A method for formulating a winning strategy based on a track two-to-one pursuit and evasion game

Abstract

This invention discloses a method for formulating a winning strategy based on a two-on-one pursuit-escape game in orbit, belonging to the field of aerospace technology. The method includes acquiring parameter information of the participants in the two-on-one pursuit-escape game; analyzing the impact of the participants' parameter information on the game outcome to generate an analytical game result; and formulating a winning strategy based on the analytical game result. This invention, through a comprehensive consideration of multiple key factors, can provide targeted winning strategies for different pursuit-escape scenarios.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically to a method for formulating a winning strategy based on a two-to-one pursuit-escape game in orbit. Background Technology

[0002] In the space domain, the pursuit-escape game, as a highly challenging strategic problem, is receiving increasing attention. This type of problem involves a complex and dynamic confrontation between the pursuer and the escapee, especially under the constraints of limited resources, vast distances, and communication delays, making the pursuit process even more complex and unpredictable.

[0003] In a two-on-one pursuit game on a track, the two pursuers not only need to formulate their own independent pursuit strategies, but also need to achieve efficient coordination. This coordination requires both sides to accurately judge the escapee's trajectory and to quickly adjust their strategies based on the escapee's real-time changes in order to achieve the best pursuit effect. At the same time, the choice of game parameters is also crucial, as it directly affects the strategy formulation of both sides and the final outcome.

[0004] However, currently, no effective research method has been established to study the winning mechanism in two-on-one pursuit-escape games in orbit. Existing research mainly focuses on strategy design in single pursuit-escape scenarios, lacking a systematic understanding and comprehensive optimization of the overall pursuit-escape game process. This limitation makes it difficult for us to grasp the evolutionary laws of the pursuit-escape game from a global perspective, and even more difficult to formulate efficient pursuit-escape strategies for the complex space environment. Therefore, how to construct an effective research method for the winning mechanism and achieve a systematic understanding and comprehensive optimization of the overall pursuit-escape game process has become an urgent problem to be solved. Summary of the Invention

[0005] Existing technologies for two-on-one pursuit and escape games in orbit primarily focus on strategy design within a single pursuit scenario, making it difficult to grasp the evolutionary patterns of the pursuit and escape game from a global perspective. This results in the inability to formulate efficient pursuit and escape strategies for the complex space environment. This invention provides a method for formulating winning strategies based on orbital two-on-one pursuit and escape games. It is no longer limited to a single factor or simplified model, but rather, through a comprehensive consideration of multiple key factors, it can provide targeted winning strategies for different pursuit and escape scenarios.

[0006] To achieve the above objectives, the present invention provides the following technical solution.

[0007] In a first aspect, the present invention provides a method for formulating a winning strategy based on a two-to-one pursuit-escape game, comprising:

[0008] Obtain parameter information of participants in a two-to-one pursuit and escape game on the track;

[0009] Based on the parameter information of the participants in the two-to-one pursuit game, the impact on the game outcome is analyzed, and the game results are generated.

[0010] Develop winning strategies based on the analysis of the game's outcome.

[0011] As a further improvement of the present invention, the parameter information of the participants in the two-to-one pursuit-escape game includes the orbital altitude of the reference spacecraft, the difference in orbital altitude between the pursuing spacecraft and the reference spacecraft, the initial states of the pursuer and the escapee, the pulse velocity increment, and the pulse time interval.

[0012] As a further improvement of the present invention, the analysis of the influence of the initial relative positions of the pursuer and the escapee on the game outcome based on the parameter information of the participants in the two-to-one pursuit-escape game includes:

[0013] Given that the pulse time intervals of the participants in a two-on-one pursuit-escape game and the maneuverability of both the pursuer and the escapee are determined, the minimum relative distance between the pursuer and the escapee in a certain location area during the entire game process can be statistically determined using the Monte Carlo method.

[0014] Plot a graph showing the relationship between the minimum relative distance between the pursuer and the escapee and the initial position of the pursuer;

[0015] Based on the aforementioned relationship diagram, the impact of the pursuer's initial position relative to the escapee on the game outcome is analyzed by comparing the results.

[0016] Among them, the minimum relative distance between the pursuer and the escapee includes:

[0017]

[0018] In the formula: E represents the player; P represents the pursuer; X represents the player. P For the pursuer's state variables; : X E The state variables of the players.

[0019] As a further improvement of the present invention, the analysis of the impact of pulse time intervals on the game outcome based on the parameter information of the participants in the two-to-one pursuit game includes:

[0020] In a two-on-one chase game, given a fixed increment in the pursuer's pulse velocity, the relationship between the proportion of the pursuer's winning area and the pulse time interval is statistically analyzed when the initial relative distance between the pursuers changes.

[0021] Based on the relationship between the percentage of winning areas for the pursuers and the pulse time interval, the influence of the size of different pulse time intervals on the game outcome under different initial relative distances is analyzed.

[0022] The percentage of areas where the pursuers won was as follows:

[0023] In the formula, R Pw To determine the percentage of the chaser's winning area, each L 12 The game theory under these circumstances is condensed into a single data point; L 12 A represents the relative distance between the two pursuers. Pw The initial number of successful pursuits within the current location range; A t This represents the total number of initial positions considered in the simulation.

[0024] As a further improvement of the present invention, the analysis of the impact of maneuverability on the game outcome based on the parameter information of the participants in the two-to-one pursuit game includes:

[0025] The relative distance L between the two pursuers 12 With the pulse magnitudes of the two pursuers fixed, the pulse velocity increment ΔV for each pursuer is selected. P The pulse velocity increment ΔV of the escapee E The ratio;

[0026] Based on the selected pursuer's pulse velocity increment ΔV P The pulse velocity increment ΔV of the escapee E The ratio of the two values ​​is used to plot the percentage of the pursuer's winning area, R. Pw The curve showing the change in pulse interval;

[0027] According to the aforementioned drawing, the percentage of the pursuer's winning area R... Pw The curves showing the changes in maneuverability and pulse interval are used to analyze the impact of maneuverability on the game outcome.

[0028] As a further improvement of the present invention, the winning strategy is formulated based on the analysis of the game results, thereby obtaining the optimal initial relative distance of the pursuer, the optimal pulse time interval, and the optimal maneuverability.

[0029] A method for formulating a winning strategy based on a two-to-one pursuit-escape game, comprising:

[0030] Obtain parameter information of participants in a two-to-one pursuit and escape game on the track;

[0031] Based on the parameter information of the participants in the two-to-one pursuit game, the impact on the game outcome is analyzed, and the game results are generated.

[0032] Develop winning strategies based on the analysis of the game's outcome.

[0033] As a further improvement of the present invention, the parameter information of the participants in the two-to-one pursuit-escape game includes the orbital altitude of the reference spacecraft, the difference in orbital altitude between the pursuing spacecraft and the reference spacecraft, the initial states of the pursuer and the escapee, the pulse velocity increment, and the pulse time interval.

[0034] As a further improvement of the present invention, the analysis of the initial relative positions of the pursuer and the escapee on the game outcome based on the parameter information of the participants in the two-to-one pursuit game includes:

[0035] Given that the pulse time intervals of the participants in a two-on-one pursuit-escape game and the maneuverability of both the pursuer and the escapee are determined, the minimum relative distance between the pursuer and the escapee in a certain location area during the entire game process can be statistically determined using the Monte Carlo method.

[0036] Plot a graph showing the relationship between the minimum relative distance between the pursuer and the escapee and the initial position of the pursuer;

[0037] Based on the relationship diagram, the impact of the pursuer's initial position relative to the escapee on the game outcome is analyzed by comparing the results.

[0038] As a further improvement of the present invention, the analysis of the impact of pulse time intervals on the game outcome based on the parameter information of the participants in the two-to-one pursuit game includes:

[0039] In a two-on-one pursuit game, given a fixed increment in the pursuer's pulse velocity, the impact of different pulse time intervals on the game outcome is statistically analyzed under different initial relative distances.

[0040] As a further improvement of the present invention, the analysis of maneuverability based on the parameter information of the participants in the two-to-one pursuit game on the track, and its impact on the game outcome, includes:

[0041] Given a fixed initial relative distance, the impact of different maneuvering capabilities on the game outcome is statistically analyzed.

[0042] As a further improvement of the present invention, the formulation of winning strategies based on the analysis of game results includes the optimal initial relative distance of the pursuer, the optimal pulse time interval, and the optimal maneuverability.

[0043] Secondly, the present invention provides a system for formulating a winning strategy based on a two-to-one pursuit-escape game, comprising:

[0044] Information Acquisition Module: Used to acquire parameter information of participants in the two-on-one pursuit and escape game on the track;

[0045] Analysis Results Module: Used to analyze the impact of parameter information of participants in a two-to-one pursuit game on the game outcome and generate analysis results.

[0046] Strategy formulation module: Used to formulate winning strategies based on the analysis of game results.

[0047] Thirdly, the present invention provides an electronic device, characterized in that it includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for formulating a winning strategy based on a two-to-one pursuit and escape game.

[0048] Fourthly, the present invention provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for formulating a winning strategy based on a two-to-one pursuit and escape game of orbits.

[0049] Fifthly, the present invention provides a computer program product, characterized in that it includes computer instructions, which, when executed by a processor, implement the steps of the method for formulating a winning strategy based on a two-to-one pursuit and escape game.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] This invention goes beyond a single pursuit scenario or simplified model, taking a global perspective and comprehensively considering key factors such as the initial relative positions of the participants, pulse time intervals, and maneuverability. This allows for more comprehensive and in-depth strategy formulation, enabling a more accurate grasp of the evolutionary patterns of the pursuit game. The method of this invention can adapt to such complex environments, developing winning strategies for specific scenarios through comprehensive analysis of multiple key factors, thus improving the effectiveness and practicality of the strategies. By comprehensively considering multiple key factors and generating analytical game results, this invention can formulate more efficient pursuit strategies. This not only reduces resource waste during the pursuit process but also shortens pursuit time and improves pursuit efficiency. Because this invention considers multiple key factors, it can formulate targeted winning strategies based on the characteristics of different pursuit scenarios. This makes the strategies more realistic, improving their operability and practicality. Therefore, in decision-making processes involving two-to-one pursuit games, this invention provides more comprehensive and in-depth analytical results, helping decision-makers better understand the essence and evolutionary patterns of the problem, thereby making more informed and accurate decisions. Attached Figure Description

[0052] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. In the drawings:

[0053] Figure 1 This is a flowchart illustrating a method for formulating a winning strategy based on a two-to-one pursuit and escape game in the present invention.

[0054] Figure 2 This is a simulation of the initial state of a method for formulating a winning strategy based on a two-to-one pursuit and escape game according to the present invention.

[0055] Figure 3 This invention presents a method for formulating a winning strategy in a two-to-one pursuit-escape game based on orbital dynamics, showing the game results of the pursuer under different initial positions; where: (a) is L 12 =0km when D min Midpoint x between the two pursuers p The relationship between (h,l,0) is shown in (b); (b) represents L. 12 =10km D min Midpoint x between the two pursuers p The relationship between (h,l,0);

[0056] Figure 4 This invention relates to a method for formulating a winning strategy based on a two-to-one pursuit-escape game in orbital dynamics. 12 Different times R Pw Curve showing the change with Δt;

[0057] Figure 5 This invention provides a method for formulating a winning strategy based on a two-to-one pursuit and escape game on an orbital plane, under different maneuverability conditions for R. Pw Curve showing the change with Δt;

[0058] Figure 6 This is a schematic diagram of the system for formulating a winning strategy based on a two-to-one pursuit and escape game of the present invention.

[0059] Figure 7 This is a schematic diagram of an electronic device in an embodiment of the present invention. Detailed Implementation

[0060] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0061] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0062] Existing technologies for two-on-one pursuit and escape games in orbit primarily focus on strategy design within a single pursuit scenario, making it difficult to grasp the evolutionary patterns of the pursuit and escape game from a global perspective. This results in the inability to formulate efficient pursuit and escape strategies for the complex space environment. This invention provides a method for formulating a winning strategy based on a two-on-one pursuit and escape game in orbit, comprising:

[0063] Obtain parameter information of participants in a two-to-one pursuit and escape game on the track;

[0064] Based on the parameter information of the participants in the two-to-one pursuit game, the impact on the game outcome is analyzed, and the game results are generated.

[0065] Develop winning strategies based on the analysis of the game's outcome.

[0066] The present invention will be explained in detail below.

[0067] This invention provides a method for studying the winning mechanism of a two-to-one pursuit-escape game, comprising the following steps:

[0068] S1: Obtain parameter information of the game participants, including the reference spacecraft's orbital altitude H, the orbital altitude difference h between the pursuing spacecraft and the reference spacecraft, and the initial states X of the first pursuer P1, the second pursuer P2, and the escapee E. P1 ,X P2 ,X E Pulse velocity increment ΔV, pulse time interval Δt, etc.

[0069] Assuming the reference spacecraft's orbit is a geostationary orbit (GEO), its orbital radius is denoted as R. e +H, where R e Let R represent the Earth's radius, and H represent the altitude of the geostationary orbit. The first pursuer P1 and the second pursuer P2 are located in the same orbital plane as the escapee E, but at different orbital altitudes. Their orbital radii are denoted as R. e+H+h, where h is the vertical height difference between the two pursuers relative to the escapee E. The two pursuers are at horizontal distances from the escapee, denoted as L1 and L2, where L1 is the horizontal distance between the first pursuer P1 and the escapee E, and L2 is the horizontal distance between the second pursuer P2 and the escapee E. The relative distance between the two pursuers is L. 12 =L1-L2. The escapee E starts at the origin of the local vertical-horizontal coordinate system (LVLH), and its orbital radius is denoted as R. e +H, the state of the escapee E in the game process can be represented as: The initial positions of the two pursuers are determined based on their respective orbital altitudes, and their state variables can be expressed as: the state variable of the first pursuer. The state quantity of the second pursuer Since the two pursuers differ from the escapee E only in orbital altitude, according to orbital dynamics theory, their initial state exhibits a constant horizontal drift relative to the escapee, known as east-west drift. The simulation conditions for the initial east-west drift scenario are shown in Table 1.

[0070] Table 1 Initial conditions for simulation

[0071]

[0072] S2: Analyze the impact of initial relative positions on the game outcome.

[0073] Given a fixed pulse time interval Δt and the magnitude of the pulse velocity increments for both the pursuer and the pursuer, the Monte Carlo method is used to calculate the relative minimum distances between points within a certain location area.

[0074] S21: Set the initial relative distance L between the two pursuers. 12 And calculate the minimum relative distance between the pursuer and the escapee throughout the entire game, denoted as D. min .

[0075] D min The formula is given by formula (1). When performing the calculation, the initial midpoint position x of the two pursuers should be ensured. P (h,l,0) falls within a specific region of the orbital plane, where

[0076]

[0077] The method for calculating the positions of the first pursuer P1, the second pursuer P2, and the escapee E during the game is shown in formula (2):

[0078]

[0079] For spacecraft state variables; n is the total number of pulse control applications; B = [0 3×3 ;I 3×3 ];ΔV(t j ) for the spacecraft at t j The pulse velocity increment applied at time t; Φ(t) f ,t j ) indicates from t f to t j The state transition matrix under the given state is represented as shown in equation (3):

[0080]

[0081] S22: Draw D min A graph showing the relationship between the value and various initial positions of the pursuers. The l and h values ​​at the midpoint of the two pursuers are used as the x and y axes, respectively, with different colors representing different values ​​of D. min The magnitude of the value.

[0082] S23: Modify the relative distance between the two pursuers. 12 Given the value of E, repeat the previous steps and analyze how the initial position of the pursuer relative to the escapee E will affect the game outcome by comparing the results.

[0083] S3: Analyze the impact of pulse time intervals on the game outcome. Given a fixed magnitude of the pursuer's pulse velocity increment, statistically analyze the impact of different pulse time intervals on the game outcome under different initial relative distances.

[0084] S31: To more conveniently and effectively assess the correlation between parameter changes and game outcomes, the "pursuer's winning area percentage" (R) is introduced. Pw This indicator measures the relative distance L between the two pursuers. 12 The game in each scenario is condensed into a single data point. R Pw This ratio is defined as follows:

[0085]

[0086] Among them, A Pw A represents the number of initial positions successfully pursued within the current location range. t This represents the total number of initial positions considered in the simulation. Then, the average minimum relative distance between the pursuer and the escapee at all initial positions in the game is calculated, denoted as...

[0087] S32: When the initial relative distance between the pursuer and the pursuer changes, respectively, calculate the relationship between the proportion of the pursuer's winning area and the pulse time interval.

[0088] S4: Analyze the impact of maneuverability on the game outcome. Given a fixed initial relative distance, statistically analyze the impact of different maneuverability levels on the game outcome.

[0089] First, determine the relative distance L between the two pursuers. 12 We assume a fixed scenario and only consider the case where both pursuers have the same pulse magnitude. Based on this, we analyze the combined effect of pulse interval and pulse magnitude. Due to mobility limitations, we select the pursuer's pulse velocity increment ΔV. P The pulse velocity increment ΔV of the escapee E The ratios are 1, 2, 3, 4, and 5, and the percentage of the pursuer's winning area (R) is plotted for each of these scenarios. Pw The curves showing the changes in pulse interval and their trends were analyzed.

[0090] S5: Develop winning strategies. Based on the simulation results, develop effective pursuit and winning strategies, including the optimal initial relative distance of the pursuer, the optimal pulse time interval, and the optimal maneuverability.

[0091] In summary, this invention provides a method for studying the winning mechanism of a two-to-one pursuit-escape game in orbit. Compared with traditional methods, it is no longer limited to a single factor or simplified model, but establishes a more comprehensive and systematic game strategy by fully considering multiple key factors. Through simulation analysis of factors such as initial relative position, pulse time interval, and maneuverability, this invention can provide targeted winning strategies for different pursuit-escape scenarios, improving the success rate and efficiency of operations. This invention fully utilizes the orbital dynamics characteristics of spacecraft, and its research method is relatively simple and widely applicable, filling a gap in current research and providing a theoretical basis for practical space orbital game missions.

[0092] The present invention will be further explained and illustrated below with reference to specific embodiments.

[0093] Example

[0094] To demonstrate the effectiveness of the algorithm, a two-to-one pulsed cooperative game scenario occurring within the GEO orbital plane is used as an example to verify its effectiveness. First, the game scenario parameter settings are given, as shown in Table 2:

[0095] Table 2 Reference Spacecraft Orbital Elements

[0096] orbital elements a / km e / 1 i / rad Ω / rad ω / rad <![CDATA[f0 / rad]]> Reference spacecraft 35786 0 0 0 0 0

[0097] In this example, during the orbital game, three spacecraft—P1, P2, and E—simultaneously apply pulses, with a maximum number of pulses of N = 20 for each spacecraft and a fixed pulse interval. The pulse sizes of P1, P2, and E are fixed, with the pulse sizes of the two pursuers being equal each time, and each spacecraft can only apply a pulse in one direction at a time. The orbital game task now requires either P1 or P2 to get as close as possible to E before the task ends, while E must get as far away as possible from both P1 and P2.

[0098] The specific implementation steps of this invention are given below:

[0099] S1: Obtain parameter information of the game participants, including the reference spacecraft's orbital altitude H, the orbital altitude difference h between the pursuing spacecraft and the reference spacecraft, and the initial states of the first pursuer P1, the second pursuer P2, and the escapee E. Pulse velocity increment ΔV, pulse time interval Δt, etc.

[0100] Assuming the reference spacecraft's orbit is a geostationary orbit (GEO), its orbital radius is denoted as R. e +H, where R e Let R represent the Earth's radius, and H represent the altitude of the geostationary orbit. The first pursuer P1 and the second pursuer P2 are located in the same orbital plane as the escapee E, but at different orbital altitudes. Their orbital radii are denoted as R. e +H+h, where h is the vertical height difference between the two pursuers relative to the escapee E. For example... Figure 2 As shown, the two pursuers are at horizontal distances from the escapee, denoted as L1 and L2. L1 is the horizontal distance between the first pursuer P1 and the escapee E, and L2 is the horizontal distance between the second pursuer P2 and the escapee E. The relative distance between the two pursuers is L. 12 =L1-L2. The escapee E starts at the origin of the local vertical-horizontal coordinate system (LVLH), and its orbital radius is denoted as R. e +H, the state of the escapee E in the game process can be represented as: The initial positions of the two pursuers are determined based on their respective orbital altitudes, and their state variables can be expressed as: the state variable of the first pursuer. The state quantity of the second pursuer Since the two pursuers differ from the escapee E only in orbital altitude, according to orbital dynamics theory, their initial states exhibit a constant horizontal drift relative to the escapee, known as east-west drift.

[0101] S2: Analyze the impact of initial relative positions on the game outcome. Given a fixed pulse time interval Δt and the magnitude of the pulse velocity increment ΔV for both the pursuer and the pursuer, use the Monte Carlo method to calculate the minimum relative distances between points within a certain location area.

[0102] S21: Set the initial relative distance L between the two pursuers. 12 And calculate the minimum relative distance between the pursuer and the escapee throughout the entire game, denoted as D. min D min The formula is given by formula (1). When performing the calculation, the initial midpoint position x of the two pursuers should be ensured. P (h,l,0) falls within a specific region of the orbital plane, where

[0103]

[0104] The method for calculating the positions of the first pursuer P1, the second pursuer P2, and the escapee E during the game is shown in formula (2):

[0105]

[0106] For spacecraft state variables; n is the total number of pulse control applications; B = [0 3×3 ;I 3×3 ];ΔV(t j ) for the spacecraft at t j The pulse velocity increment applied at time t; Φ(t) f ,t j ) indicates from t f to t j The state transition matrix under the given state is represented as shown in equation (3):

[0107]

[0108] Δt = t - t0;

[0109] S22: Draw D min A graph showing the relationship between the value and various initial positions of the pursuers. The l and h values ​​at the midpoint of the two pursuers are used as the x and y axes, respectively, with different colors representing different values ​​of D. min The magnitude of the value.

[0110] S23: Modify the relative distance between the two pursuers. 12 Given the value of E, repeat the previous steps and analyze how the initial position of the pursuer relative to the escapee E will affect the game outcome by comparing the results.

[0111] Figure 3It represents the relative distance L between the two pursuers. 12 What is the minimum relative distance D between the midpoint of the two pursuers and the pursuer and the escapee, given distances of 0km and 10km respectively? min The diagram shows the relationship between the two pursuers, with the dark purple area representing successful pursuit scenarios. It can be seen that for the pursuers, their optimal starting position should be as close to the minor axis as possible. Furthermore, with the initial relative distance L between the two pursuers... 12 With the increase in the number of targets, the winning area of ​​the pursuer expands accordingly, and the overall success rate also increases accordingly.

[0112] S3: Analyze the impact of pulse time intervals on the game outcome. Given a fixed magnitude of the pulse velocity increments for both the pursuer and the escapee, statistically analyze the impact of different pulse time intervals on the game outcome under varying initial relative distances.

[0113] S31: To more conveniently and effectively assess the correlation between parameter changes and game outcomes, the "pursuer's winning area percentage" (R) is introduced. Pw This indicator measures the relative distance L between the two pursuers. 12 The game in each scenario is condensed into a single data point. R Pw The definition is as follows:

[0114]

[0115] Among them, A Pw A represents the number of initial positions successfully pursued within the current location range. t This represents the total number of initial positions considered in the simulation. Then, the average minimum relative distance between the pursuer and the escapee at all initial positions in the game is calculated, denoted as...

[0116] S32: When the initial relative distance between the pursuer and the pursuer changes, respectively, calculate the relationship between the proportion of the pursuer's winning area and the pulse time interval.

[0117] like Figure 4 As shown, the relative distance L between the two pursuers 12 The percentage of the pursuer's winning area R when the distances are 0km, 10km, 30km, and 50km respectively. PwThe pulse interval exhibits a certain linear relationship. When the pulse interval is extremely short, due to fuel limitations, the total number of rounds n is constant, resulting in a very short total game time, leaving the pursuer insufficient time for natural orbital transfer. As the pulse interval increases to its maximum value, the influence of pulse control counteracts the influence of orbital dynamics, increasing the success rate of the pursuit. However, as the pulse interval continues to increase, the spacecraft's position change due to natural transfer becomes more significant. At this stage, the game outcome is mainly affected by the initial distance between the pursuer and the escapee, leading to a decrease in the proportion of the pursuer's winning area R. Pw It gradually decreases. It is worth noting that when the pursuers do not initially start from the same location, the relative distance L between the two pursuers... 12 Increasing the value of the pulse interval will result in a slight increase in the optimal pulse interval, and the success rate will also increase accordingly.

[0118] S4: Analyze the impact of maneuverability on the game outcome. Given a fixed initial relative distance, statistically analyze the impact of different maneuverability levels on the game outcome.

[0119] First, we fix the situation and only consider the case where both pursuers have the same pulse magnitude. Based on this, we analyze the combined effect of pulse interval and pulse magnitude. Due to mobility limitations, we select the pulse velocity increment ΔV of the pursuer. P The pulse velocity increment ΔV of the escapee E The ratios are 1, 2, 3, 4, and 5, and the percentage of the pursuer's winning area (R) is plotted for each of these scenarios. Pw The curves showing the changes in pulse interval and their trends were analyzed.

[0120] like Figure 5 The given curves represent the percentage of the pursuer's winning region R when the pursuer's pulse velocity increments are 1 m / s, 2 m / s, 3 m / s, 4 m / s, and 5 m / s. Pw The trend of change with pulse interval. Except for ΔV P / ΔV E Except when the value is 1, as the pulse time interval increases, the percentage of the pursuer's winning area R increases. Pw The trend is an initial increase followed by a decrease. This overall trend resembles a downward-opening quadratic curve. Therefore, we can analyze and conclude that a larger or smaller pulse interval is not necessarily better; rather, there exists an optimal intermediate value that depends on the ratio of the pulse velocity increments between the pursuer and the escapee. The smaller this ratio, the smaller the optimal pulse interval; conversely, the larger this ratio, the larger the optimal pulse interval. In our given example, the optimal pulse interval is approximately in the range of 15 to 25 minutes.

[0121] S5: Develop winning strategies. Based on the simulation results, develop effective pursuit and winning strategies, including the optimal initial relative distance of the pursuer, the optimal pulse time interval, and the optimal maneuverability.

[0122] The simulation results from the above steps show that, in order to achieve a better pursuit effect, the two pursuers should start from different positions on the same track and be spaced a distance apart. At the same time, the pulse time interval should ideally be between 15 and 25 minutes and should be slightly adjusted according to the maneuverability to deal with the coupling effect between the two and improve the success rate of the pursuit.

[0123] The second objective of this invention is to propose a system for formulating winning strategies based on a two-to-one pursuit-escape game, such as... Figure 6 As shown, it includes:

[0124] Information Acquisition Module: Used to acquire parameter information of participants in the two-on-one pursuit and escape game on the track;

[0125] Analysis Results Module: Used to analyze the impact of parameter information of participants in a two-to-one pursuit game on the game outcome and generate analysis results.

[0126] Strategy formulation module: Used to formulate winning strategies based on the analysis of game results.

[0127] like Figure 7 As shown, a third objective of this invention is to provide an electronic device comprising a processor, a memory, and a display screen. The memory and display screen are both connected to the processor, such as via a bus. Optionally, the electronic device may further include a transceiver. It should be noted that in practical applications, the transceiver is not limited to one unit, and the structure of this electronic device does not constitute a limitation on the embodiments of this application.

[0128] The processor can be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. The processor can also be a combination that implements computational functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0129] A bus can include a pathway for transmitting information between the aforementioned components. The bus can be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc.

[0130] The memory may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited to these.

[0131] The memory stores the application code that executes the solution of this application, and its execution is controlled by the processor. The processor executes the application code stored in the memory to implement the content shown in the foregoing method embodiments.

[0132] Figure 7 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0133] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, performs the aforementioned functions. Figure 1 The illustrated method embodiments include various processes. For example, a memory may include instructions that can be executed by a processor of an electronic device to perform the described method.

[0134] A computer-readable storage medium can be a tangible device that holds and stores instructions used by an instruction execution device. A computer-readable storage medium can be, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof. Specifically, a computer-readable storage medium can be a portable computer disk, a hard disk, a USB flash drive, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), staging random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory stick, floppy disk, optical disk, magnetic disk, mechanical encoding device, or any combination thereof.

[0135] A fifth objective of this invention is to provide a computer program product comprising computer instructions that, when executed by a processor, implement the above-described... Figure 1 The various processes of the method embodiments shown can achieve the same technical effect, and will not be described again here to avoid repetition.

[0136] Many embodiments and applications beyond the examples provided will be apparent to those skilled in the art upon reading the foregoing description. Therefore, the scope of this teaching should not be determined by reference to the foregoing description, but rather by reference to the foregoing claims and the full scope of their equivalents. For purposes of completeness, all articles and references, including patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended as a waiver of that subject matter, nor should it be construed as an indication that the applicant has not considered that subject matter as part of the disclosed inventive subject matter.

[0137] The above content provides a further detailed description of the present invention. It should not be construed that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention as defined by the submitted claims.

Claims

1. A method for formulating a winning strategy based on a two-to-one pursuit-escape game, characterized in that, include: Obtain parameter information of participants in a two-to-one pursuit and escape game on the track; Based on the parameter information of the participants in the two-to-one pursuit game, the impact on the game outcome is analyzed, and the game results are generated. Develop winning strategies based on the analysis of the game's outcome; The parameter information of the participants in the two-to-one pursuit and escape game is obtained, including the orbital altitude of the reference spacecraft, the difference in orbital altitude between the pursuing spacecraft and the reference spacecraft, the initial states of the pursuer and the escapee, the pulse velocity increment, and the pulse time interval. The analysis of the impact of the initial relative positions of the pursuer and the escapee on the game outcome, based on the parameter information of the participants in a two-to-one pursuit game, includes: Given that the pulse time intervals of the participants in a two-on-one pursuit-escape game and the maneuverability of both the pursuer and the escapee are determined, the minimum relative distance between the pursuer and the escapee in a certain location area during the entire game process can be statistically determined using the Monte Carlo method. Plot a graph showing the relationship between the minimum relative distance between the pursuer and the escapee and the initial position of the pursuer; Based on the aforementioned relationship diagram, the impact of the pursuer's initial position relative to the escapee on the game outcome is analyzed by comparing the results. Among them, the minimum relative distance between the pursuer and the escapee includes: In the formula: E represents the player; P represents the pursuer; For the pursuer's state variables; The state variables of the game players; The analysis of the impact of pulse time intervals on the game outcome based on the parameter information of the participants in the two-to-one pursuit game includes: In a two-on-one chase game, given a fixed increment in the pursuer's pulse velocity, the relationship between the proportion of the pursuer's winning area and the pulse time interval is statistically analyzed when the initial relative distance between the pursuers changes. Based on the relationship between the percentage of winning areas for the pursuers and the pulse time interval, the influence of the size of different pulse time intervals on the game outcome under different initial relative distances is analyzed. The percentage of areas where the pursuers won was [percentage missing]. In the formula, To determine the percentage of the area where the pursuer wins, each The game-playing situation is condensed into a single data point; The relative distance between the two pursuers; The initial number of successful pursuits within the current location range; This represents the total number of initial positions considered in the simulation. The analysis of the impact of maneuverability on the game outcome based on the parameter information of the participants in the two-to-one pursuit game includes: The relative distance between the two pursuers With the pulse magnitudes of the two pursuers fixed, the pulse velocity increment for each pursuer is selected. Pulse velocity increment of the escapee The ratio; Based on the selected pursuer's pulse velocity increment Pulse velocity increment of the escapee The ratio of the two values ​​is used to plot the percentage of the pursuer's winning area. The curve showing the change in pulse interval; Based on the percentage of the pursuer's winning area... The curves showing the changes in maneuverability and pulse interval are used to analyze the impact of maneuverability on the game outcome.

2. The method for formulating a winning strategy based on a two-to-one pursuit-escape game according to claim 1, characterized in that, The winning strategy is formulated based on the analysis of the game results, which yields the optimal initial relative distance of the pursuer, the optimal pulse time interval, and the optimal maneuverability.

3. A system for formulating a winning strategy based on a two-to-one pursuit and escape game, based on the method for formulating a winning strategy based on a two-to-one pursuit and escape game according to any one of claims 1-2, characterized in that, include: Information Acquisition Module: Used to acquire parameter information of participants in the two-on-one pursuit and escape game on the track; Analysis Results Module: Used to analyze the impact of parameter information of participants in a two-to-one pursuit game on the game outcome and generate analysis results. Strategy formulation module: Used to formulate winning strategies based on the analysis of game results.

4. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for formulating a winning strategy based on a two-to-one pursuit game of orbits as described in any one of claims 1-2.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method for formulating a winning strategy based on a two-to-one pursuit and escape game according to any one of claims 1-2.

6. A computer program product, characterized in that, The method includes computer instructions that, when executed by a processor, implement the steps of a method for formulating a winning strategy based on a two-to-one pursuit game of orbits as described in any one of claims 1-2.

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