A high-orbit satellite pulse pursuit game strategy solving method based on mixed game

Abstract

The application discloses a high-orbit satellite pursuit-escape game strategy solving method based on a mixed game, belongs to the technical field of spaceflight, and is characterized in that, according to the characteristic that a high-orbit satellite needs to return to an original orbit in a pulse maneuver, the special situation is analyzed, the pursuit-escape strategy of a pursuit satellite and an escape satellite is determined, a pursuit-escape game model is designed by using a simple two-pulse maneuver mode, the idea of the mixed game is introduced, a linear programming method is adopted, the solving idea of the high-orbit satellite game is specifically analyzed, the best mixed game solution is obtained, and the method has the advantages of being intuitive and convenient to solve. Meanwhile, the application supplements the related design method of the existing high-orbit satellite pursuit-escape game strategy research, and provides ideas and technical support for subsequent engineering application.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a method for solving a high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory. Background Technology

[0002] For rendezvous problems involving non-cooperative targets, such as approaching or capturing out-of-control or malfunctioning spacecraft or space debris, the problem requiring active maneuvering of the spacecraft to approach can be regarded as a typical orbital pursuit and escape problem.

[0003] Current research on spacecraft pursuit-escape game theory largely employs differential strategies, with some using classical guidance and control theory and optimal guidance and control theory. However, while spacecraft in-orbit transfers frequently utilize pulse maneuvers, research on pursuit-escape game strategies for these pulse maneuvers is limited. Therefore, studying pulse-based pursuit-escape game theory is highly significant. Since the target is a high-orbit satellite, which requires its original orbit to perform its specific functions, it will eventually return to its original orbit during the pursuit process. For this special case, game theory can be applied to study pursuit-escape game strategies. To fill this research gap, this invention proposes a method for solving high-orbit satellite pulse pursuit-escape game strategies based on hybrid game theory. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a solution method for high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory, so as to solve the technical problem that the research on the pursuit and escape game strategy of spacecraft pulse maneuvering in the prior art is not intuitive.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for solving a high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory includes:

[0007] Obtain the orbital altitude and the initial status of the pursuing and escaping satellites;

[0008] The pursuit and escape strategies for the pursuing and escaping satellites are determined based on their orbital altitudes.

[0009] The pulse velocity increment under different pursuit and escape strategies was calculated using a two-pulse maneuver method.

[0010] Based on the determined pursuit strategy and the calculated pulse velocity increment, a hybrid strategy matrix game is established, and the hybrid strategy solution is calculated.

[0011] Preferably, the determined pursuit strategy for the pursuing satellite P and the escaping satellite E is as follows:

[0012] Pursuit Strategy

[0013] escape strategy

[0014] Where m is the total number of strategies available for pursuing satellites, and n is the total number of strategies available for escaping satellites.

[0015] Preferably, the pulse velocity increment under different pursuit and escape strategies is calculated using a two-pulse method, specifically including:

[0016]

[0017] in

[0018]

[0019] at the same time

[0020]

[0021] Substituting the initial and final states of the pursuing satellite and the escaping satellite into the above equation, we obtain the corresponding two-pulse pulses. , ;

[0022] in, For the initial pulse velocity increment, The second pulse velocity increment, P is the index of the pursuing satellite, and E is the index of the escaping satellite. The state at time t, For arrival time, Here is the state transition matrix of the CW equation. This is the pulse transition time.

[0023] Preferably, a hybrid strategy matrix game is established based on the determined pursuit and escape strategy and the calculated pulse velocity increment. ,

[0024] , ,

[0025] in As a pursuit strategy, For the escape strategy, m is the total number of existing strategies for pursuing the satellite, and n is the total number of existing strategies for escaping the satellite. A hybrid strategy set for tracking satellites. A set of hybrid strategies for escaping satellites.

[0026] Preferably,

[0027]

[0028]

[0029] , This refers to a hybrid strategy that involves both pursuing and escaping satellites.

[0030]

[0031] The expected payoff function for the escaping satellite;

[0032] in, The game value.

[0033] Preferably, both sides in the pursuit and manhunt select their strategies based on the principle of "choosing the most favorable outcome from the worst-case scenario."

[0034] The decision-making criteria for tracking satellites are to adopt a hybrid strategy. This makes the expected payoff function at most 1. ,

[0035] The decision-making criterion for escape satellites is to adopt a hybrid strategy. Such that the expected payoff function is not less than

[0036] in, A hybrid strategy for tracking satellites, A hybrid strategy for escaping satellites.

[0037] Preferably, the mixed strategy matrix game is obtained. Solution Make

[0038]

[0039] Game value for

[0040]

[0041] in To track satellites Strategy, escaping satellite adopts After the strategy is implemented, the relative distance at the final state of the pursuing satellite is as follows:

[0042]

[0043] in

[0044]

[0045]

[0046] It is the relative distance weighting coefficient of the pursuit satellite. It is the fuel weighting coefficient for tracking satellites. It is the fuel weighting coefficient for escape satellites. For the initial pulse velocity increment, The second pulse velocity increment is represented by P, which is the index of the pursuing satellite, and E is the index of the escaping satellite.

[0047] Preferably, when matrix game If there are non-positive elements in A, add a sufficiently large positive number M to all elements in A. , At this point, all elements in B are positive. The matrix game problem is then solved using linear programming.

[0048]

[0049] and

[0050]

[0051] Find the optimal solution , Matrix game The value is:

[0052]

[0053] Matrix Game Solution for:

[0054] ,

[0055] When matrix game The solution when there are non-positive elements in A is:

[0056]

[0057] in, The optimal hybrid strategy for tracking satellites, The optimal hybrid strategy for escaping satellites is... Let i be the probability of choosing pursuit strategy i. Let i be the probability of choosing escape strategy i. , All of these are optimal solutions.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] This invention presents a method for solving a high-orbit satellite pulse pursuit-escape game strategy based on hybrid game theory. Taking into account the characteristic that high-orbit satellites need to return to their original orbit during pulse maneuvers, this special case is analyzed to determine the pursuit and escape strategies of the pursuing and escaping satellites. A pursuit-escape game model is designed using a simple two-pulse maneuver, and the concept of hybrid game theory is introduced. A linear programming method is employed to specifically analyze the solution approach for the high-orbit satellite game, obtaining the optimal hybrid game solution. This method has the advantages of being intuitive and easy to solve. Furthermore, this invention supplements existing design methods for high-orbit satellite pursuit-escape game strategies, providing ideas and technical support for subsequent engineering applications. Attached Figure Description

[0060] Figure 1 This is the main flowchart of the present invention;

[0061] Figure 2 This is the main flowchart of the hybrid strategy matrix game of the present invention;

[0062] Figure 3 This is a schematic diagram of the satellite pursuit strategy of the present invention;

[0063] Figure 4 This is a schematic diagram of the escape strategy for the escape satellite of the present invention. Detailed Implementation

[0064] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0065] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0066] The present invention will now be described in further detail with reference to the accompanying drawings:

[0067] The purpose of this invention is to construct a method for solving a high-orbit satellite pulse pursuit-escape game strategy based on hybrid game theory, focusing on the pursuit-escape game problem between non-cooperative targets in high-orbit satellites. The specific research steps are as follows:

[0068] Obtain the orbital altitude and the initial status of the pursuing and escaping satellites;

[0069] The pursuit and escape strategies for the pursuing and escaping satellites are determined based on their orbital altitudes.

[0070] Calculate the pulse velocity increment under different pursuit and escape strategies;

[0071] Based on the determined pursuit strategy and the calculated pulse velocity increment, a hybrid strategy matrix game is established, and the hybrid strategy solution is calculated.

[0072] Given the orbital altitude H of the high-orbit satellite, the initial state of the pursuing satellite is: The initial state of the escaping satellite is First, establish the existing pursuit strategies for the pursuing satellite P and the fleeing satellite E. and escape strategy , where m is the total number of existing strategies for pursuing satellites, and n is the total number of existing strategies for escaping satellites.

[0073] Assuming both sides implement pursuit strategies simultaneously. and escape strategy All have gone through Arrive at the corresponding location after the time has elapsed. and The spacecraft orbit transfers here are all performed using a two-pulse method, as shown in the following equations:

[0074]

[0075] in

[0076]

[0077] at the same time

[0078]

[0079] Substituting the initial and final states of the pursuing satellite and the escaping satellite into the above equation, we obtain the corresponding two-pulse pulses. , .

[0080] Establishing a hybrid strategy matrix game ,in

[0081] , ,

[0082] remember

[0083]

[0084]

[0085] Then it is called and These are hybrid strategy sets for pursuing satellites and escaping satellites, respectively. , This refers to a hybrid strategy that involves both pursuing and escaping satellites.

[0086]

[0087] Let the expected payoff function be the payoff function for the escaping satellite. Both the pursuer and the pursuer choose strategies based on the principle of "selecting the most favorable outcome from the worst-case scenario." The decision criterion for pursuing the satellite is to find a hybrid strategy. This makes the expected payoff function at most 1. The decision-making criteria for escaping satellites are to adopt a hybrid strategy. Such that the expected payoff function is not less than .

[0088] Find the mixed strategy matrix game Solution Make

[0089]

[0090] Let the game value be... for

[0091]

[0092] Game value It is related to the relative distance between the pursuing and fugitive parties and fuel consumption. Among them To track satellites Strategy, escaping satellite adopts After the strategy is implemented, the relative distance at the final state of the pursuing satellite is as follows:

[0093]

[0094] in

[0095]

[0096]

[0097] It is the relative distance weighting coefficient of the pursuit satellite. It is the fuel weighting coefficient for tracking satellites. It is the fuel weighting coefficient for the escape satellite.

[0098] When matrix game If there are non-positive elements in A, add a sufficiently large positive number M to all elements in A. , At this point, all elements in B are positive numbers. The above matrix game problem is then solved using linear programming.

[0099]

[0100] and

[0101]

[0102] Find the optimal solution , Matrix game The value is:

[0103]

[0104] Matrix Game Solution for:

[0105] ,

[0106] The value of the original problem is:

[0107]

Example

[0108] See Figures 1-4 Assume that both the pursuing satellite P and the escaping satellite E are in a circular orbit with an altitude of 42,000 km, and their initial states are shown in Table 1.

[0109] Table 1. Initial relative position and velocity (km, km / s) between the pursuing satellite P and the fleeing satellite E

[0110]

[0111] At a certain initial moment The pursuing satellite and the escape satellite simultaneously make pursuit decisions at their respective locations. and Both employ a two-pulse transfer, and after the transfer pulse time... Then it returned to the original track.

[0112] First, assume that the pursuing satellite P and the fleeing satellite E have existing pursuit strategies. and escape strategy The pursuit strategies represent:

[0113] Tracking in the positive Y-axis direction Strategy :

[0114] Tracking in the positive Y-axis direction Strategy :

[0115] Tracking in the positive Y-axis direction Strategy :

[0116] Among them, take , , .

[0117] The escape strategies represent:

[0118] Y-axis positive direction escape strategy :

[0119] non-maneuvering strategy :

[0120] Y-axis negative direction tracking strategy :

[0121] The initial state of the pursuing satellite is known to be The initial state of the escaping satellite is At the same time, a pursuit strategy was implemented. and escape strategy All have gone through Arrive at the corresponding location after the time has elapsed. and The spacecraft orbit transfers here are all performed using a two-pulse method, as shown in the following equations:

[0122]

[0123] in

[0124]

[0125] at the same time

[0126]

[0127] Different strategies for pursuing satellites result in different final states. Substituting the initial and final states of pursuing satellites in all cases into the above formula, the corresponding two pulses are obtained as shown in Table 2 below.

[0128] Table 2. Pulse velocity increments (m / s) under different strategies for pursuing satellite P and escaping satellite E.

[0129]

[0130] Establishing a hybrid strategy matrix game ,in

[0131] , ,

[0132] remember

[0133]

[0134]

[0135] Then it is called and These are hybrid strategy sets for pursuing satellites and escaping satellites, respectively. , This refers to a hybrid strategy that involves both pursuing and escaping satellites.

[0136]

[0137] Let the expected payoff function be the payoff function for the escaping satellite. Both the pursuer and the pursuer choose strategies based on the principle of "selecting the most favorable outcome from the worst-case scenario." The decision criterion for pursuing the satellite is to find a hybrid strategy. This makes the expected payoff function at most 1. The decision-making criteria for escaping satellites are to adopt a hybrid strategy. Such that the expected payoff function is not less than .

[0138] Find the mixed strategy matrix game Solution Make

[0139]

[0140] Let the game value be... for

[0141]

[0142] Game value It is related to the relative distance between the pursuing and fugitive parties and fuel consumption. Among them To track satellites Strategy, escaping satellite adopts After the strategy is implemented, the relative distance at the final state of the pursuing satellite is as follows:

[0143]

[0144] in

[0145]

[0146]

[0147] It is the relative distance weighting coefficient of the pursuit satellite. It is the fuel weighting coefficient for tracking satellites. It is the fuel weighting coefficient for the escape satellite.

[0148] This makes , , Substitute to obtain the game value The matrix is ​​shown in Table 3 below.

[0149] Table 3. Game values ​​under different strategies for pursuing satellite P and fleeing satellite E.

[0150]

[0151] When matrix game If there are non-positive elements in A, add a sufficiently large positive number M=10000 to all elements in A. , At this point, all elements in B are positive numbers, as shown in Table 4 below.

[0152] Table 4. Game values ​​under different strategies for pursuing satellite P and fleeing satellite E.

[0153]

[0154] The matrix game problem is then solved using linear programming.

[0155]

[0156] and

[0157]

[0158] Find the optimal solution , , Matrix game The value is:

[0159]

[0160] so .

[0161] Similarly, find , , Matrix game The value is:

[0162]

[0163] so .

[0164] The value of the original problem is:

[0165]

[0166] In summary, this invention discloses a method for solving a pursuit-escape game strategy for high-orbit satellite pulses based on hybrid game theory. The discussion concerns a pursuit-escape game problem between non-cooperative targets in high-orbit satellites. Due to the unique characteristics of high-orbit satellites, the pursuit and escape strategies require returning to the original orbit. Based on this characteristic, specific pursuit-escape strategies are designed, employing a two-pulse maneuver for orbital transfer. Then, hybrid game theory is used to analyze the strategies of both sides, obtaining the optimal probability distribution solution for selecting the pursuit-escape game strategy in this scenario. Specifically, the method includes the following steps:

[0167] 1. Determine the orbital altitude of the high-orbit satellite and the initial state of the satellites of both the pursuing and fleeing parties;

[0168] 2. First, set specific pursuit strategies for both sides of the pursuit satellite, and obtain the corresponding two-pulse velocity increments under different strategies;

[0169] 3. Establish a hybrid game matrix model and set the corresponding game values;

[0170] 4. Substitute the pursuit strategy into the game matrix to obtain the corresponding game matrix. Then, use linear programming to obtain the optimal probability distribution for selecting the pursuit strategy.

[0171] This invention utilizes the ideas of game theory to solve the high-orbit satellite pursuit and escape game problem, and presents a solution method for the high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory, providing design methods and ideas for subsequent high-orbit space attack and defense.

[0172] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for solving a high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory, characterized in that, include: Obtain the orbital altitude and the initial status of the pursuing and escaping satellites; The pursuit and escape strategies for the pursuing and escaping satellites are determined based on their orbital altitudes. The calculation of pulse velocity increments under different pursuit strategies using a two-pulse maneuver method specifically includes: in at the same time Substituting the initial and final states of the pursuing satellite and the escaping satellite into the above equation, we obtain the corresponding two pulses [Δv]. P0 ,Δv P1 ] -1 ,[Δv E0 ,Δv E1 ] -1 ; Based on the determined pursuit strategy and the calculated pulse velocity increment, a hybrid strategy matrix game is established, and the hybrid strategy solution is calculated; specifically including: Mixed strategy matrix game Γ=(U P U E ;A;U′ P ,U′ E ), U P ={U P1 ,U P2 ,…,U Pm },U E ={U E1 ,U E2 ,…,U En },A=(a ij ) m×n X∈U′ P ,Y∈U′ E This refers to a hybrid strategy that involves both pursuing and escaping satellites. The expected payoff function for the escaping satellite; Where Δv0 is the initial pulse velocity increment, Δv1 is the second pulse velocity increment, P is the index of the pursuing satellite, E is the index of the escaping satellite, X(t) is the state at time t, and t is the arrival time. U is the state transition matrix of the CW equation, where Δt is the pulse transition time; P For the pursuit strategy, U E For the escape strategy, m is the total number of existing strategies for pursuing the satellite, n is the total number of existing strategies for escaping the satellite, and U′ P For a hybrid strategy set to track satellites, U′ E A set of hybrid strategies for escaping satellites; a ij The game value.

2. The method for solving the high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory according to claim 1, characterized in that, The established pursuit and escape strategies for the pursuing satellite P and the escaping satellite E are as follows: Chasing Strategy U P ={U P1 ,U P2 ,…,U Pm } Escape Strategy U E ={U E1 U E2 ,…,U En } Where m is the total number of strategies available for pursuing satellites, and n is the total number of strategies available for escaping satellites.

3. The method for solving the high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory according to claim 1, characterized in that, Both sides in the pursuit and manhunt selected their strategies based on the principle of "choosing the most favorable outcome from the worst-case scenario." The decision-making criterion for tracking satellites is to seek a hybrid strategy X. * This makes the expected payoff function at most 1. The decision criterion for the escaping satellite is to seek a hybrid strategy Y. * Such that the expected payoff function is not less than Where X is the hybrid strategy for pursuing satellites, and Y is the hybrid strategy for escaping satellites.

4. The method for solving the high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory according to claim 3, characterized in that, Find the mixed strategy matrix game Γ=(U P U E ;A;U′ P ,U′ E The solution (X) * ,Y * ) makes Game value a ij for Where d ij To track satellites, U-shaped Pi Strategy: Escape satellite uses U Ej After the strategy is implemented, the relative distance at the final state of the pursuing satellite is as follows: in k1 is the weighting coefficient for the relative distance between the tracking satellites, k P It is the fuel weighting coefficient for the pursuit satellite, k E Δv0 is the fuel weighting coefficient of the escaping satellite, Δv1 is the velocity increment of the first pulse, P is the index of the pursuing satellite, and E is the index of the escaping satellite.

5. The method for solving a high-orbit satellite pulse pursuit and escape game strategy based on hybrid game theory according to claim 1, characterized in that, When there are non-positive elements in A in a matrix game Γ, add a sufficiently large positive number M to all elements in A, then B = (b ij ) m×n b ij =a ij +M, at this point, all elements in B are positive. Solving the matrix game problem using linear programming: and Find the optimal solution u * ,w * The value of Γ in the matrix game is: Solution (X) of matrix game Γ * ,Y * )for: The solution to the matrix game Γ when A contains non-positive elements is: Among them, X * To determine the optimal hybrid strategy for tracking satellites, Y * The optimal hybrid strategy for escaping satellites, u i w represents the probability of choosing pursuit strategy i. i For the probability of choosing escape strategy i, u * w * All of these are optimal solutions.

Images