A track pursuit and evasion game strategy solving method based on dynamic game tree search

Abstract

The application discloses a pursuit-escape game strategy solving method based on a dynamic game tree search, and belongs to the technical field of space design. The method comprises the following steps: establishing a pursuit-escape game tree; based on the pursuit-escape game tree and by using a maximum-minimum value search method, a pursuit spacecraft firstly selects a pursuit strategy and outputs a pursuit action in a round; after detecting a maneuver of the pursuit spacecraft, an escape spacecraft selects an escape strategy and outputs an escape action in the round; the pursuit spacecraft and the escape spacecraft sequentially perform game respectively, and whether a pursuit success condition is met is judged, so that the best strategy of the pursuit spacecraft and the escape spacecraft is obtained.

Description

Technical Field

[0001] This invention belongs to the field of aerospace design technology, specifically relating to a method for solving orbital pursuit and escape game strategies based on dynamic game tree search. Background Technology

[0002] Orbital pursuit and escape game is the most common orbital game problem in space games. Specifically, it manifests as a pursuing spacecraft actively approaching an escape spacecraft or an escape spacecraft actively moving away from the pursuer.

[0003] Because there is a time delay in spacecraft sensing the opponent's situation during a chase-escape game, and if the satellite cannot perform autonomous relative navigation and decision-making control in orbit but requires ground station assistance for sensing, decision-making, and remote control, there is a time delay between two adjacent maneuvers. Current research on spacecraft chase-escape games often uses differential game theory, neglecting the time delay between sensing and decision-making between chasing and fleeing spacecraft, and assuming that the chase-escape game is instantaneous and continuous, which does not conform to reality. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to provide a method for solving orbital pursuit and escape game strategies based on dynamic game tree search. Based on the characteristics of satellite pursuit and escape games, a sequential turn-based game is proposed, in which one party performs an orbital maneuver first, and the other party needs a certain delay before it can perform an orbital maneuver. Furthermore, due to the delay of the turn-based system, pulse control is adopted. It is only necessary to know the initial and final states of the orbital transfer and the states of several intermediate points to obtain the pulse control to be applied, thus solving the problem of pulse pursuit and escape game strategy.

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

[0006] This invention provides a method for solving orbital pursuit and escape game strategies based on dynamic game tree search, comprising the following steps:

[0007] S1: Establish the pursuit and escape game tree;

[0008] S2: Based on the pursuit-escape game tree and using the minimax search method, the pursuing spacecraft first selects a pursuit strategy and outputs the pursuit action for the current round; the escaping spacecraft selects an escape strategy after detecting the maneuver of the pursuing spacecraft and outputs the escape action for the current round.

[0009] S3: The pursuing spacecraft and the escaping spacecraft engage in sequential gameplay to determine whether the conditions for a successful pursuit are met, and to obtain the optimal strategies for the pursuing and escaping spacecraft.

[0010] In the specific implementation process, the establishment of the pursuit game tree includes the following steps:

[0011] S11: Establish an orbital coordinate system based on orbital altitude a and with the initial position of the escaped spacecraft as the origin. In the orbital coordinate system, the X-axis points from the Earth's center to the escaped spacecraft, and the Y-axis points to the velocity direction within the orbital plane where the escaped spacecraft is located.

[0012] S12: Set the existing escape action set for each round of the escape spacecraft U E ={U E1 U E2 ,…,U Ed} and the existing set of pursuit actions U for each round of pursuing the spacecraft P ={U P1 U P2 ,…,U Pk}; Set the game search depth n for the escaping spacecraft, the game search depth m for the pursuing spacecraft, and the conditions for successful pursuit; set the pulse transfer time ΔT and the reaction time Δt;

[0013] S13: Based on the orbital coordinate system, the existing set of escape actions U for each round of the escape spacecraft. E ={U E1 U E2 ,…,U Ed} and the existing set of pursuit actions U for each round of pursuing the spacecraft P ={U P1 U P2 ,…,U Pk The game-theoretic search depth n of the escaping spacecraft, the game-theoretic search depth m of the pursuing spacecraft, the conditions for successful pursuit, the pulse transition time ΔT, and the reaction time Δt are used to construct the pursuit-escape game tree;

[0014] In the above, P represents the pursuing spacecraft; E represents the escaping spacecraft; where d represents the total number of actions taken by the escaping spacecraft, and k represents the total number of actions taken by the pursuing spacecraft.

[0015] In the specific implementation process, the conditions for successful pursuit are as follows:

[0016] The pursuit is successful when the relative distance between the pursuing spacecraft and the fleeing spacecraft is r; the pursuit fails if the pursuing spacecraft fails to catch up with the fleeing spacecraft within N rounds.

[0017] In practice, the pursuit game tree includes the corresponding position X of the pursuing spacecraft after each round of the game. P (t0+ΔT) and the state of the pursuing spacecraft after each round of the game;

[0018] The corresponding position X of the escaping spacecraft after each round of the game. E (t0+Δt+ΔT) and the state of the escaping spacecraft after each round of the game;

[0019] It also includes the relative distances obtained from all combinations of pursuit and escape actions based on the game search depth m of the pursuing spacecraft, and the relative distances obtained from all combinations of pursuit and escape actions based on the game search depth n of the escaping spacecraft.

[0020] In the specific implementation process, the game-theoretic search depth based on the pursuing spacecraft... m The relative distances obtained from all the pursuit and escape actions are as follows:

[0021] Based on the game-theoretic search depth m of the pursuing spacecraft, the relative distance between the pursuer and the fleeing party after m rounds of pulses is obtained as the optimization objective. The relative distance is obtained by calculating the combination of all pursuit and fleeing actions in m rounds of pulses.

[0022] Optimization objective J of pursuing spacecraft P Represented as:

[0023] J P =||M·(X) P (t M )-X E (t M ))||2,t M = t0 + Δt + m·ΔT;

[0024] in:

[0025]

[0026]

[0027] t m =t0+m·ΔT;

[0028] Among them, X P (t M ) is the pursuit spacecraft in t M The state at any given moment; X E (t M ) is the escape spacecraft in t M The state at any given moment; X P (t0) represents the state of the pursuing spacecraft at time t0; X E (t0) is the state of the escaping spacecraft at time t0; M is the matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference; Φ(t M (t0) represents the time from t0 to t... M The CW equation transition matrix at time t; Φ v (t m ,t i-1 ) is t i-1 The velocity transfer matrix of the CW equation from time tm to time tm; Φ v (t M ,ti-1 +Δt) is t i-1 +Δt time to t M The velocity transfer matrix of the CW equation at time t;

[0029] The relative distances obtained from all combinations of pursuit and escape actions based on the game-theoretic search depth n of the escape spacecraft are as follows:

[0030] Based on the game-theoretic search depth n of the escape spacecraft, the relative distance between the pursuer and the escaper after n rounds of pulses is the optimization objective. The relative distance is obtained by calculating the combination of all pursuit and escape actions in n rounds of pulses.

[0031] Optimization objective J E It can be represented as:

[0032] J E =||M·(X) P (t N )-X E (t N ))||2,t N = t0 + Δt + n·ΔT

[0033] in,

[0034]

[0035]

[0036] t n =t0+n·ΔT;

[0037] Among them, X P (t N ) is the pursuit spacecraft in t N The state at any given moment; X E (t N ) is the escape spacecraft in t N The state at time t; Φ(t) N (t0) represents the time from t0 to t... N The CW equation transition matrix at time t; Φ v (t N ,t i-1 +Δt) is t i-1 +Δt time to t N The velocity transfer matrix of the CW equation at time Φ v (t n ,t i-1 ) is t i-1 Time to t n The velocity transfer matrix of the CW equation at time t;

[0038] In the above formula,

[0039] Δv Pi In the chase action series U P ={U P1 U P2 ,…,U Pk Choose from}, and Δv Ei In the escape action series U E ={U E1 U E2 ,…,U Ed Choose from}

[0040] In the specific implementation process, the strategy selection process of the pursuing spacecraft in S2 is as follows:

[0041] Based on the game-theoretic search depth m of the pursuing spacecraft, the relative distance between the pursuer and the pursuer after m rounds of pulses is obtained as the optimization objective. The minimax game tree search method is adopted to search from all nodes after m rounds of pulses. First, the maxima layer search is performed, and then the minima layer search is performed to obtain the corresponding strategy ranking. The strategy of the first round is selected and the corresponding relative distance solution is obtained.

[0042] In the specific implementation process, the method of using the minimax game tree search is adopted. The search is performed from all nodes after the m-round impulse, first a minimax search, then a minimax search, to obtain the corresponding strategy ranking. The process of selecting the strategy for the first round and obtaining the corresponding relative distance solution is as follows:

[0043] Based on the game search depth m of the pursuing spacecraft, the game rounds for both the pursuing and escaping spacecraft are predicted to be m rounds. The number of rounds k is obtained from all strategy combinations. m ·d m One root node;

[0044] Performing a search at the maxima level, when selecting an escape spacecraft pulse, there are d possible escape actions, and k... m ·d m The root nodes are divided into k according to their sorting. m ·d m-1 Each part contains d nodes. The maximum value among these d nodes is selected as the child node of the maxima level, thus obtaining k. m ·d m-1 Number of child nodes;

[0045] Performing a search at the minimum level, when selecting a spacecraft pulse to pursue, there are k possible pursuit actions. The k obtained from the maximum level... m ·d m-1 The child nodes are divided into k according to their sorting. m-1 ·d m-1 Each part contains k nodes. The minimum value among the k nodes is selected as the child node of the minimum layer.

[0046] Similarly, select nodes at the minimum and maximum levels to obtain the solution of the chase-escape game tree for the final m rounds, and output the chase action of the first round.

[0047] In the specific implementation process, in S2, the process by which the escaping spacecraft selects an escape strategy after detecting the maneuvering of the pursuing spacecraft is as follows:

[0048] After detecting the maneuver of the pursuing spacecraft, the escaping spacecraft, based on the game search depth n of the escaping spacecraft, obtains the relative distance between the pursuer and the escaping spacecraft after n rounds of pulses as the optimization objective. It adopts the minimax game tree search method, searches from all nodes after n rounds, first performs the minimax search, then the maxima search, obtains the corresponding strategy ranking, selects the strategy of the first round, and obtains the corresponding relative distance solution.

[0049] In the specific implementation process, the method of using the minimax game tree search is adopted. The search is performed from all nodes after n rounds, first a minimax search, then a maxima search, to obtain the corresponding strategy ranking. The process of selecting the strategy for the first round and obtaining the corresponding relative distance solution is as follows:

[0050] Based on the game search depth n of the escaping spacecraft, the game rounds for both the pursuing and escaping spacecraft are predicted to be n rounds. The number of rounds (k) is obtained from all strategy combinations. n ·d n One root node;

[0051] Performing a search at the minimum level, when selecting a pursuit pulse for the spacecraft, there are k possible pursuit actions. Let k... n ·d n The root nodes are divided into k according to their sorting. n-1 ·d n Each part contains k nodes. The minimum value among these k nodes is selected as the child node of the minimum layer, thus obtaining kmin. n-1 ·d n Number of child nodes;

[0052] When performing a search at the maxima level and selecting an escape spacecraft pulse, there are d possible escape actions. The k obtained from the minima level... n-1 ·d n The child nodes are divided into k according to their sorting. n-1 ·d n-1 There are d parts, each with d nodes. The maximum value among the d parts is selected as the child node of the maxima level.

[0053] Similarly, perform node selection for the minimum and maximum layers to obtain the solution of the chase-escape game tree for the final n rounds, and output the chase action of the first round.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] This invention provides a method for solving orbital pursuit-escape game strategies based on dynamic game tree search, considering the time delay between perception and decision-making, and employing pulse control to address the problem. Due to the perception and decision-making delays, the pursuing spacecraft engages in a sequential game, utilizing pulse maneuvers. The dynamic game tree search method selects solutions satisfying the search criteria from discrete pure strategies, effectively demonstrating the pulse pursuit-escape game scenario. Both sides choose their optimal actions for each round based on their respective game depths, playing within a certain safe distance and a finite number of rounds. Reaching the safe distance within the finite number of rounds results in a successful pursuit; otherwise, the pursuit fails. Finally, the strategies of both pursuing and escape spacecraft are obtained, offering advantages such as intuitiveness and ease of solution, providing ideas and technical support for subsequent engineering applications. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method for solving the orbital pursuit and escape game strategy based on dynamic game tree search according to the present invention.

[0057] Figure 2 This is a schematic diagram of the orbital coordinate system established by the initial position of the escaped spacecraft according to the present invention;

[0058] Figure 3 This is a schematic diagram of the trajectory in the pursuit-escape game of the present invention;

[0059] Figure 4 This is a schematic diagram illustrating the change in the relative distance between the pursuing and fleeing parties in this invention.

[0060] Figure 5 This is a schematic diagram of the pursuit and escape game tree for m rounds according to the present invention;

[0061] Figure 6 This is a schematic diagram of the n-round chase-escape game tree of the present invention;

[0062] Figure 7 This is a schematic diagram of a 3-round chase-escape game tree in an embodiment of the present invention;

[0063] Figure 8 This is a schematic diagram of a one-round chase-escape game tree in an embodiment 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] like Figure 1 As shown, this invention provides a method for solving orbital pursuit-escape game strategies based on dynamic game tree search. In the pursuit-escape problem between non-cooperative satellites, the pursuing spacecraft first performs a pulse maneuver, and then the escaping spacecraft senses the pursuit and attempts to escape. The sequential orbital pursuit-escape game design includes the following steps:

[0068] S1: Establish the pursuit and escape game tree;

[0069] S2: Based on the pursuit-escape game tree and using the minimax search method, the pursuing spacecraft first selects a pursuit strategy and outputs the pursuit action for the current round; the escaping spacecraft selects an escape strategy after detecting the maneuver of the pursuing spacecraft and outputs the escape action for the current round.

[0070] Specifically, based on the game search depth m of the pursuing spacecraft, the relative distance between the pursuer and the fleeing party after m rounds of pulses is obtained as the optimization objective. The minimax game tree search method is adopted to search from all nodes after m rounds of pulses. First, the maxima layer search is performed, and then the minima layer search is performed to obtain the corresponding strategy ranking. The strategy of the first round is selected and the corresponding relative distance solution is obtained.

[0071] After detecting the maneuver of the pursuing spacecraft, the escaping spacecraft, based on the game search depth n of the escaping spacecraft, obtains the relative distance between the pursuer and the escaping spacecraft after n rounds of pulses as the optimization objective. It adopts the minimax game tree search method, searches from all nodes after n rounds, first performs the minimax search, then the maxima search, obtains the corresponding strategy ranking, selects the strategy of the first round, and obtains the corresponding relative distance solution.

[0072] S3: The pursuing and escaping spacecraft sequentially engage in a game to determine if the conditions for a successful pursuit are met, obtaining the optimal strategies for both. Specifically, the pursuing and escaping spacecraft sequentially engage in the game. If, at any given moment, the relative distance between the two spacecraft is less than *r*, the game ends, and the pursuit is successful. If both spacecraft make N decisions but fail to catch up, the pursuit fails. Finally, input the pursuit-escape game strategy for either success or failure.

[0073] The steps involved in establishing the fugitive pursuit game tree are as follows:

[0074] S11: Establish an orbital coordinate system based on orbital altitude a and with the initial position of the escaped spacecraft as the origin. In the orbital coordinate system, the X-axis points from the Earth's center to the escaped spacecraft, and the Y-axis points to the velocity direction within the orbital plane where the escaped spacecraft is located.

[0075] like Figure 2 As shown, the initial state of the escape spacecraft is set as follows: The initial state of the pursuing spacecraft is

[0076] S12: Set the existing escape action set for each round of the escape spacecraft U E ={U E1 U E2 ,…,U Ed} and the existing set of pursuit actions U for each round of pursuing the spacecraft P ={U P1 U P2 ,…,U Pk The game search depth n for the escaping spacecraft and the game search depth m for the pursuing spacecraft are set. The success condition for the pursuit is that the relative distance between the pursuing and escaping spacecraft is r. If the pursuing spacecraft fails to catch up with the escaping spacecraft within N rounds, the pursuit fails. The pulse transfer time ΔT and reaction time Δt for each round are set for the pursuing and escaping spacecraft. After the opponent makes a pulse maneuver, the pursuing spacecraft makes a corresponding pursuit and escape strategy and performs the corresponding pulse maneuver. It is assumed that the pursuing spacecraft is the one that makes the pulse maneuver first.

[0077] S13: Based on the orbital coordinate system, the existing set of escape actions U for each round of the escape spacecraft. E ={UE1 U E2 ,…,U Ed} and the existing set of pursuit actions U for each round of pursuing the spacecraft P ={U P1 U P2 ,…,U Pk The game search depth n of the escape spacecraft, the game search depth m of the pursuing spacecraft, and the pursuit success condition (i.e., the pursuit is successful when the relative distance between the pursuing spacecraft and the escape spacecraft is r; if the pursuing spacecraft fails to catch up with the escape spacecraft within N rounds, the pursuit fails) are established using the pulse transfer time ΔT and the reaction time Δt.

[0078] In the above, P represents the pursuing spacecraft; E represents the escaping spacecraft; where d represents the total number of actions taken by the escaping spacecraft, and k represents the total number of actions taken by the pursuing spacecraft.

[0079] The aforementioned pursuit game tree includes the corresponding position X of the pursuing spacecraft after each round of the game. P (t0+ΔT) and the state of the pursuing spacecraft after each round of the game;

[0080] The corresponding position X of the escaping spacecraft after each round of the game. E (t0+Δt+ΔT) and the state of the escaping spacecraft after each round of the game;

[0081] It also includes the relative distances obtained from all combinations of pursuit and escape actions based on the game search depth m of the pursuing spacecraft, and the relative distances obtained from all combinations of pursuit and escape actions based on the game search depth n of the escaping spacecraft.

[0082] Among them, the existing pursuit motion set U of the pursuing spacecraft P and the escaping spacecraft E is set. P ={U P1 U P2 ,…,U Pk} and escape action set U E ={U E1 U E2 ,…,U Ed}, where k is the total number of actions already performed by the pursuing satellite, and d is the total number of actions already performed by the escaping satellite. Each action has a corresponding pulse pattern.

[0083] The pursuit of the spacecraft was first carried out by executing the pursuit maneuver. Pi After a time interval ΔT, it reaches the corresponding position X. P (t0+ΔT). The spacecraft orbit transfers here are all performed using a single-pulse method, as shown in the following equations:

[0084] X P(t0+ΔT)=Φ(t0+ΔT,t0)·X P (t0)+Φ v (t0+ΔT,t0)Δv Pi

[0085] in,

[0086]

[0087]

[0088] Substituting the state of the pursuing spacecraft and the pulse increment corresponding to the pursuit action into the above formula, we can obtain the state of the pursuing spacecraft after one round.

[0089] Then, after the pursuing spacecraft performs a maneuver Δt, the escaping spacecraft performs its escape maneuver and reaches the corresponding position X after a time interval ΔT. E (t0+Δt+ΔT). Similarly, the state of the pursuing spacecraft is solved to obtain the state of the escaping spacecraft after one round.

[0090] The relative distances obtained from all combinations of pursuit and escape actions at a game-theoretic search depth m for the pursuing spacecraft are as follows:

[0091] Based on the game-theoretic search depth m of the pursuing spacecraft, the relative distance between the pursuer and the fleeing party after m rounds of pulses is obtained as the optimization objective. The relative distance is obtained by calculating the combination of all pursuit and fleeing actions in m rounds of pulses.

[0092] Optimization objective J of pursuing spacecraft P Represented as:

[0093] J P =||M·(X) P (t M )-X E (t M ))||2,t M = t0 + Δt + m·ΔT;

[0094] in:

[0095]

[0096]

[0097] t m =t0+m·ΔT;

[0098] X P (t M ) is the pursuit spacecraft in t M The state at any given moment; X E (t M ) is the escape spacecraft in t MThe state at any given moment; X P (t0) represents the state of the pursuing spacecraft at time t0; X E (t0) is the state of the escaping spacecraft at time t0; M is the matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference; Φ(t M (t0) represents the time from t0 to t... M The CW equation transition matrix at time t; Φ v (t m ,t i-1 ) is t i-1 Time to t m The velocity transfer matrix of the CW equation at time Φ v (t M ,t i-1 +Δt) is t i-1 +Δt time to t M The velocity transfer matrix of the CW equation at time t;

[0099] The relative distances obtained from all combinations of pursuit and escape actions based on the game-theoretic search depth n of the escape spacecraft are as follows:

[0100] Based on the game-theoretic search depth n of the escape spacecraft, the relative distance between the pursuer and the escaper after n rounds of pulses is the optimization objective. The relative distance is obtained by calculating the combination of all pursuit and escape actions in n rounds of pulses.

[0101] Optimization objective J E It can be represented as:

[0102] J E =||M·(X) P (t N )-X E (t N ))||2,t N = t0 + Δt + n·ΔT

[0103] in,

[0104]

[0105]

[0106] t n =t0+n·ΔT;

[0107] X P (t N ) is the pursuit spacecraft in t N The state at any given moment; X E (t N ) is the escape spacecraft in t N The state at time t; Φ(t) N (t0) represents the time from t0 to t...N The CW equation transition matrix at time t; Φ v (t N ,t i-1 +Δt) is t i-1 +Δt time to t N The velocity transfer matrix of the CW equation at time Φ v (t n ,t i-1 ) is t i-1 Time to t n The velocity transfer matrix of the CW equation at time t;

[0108] In the above formula,

[0109] Δv Pi In the chase action series U P ={U P1 U P2 ,…,U Pk Choose from}, and Δv Ei In the escape action series U E ={U E1 U E2 ,…,U Ed Choose from}

[0110] The trajectory of the pursuit and escape game and the changes in the relative distance between the pursuers and the escapees are as follows: Figure 3 , 4 As shown.

[0111] More specifically, an m-round pursuit / escape game tree is established to perform the first round action search for the pursuing spacecraft, such as... Figure 5 As shown. The pursuing spacecraft aims to minimize the relative distance after m rounds of pulses, employing a max-min game tree search approach, starting from k... m ·d m The following steps are taken to find the pursuit-escape game strategy that satisfies the search method in each root node and obtain the corresponding relative distance solution. Using the minimax game tree search method, the search proceeds from all nodes after the m-round impulse, first performing a maxima-level search, then a minima-level search, to obtain the corresponding strategy ranking. The process of selecting the strategy for the first round and obtaining the corresponding relative distance solution is as follows:

[0112] like Figure 5 As shown, based on the game search depth m of the pursuing spacecraft, the predicted game rounds for both the pursuing and escaping spacecraft are m rounds. Based on all strategy combinations, k is obtained. m ·d m One root node;

[0113] Performing a search at the maxima level, when selecting an escape spacecraft pulse, there are d possible escape actions, and k... m ·dm The root nodes are divided into k according to their sorting. m ·d m-1 Each part contains d nodes. The maximum value among these d nodes is selected as the child node of the maxima level, thus obtaining k. m ·d m-1 Number of child nodes;

[0114] Performing a search at the minimum level, when selecting a spacecraft pulse to pursue, there are k possible pursuit actions. The k obtained from the maximum level... m ·d m-1 The child nodes are divided into k according to their sorting. m-1 ·d m-1 Each part contains k nodes. The minimum value among the k nodes is selected as the child node of the minimum layer.

[0115] Similarly, select nodes at the minimum and maximum levels to obtain the solution of the chase-escape game tree for the final m rounds, and output the chase action of the first round.

[0116] More specifically, an n-round pursuit-escape game tree is constructed to search for the first round action of the escaping spacecraft, such as... Figure 6 As shown. The escaping spacecraft wants the relative distance after n rounds of pulses to be as large as possible, and uses a minmax game tree search method, starting from k n ·d n Find the pursuit-escape game strategy that satisfies the search method in each root node, and obtain the corresponding relative distance solution.

[0117] The minimax game tree search method is used to search all nodes after n rounds. First, a minimax search is performed, then a maxima search is performed to obtain the corresponding strategy ranking. The process of selecting the strategy for the first round and obtaining the corresponding relative distance solution is as follows:

[0118] like Figure 6 As shown, based on the game search depth n of the escaping spacecraft, the game rounds for both the pursuing and escaping spacecraft are predicted to be n rounds. Based on all strategy combinations, k is obtained. n ·d n One root node;

[0119] Performing a search at the minimum level, when selecting a pursuit pulse for the spacecraft, there are k possible pursuit actions. Let k... n ·d n The root nodes are divided into k according to their sorting. n-1 ·d n Each part contains k nodes. The minimum value among these k nodes is selected as the child node of the minimum layer, thus obtaining kmin. n-1 ·d n Number of child nodes;

[0120] When performing a search at the maxima level and selecting an escape spacecraft pulse, there are d possible escape actions. The k obtained from the minima level... n-1 ·d n The child nodes are divided into k according to their sorting. n-1 ·d n-1 There are d parts, each with d nodes. The maximum value among the d parts is selected as the child node of the maxima level.

[0121] Similarly, perform node selection for the minimum and maximum layers to obtain the solution of the chase-escape game tree for the final n rounds, and output the chase action of the first round.

[0122] Example

[0123] This embodiment provides a method for solving the orbital pursuit and escape game strategy based on dynamic game tree search. The specific steps are as follows:

[0124] S1: Input orbital altitude a = 42000km and establish an orbital coordinate system with the initial position of the escaped spacecraft as the origin. The X-axis points from the Earth's center to the direction of the escaped spacecraft, and the Y-axis is the velocity direction within the orbital plane of the escaped spacecraft. (Specific details are as follows...) Figure 2 As shown.

[0125] Let the initial state of the escape spacecraft be X. E0 =[0,0,0,0,0,0] T The initial state of the pursuing spacecraft is X P0 =[10km,0,0,-1.1002m / s,0,0] T ;

[0126] S2: Set the escape action set U for each round of the escape spacecraft. E ={U E1 U E2 ,…,U E9} and the existing set of pursuit actions for each round of the pursuing spacecraft U P ={U P1 U P2 ,…,U P9}, where 9 is the total number of actions taken by the escaping spacecraft and 9 is the total number of actions taken by the pursuing spacecraft;

[0127] S3: Set the game search depth for the escaping spacecraft to 1, and the game search depth for the pursuing spacecraft to 3.

[0128] A successful pursuit occurs when the relative distance between the pursuing and escaping spacecraft is set to r. A pursuit fails if the pursuing spacecraft fails to catch up with the escaping spacecraft within K rounds.

[0129] S4: Set the pulse transition time for each pulse between the pursuing and escaping spacecraft to ΔT = 3600s.

[0130] The pursuing spacecraft adopts a corresponding pursuit strategy and performs a pulse maneuver Δt = 1800s after the other spacecraft performs a pulse maneuver. Assume the pursuing spacecraft initiates the pulse maneuver first.

[0131] S5: Based on S2, S3, and S4, construct the game tree and use the minimax search method to solve the impulse chase-escape game strategy. The specific steps are as follows:

[0132] S5.1: The first step in pursuing the spacecraft is to select a strategy. Using the relative distance between the pursuing and fleeing parties after 3 rounds of pulses as the optimization objective, a max-min game tree search method is employed. The search proceeds from all nodes after 3 rounds, first performing a max-level search, then a min-level search, to obtain the corresponding strategy ranking. Only the strategy from the first round is selected.

[0133] S5.2: After detecting the maneuver of the pursuing spacecraft, the escaping spacecraft selects an escape strategy. Using the relative distance between the pursuer and the escaping spacecraft after one round pulse as the optimization objective, a minmax game tree search method is employed. The search proceeds from all nodes after one round, first performing a min-level search, then a max-level search, to obtain the corresponding strategy ranking. Only the strategy from the first round is selected.

[0134] S5.3: Based on the total number of rounds (10) set in S3 above, the pursuing and fleeing spacecraft sequentially engage in the game. If the relative distance between the two sides is less than r = 1000m at any given moment, the game ends, and the pursuit is successful. If both sides make 10 decisions but fail to catch up, the pursuit fails. The strategies obtained through the game tree search method described above represent the optimal strategies for both the pursuing and fleeing spacecraft.

[0135] Specifically, step S2 is as follows:

[0136] First, set up the existing pursuit motion set U for the pursuing spacecraft P and the escaping spacecraft E. P ={U P1 U P2 ,…,U P9} and escape action set U E ={U E1 U E2 ,…,U E9}, where the pursuit strategies represent:

[0137]

[0138]

[0139] The escape strategies represent:

[0140]

[0141]

[0142] The pursuit of the spacecraft was first carried out by executing the pursuit maneuver. Pi After a time interval ΔT, it reaches the corresponding position X. P (t0+ΔT). The spacecraft orbit transfers here are all performed using a single-pulse method, as shown in the following equations:

[0143] X P (t0+ΔT)=Φ(t0+ΔT,t0)·X P (t0)+Φ v (t0+ΔT,t0)Δv Pi

[0144] in

[0145]

[0146] at the same time

[0147]

[0148] Substituting the state of the pursuing spacecraft and the pulse increment corresponding to the pursuit action into the above formula, we can obtain the state of the pursuing spacecraft after one round.

[0149] Then, after the pursuing spacecraft performs a maneuver Δt, the escaping spacecraft performs its escape maneuver and reaches the corresponding position X after a time interval ΔT. E (t0+Δt+ΔT). Similarly, the state of the pursuing spacecraft is solved to obtain the state of the escaping spacecraft after one round.

[0150] Specifically, step S3 is as follows:

[0151] S3.1 The pursuing spacecraft uses the relative distance between the pursuing and fleeing parties after 3 rounds of pulses as the optimization target, and calculates the relative distance obtained by the combination of all pursuing and fleeing actions in 3 rounds.

[0152] Optimization objective J P It can be represented as:

[0153] J P =||M·(X) P (t M )-X E (t M ))||2,t M = t0 + Δt + 3·ΔT

[0154] in

[0155]

[0156]

[0157] t3=t0+3·ΔT

[0158] X P (t M ) is the pursuit spacecraft in t M The state at any given moment; X E (t M ) is the escape spacecraft in t M The state at any given moment; X P (t0) represents the state of the pursuing spacecraft at time t0; X E (t0) is the state of the escaping spacecraft at time t0; M is the matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference; Φ(t M (t0) represents the time from t0 to t... M The CW equation transition matrix at time t; Φ v (t3,t i-1 ) is t i-1 The velocity transfer matrix of the CW equation from time t1 to time t3; Φ v (t M ,t i-1 +Δt) is t i-1 +Δt time to t M The velocity transfer matrix of the CW equation at time t;

[0159] Δv Pi In the chase action series U P ={U P1 U P2 ,…,U P9 Choose from}, and Δv Ei In the escape action U E ={U E1 U E2 ,…,U E9 Choose from}

[0160] S3.2, the escape spacecraft uses the relative distance between the pursuer and the escaper after one round of pulse as the optimization target, and calculates the relative distance obtained by the combination of all pursuit and escape actions in one round.

[0161] Optimization objective J E It can be represented as:

[0162] J E =||M·(X) P (t N )-X E (t N ))||2,t N = t0 + Δt + ΔT

[0163] in

[0164]

[0165]

[0166] t1 = t0 + ΔT

[0167] X P (t N ) is the pursuit spacecraft in t N The state at any given moment; X E (t N ) is the escape spacecraft in t N The state at time t; Φ(t) N (t0) represents the time from t0 to t... N The CW equation transition matrix at time t; Φ v (t N ,t i-1 +Δt) is t i-1 +Δt time to t N The velocity transfer matrix of the CW equation at time Φ v (t1,t i-1 ) is t i-1 The velocity transfer matrix of the CW equation from time t1 to time t2; Δv Pi In the chase action series U P ={U P1 U P2 ,…,U P9 Choose from}, and Δv Ei In the escape action U E ={U E1 U E2 ,…,U E9 Choose from}

[0168] Specifically, step S5 is as follows:

[0169] S5.1, establish a 3-round pursuit-escape game tree, and conduct the first round action search for the spacecraft, as follows: Figure 7 The game tree for a 3-round chase is shown.

[0170] The pursuing spacecraft aims to minimize the relative distance after three pulses. Therefore, a maxmin game tree search method is used to find the pursuit-escape game strategy that satisfies the search method from 531,441 root nodes, and obtain the corresponding relative distance solution.

[0171] The search method for the max-min game tree is as follows: First, predict the 531441 root nodes obtained from all strategy combinations in the 3-round game between the pursuer and the pursuer. Then, perform a search at the max level. Since there are 9 escape actions, there are 9 choices when selecting the escape spacecraft pulse. Divide the root nodes into 59049 groups, each with 9 nodes. Select the maximum value among the 9 as the child node of the max level, thus obtaining 59049 child nodes. Similarly, when performing a search at the min level, since there are 9 pursuit actions, there are 9 choices when selecting the pursuit spacecraft pulse. Divide the 59049 child nodes obtained from the max level into 6561 groups, each with 9 nodes. Select the minimum value among the 9 as the child node of the min level. Repeat the node selection for the min and max levels to obtain the solution for the final 3-round pursuit-escape game tree. Output U as the pursuit action of the first round. P1 .

[0172] S5.2, establish a 1-round pursuit / escape game tree, and perform the first-round action search for the escaping spacecraft, as follows: Figure 8 As shown, this is the game tree for a 1-round chase / escape scenario.

[0173] The escaping spacecraft wants to maximize the relative distance after one pulse. Therefore, the minmax game tree search method is used to find the pursuit-escape game strategy that satisfies the search method from 81 root nodes and obtain the corresponding relative distance solution.

[0174] The minmax game tree search method is as follows: First, predict the 81 root nodes obtained from all strategy combinations in one round of the game between the pursuer and the escaper. Then, perform a search at the min level. Since there are 9 pursuit actions, there are 9 choices when selecting the spacecraft pulse to pursue. Divide the root nodes into 9 groups, each with 9 nodes. Select the minimum value among these 9 as the child node of the min level, thus obtaining 9 child nodes. Similarly, when performing a search at the max level, since there are 9 escape actions, there are 9 choices when selecting the spacecraft pulse to escape. Divide the 9 child nodes obtained from the min level into 1 group, each with 9 nodes. Select the maximum value among these 9 as the child node of the max level. Repeat the node selection process for both the min and max levels to obtain the solution for the final round of the pursuit-escape game tree. Output U as the escape action from the first round. E1 .

[0175] S5.3, the pursuing and fleeing spacecraft sequentially engage in a game, and it is found that at t = 35280s, the relative distance between the pursuing and fleeing spacecraft is less than r = 1000m, indicating a successful pursuit. The strategies of both the pursuing and fleeing spacecraft are as follows:

[0176]

[0177]

[0178] 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 orbital pursuit and escape game strategies based on dynamic game tree search, characterized in that, Includes the following steps: S1: Establish the pursuit and escape game tree; The establishment of the pursuit and escape game tree includes the following steps: S11: Establish an orbital coordinate system based on orbital altitude a and with the initial position of the escaped spacecraft as the origin. In the orbital coordinate system, the X-axis points from the Earth's center to the escaped spacecraft, and the Y-axis points to the velocity direction within the orbital plane where the escaped spacecraft is located. S12: Set the existing escape action set for each round of the escape spacecraft. And the existing set of pursuit actions for each round of pursuing the spacecraft. ; Set the game-theoretic search depth for the escape spacecraft The game of searching for spacecraft depth And the conditions for successful pursuit, setting the pulse transfer time. and reaction time ; S13: Based on the orbital coordinate system, the existing set of escape actions for each round of the escape spacecraft. And the existing set of pursuit actions for each round of pursuing the spacecraft. The depth of the game search for escaped spacecraft The depth of the game of chasing spacecraft And the conditions for successful pursuit, pulse transfer time and reaction time Establish a fugitive pursuit game tree; P represents the pursuing spacecraft; E represents the escaping spacecraft; where This represents the total number of actions already taken by the escape spacecraft. To keep up with the total number of maneuvers already performed by the spacecraft; The conditions for a successful pursuit are as follows: When the relative distance between the pursuing spacecraft and the escaping spacecraft is At that time, the pursuit was successful; if in If the pursuing spacecraft fails to catch up with the fleeing spacecraft within the round, the pursuit fails. The pursuit game tree includes the corresponding positions of the pursuing spacecraft after each round of the game. And the status of the pursuing spacecraft after each round of the game; The corresponding positions of the escaping spacecraft after each round of the game And the status of the escaping spacecraft after each round of the game; It also includes game-theoretic search depth based on the pursuing spacecraft. The relative distance obtained from all combinations of pursuit and escape actions, and the game-theoretic search depth based on the escaping spacecraft. The relative distance obtained by combining all the pursuit and escape actions; S2: Based on the pursuit-escape game tree and using the minimax search method, the pursuing spacecraft first selects a pursuit strategy and outputs the pursuit action for the current round; the escaping spacecraft selects an escape strategy after detecting the maneuver of the pursuing spacecraft and outputs the escape action for the current round. In step S2, the process by which the pursuing spacecraft selects a strategy is as follows: Game-theoretic search depth based on pursuing spacecraft get The relative distance between the pursuer and pursuer after the round pulse is the optimization objective. A minimax game tree search method is employed, starting from... Search all nodes after the round pulse, first perform maximal search, then minimum search, to obtain the corresponding strategy ranking, select the strategy of the first round and obtain the corresponding relative distance solution; The method employing the minimax game tree search approach is as follows: The process of searching all nodes after the round pulse, first performing a maximal search and then a minimum search, to obtain the corresponding policy ranking, selecting the policy for the first round, and obtaining the corresponding relative distance solution is as follows: Based on the game-like search depth of the pursuing spacecraft The predicted number of rounds in the game between the pursuing and escaping spacecraft is as follows: Rounds, obtained based on all strategy combinations km dm One root node; When performing a maximum-level search and selecting an escape spacecraft pulse, there are d possible escape actions. km dm The root nodes are divided into sorted groups. k m d m-1 Each part contains d nodes. The maximum value among these d nodes is selected as the child node of the maxima level. k m d m-1 Number of child nodes; Performing a search at the minimum level, when selecting a pursuit pulse for the spacecraft, there are k possible pursuit actions. The maximum level will then be used to obtain... k m d m-1 The child nodes are divided into sorted groups. k m-1 d m-1 Each part contains k nodes. The minimum value among the k nodes is selected as the child node of the minimum layer. Similarly, node selection is performed at the minimum and maximum levels to obtain the final result. Solve the game tree of the chase and escape rounds and output the chase action of the first round; In step S2, the process by which the escaping spacecraft selects an escape strategy after detecting the maneuvering of the pursuing spacecraft is as follows: After detecting the maneuvering of the pursuing spacecraft, the escaping spacecraft performs a game-theoretic search based on the depth of its movements. get The relative distance between the pursuer and pursuer after the round pulse is the optimization objective. A minimax game tree search method is employed, starting from... After each round, all nodes are searched. First, a minimum level search is performed, then a maximum level search is performed to obtain the corresponding strategy ranking. The strategy for the first round is selected and the corresponding relative distance solution is obtained. The method employing the minimax game tree search approach is as follows: The process of searching all nodes after each round, first performing a minimum-level search and then a maximum-level search, to obtain the corresponding policy ranking, selecting the policy for the first round, and obtaining the corresponding relative distance solution is as follows: Based on the game search depth of the escaped spacecraft The predicted number of rounds in the game between the pursuing and escaping spacecraft is as follows: Rounds, obtained based on all strategy combinations kn dn One root node; Performing a search at the minimum level, when selecting the spacecraft pulse to pursue, there are k possible pursuit actions. kn dn The root nodes are divided into sorted groups. kn-1 dn Each part contains k nodes. The minimum value among these k nodes is selected as the child node of the minimum layer. kn-1 dn Number of child nodes; When performing a search at the maxima level and selecting an escape spacecraft pulse, there are d possible escape actions. The results obtained at the minima level will be used to determine the escape actions. kn-1 dn The child nodes are divided into sorted groups. kn-1 dn-1 There are d parts, each with d nodes. The maximum value among the d parts is selected as the child node of the maxima level. Similarly, node selection is performed at the minimum and maximum levels to obtain the final result. Solve the game tree of the chase and escape rounds and output the chase action of the first round; S3: The pursuing spacecraft and the escaping spacecraft engage in sequential gameplay to determine whether the conditions for a successful pursuit are met, and to obtain the optimal strategies for the pursuing and escaping spacecraft.

2. The method for solving the orbital pursuit and escape game strategy based on dynamic game tree search according to claim 1, characterized in that, The game-theoretic search depth based on the chasing spacecraft The relative distances obtained from all the pursuit and escape actions are as follows: Game-theoretic search depth based on pursuing spacecraft get The relative distance between the pursuing and fleeing parties after the round pulse is the optimization target, and the calculation is performed. The relative distance obtained by combining all pursuit and escape actions in a round pulse; Pursuing the optimization goals of spacecraft Represented as: ； in: ； in, It is a spacecraft in pursuit The state at any given moment; Is it an escape spacecraft? The state at any given moment; It is a spacecraft in pursuit The state at any given moment; Is it an escape spacecraft? The state at any given moment; It is a matrix that transforms the state difference between the pursuer and the pursuer into a relative position difference; yes Time's up The CW equation transition matrix at time t; yes Time's up The velocity transfer matrix of the CW equation at time t; yes Time's up The velocity transfer matrix of the CW equation at time t; The game-theoretic search depth based on escaped spacecraft The relative distances obtained from all the pursuit and escape actions are as follows: Game-theoretic search depth based on escaped spacecraft get The relative distance between the pursuing and fleeing parties after the round pulse is the optimization target, and the calculation is performed. The relative distance obtained by combining all pursuit and escape actions in a round pulse; Optimization Objective It can be represented as: in, ； in, It is a spacecraft in pursuit The state at any given moment; Is it an escape spacecraft? The state at any given moment; yes Time's up The CW equation transition matrix at time t; yes Time's up The velocity transfer matrix of the CW equation at time t; yes Time's up The velocity transfer matrix of the CW equation at time t; In the above formula, ; In the chase action series Choose from, and In the Escape Action Collection Choose from.

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