An on-orbit three-party game control method considering the sunlight angle constraint

Abstract

The present invention discloses an on-orbit three-party game control method considering solar angle constraints, which includes establishing an optimal control model for each participant in the "pursue-defend-escape" on-orbit three-party game problem of a pursuit spacecraft, a defense spacecraft and a target spacecraft; constructing the "pursue-defend" problem and the "pursue-escape" problem, and respectively solving the optimal controls of the two problems based on the optimal control model; using weight coefficients to perform weighted combination on the optimal controls of the two problems, thereby reducing the solution dimension of the original problem from 36 dimensions to 12 dimensions, greatly improving the calculation efficiency, while ensuring the optimality of the control index and significantly reducing the amount of calculation; designing a solar angle correction strategy, adding the solar avoidance vector to the control quantity for correction to obtain the final game control quantity of each participant, and ensuring 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 the on-orbit three-party game control that satisfies the process solar angle constraints.

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 Art

[0002] In recent years, with the increasing complexity of space game tasks, the research on on-orbit pursuit-evasion games has gradually expanded from traditional two-party games to multi-party collaborative game fields, 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 game lacks a systematic solution to the problem of high-dimensional optimal control equations and difficult solutions in multi-party games, resulting in limited real-time decision-making ability in 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 threats in time and implement maneuvers, thereby significantly changing the game result. Such an orbit pursuit-evasion game model including 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 lacking. 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. In 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 high-dimensional two-point boundary value problems 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 solutions often destroys the optimality and even causes control conflicts. This limitation makes it difficult to reduce the computational amount through direct splitting methods.

[0004] In addition, prior art research unified complex game indicators such as the solar aspect angle and the energy of the target orbit 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 uses other forms of game indicators as terminal indicators is that the process game indicators need to be expressed in integral form in the cost function of the game participants. However, for game indicators with complex mathematical expressions such as angle constraints, it is difficult to analytically solve the optimal control differential equation when solving the control strategies of the participants. 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 solar aspect angle constraint, which can effectively solve the problems raised in the above background technology.

[0006] To solve the above technical problems, the invention adopts the following technical solutions: An on-orbit three-party game control method considering the solar aspect angle constraint, establishing an optimal control model for each participant in the "chase-defend-escape" on-orbit three-party game problem of the pursuit spacecraft, the defense spacecraft and the target spacecraft; and constructing the "chase-defend" problem and the "chase-escape" problem, and respectively solving the optimal controls of the two problems based on the optimal control model;

[0007] Introducing a weight coefficient to perform weighted combination on the optimal controls of the two problems;

[0008] Designing a solar aspect angle correction strategy, adding the solar avoidance vector to the control quantity for correction to obtain the final game control quantity for each participant.

[0009] Preferably, an optimal control model is established:

[0010] Selecting a virtual reference point, and taking the virtual reference point as the center of the coordinate system, establishing 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:

[0011] ;

[0012] Among them, represents the state vector of each 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 each 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;

[0013] Define the cost functions of each participant , and , which are respectively expressed as:

[0014] ;

[0015] Among them, and are weight coefficients; is the set terminal time of the game; the superscript T represents transpose; the goal of the game participants is to minimize their respective cost functions;

[0016] 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:

[0017] ;

[0018] 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;

[0019] Construct the Hamiltonian functions of each participant:

[0020] ;

[0021] Among them, and are the optimal control co-state quantities of the three-party game, satisfying the following recurrence relation:

[0022] ;

[0023] According to the optimal control principle, obtain the optimal controls , and of each game participant:

[0024] ;

[0025] 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 each participant corresponding to the Hamiltonian function;

[0026] Among them, the calculation methods of A and B are as follows:

[0027] , ;

[0028] Among them, 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; if the virtual reference center point is taken as a circular orbit, then r , , does not change with time, and A( t ) = A is a constant value.

[0029] Preferably, the "chase - defense - escape" three - party in - orbit game problem of the optimal control model is decoupled, so as to construct the "chase - defense" problem and the "chase - escape" problem.

[0030] Preferably, the optimal control of the "chase - defense" problem and the "chase - escape" problem is calculated based on the Riccati equation method.

[0031] Further preferably, the "chase - escape" problem and the "chase - defense" problem are respectively expressed as:

[0032] , ;

[0033] Among them, , , are the weights measuring the importance of each participant to the game state and control cost. The subscripts P1 and P2 respectively correspond to the "chase - escape" problem and the "chase - defense" problem;

[0034] The optimal controls of the "chase - escape" problem and the "chase - defense" problem are respectively expressed as:

[0035] , ;

[0036] Among them, , 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.

[0037] Preferably, the weight coefficients are weighted and combined as:

[0038] ;

[0039] Among them, , are respectively the optimal controls of the pursuit spacecraft in the "chase - escape" problem and the "chase - defense" problem. When When it is the case, it indicates that the pursuit spacecraft expects to reduce the terminal distance from the target spacecraft; when it is the case, it indicates that the pursuit spacecraft expects to increase the terminal distance from the defense spacecraft.

[0040] Preferably, define the sun avoidance angle of "our spacecraft - enemy spacecraft" in the game process;

[0041] ;

[0042] Among them, is the sun position vector in the geocentric inertial system, is the relative position vector pointing from our spacecraft to the enemy spacecraft;

[0043] According to the performance of the optical imaging instrument adopted by the game participants, set the upper limit of the sun avoidance angle threshold. When the angle between the spacecraft performing the task, the enemy spacecraft and the sun is less than the upper limit of the sun avoidance angle threshold, the imaging of the enemy 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 enemy spacecraft. Therefore, the game process should complete the approach against the light of the target, that is, it is necessary to satisfy:

[0044] ;

[0045] Among them, is the upper limit of the sun avoidance angle threshold;

[0046] Add the sun avoidance vector to the control quantity for correction to obtain the final game control quantity of each participant:

[0047] ;

[0048] ;

[0049] Among them, is the game control without considering sunlight conditions, which are respectively , and [[ID=D49]] ; 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 index magnitudes of the control term and the angle term consistent.

[0050] Preferably, based on the requirements of the on-orbit game mission, when our spacecraft is outside the sun avoidance angle range of the enemy spacecraft (i.e., ), our spacecraft executes the sun avoidance strategy, and the specific maneuver strategy for sun avoidance is:

[0051] ;

[0052] Among them, h is the normal vector perpendicular to the orbital plane formed by both sides; is the solar avoidance maneuver direction vector.

[0053] Beneficial effects: The method of the present invention replaces the original "pursue - defend - escape" problem by constructing "pursue - defend" 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 control indicators, and providing a feasible solution for the online correction control of complex on - orbit game scenarios;

[0054] In addition, a sunlight angle correction strategy is designed. By dynamically adjusting the game control direction, it ensures that the pursuer approaches the target in the backlight area, weakens the optical observation conditions of the enemy, and realizes the on - orbit three - party game control that meets the process sunlight angle constraint. Brief Description of the Drawings

[0055] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation to the present invention.

[0056] In the drawings:

[0057] Figure 1 is the flowchart of a method for on - orbit three - party game control considering sunlight angle constraint of the present invention;

[0058] Figure 2 is the geometric schematic diagram of the solar avoidance maneuver vector of the invention.

[0059] Figure 3 is the image of the relative distance change between the defensive spacecraft and the pursuing spacecraft in the test case of the invention.

[0060] Figure 4 is the image of the solar avoidance angle change between the defensive spacecraft and the pursuing spacecraft in the test case of the invention.

[0061] Figure 5 is the box plot of the solution duration statistical results of the method of the present invention and the non - dimensionality - reduced method in the Monte Carlo simulation.

[0062] Figure 6 is the scatter plot of the solution duration statistical results of the method of the present invention and the non - dimensionality - reduced method in the Monte Carlo simulation.

[0063] Figure 7 is the image of the relative distance change between the defensive spacecraft and the pursuing spacecraft of the method of the present invention and the non - dimensionality - reduced method in the verification case. Detailed Embodiments

[0064] The embodiments of the present invention will be described below in conjunction with 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, and are not intended to limit the present invention. The embodiments of the present application will be described below in conjunction with the accompanying drawings.

[0065] As Figure 1 shown, a on-orbit three-party game control method considering solar angle constraints includes:

[0066] Step S1. For the on-orbit three-party game problem, according to the game objectives of the pursuit spacecraft, the defense spacecraft, and the target spacecraft, establish the optimal control model for each participant in the on-orbit three-party game problem;

[0067] 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:

[0068] ;

[0069] Among them, represents the state vector of each 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 each participant, , when the subscript i takes P, D, and E, it represents the pursuit spacecraft, the defense 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:

[0070] , ;

[0071] Among them, θ is the true anomaly of the orbit 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 , , does not change with time. One dot represents the first derivative, and two dots represent the second derivative, is a fixed value;

[0072] S1.2. Define the cost functions , and , which are respectively expressed as:

[0073] ;

[0074] wherein, and are weight coefficients; is the set terminal moment of the game; the superscript T represents 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;

[0075] S1.3. Since the game process only focuses on the relative states between game participants, therefore, the relative states are defined to describe the dynamics of the three-party game scenario:

[0076] ;

[0077] 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;

[0078] On this basis, the respective Hamiltonian functions of the participants are constructed:

[0079] ;

[0080] wherein, and are the optimal control co-state variables of the three-party game, satisfying the following recurrence relations:

[0081] ;

[0082] S1.4. The respective optimal controls , and of the game participants are obtained by variational calculus of the Hamiltonian function:

[0083] ;

[0084] wherein, is the optimal control of the pursuit spacecraft, is the optimal control of the target spacecraft, is the optimal control of the defense spacecraft, and the superscript * indicates that this control is the optimal control of the participant corresponding to the Hamiltonian function.

[0085] Step S2. Decouple and split the solution to the original "pursuit-defense-evasion" on-orbit three-party game control problem described in Step S1 into a "pursuit-defense" problem and a "pursuit-evasion" problem, and respectively solve the respective optimal controls of the three parties of pursuit, defense, and evasion in the two sub-problems;

[0086] S2.1. Define the cost functions of two game sub-problems according to the requirements of the original "pursuit-evasion-defense" three-party game problem:

[0087] , ;

[0088] Among them, , , To measure the degree of importance of each participant to the game state and control cost, the larger its value, the more inclined the participant is to use less control cost to maintain the relative state of the current game. The subscripts P1 and P2 correspond to the "pursuit-evasion" problem and the "pursuit-defense" problem respectively;

[0089] 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:

[0090] , ;

[0091] Among them, , is the Riccati matrix, and after determining the game duration, it is integrated backward from the terminal value to obtain the process Riccati matrix; I is the identity matrix.

[0092] Step S3. Introduce weight coefficients, and combine the optimal controls obtained 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;

[0093] S3.1. The control quantity of the pursuit spacecraft obtained in Step S2.2 consists of and These two parts are the optimal controls corresponding to their cost functions in their respective sub-problems. Introduce weight coefficients to weight the two parts:

[0094] ;

[0095] Among them, , are the optimal controls of the pursuit spacecraft in the "pursuit-evasion" problem and the "pursuit-defense" problem respectively. The parameter , representing the weight of the pursuit spacecraft in measuring the two parts of the countermeasures when making decisions; 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.

[0096] Step S4: Design a sun angle correction strategy to obtain the optimal on-orbit three-party game control that meets the requirements of the process sun angle game.

[0097] S4.1: Define the sun avoidance angle between "one's own spacecraft - enemy spacecraft" in the game process:

[0098] ;

[0099] where is the sun position vector in the geocentric inertial coordinate system, is the relative position vector from one's own spacecraft to the enemy spacecraft;

[0100] S4.2: Set the upper limit of the sun avoidance angle threshold according to the performance of the optical imaging instrument adopted by the game participants. When the angle between the spacecraft performing the task, the enemy spacecraft, and the sun is less than the upper limit of the sun avoidance angle threshold, the imaging of the enemy spacecraft may be difficult to distinguish due to excessive background light (i.e., the "overexposure" phenomenon), resulting in the inability to effectively observe the enemy spacecraft. Therefore, the backlight approach to the target should be completed during the game process, that is, it is necessary to satisfy:

[0101] ;

[0102] where is the upper limit of the sun avoidance angle threshold;

[0103] S4.3: Set the sun avoidance strategy during the on-orbit game as follows:

[0104]

[0105] 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 one's own spacecraft is outside the sun angle line of sight of the enemy spacecraft, the maneuver trigger condition of the sun avoidance strategy is as follows:

[0106] ;

[0107] where is the correction control considering only the sun angle, is the control coefficient parameter used to keep the order of magnitude of the control term and the angle term indicators consistent.

[0108] S4.4: Add the sun avoidance vector to the control quantity for correction to obtain the final game control quantity of each participant:

[0109] ;

[0110] Among them, the game control without considering sunlight conditions are respectively , and ; is the solar angle correction weight coefficient.

[0111] In a specific test case, the simulation sets the initial moment of the target spacecraft to be 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: , and the gravitational constant of the earth μ = 398600 km3 / s2.

[0112] 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° included 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].

[0113] 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 of the solar avoidance angle of the chasing side relative to the defensive side. Due to the large solar avoidance angle threshold, within the 426 s game duration, the chasing spacecraft triggers the solar 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.

[0114] To verify the solution efficiency of the method, the state of the target spacecraft is set to [0 km, 0 km, 0 km, 0 km / s, 0 km / s, 0 km / s]; the initial three-axis direction positions of the chasing spacecraft are within ±[30, 60] km, and the initial velocity states are within ±[0.01, 0.05] km / s; the initial three-axis direction positions of the defensive spacecraft are within ±[30, 60] km, and the initial velocity states are within ±[0.01, 0.05] km / s. 100 Monte Carlo simulations are performed, and the game planning is carried out using the non-dimensional reduction method and the method of the present invention respectively, and the calculation durations of the two methods are statistically analyzed.

[0115] 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 time 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 randomness, and 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 time 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 paper 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 time 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.

[0116] 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" on-orbit three-party game problem of the pursuit spacecraft, defense spacecraft, and 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 model; 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; 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, defense spacecraft, and 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 control models for each participant; The "chase-evasion" problem and the "chase-defense" problem are respectively expressed as: ； Among them, represents the control vectors of each participant. 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 each participant. 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. , , are used to measure the degree of importance of each participant to the game state and the control cost. The superscript T represents the transpose; The optimal controls of 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.

2. The on-orbit three-party game control method considering the sunlight angle constraint according to claim 1, characterized in that: Decouple the "chase-defense-evasion" on-orbit three-party game problem of the optimal control model, so as to construct the "chase-defense" problem and the "chase-evasion" problem.

3. The on-orbit three-party game control method considering the sunlight angle constraint according to claim 2, characterized in that: Calculate the optimal controls of the "chase-defense" problem and the "chase-evasion" problem based on the Riccati equation method.

4. The on-orbit three-party game control method considering sunlight angle constraints according to claim 3, characterized in that: The calculation methods of A 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, and μ is the gravitational constant of the central celestial body.

5. The on-orbit three-party game control method considering the sunlight angle constraint according to claim 3, characterized in that: Weight coefficient , and the weighted combination is expressed as: ； Among them, , are the optimal controls of the pursuing spacecraft in the "pursuit-evasion" problem and the "pursuit-defense" problem respectively. When , it indicates that the pursuing spacecraft expects to reduce the terminal distance from the target spacecraft; when , it indicates that the pursuing spacecraft expects to increase the terminal distance from the defensive spacecraft.

6. According to the on-orbit three-party game control method considering sun angle constraints described in claim 3, it is characterized in that: Define the solar avoidance angle of the "own spacecraft - enemy 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; 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.

7. A method for on-orbit three-party game control considering solar angle constraints according to claim 6, characterized in that: 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 enemy 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 sides; is the solar avoidance maneuver direction vector, is the solar position vector in the geocentric inertial system, is the relative position vector from one's own spacecraft to the enemy spacecraft.

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