A three-way orbital game control method based on pulse control

Abstract

This invention discloses a three-party orbital game control method based on pulse control, belonging to the field of aerospace technology. It includes the following steps: establishing a basic model of a three-party game in space orbit; obtaining parameter information of the game participants; inputting the parameter information of the game participants into the basic model of the three-party game in space orbit; obtaining the optimal strategy solution methods for the coordinated pursuit of the pursuing satellite and the interceptor satellite, as well as the optimal strategy solution methods for the escape satellite to evade the coordinated pursuit; and obtaining the optimal strategies of the game participants to complete the three-party orbital game control.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a three-party orbital game control method based on pulse control. Background Technology

[0002] In recent years, the proliferation of faulty and maliciously resisting spacecraft in space has threatened space security. To more efficiently address the problem of capturing non-cooperative spacecraft, a more effective approach is needed. However, the maneuverability of spacecraft is limited when using pulse control. In orbital pursuit-escape games where both sides possess maneuverability, the difficulty in predicting the opponent's maneuvering strategies poses a challenge to model building. Current research on pulse-controlled orbital games is limited, and most studies only involve two parties (pursuer and pursuer). Minimax game tree search methods are commonly used for strategy solving, but these methods are only applicable to zero-sum games between two parties and are difficult to apply to multi-party games. Furthermore, the computational complexity increases exponentially with the number of rounds, making them difficult to solve. For the three-spacecraft orbital "pursuit-escape-interception" problem, there is still no clear cooperative pursuit method or escape strategy. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, the present invention aims to provide a three-way orbital game control method based on pulse control. This method employs a three-spacecraft orbital "chase-escape-intercept" game strategy based on pulse control, considering the coordinated action of two pursuing spacecraft to pursue the escaping spacecraft from different directions. This adds an interceptor to the existing two-way pursuit-escape strategy, establishing a "chase-intercept" coordinated strategy model and solving for the optimal control strategy, thus providing a strategic solution for space orbital pursuit-escape missions.

[0004] To achieve the above objectives, the present invention employs the following technical solution:

[0005] This invention provides a three-way orbital game control method based on pulse control, comprising the following steps:

[0006] S1: Establish a basic model of a three-way game in space orbit;

[0007] S2: Obtain the parameter information of the game participants, input the parameter information of the game participants into the basic model of the three-party game in space orbit, obtain the optimal strategy solution method for the coordinated pursuit of the chasing star and the intercepting star among the game participants, and the optimal strategy solution method for the escape star to evade the coordinated pursuit, obtain the optimal strategy of the game participants, and complete the control of the three-party orbit game.

[0008] In the specific implementation process, the process of establishing the basic model of the three-party game in space orbit in S1 is as follows:

[0009] A circular orbit near the spacecraft is selected as the reference orbit. Based on the CW equation, dynamic modeling of relative motion under pulse velocity increment is performed, and a state transition model under pulse velocity increment is established.

[0010] Based on the different needs of the game participants for the distance between pursuit and escape during the game process, the optimization objectives of the game participants are established;

[0011] Obtain the orbital dynamics constraints imposed on the game participants during the game process, the upper limit constraints on the magnitude of a single pulse velocity increment during orbital maneuvers, and the upper limit constraints on the total consumption of pulse velocity increments;

[0012] A basic model of a three-way game in space orbit is established based on the state transition model under pulse velocity increment, the optimization objectives of the game participants, the orbital dynamics constraints imposed on the game participants during the game, the upper limit constraint on the magnitude of a single pulse velocity increment during orbital maneuvering, and the upper limit constraint on the total consumption of pulse velocity increment.

[0013] In practical implementation, the state transition model under the pulse velocity increment is as follows:

[0014]

[0015] Define the state quantities of relative motion 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 any given time;

[0016]

[0017] Δt = t - t0;

[0018] In the above formula, Φ(t,t0) represents the state transition matrix from state t0 to state t.

[0019] In the specific implementation process, the game participants include: the pursuing star, the intercepting star, and the escaping star;

[0020] The optimization objective of the tracking star is:

[0021] min J P1 =J(ΔV) P1 ,ΔV E )=||M·(X P1 (t f )-X E (t f ))||2;

[0022] The optimization objective of the interceptor is:

[0023] min J P2 =J(ΔV) P2 ,ΔV E )=||M·(X P2 (t f )-X E (t f ))||2;

[0024] The optimization objective of the escape star is:

[0025] maxJ(ΔV P ,ΔV E ) = max min(J P1 J P2 );

[0026] The orbital dynamics constraints imposed on the participants in the game during the game process are as follows:

[0027]

[0028] In the above formula, M = [I 3×3 ,0 3×3 J represents the payoff metrics for both the pursuer and the fugitive; P1 represents the pursuing star; P2 represents the intercepting star; E represents the escaping star; t0 is the start of the game; t f The moment when the game ends; t j X is the time when the j-th pulse is applied; P1 X P2 and X E These represent the state vectors of the tracking star, the interceptor star, and the escape star, respectively; ΔV P1 (t j ), ΔV P2 (t j ) and ΔV E (t j ) represent the tracking star, interceptor star, and escape star at t, respectively. j The velocity increment applied at any given moment.

[0029] In the specific implementation process, the upper limit constraint on the control magnitude of the single pulse velocity increment during the orbital maneuver is specifically as follows:

[0030]

[0031] The total consumption limit constraint for the pulse velocity increment is specifically in the following form:

[0032]

[0033] In the above formula, and ΔV represents the maximum value of the velocity increment for each pulse of the tracking star, the intercepting star, and the escaping star, respectively. P1max ΔV P2max and ΔV Emax These represent the maximum total reserves of pulse velocity increments for the pursuing star, the intercepting star, and the escaping star, respectively.

[0034] In the specific implementation process, the optimal strategy for coordinated pursuit by the tracking satellite and the interceptor satellite is solved as follows:

[0035] The roles of the pursuing and intercepting satellites in the pursuing spacecraft are determined. The spacecraft that is closer to the escape satellite at the current moment is selected as the intercepting satellite, and the spacecraft that is farther away is selected as the pursuing satellite. The pursuing satellite uses the MinMax algorithm to determine the optimal strategy and predict the optimal strategy of the escape satellite. Based on the predicted optimal strategy of the escape satellite, the optimal strategy of the intercepting satellite is determined, so that the relative distance between the intercepting satellite and the escape satellite is minimized after this round.

[0036] In the specific implementation process, the selection process for the optimal strategy solution method of the coordinated pursuit by the tracking satellite and the interceptor satellite is as follows:

[0037] The game process involves obtaining the initial states of the game participants and determining the maximum number of rounds. It also involves identifying the roles of the pursuing and intercepting satellites within the pursuing spacecraft, using single-round pulse optimization to predict the positions of the game participants before the next pulse maneuver, and determining the optimal strategy at the current moment. After the pulse maneuver, the game process involves obtaining the states of the game participants at each moment, determining whether the pursuit is successful, and ending the game when the pursuit is successful or the maximum number of rounds is reached.

[0038] In practical implementation, the optimal strategy for coordinated pursuit by the tracking satellite and the interceptor satellite satisfies the following conditions:

[0039]

[0040] In the above formula, These represent the optimal strategies for the pursuing satellite and the intercepting satellite, respectively. This represents the optimal strategy predicted by the pursuing star for the escape star.

[0041] In the specific implementation process, the optimal strategy for the escape star to evade coordinated pursuit is solved as follows:

[0042] The MinMax algorithm is used to predict the maneuver strategies of the pursuing and intercepting satellites, and to obtain the first strategy and the second strategy of the escaping satellite when facing the pursuing satellite.

[0043] The distances between the escape star and the pursuing and intercepting stars, respectively, when selecting the first and second strategies;

[0044] The strategy with the largest distance between the pursuing star and the escaping star under the first strategy and the second strategy is selected as the optimal strategy for the escaping star.

[0045] The process for selecting the optimal strategy for the escape star to evade coordinated pursuit is as follows:

[0046] The game begins by obtaining the initial states of the players and determining the maximum number of rounds. Single-round pulse optimization is used to predict the positions of the players before the next pulse maneuver, obtaining the relative distances between the escape star and the pursuing and intercepting stars, and determining the optimal strategy at the current moment. After the pulse maneuver, the game states of the players at each moment are obtained, and it is determined whether the escape was successful. The game ends when the escape star fails to escape or the maximum number of rounds is reached.

[0047] In practical implementation, the optimal strategy for the escape star to evade coordinated pursuit satisfies the following conditions:

[0048]

[0049] Among them, the first strategy chosen by the escape star when facing the pursuing star is The second strategy chosen by the escape star when facing the interceptor star is The distances between the escape star and the pursuing star when the escape star chooses the first strategy, and the distances between the escape star and the intercepting star when the escape star chooses the first strategy, are respectively The distances between the escape satellite and the pursuing satellite when the second strategy is selected, and the distances between the escape satellite and the intercepting satellite when the second strategy is selected, are respectively:

[0050]

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] This invention provides a three-way orbital game control method based on pulse control. It designs the game payoff index of the three spacecraft in the game with the terminal distance as a parameter. Based on the established game model, it introduces relevant methods of game theory to transform the 2-chase 1-escape game problem into a composite chase 1-escape game problem. Based on the MinMax bilateral optimization algorithm, it realizes the strategy design of cooperative game by predicting and tracking the results.

[0053] The method described in this invention fully utilizes the orbital dynamics characteristics of spacecraft, establishing a relatively simple and widely applicable game model, while also providing relevant constraints. Furthermore, by introducing relevant ideas and methods from game theory, a cooperative mechanism is designed, filling a gap in current research and providing a theoretical foundation for practical space orbital game-theoretic tasks. Attached Figure Description

[0054] Figure 1This is a flowchart illustrating the design of a pulse-controlled track "chase-escape-block" game algorithm according to an embodiment of the present invention.

[0055] Figure 2 This is a schematic diagram of the MinMax algorithm of the present invention;

[0056] Figure 3 This is a flowchart of the strategy selection process for the chasing game according to the present invention;

[0057] Figure 4 This is a schematic diagram of the optimal strategy solution method for the pursuit of the square according to the present invention;

[0058] Figure 5 This is a flowchart illustrating the escape strategy selection process of the present invention.

[0059] Figure 6 This is a schematic diagram of the escape optimal strategy solution method of the present invention;

[0060] Figure 7 This is a schematic diagram of the two-to-one pursuit and escape trajectory of the pursuer in this invention;

[0061] Figure 8 This is a schematic diagram of the two-on-one pursuit trajectory of the escapee in this invention. Detailed Implementation

[0062] 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.

[0063] 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.

[0064] This invention provides a three-way orbital game control method based on pulse control, comprising the following steps:

[0065] S1: Establish a basic model of a three-way game in space orbit;

[0066] Specifically, a circular orbit near the spacecraft in the game is selected as the reference orbit. Dynamic modeling of relative motion under pulse velocity increments is performed based on the CW equations, establishing a state transition model under pulse velocity increments. Based on the different needs of the game participants for the distance between pursuit and escape during the game, optimization objectives for the game participants are established. The orbital dynamic constraints, the upper limit constraints on the magnitude of a single pulse velocity increment during orbital maneuvers, and the upper limit constraints on the total consumption of pulse velocity increments are obtained for the game participants during the game. Based on the state transition model under pulse velocity increments, the optimization objectives of the game participants, and the orbital dynamic constraints, the upper limit constraints on the magnitude of a single pulse velocity increment during orbital maneuvers, and the upper limit constraints on the total consumption of pulse velocity increments, a basic model of a three-way game in space orbits is established.

[0067] S2: Obtain the parameter information of the game participants, input the parameter information of the game participants into the basic model of the three-party game in space orbit, obtain the optimal strategy solution method for the coordinated pursuit of the chasing star and the intercepting star and the optimal strategy solution method for the escape star to evade the coordinated pursuit among the game participants, obtain the optimal strategy of the game participants, and complete the three-party orbit game control based on the optimal strategy of the game participants.

[0068] The present invention will now be described in further detail with reference to the accompanying drawings:

[0069] See Figures 1 to 6 As shown, this invention provides a three-way orbital game control method based on pulse control, the specific steps of which are as follows:

[0070] S1, Establish the basic model of the three-way game in space orbit, namely the basic model of the "chase-escape-block" game;

[0071] The process of establishing the basic model of the three-way game in space orbit is as follows:

[0072] S11: In the "chase-escape-intercept" game scenario of in-plane orbit, the relative distance between spacecraft is relatively close to the orbital altitude. Therefore, a circular orbit near the game spacecraft can be selected as the reference orbit, and a state transition model under pulse velocity increment can be established based on the CW equation. At the instant the pulse velocity increment is applied, the spacecraft's velocity changes but its position remains unchanged. The motion between the pulse maneuvering points is the spacecraft's natural transfer motion.

[0073] The state transition model under the above pulse velocity increment is as follows:

[0074]

[0075] Define the state quantities of relative motion 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 any given time;

[0076]

[0077] Δt = t - t0;

[0078] In the above formula, Φ(t,t0) represents the state transition matrix from state t0 to state t.

[0079] S12: Based on the different needs of the game participants for the distance between pursuit and escape during the game process, establish the optimization objectives of the game participants; obtain the orbital dynamics constraints, the upper limit constraints on the magnitude of the single pulse velocity increment during the orbital maneuver, and the upper limit constraints on the total consumption of the pulse velocity increment during the game process.

[0080] In designing the game theory model, the basic assumptions required for its establishment are first given. It is assumed that all spacecraft in the game process are considered point masses, their attitude changes are ignored, and they all move within the same plane; during pulse maneuvers, all spacecraft simultaneously apply pulses at equal time intervals, with each pulse increment being the same in magnitude; the direction of the pulse control is fixed, including V... x+ V x- V y+ V y- Pulses are applied in four directions, but only in one direction at a time.

[0081] The game participants mentioned above include: the pursuing star P1, the intercepting star P2, and the escaping star E; based on the different needs of the game participants for the distance between pursuit and escape during the game process, the optimization objectives of the game participants are established.

[0082] The optimization objective for the Chaser Star is as follows:

[0083] min J P1 =J(ΔV) P1 ,ΔV E )=||M·(X P1 (t f )-X E (t f ))||2; (2)

[0084] The optimization objective for the interceptor is as follows:

[0085] min J P2 =J(ΔV) P2 ,ΔV E )=||M·(X P2(t f )-X E (t f ))||2; (3)

[0086] The optimization objective for the escape star is as follows:

[0087] maxJ(ΔV P ,ΔV E ) = maxmin(J P1 J P2 (4)

[0088] The orbital dynamics constraints imposed on the participants in the game are as follows:

[0089]

[0090] In the above formula, M = [I 3×3 ,0 3×3 J represents the payoff metrics for both the pursuer and the fugitive; P1 represents the pursuing star; P2 represents the intercepting star; E represents the escaping star; t0 is the start of the game; t f The moment when the game ends; t j X is the time when the j-th pulse is applied; P1 X P2 and X E These represent the state vectors of the tracking star, the interceptor star, and the escape star, respectively; ΔV P1 (t j ), ΔV P2 (t j ) and ΔV E (t j ) represent the tracking star, interceptor star, and escape star at t, respectively. j The velocity increment applied at any given moment.

[0091] The upper limit constraint on the magnitude of the single pulse velocity increment during orbital maneuvering is as follows:

[0092]

[0093] The total consumption limit constraint for pulse velocity increment is specifically in the following form:

[0094]

[0095] In the above formula, and ΔV represents the maximum value of the velocity increment for each pulse of the tracking star, the intercepting star, and the escaping star, respectively. P1max ΔV P2max and ΔV Emax These represent the maximum total reserves of pulse velocity increments for the pursuing star, the intercepting star, and the escaping star, respectively.

[0096] S13: Based on the state transition model under pulse velocity increment, the optimization objectives of the game participants, the orbital dynamics constraints imposed on the game participants during the game, the upper limit constraint on the magnitude of a single pulse velocity increment during orbital maneuvering, and the upper limit constraint on the total consumption of pulse velocity increment, a basic model of three-party game in space orbit is established.

[0097] S2: Obtain the parameter information of the game participants, input the parameter information of the game participants into the basic model of the three-party game of space orbit, obtain the optimal strategy of the game participants, and complete the control of the three-party orbit game.

[0098] Based on the optimal strategy solution method for pursuit and escape by both the pursuing star and the escape star, we obtain the optimal strategy solution method for coordinated pursuit by the pursuing star and the intercepting star, as well as the optimal strategy solution method for the escape star to evade coordinated pursuit.

[0099] The optimal strategy for both the pursuing and escaping stars is determined as follows:

[0100] Based on the MinMax algorithm, the corresponding profit index is obtained after combining each maneuver strategy that can be executed by both the pursuing star and the escaping star. The profit matrix is ​​constructed by using each maneuver strategy that can be executed by both the pursuing star and the escaping star as the row coordinates and column coordinates, respectively.

[0101] Obtain the minimum value in each column of the profit matrix, and then select the maximum value from the minimum values ​​in each column; select the row and column coordinates of the maximum value as the optimal strategy for the pursuit and escape of both the pursuing and escape stars.

[0102] The optimal strategy for coordinated pursuit by the tracking satellite and the interceptor satellite described in this invention is as follows:

[0103] The roles of the pursuing and intercepting satellites in the pursuing spacecraft are determined. The spacecraft that is closer to the escape satellite at the current moment is selected as the intercepting satellite, and the spacecraft that is farther away is selected as the pursuing satellite. The pursuing satellite uses the MinMax algorithm to determine the optimal strategy and predict the optimal strategy of the escape satellite. Based on the predicted optimal strategy of the escape satellite, the optimal strategy of the intercepting satellite is determined, so that the relative distance between the intercepting satellite and the escape satellite is minimized after this round.

[0104] The selection process for the optimal strategy solution method of the above-mentioned coordinated pursuit by the pursuit satellite and the interceptor satellite in this invention is as follows:

[0105] The game process involves obtaining the initial states of the game participants and determining the maximum number of rounds. It also involves identifying the roles of the pursuing and intercepting satellites in the pursuing spacecraft, using single-round pulse optimization to predict the positions of the game participants before the next pulse maneuver, and determining the optimal strategy at the current moment. After the pulse maneuver, the game process involves obtaining the states of the game participants at each moment, determining whether the pursuit is successful (i.e., whether the relative distance D(t) between the escape satellite and the pursuing and intercepting satellites is less than 2km), and ending the game when the escape satellite is captured or the maximum number of rounds is reached.

[0106] The optimal strategy for coordinated pursuit by the aforementioned tracking and intercepting satellites in this invention satisfies the following conditions:

[0107]

[0108] In the above formula, These represent the optimal strategies for the pursuing satellite and the intercepting satellite, respectively. This represents the optimal strategy predicted by the pursuing star for the escape star.

[0109] The optimal strategy for evading coordinated pursuit by the escape star described in this invention is as follows:

[0110] The MinMax algorithm is used to predict the maneuver strategies of the pursuing and intercepting satellites, and to obtain the first strategy and the second strategy of the escaping satellite when facing the pursuing satellite.

[0111] The distances between the escape star and the pursuing and intercepting stars, respectively, when selecting the first and second strategies;

[0112] The strategy with the largest distance between the pursuing star and the escaping star under the first strategy and the second strategy is selected as the optimal strategy for the escaping star.

[0113] The process of selecting the optimal strategy for the escape star to evade coordinated pursuit is as follows:

[0114] The game begins by obtaining the initial states of the players and determining the maximum number of rounds. Single-round pulse optimization is used to predict the positions of the players before the next pulse maneuver, obtaining the relative distances between the escape star and the pursuing and intercepting stars, and determining the optimal strategy at the current moment. After the pulse maneuver, the game begins by obtaining the states of the players at each moment and determining whether the escape was successful, i.e., whether the relative distance D(t) between the escape star and the pursuing and intercepting stars is greater than or equal to 2km. The game ends when the escape star fails to escape or when the maximum number of rounds is reached.

[0115] The optimal strategy for the escape star to evade coordinated pursuit satisfies the following conditions:

[0116]

[0117] Among them, the first strategy chosen by the escape star when facing the pursuing star is The second strategy chosen by the escape star when facing the interceptor star is The distances between the escape star and the pursuing star when the escape star chooses the first strategy, and the distances between the escape star and the intercepting star when the escape star chooses the first strategy, are respectively The distances between the escape satellite and the pursuing satellite when the second strategy is selected, and the distances between the escape satellite and the intercepting satellite when the second strategy is selected, are respectively:

[0118]

[0119] In the specific implementation of the above S2, based on the optimal strategy solution method for the two parties in a one-to-one pursuit-escape game, after obtaining the parameter information of the game participants, a strategy solution method for the coordinated pursuit of the pursuing star and the intercepting star is designed; a strategy solution method for the escape star to evade the coordinated pursuit is designed, the optimal strategy of the game participants is obtained, and the three-party orbital game control is completed.

[0120] In orbital pursuit and escape games between two spacecraft, the MinMax algorithm is often used to solve for the optimal strategy. The process for selecting maneuver schemes in designing a method to solve for the optimal strategy between the pursuing and escaping parties in a one-to-one pursuit and escape game is as follows: Figure 2 As shown, specifically:

[0121] Step 1: First, calculate the corresponding profit index J after combining each maneuver strategy that can be executed by both the pursuer and the pursuer, and construct a profit matrix using the multiple strategies of the pursuer and the pursuer as column and row coordinates.

[0122] Step 2: After obtaining the profit matrix, select the smallest value from each column of the matrix.

[0123] Step 3: Select the largest value from the smallest values ​​selected in each column in the previous step. The row and column coordinates of the final selected value are the optimal strategies for the pursuer and the fleeing player.

[0124] Furthermore, this invention considers the synergistic effect of the two spacecraft, the pursuing satellite and the interceptor satellite, and determines the solution process for the optimal game strategy between the two satellites, such as... Figure 4 As shown, the specific solution method for the strategy of coordinated pursuit by the tracking satellite and the interceptor satellite is as follows:

[0125] Step 1: First, determine the roles of the pursuing spacecraft P1 and P2, selecting the one that is closer to the pursuing satellite at the current moment as the interceptor satellite and the one that is farther away as the pursuing satellite.

[0126] Step 2: The pursuing star uses the MinMax algorithm to determine its optimal maneuver strategy, and at the same time predicts the optimal strategy that the escaping star may take (i.e. (P1-E)).

[0127] Step 3: The interceptor star uses the optimal maneuver strategy of the escape star predicted above to determine its own strategy (i.e., P2(P1-E)) so that the relative distance between the interceptor star and the escape star is minimized at the end of this round.

[0128] like Figure 3 As shown, the specific steps for selecting the chasing strategy in the entire game process are as follows: In the orbital game, the number of pulse maneuvers of the three satellites, i.e., the number of game rounds, is N. Single-round pulse optimization is adopted, that is, at the beginning of each round, the chasing and intercepting roles of the two spacecraft are first determined, and then the optimal strategy at the current moment is determined by predicting the position of the three satellites before the next pulse maneuver. The game ends when the escape satellite is captured or when the maximum number of game rounds is reached.

[0129] Among them, such as Figure 6 As shown, the specific solution method for designing the optimal strategy for an escape star to evade coordinated pursuit is as follows:

[0130] Step 1: The MinMax algorithm is used to predict the maneuver strategies of the escape satellite and the pursuing satellite, as well as the interceptor satellite, and to obtain two possible strategies for the escape satellite in relation to the pursuing and interceptor satellites, respectively.

[0131] Step 2: Calculate the distances between the escape satellite and the pursuing and intercepting satellites when the above two strategies are selected.

[0132] Step 3: Select the strategy with the largest relative minimum distance between the pursuer and the escaper under each strategy. This strategy is the escape star's maneuver strategy.

[0133] like Figure 5 As shown, the method for selecting the escaper's strategy in the game is as follows:

[0134] Considering the synergistic effect of the pursuing and intercepting spacecraft, the solution process for the optimal game strategy of the escape spacecraft is determined. Similar to the strategy solution process of the pursuing spacecraft, a single-round pulse optimization is adopted. At the beginning of each round, the relative distance between the pursuing and escape spacecraft is calculated by predicting the positions of the three satellites before the next pulse maneuver, thereby determining the optimal strategy of the escape spacecraft at the current moment. The game ends when the escape spacecraft fails to escape or the maximum number of rounds in the game is reached.

[0135] Example

[0136] To demonstrate the effectiveness of the algorithm, a two-to-one pulsed "chase-escape-interception" 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:

[0137] Table 1 Reference Spacecraft Orbital Elements

[0138] orbital elements a / km e / 1 i / rad Ω / rad ω / rad <![CDATA[f0 / rad]]> Reference spacecraft 35786 0 0 0 0 0

[0139] Table 2 Initial relative position and velocity of the spacecraft

[0140]

[0141] In this example, during the orbital game, the spacecraft simultaneously applies pulses to the pursuing, escaping, and intercepting three satellites, with a total of N=4 pulses for each satellite and a fixed pulse interval of 30 minutes. The entire game lasts for 2 hours. The pulse magnitudes of the pursuing, escaping, and intercepting spacecraft are fixed at 3 m / s, 1 m / s, and 3 m / s, respectively. Each spacecraft can only apply a pulse in one direction at a time, including four scenarios: positive and negative directions of the x-axis and y-axis in the relative coordinate system. The orbital game task now requires the pursuing or intercepting satellite to get as close as possible to the escaping satellite before the mission ends, while the escaping satellite must move as far away as possible from the pursuing and intercepting satellites.

[0142] The specific implementation steps of this invention are given below:

[0143] S1, establish a basic model of the "pursuit-escape-interception" game in space orbit;

[0144] In the "chase-escape-interception" game scenario within a plane orbit, the relative distance between spacecraft is relatively short compared to the orbital altitude. Therefore, a circular orbit near the spacecraft in the game can be selected as the reference orbit, and a state transition model under pulse velocity increments can be established based on the CW equations. At the instant the pulse velocity increment is applied, the spacecraft's velocity changes, but its position remains unchanged. The motion between the pulse maneuvering points is the spacecraft's natural transition motion.

[0145] The state transition model under the above pulse velocity increment is as follows:

[0146]

[0147] Define the state quantities of relative motion 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 any given time;

[0148]

[0149] Δt = t - t0;

[0150] In the above formula, Φ(t,t0) represents the state transition matrix from state t0 to state t.

[0151] When designing the game theory model, based on the different requirements of the pursuit, escape, and interception parties regarding the distance between the pursuit and escape, the optimization objective is established as follows:

[0152] The optimization objective for the Chaser Star is as follows:

[0153] min J P1 =J(ΔV) P1 ,ΔV E )=||M·(X P1 (t f )-X E (t f ))||2; (2)

[0154] The optimization objective for the interceptor is as follows:

[0155] min J P2 =J(ΔV) P2 ,ΔV E )=||M·(X P2 (t f )-X E (t f ))||2; (3)

[0156] The optimization objective for the escape star is as follows:

[0157] maxJ(ΔV P ,ΔV E ) = maxmin(J P1 J P2 (4)

[0158] The constraints in orbital maneuvers are as follows:

[0159] The orbital dynamics constraints imposed on the participants in the game are as follows:

[0160]

[0161] In the above formula, M = [I 3×3 ,0 3×3 J represents the payoff metrics for both the pursuer and the fugitive; P1 represents the pursuing star; P2 represents the intercepting star; E represents the escaping star; t0 is the start of the game; t f The moment when the game ends; t j X is the time when the j-th pulse is applied; P1 X P2 and X E These represent the state vectors of the tracking star, the interceptor star, and the escape star, respectively; ΔV P1 (t j ), ΔV P2 (t j ) and ΔV E (t j ) represent the tracking star, interceptor star, and escape star at t, respectively. j The velocity increment applied at any given moment.

[0162] During orbital maneuvers, there is an upper limit constraint on the magnitude of the single pulse velocity increment, specifically in the form of:

[0163]

[0164] The total consumption of pulse velocity increments is subject to an upper limit constraint, specifically in the form of:

[0165]

[0166] In the above formula, and ΔV represents the maximum value of the velocity increment for each pulse of the tracking star, the intercepting star, and the escaping star, respectively. P1max ΔV P2max and ΔV Emax These represent the maximum total reserves of pulse velocity increments for the pursuing star, the intercepting star, and the escaping star, respectively.

[0167] S2, based on the optimal strategy solution method for the two sides in a one-to-one pursuit and escape game, designs a strategy solution method for the coordinated pursuit of the pursuing star and the intercepting star, and a strategy solution method for the escape star to evade the coordinated pursuit.

[0168] In the one-to-one pursuit and escape game, the MinMax algorithm is often used to solve the optimal strategy for the pursuit and escape of two spacecraft in the orbital pursuit and escape game.

[0169] Step 1: First, calculate the corresponding profit index J after combining each maneuver strategy that can be executed by both the pursuer and the pursuer, and construct a profit matrix using the multiple strategies of the pursuer and the pursuer as column coordinates and row coordinates.

[0170] Step 2: After obtaining the profit matrix, select the smallest value from each column of the matrix.

[0171] Step 3: Select the largest value from the smallest values ​​selected in each column in the previous step. The row and column coordinates of the final selected value are the optimal strategies for the pursuer and the fleeing player.

[0172] Among them, a solution method for designing a strategy for coordinated pursuit by both the pursuing satellite and the interceptor satellite is proposed.

[0173] Round 1:

[0174] Step 1: First, determine the roles of the pursuing spacecraft P1 and P2: At the current moment, the pursuing spacecraft P1 is closer to the escape star and acts as the interceptor star, while the pursuing spacecraft P2 is farther from the escape star and acts as the pursuer star.

[0175] Step 2: The pursuing star uses the MinMax algorithm to determine its optimal maneuver strategy, while simultaneously predicting the optimal strategy (i.e., (P1-E)) that the escaping star might adopt. The resulting payoff matrix and maneuver strategies are as follows:

[0176] Table 3. Payoff Matrix for Chasing Star and Escape Star Strategies

[0177]

[0178] Pursuing star P1 maneuvers in the positive y-axis direction, and predicted escape star E maneuvers in the positive y-axis direction.

[0179] Step 3: The interceptor star uses the optimal maneuver strategy of the escape star predicted above to determine its own strategy (i.e., P2(P1-E)) so that the relative distance between the interceptor star and the escape star is minimized at the end of this round.

[0180] The optimal strategy for coordinated pursuit by the aforementioned tracking and intercepting satellites satisfies the following conditions:

[0181]

[0182] In the above formula, These represent the optimal strategies for the pursuing satellite and the intercepting satellite, respectively. This represents the optimal strategy predicted by the pursuing star for the escape star.

[0183] The payoff matrix and interceptor strategies for using different maneuvering tactics are obtained as follows:

[0184] Table 4. Payoff Matrix for Interceptor and Escape Star Strategies

[0185]

[0186] The interceptor chooses to maneuver in the positive y-axis direction. After both the pursuer and interceptor have chosen their strategies, they maneuver simultaneously, and then after 30 minutes of natural transition, they enter the next round. Repeating the above steps, the four pulse maneuver strategies of the pursuer and interceptor during the entire game are obtained, and the two-on-one pursuit and escape trajectory of the pursuer is plotted as shown in Figure 7.

[0187] The specific solution method for designing the escape star's strategy to evade coordinated pursuit is as follows:

[0188] Round 1:

[0189] Step 1: The MinMax algorithm is used to predict the maneuver strategies of the escape satellite and the pursuing satellite, as well as the interceptor satellite, and to obtain the first strategy chosen by the escape satellite when facing the pursuing satellite and the second strategy chosen by the escape satellite when facing the interceptor satellite.

[0190] Table 5. Escape Star and Chase Star Strategy Payoff Matrix

[0191]

[0192] Table 6. Escape Star and Interceptor Star Strategy Profit Matrix

[0193]

[0194]

[0195] The pursuing star is predicted to maneuver in the positive y-axis direction, while the intercepting star is predicted to maneuver in the negative y-axis direction. The escaping star can choose to maneuver in either the positive or negative y-axis direction.

[0196] Step 2: Calculate the distances between the escape satellite and the pursuing and intercepting satellites when the above two strategies are selected.

[0197]

[0198] Step 3: Select the strategy with the largest relative minimum distance between the pursuer and the fleeing star under each strategy. This strategy is the escape star's maneuver strategy. The optimal strategy for the escape star to evade coordinated pursuit satisfies the following conditions:

[0199]

[0200] Among them, the first strategy chosen by the escape star when facing the pursuing star is The second strategy chosen by the escape star when facing the interceptor star is The distances between the escape star and the pursuing star when the escape star chooses the first strategy, and the distances between the escape star and the intercepting star when the escape star chooses the first strategy, are respectively The distances between the escape satellite and the pursuing satellite when the second strategy is selected, and the distances between the escape satellite and the intercepting satellite when the second strategy is selected, are respectively:

[0201]

[0202] The escape star's maneuver strategy is obtained as follows: maneuver in the positive y-axis direction. After choosing its strategy, the escape star maneuvers and then undergoes a 30-minute natural transition before entering the next round. Repeating the above steps yields the escape star's four impulse maneuver strategies throughout the game, and the escaper's two-on-one pursuit trajectory is plotted as shown in Figure 8.

[0203] 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 three-way orbital game control method based on pulse control, characterized in that, Includes the following steps: S1: Establish a basic model of a three-way game in space orbit; In S1, the process of establishing the basic model of the three-way game in space orbit is as follows: The circular orbits near the game participants are selected as reference orbits. Based on the CW equation, the dynamics of the relative motion under the pulse velocity increment are modeled, and the state transition model under the pulse velocity increment is established. Based on the different needs of the game participants for the distance between pursuit and escape during the game process, the optimization objectives of the game participants are established; Obtain the orbital dynamics constraints imposed on the game participants during the game process, the upper limit constraints on the magnitude of a single pulse velocity increment during orbital maneuvers, and the upper limit constraints on the total consumption of pulse velocity increments; A basic model of a three-way game in space orbit is established based on the state transition model under pulse velocity increment, the optimization objectives of the game participants, the orbital dynamics constraints imposed on the game participants during the game, the upper limit constraint on the magnitude of a single pulse velocity increment during orbital maneuvering, and the upper limit constraint on the total consumption of pulse velocity increment. S2: Obtain the parameter information of the game participants, input the parameter information of the game participants into the basic model of the three-party game in space orbit, obtain the optimal strategy solution method for the coordinated pursuit of the chasing star and the intercepting star among the game participants, and the optimal strategy solution method for the escape star to evade the coordinated pursuit, obtain the optimal strategy of the game participants, and complete the control of the three-party orbit game. The optimal strategy for coordinated pursuit by the tracking and intercepting satellites is solved as follows: The roles of the pursuing and intercepting satellites in the pursuing spacecraft are determined. The spacecraft that is closer to the escape satellite at the current moment is selected as the intercepting satellite, and the spacecraft that is farther away is selected as the pursuing satellite. The pursuing satellite uses the MinMax algorithm to determine the optimal strategy and predict the optimal strategy of the escape satellite. Based on the predicted optimal strategy of the escape satellite, the optimal strategy of the intercepting satellite is determined, so that the relative distance between the intercepting satellite and the escape satellite is minimized after this round. The optimal strategy for the escape star to evade coordinated pursuit is solved as follows: The MinMax algorithm is used to predict the maneuver strategies of the pursuing and intercepting satellites, and to obtain the first strategy and the second strategy of the escaping satellite when facing the pursuing satellite. The distances between the escape star and the pursuing and intercepting stars, respectively, when selecting the first and second strategies; The strategy with the largest distance between the pursuing star and the escaping star under the first strategy and the second strategy is selected as the optimal strategy for the escaping star.

2. The three-party orbital game control method based on pulse control according to claim 1, characterized in that, The state transition model under the pulse velocity increment is as follows: ； Define the state quantities of relative motion ; N The total number of pulse control applications; ; For the spacecraft in the The pulse velocity increment applied at any given time; ； ； In the above formula, Indicates from arrive The state transition matrix under the given state; The moment the game begins; For the first j The moment when the pulse is applied.

3. The three-party orbital game control method based on pulse control according to claim 2, characterized in that, The game participants include: the chasing star, the intercepting star, and the escaping star; The optimization objective of the tracking star is: ； The optimization objective of the interceptor is: ； The optimization objective of the escape star is: ； The orbital dynamics constraints imposed on the participants in the game during the game process are as follows: ； In the above formula, ; J Indicators representing the profits of both sides in the manhunt; Represents the pursuit star; E represents the interceptor star; E represents the escape star. The moment the game begins; The moment when the game ends; For the first j The moment when the pulse is applied; and These represent the state vectors of the tracking star, the intercepting star, and the escape star, respectively. , and These respectively represent the tracking star, interceptor star, and escape star in... The velocity increment applied at any given moment.

4. The three-party orbital game control method based on pulse control according to claim 3, characterized in that, The upper limit constraint on the control magnitude of the single pulse velocity increment during the orbital maneuver is specifically in the form of: ； The total consumption limit constraint for the pulse velocity increment is specifically in the following form: ； In the above formula, and These represent the maximum value of the velocity increment for each pulse of the tracking star, the intercepting star, and the escaping star, respectively. , and These represent the maximum total reserves of pulse velocity increments for the pursuing star, the intercepting star, and the escaping star, respectively.

5. The three-party orbital game control method based on pulse control according to claim 4, characterized in that, The selection process for the optimal strategy solution method of coordinated pursuit by the tracking satellite and the interceptor satellite is as follows: The game process involves obtaining the initial states of the game participants and determining the maximum number of rounds. It also involves identifying the roles of the pursuing and intercepting satellites in the pursuing spacecraft, using single-round pulse optimization to predict the positions of the game participants before the next pulse maneuver, and determining the optimal strategy at the current moment. After the pulse maneuver, the game process involves obtaining the states of the game participants at each moment, determining whether the pursuit is successful, and ending the game when the escape satellite is captured or the maximum number of rounds is reached.

6. The three-party orbital game control method based on pulse control according to claim 5, characterized in that, The optimal strategy for coordinated pursuit by the tracking and intercepting satellites satisfies the following conditions: ； In the above formula, These represent the optimal strategies for the pursuing satellite and the intercepting satellite, respectively. This represents the optimal strategy predicted by the pursuing star for the escape star.

7. The three-party orbital game control method based on pulse control according to claim 6, characterized in that, The process for selecting the optimal strategy for the escape star to evade coordinated pursuit is as follows: The game begins by obtaining the initial states of the players and determining the maximum number of rounds. Single-round pulse optimization is used to predict the positions of the players before the next pulse maneuver, obtaining the relative distances between the escape star and the pursuing and intercepting stars, and determining the optimal strategy at the current moment. After the pulse maneuver, the game states of the players at each moment are obtained, and it is determined whether the escape was successful. The game ends when the escape star fails to escape or the maximum number of rounds is reached.

8. The three-party orbital game control method based on pulse control according to claim 7, characterized in that, The optimal strategy for the escape star to evade coordinated pursuit satisfies the following conditions: ； Among them, the first strategy chosen by the escape star when facing the pursuing star is The second strategy chosen by the escape star when facing the interceptor star is... The distances between the escape satellite and the pursuing satellite when the escape satellite chooses the first strategy, and the distances between the escape satellite and the intercepting satellite when the escape satellite chooses the first strategy, are respectively... The distances between the escape satellite and the pursuing satellite when the second strategy is selected, and the distances between the escape satellite and the intercepting satellite when the second strategy is selected, are respectively... .

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