in the complexity of space game tasks, the research on on-orbit pursuit-evasion games has gradually expanded from traditional two-party games to the field of multi-party collaborative games, among which the "pursuit-defense-evasion" three-party game scenario is the most representative. For such game scenarios, there are mainly two technical bottlenecks in existing research: First, the game control strategy based on differential games lacks a systematic solution to the problems of high dimension and difficult solution of the optimal control equation for multi-party games, resulting in limited real-time decision-making ability for multi-party games; Second, due to the difficulty of solving high-dimensional equations, it is difficult for existing methods to introduce game indicators such as optical constraints that have a key impact on the game situation. It should be particularly noted that if the game player can approach the target spacecraft along the backlight area, it will cause the target to be unable to detect the threat in time and implement maneuvers, thus significantly changing the game result. Such an orbit pursuit-evasion game model with optical constraints has higher complexity, involving not only the game in the distance dimension but also the game in the angle dimension. However, traditional differential game models mainly focus on parameters such as the relative distance and speed of spacecraft at the game process and terminal time, and the research on environmental factors such as lighting conditions is relatively scarce. This theoretical limitation makes it difficult for existing models to accurately reflect the multi-dimensional game characteristics in actual space missions.

[0003] In the three-party orbit game scenario, each participant has 6 state variables including position components and velocity components, for a total of 18-dimensional state variables. During the numerical solution process, co-state variables corresponding to these state variables will be introduced simultaneously, transforming the on-orbit three-party game optimal control problem into a 36-dimensional two-point boundary value problem. Solving the high-dimensional two-point boundary value problem is very challenging and requires a large amount of computing resources, making it difficult to be used for online correction guidance. Moreover, since the control strategies obtained under different sub-games do not have consistency or compatibility, simply superimposing them after separate solution often destroys the optimality and even causes control conflicts. This limitation makes it difficult to reduce the computational amount through direct splitting.

[0004] In addition, prior art research unified complex game indicators such as the sun angle and target orbit energy into the form of the terminal miss distance. Although this processing method can ensure that the game participants achieve the preset terminal indicators at the end, it cannot make the game process meet the indicator requirements. The reason why prior art research only regards other forms of game indicators as terminal indicators is that the process game indicators need to be expressed as an integral form in the cost function of the game participants. However, for game indicators with complex mathematical expressions such as angle constraints, when solving the control strategy of the participants, it will lead to difficulties in analytically solving the optimal control differential equation. Therefore, prior research generally chooses to handle such indicators as terminal indicators. Summary of the Invention

[0005] The object of the invention is to provide an on-orbit three-party game control method considering the sun angle constraint, which can effectively solve the problems raised in the above background technology.

[0006] To solve the above technical problems, the present invention adopts the following technical solutions: An on-orbit three-party game control method considering the sun angle constraint, establishing an optimal control model for each participant in the "pursue-defend-escape" on-orbit three-party game problem of the pursuit spacecraft, the defense spacecraft and the target spacecraft; and constructing the "pursue-defend" problem and the "pursue-escape" problem, and respectively solving the optimal control of the two problems based on the optimal control model; Introducing a weight coefficient to perform weighted combination on the optimal control of the two problems; Designing a sun angle correction strategy, adding the sun avoidance vector to the control quantity for correction to obtain the final game control quantity of each participant.

[0007] Preferably, an optimal control model is established: Selecting a virtual reference point, and taking the virtual reference point as the center of the coordinate system to establish a LVLH coordinate system, and respectively describing the motion states of the pursuit spacecraft, the defense spacecraft and the target spacecraft in the LVLH coordinate system; the motion equations of each game participant in the LVLH coordinate system are: ; Among them, represents the state vector of the game participant, is the position and velocity difference between the spacecraft and the virtual reference point, is the position difference component, v is the velocity difference component; u represents the control vector of the game participant, , when the subscript i takes P, D, and E, it represents the pursuit spacecraft, the defense spacecraft and the target spacecraft respectively, and the values of B correspond to describing the orbital state of the virtual center point at the moment; Defining the cost function of each participant , and , which are respectively expressed as: ; Among them, and are weight coefficients; is the set terminal moment of the game; the superscript T represents transpose; the goal of the game participants is to minimize their respective cost functions; Convert the absolute coordinates in the cost function into the difference in the state quantities between the participants, that is, the relative state; the relative state dynamically describes the three-party game scenario: ; Among them, is the difference in the state vectors between the pursuit spacecraft and the target spacecraft, is the difference in the state vectors between the defense spacecraft and the pursuit spacecraft; Construct the respective Hamiltonian functions of the participants: ; Among them, and are the optimal control co-state quantities of the three-party game, satisfying the following recurrence relation: ; According to the optimal control principle, the optimal controls of the game participants are obtained , and : ; Among them, is the optimal control of the pursuit spacecraft, is the optimal control of the target spacecraft, is the optimal control of the defense spacecraft; the superscript * indicates that this control is the optimal control of the participant corresponding to the Hamiltonian function; Among them, the calculation methods of A and B are as follows: , ; Among them, is the true anomaly of the orbit of the virtual reference center point at the described moment, is the geocentric distance of the virtual reference center point at the described moment, μ is the gravitational constant of the central celestial body; if the virtual reference center point is taken as a circular orbit, then r , , does not change with time, A( t ) = A is a constant value.

[0008] Preferably, decouple the "pursuit - defense - escape" problem of the optimal control model, so as to construct the "pursuit - defense" problem and the "pursuit - escape" problem.

[0009] Preferably, the optimal control of the "chase - defense" problem and the "chase - escape" problem is calculated based on the Riccati equation method.

[0010] Further preferably, the "chase - escape" problem and the "chase - defense" problem are respectively expressed as: , ; where, , , is to measure the degree of importance of the participants to the game state and control cost. The subscripts P1 and P2 respectively correspond to the "chase - escape" problem and the "chase - defense" problem; The optimal controls of the "chase - escape" problem and the "chase - defense" problem are respectively expressed as: , ; where, , is the Riccati matrix, which is obtained by backward integration from the terminal value after determining the game duration to obtain the process Riccati matrix; I is the identity matrix.

[0011] Preferably, the weight coefficient , and the weighted combination is expressed as: ; where, , are respectively the optimal controls of the pursuit spacecraft in the "chase - escape" problem and the "chase - defense" problem. When , it indicates that the pursuit spacecraft expects to reduce the terminal distance from the target spacecraft; when , it indicates that the pursuit spacecraft expects to increase the terminal distance from the defense spacecraft.

[0012] Preferably, the sun avoidance angle between the "own spacecraft - target spacecraft" is defined during the game process; ; where, is the sun position vector in the geocentric inertial system, is the relative position vector from the own spacecraft to the target spacecraft; According to the performance of the optical imaging instrument adopted by the game participants, the upper limit of the sun avoidance angle threshold is set. When the angle between the spacecraft performing the task, the target spacecraft, and the sun is less than the upper limit of the sun avoidance angle threshold, the imaging of the target spacecraft may be difficult to distinguish due to too strong background light (i.e., the "overexposure" phenomenon), resulting in the inability to effectively observe the target spacecraft. Therefore, the game process should complete the backlight approach to the target, that is, it is necessary to satisfy: ; Among them, is the upper limit of the sun avoidance angle threshold; Add the sun avoidance vector to the control quantity for correction to obtain the final game control quantity of each participant: ; ; Among them, is the game control without considering sunlight conditions, which are respectively , and ; is the sun angle correction weight coefficient; , is the correction control considering only the sun angle, is the control coefficient parameter used to keep the magnitudes of the control term and the angle term indicators consistent.

[0013] Preferably, based on the on-orbit game task requirements, when the own spacecraft is outside the sun avoidance angle range of the target spacecraft (i.e., ), the own spacecraft executes the sun avoidance strategy, and the specific maneuver strategy for sun avoidance is: ; Among them, h is the normal vector perpendicular to the orbital plane formed by both sides; is the sun avoidance maneuver direction vector.

[0014] Beneficial effects: The method of the present invention replaces the original "pursue - defend - escape" problem by constructing "pursue - defend" problems and "pursue - escape" problems, thereby reducing the solution dimension of the original problem from 36 dimensions to 12 dimensions, greatly improving the calculation efficiency, significantly reducing the amount of calculation while ensuring the optimality of the control index, and providing a feasible solution for the online correction control of complex on-orbit game scenarios; In addition, a sun angle correction strategy is designed to ensure that the pursuer approaches the target in the backlight area by dynamically adjusting the game control direction, weakening the optical observation conditions of the enemy, and realizing on-orbit three-party game control that satisfies the process sun angle constraint. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention.

[0016] In the drawings: Figure 1 is a flowchart of an on-orbit three-party game control method considering sun angle constraints of the present invention; Figure 2 is a geometric schematic diagram of the sun avoidance maneuver vector of the invention.

[0017] Figure 3 It is the image of the relative distance change between the defensive spacecraft and the pursuing spacecraft in the test case of the invention.

[0018] Figure 4 It is the image of the sun avoidance angle change between the defensive spacecraft and the pursuing spacecraft in the test case of the invention.

[0019] Figure 5 It is the box plot of the solution time statistics of the method of the invention and the non-dimensional reduction method in the Monte Carlo simulation.

[0020] Figure 6 It is the dot plot of the solution time statistics of the method of the invention and the non-dimensional reduction method in the Monte Carlo simulation.

[0021] Figure 7 It is the image of the relative distance change between the defensive spacecraft and the pursuing spacecraft of the method of the invention and the non-dimensional reduction method in the verification case. Detailed implementation manners

[0022] The embodiments of the present invention will be described below with reference to the accompanying drawings in the embodiments of the present invention. The terms used in the embodiments of the present invention are only for explaining the specific embodiments of the present invention, rather than aiming to limit the present invention. The embodiments of the present application will be described below with reference to the accompanying drawings.

[0023] As Figure 1 shown, an on-orbit three-party game control method considering the sunlight angle constraint includes: Step S1, for the on-orbit three-party game problem, establish the optimal control models of each participant in the on-orbit three-party game problem according to the game objectives of the pursuing spacecraft, the defensive spacecraft and the target spacecraft; S1.1, select a virtual reference point, and establish a LVLH coordinate system with the virtual reference point as the center of the coordinate system. According to the Clohessy-Wiltshire equation, express the motion equations of each game participant in the above reference system as: ; Among them, represents the state vector of the game participant, is the position and velocity difference between the spacecraft and the virtual reference point, is the position difference component, v is the velocity difference component; u represents the control vector of the game participant, , when the subscript i takes P, D, and E, it represents the pursuing spacecraft, the defensive spacecraft and the target spacecraft respectively. The values of A(t) and B correspond to the orbital state of the virtual center point at the described moment. The calculation methods of A(t) and B are as follows: , ; wherein, θ is the true anomaly of the virtual reference center point at the described moment, r is the geocentric distance of the virtual reference center point at the described moment, μ is the gravitational constant of the central celestial body. If the virtual reference center point is taken as a circular orbit, then r , , do not change with time. One dot represents the first-order derivative, and two dots represent the second-order derivative, is a fixed value; S1.2. Define the cost functions of each participant , and , which are respectively expressed as: ; wherein, and are weight coefficients; is the set terminal moment of the game; the superscript T represents the transpose; the goal of each game participant is to minimize their respective cost functions. Since there are games between the pursuit spacecraft and both the target spacecraft and the defense spacecraft during the game process, in order to measure the weight relationship between the two goals, weight coefficients are used to weight them; the goal of each game participant is to minimize their respective cost functions; S1.3. Since the game process only focuses on the relative states between game participants, therefore, define the relative states to describe the dynamics of the three-party game scenario: ; wherein, is the difference in the state vectors between the pursuit spacecraft and the target spacecraft, is the difference in the state vectors between the defense spacecraft and the pursuit spacecraft; On this basis, construct the Hamiltonian functions of each participant: ; wherein, and are the optimal control co-state variables of the three-party game, satisfying the following recurrence relation: ; S1.4. The optimal controls of each game participant , and are obtained by variational calculus of the Hamiltonian function: ; wherein, is the optimal control of the pursuit spacecraft, is the optimal control of the target spacecraft, For the optimal control of a defensive spacecraft, the superscript * indicates that this control is the optimal control of the participant corresponding to the Hamiltonian function.

[0024] Step S2: Decouple and split the solution of the original "pursue-defend-evade" on-orbit three-party game control problem into a "pursue-defend" problem and a "pursue-evade" problem, and solve the optimal controls of the pursuer, defender, and evader in the two sub-problems respectively. S2.1: Define the cost functions of the two game sub-problems according to the requirements of the original "pursue-defend-evade" three-party game problem: , ; where, , , is to measure the participant's emphasis on the game state and control cost. The larger its value, the more the participant tends to maintain the relative state of the current game with less control cost. The subscripts P1 and P2 correspond to the "pursue-evade" problem and the "pursue-defend" problem respectively. S2.2: Both of the two game sub-problems are zero-sum game linear quadratic optimal control problems, which can be solved by the Riccati equation method: , ; where, , is the Riccati matrix. After determining the game duration, it is integrated backward from the terminal value to obtain the process Riccati matrix; I is the identity matrix.

[0025] Step S3: Introduce a weight coefficient, and combine the optimal controls solved under the two sub-problems according to the scenario requirements, so that the synthesized control quantity not only meets the objectives of the original problem, but also maintains the control characteristics of each sub-problem, ensuring the robustness and computational efficiency of the overall game process. S3.1: The control quantity of the pursuit spacecraft obtained in step S2.2 consists of and two parts, which are the optimal controls corresponding to their cost functions in their respective sub-problems. A weight coefficient is introduced to weight the two parts: ; where, , are the optimal controls of the pursuit spacecraft in the "pursue-evade" problem and the "pursue-defend" problem respectively. The parameter , represents the weight of the pursuit spacecraft in measuring the two countermeasures when making a decision; when , it indicates that the pursuit spacecraft expects to reduce the terminal distance from the target spacecraft; when , it indicates that the pursuit spacecraft expects to increase the terminal distance from the defensive spacecraft.

[0026] Step S4: Design a sunlight angle correction strategy to obtain the optimal on-orbit three-party game control that meets the requirements of the process sunlight angle game.

[0027] S4.1: Define the sun avoidance angle between the "own spacecraft - target spacecraft" during the game process: ; where is the sun position vector in the geocentric inertial coordinate system, is the relative position vector pointing from the own spacecraft to the target spacecraft; S4.2: Set the upper limit of the sun avoidance angle threshold according to the performance of the optical imaging instruments adopted by the game participants. When the angle between the spacecraft performing the task, the target spacecraft, and the sun is less than the upper limit of the sun avoidance angle threshold, the imaging of the target spacecraft may be difficult to distinguish due to excessive background light (i.e., the "overexposure" phenomenon), resulting in the inability to effectively observe the target spacecraft. Therefore, the game process should complete the approach against the light of the target, that is, it is necessary to satisfy: ; where is the upper limit of the sun avoidance angle threshold; S4.3: Set the sun avoidance strategy during the on-orbit game as follows:

[0028] where h is the normal vector perpendicular to the orbital plane formed by both sides; is the sun avoidance maneuver direction vector, and its schematic diagram is as shown in Figure 2 ; Since the benefits are the same as long as the own spacecraft is outside the sunlight angle line of sight of the target spacecraft, the maneuver trigger condition of the sun avoidance strategy is as follows: ; where is the correction control considering only the sunlight angle, is the control coefficient parameter used to keep the control term and the angle term index magnitudes consistent.

[0029] S4.4: Add the sun avoidance vector to the control quantity for correction to obtain the final game control quantity of each participant: ; where is the game control without considering the sunlight condition, which are respectively , and ; is the sun angle correction weight coefficient.

[0030] In a specific test case, the simulation assumes that the target spacecraft is initially located in the geosynchronous orbit, which is a nearly circular orbit with a radius of 42166.3 km and an orbital eccentricity of 0.01. Taking the state of the target spacecraft at the initial moment as the virtual reference point, the state of the chasing spacecraft at the initial moment , and the state of the defensive spacecraft at the initial moment . The strategy parameters of each participant are set as follows: . The gravitational constant of the Earth μ = 398600 km3 / s2.

[0031] In this case, each game participant has a sunlight avoidance angle constraint of 60°, that is, when the non-cooperative target is within the 60° angle range of the solar vector, the observation task of the target cannot be completed. The solar vector at the initial moment = [1, 1, 1].

[0032] As Figure 3 shown, in this scenario, the defensive spacecraft completes the interception task at 426 s; since the initial chasing spacecraft is in the sunlit position of the target spacecraft and the defensive spacecraft, Figure 4 shows the change in the sunlight avoidance angle of the chasing side relative to the defensive side. Due to the large sunlight avoidance angle threshold, within the 426 s game duration, the chasing spacecraft triggers the sunlight avoidance angle correction throughout the process; for the defensive spacecraft, the chasing spacecraft is in its backlit position, and the defensive spacecraft does not trigger its correction mechanism.

[0033] To verify the solution efficiency of the method, the state of the target spacecraft is set as [0 km, 0 km, 0 km, 0 km / s, 0 km / s, 0 km / s]; the initial three-axis position of the chasing spacecraft is within ±[30, 60] km, and the initial velocity state is within ±[0.01, 0.05] km / s; the initial three-axis position of the defensive spacecraft is within ±[30, 60] km, and the initial velocity state is within ±[0.01, 0.05] km / s. 100 Monte Carlo simulations are performed, and the game planning is carried out using the non-dimension reduction method and the method of the present invention respectively, and the calculation durations of the two methods are statistically analyzed.

[0034] As Figure 5 , Figure 6As shown, since the method of the present invention only involves the integration process, in 100 Monte Carlo simulations, the average calculation duration of the method of the present invention is 1.35 s. The non-dimensionality reduction method needs to solve the initial value of the differential equation through the differential equation solving method, and then use the shooting method with this initial value to obtain the solution of the differential equation that satisfies the terminal constraint. However, the process of solving the initial value of the differential equation has a certain degree of randomness. Usually, multiple solutions are required to obtain an initial solution with a certain range of error from the terminal constraint. Therefore, the randomness of the calculation time of the non-dimensionality reduction method is relatively large due to the indefinite number of solutions. In 100 Monte Carlo simulations, the average calculation duration of the non-dimensionality reduction method is 11.38 s. One group is selected as a case to verify the game results of the method of this article and the non-dimensionality reduction method for comparison. The results are as Figure 7 shown. The maximum error in position between the method proposed in the present invention and the non-dimensionality reduction method appears at 281.1 s, which is 0.03 km. While ensuring optimality, the average calculation duration of the method of the present invention is 11.86% of that of the non-dimensionality reduction method, improving the solution efficiency and providing a feasible solution for online correction guidance.

[0035] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. For those of ordinary skill in the art in this technical field, after learning the content recorded in the present invention, without departing from the principle of the present invention, several equivalent transformations and substitutions can still be made, and these equivalent transformations and substitutions should also be regarded as belonging to the protection scope of the present invention.

Claims

1. An on-orbit three-party game control method considering solar angle constraints, characterized in that: Establish the optimal control models for each participant in the "chase-defense-evasion" in-orbit three-party game problem of a pursuit spacecraft, a defense spacecraft, and a target spacecraft; and Construct the "chase-defense" problem and the "chase-evasion" problem, and solve the optimal controls for the two problems respectively based on the optimal control models; And introduce a weight coefficient to perform weighted combination on the optimal controls of the two problems; Design a sun angle correction strategy, add the sun avoidance vector to the control quantity for correction, and obtain the final game control quantity for each participant.

2. The on-orbit three-party game control method considering the sunlight angle constraint according to claim 1, characterized in that: Establish the optimal control model: Select a virtual reference point, and with the virtual reference point as the center of the coordinate system, establish the LVLH coordinate system, and describe the motion states of the pursuit spacecraft, the defense spacecraft, and the target spacecraft respectively in the LVLH coordinate system; Define the cost functions for each participant; Convert the absolute coordinates in the cost function into the state quantity differences between each participant, that is, the relative state, and on this basis, conduct a dynamic description of the three-party game scenario; According to the optimal control principle, obtain the optimal controls for each game participant.

3. A method for on-orbit three-party game control considering solar angle constraints according to claim 1 or 2, characterized in that: Decouple the "chase-defense-evasion" problem of the optimal control model, so as to construct the "chase-defense" problem and the "chase-evasion" problem.

4. A method for on-orbit three-party game control considering solar angle constraints according to claim 3, characterized in that: Calculate the optimal controls for the "chase-defense" problem and the "chase-evasion" problem based on the Riccati equation method.

5. The on-orbit three-party game control method considering solar angle constraints according to claim 4, characterized in that: The "chase-evasion" problem and the "chase-defense" problem are respectively expressed as: ； Among them, represents the control vector of the game participants. The subscripts P, D, and E represent the pursuit spacecraft, the defense spacecraft, and the target spacecraft respectively, , and are the cost functions of each participant. The subscripts P1 and P2 correspond to the "pursuit-evasion" problem and the "pursuit-defense" problem respectively; is the set terminal time of the game. x represents the state vector of the game participants, is the difference in the state vectors between the pursuit spacecraft and the target spacecraft, is the difference in the state vectors between the defense spacecraft and the pursuit spacecraft , , is to measure the degree of importance of the participants to the game state and the control cost. The superscript T represents the transpose; The optimal controls for the "chase-defense" problem and the "chase-evasion" problem are respectively expressed as: ， ； Among them, , is the Riccati matrix. After determining the game duration, the process Riccati matrix is obtained by backward integration from the terminal value ; is the set terminal time of the game; I is the identity matrix, and the values of A and B correspond to the description of the orbital state of the virtual center point at the corresponding time. The superscript * indicates that this control is the optimal control of the participant corresponding to the Hamiltonian function, is the optimal control of the pursuit spacecraft, is the optimal control of the target spacecraft, is the optimal control of the defense spacecraft.

6. The on-orbit three-party game control method considering solar angle constraints according to claim 5, characterized in that: The calculation methods of A and B are as follows: ， ； wherein, is the true anomaly of the virtual reference center point at the described moment, is the geocentric distance of the virtual reference center point at the described moment, and μ is the gravitational constant of the central celestial body.

7. A method for on-orbit three-party game control considering the constraint of the sun angle according to claim 5, characterized in that: Weight coefficient , the weighted combination is expressed as: ； Among them, , are the optimal controls of the pursuit spacecraft in the "pursuit-evasion" problem and the "pursuit-defense" problem respectively. When , it indicates that the pursuit spacecraft expects to reduce the terminal distance from the target spacecraft; when , it indicates that the pursuit spacecraft expects to increase the terminal distance from the defense spacecraft.

8. A method for in-orbit three-party game control considering sun angle constraints according to claim 5, characterized in that: Define the solar avoidance angle of the "own spacecraft - target spacecraft" during the game process, and preset the upper limit of the solar avoidance angle threshold ; When the solar avoidance angle is: ； Among them, is the game control without considering sunlight conditions, which are respectively , and ; is the solar angle correction weight coefficient; , is the correction control considering only the sunlight angle, is the control coefficient parameter used to keep the magnitudes of the control term and the angle term indicators consistent.

9. The on-orbit three-party game control method considering the sunlight angle constraint according to claim 8, wherein: Based on the requirements of on-orbit game tasks, set the maneuver trigger conditions for the sun avoidance strategy. When the own spacecraft is outside the sun avoidance angle range of the target spacecraft, that is , the own spacecraft executes the sun avoidance strategy. The specific maneuver strategy for sun avoidance is as follows: ； where h is the normal vector perpendicular to the orbital plane formed by both parties; is the solar avoidance maneuver direction vector, is the solar position vector in the geocentric inertial system, is the relative position vector from the own spacecraft to the target spacecraft.

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