Analysis Method for Optimal Pursuit Starting Azimuth of Orbital Pursuit and Evasion under Pulse Maneuver Conditions

Abstract

The present invention discloses a method for analyzing the optimal pursuit start azimuth based on the condition of pulsed maneuver in orbital pursuit and evasion, including: setting the pursuit and evasion to be carried out on the same orbital plane, establishing an orbital coordinate system with the initial position of the evading spacecraft as the origin based on the orbital altitude and the initial relative distance between the evading spacecraft and the pursuing spacecraft, and determining the initial states of the evading spacecraft and the pursuing spacecraft; based on the initial states of the evading spacecraft and the pursuing spacecraft, using a pulsed pursuit and evasion game strategy solution method based on game tree search to obtain the relative distance under the optimal strategy; the pursuing spacecraft starts to pursue from different start azimuths respectively, compares the relative distances at all azimuths under the optimal strategy, and obtains the optimal pursuit start azimuth under this initial condition. The present invention takes into account the limited action set of the pursuit and evasion spacecraft and the influence of the natural evolution of the spacecraft, obtains the optimal pursuit start azimuth under the same orbital plane, and is helpful for the subsequent research on the selection of the initial position in orbital pursuit and evasion.

Description

Technical Field

[0001] The present invention belongs to the field of space technology and relates to a method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition in orbital pursuit and evasion. Background Art

[0002] Many spacecraft are equipped with fixed thrusters that cannot change the thrust direction, so thrust in a limited direction is generated. If the thrust magnitude is fixed each time, then the spacecraft has only limited actions for pursuit and evasion games. During the pursuit and evasion process of the spacecraft, the pursuing spacecraft needs to catch up with the escaping spacecraft within a short time. It not only needs to rely on its own maneuverability to catch up with the escaping spacecraft, but also can rely on the characteristics of the space environment to select a suitable initial pursuit azimuth. Since the fuel of the spacecraft is precious, when conducting orbital pursuit and evasion, the pursuing spacecraft selects an appropriate pursuit start azimuth and utilizes the characteristics of space dynamics to save more fuel to pursue the escaping spacecraft and can catch up with the escaping spacecraft faster.

[0003] Currently, spacecraft all have a limited sensing range and cannot sense information about the other party outside the sensing range of the spacecraft. When the pursuing spacecraft is outside the sensing range of the escaping spacecraft, the escaping spacecraft does not maneuver, and when the pursuing spacecraft enters the sensing range, the escaping spacecraft maneuvers. Existing research lacks the research and analysis on which azimuth outside the sensing range the pursuing spacecraft starts to pursue. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art and provide a method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition in orbital pursuit and evasion, so as to solve the problem of the pursuing spacecraft selecting the optimal pursuit start azimuth in the orbital pursuit and evasion between non-cooperative satellites.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition in orbital pursuit and evasion includes:

[0007] Set the pursuit and evasion of both parties in the same orbital plane. Based on the orbital altitude and the initial relative distance between the escaping spacecraft and the pursuing spacecraft, establish an orbital coordinate system with the initial position of the escaping spacecraft as the origin, and determine the initial states of the escaping spacecraft and the pursuing spacecraft;

[0008] Based on the initial states of the escaping spacecraft and the pursuing spacecraft, adopt a pulse pursuit and evasion game strategy solving method based on game tree search to obtain the relative distance under the optimal strategy;

[0009] The pursuing spacecraft starts to pursue from different start azimuths, compares the relative distances in all azimuths under the optimal strategy, and obtains the optimal pursuit start azimuth under this initial condition.

[0010] Further, the X-axis of the orbital coordinate system points from the center of the earth to the direction of the escaping spacecraft, and the Y-axis points to the velocity direction within the orbital plane where the escaping spacecraft is located.

[0011] Further, the initial state of the escaping spacecraft is

[0012] .

[0013] Further, the initial state of the pursuing spacecraft is

[0014]

[0015] where r represents the initial relative distance between the escaping spacecraft and the pursuing spacecraft, represents the angle between the line connecting the pursuing spacecraft and the escaping spacecraft and the Y-axis.

[0016] Further, the solving process of the impulse pursuit-evasion game strategy based on game tree search includes:

[0017] Determine the finite action sets of both the pursuer and the evader;

[0018] According to the finite action sets, taking the relative distance between the pursuer and the evader after two rounds of impulses as the optimization objective, calculate the root nodes obtained by all pursuit-evasion strategy combinations in two rounds;

[0019] Establish a game tree based on the root nodes, and adopt the minmax game tree search method. Start searching from the root node for the min layer to obtain the corresponding child nodes, and then conduct a max search on the corresponding child nodes. Conduct such a minmax game tree search once;

[0020] According to the corresponding number of rounds, conduct two minmax game tree searches to obtain the optimal strategies for each round of the pursuer and the evader, as well as the relative distance after two rounds of impulses.

[0021] Further, the finite action sets of both the pursuer and the evader include the existing pursuit action set of the pursuing satellite P and the existing evasion action set

[0022] of the escaping satellite E

[0023]

[0024] where m is the total number of existing action sets of the pursuing satellite, and n is the total number of existing action sets of the escaping satellite.

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Selected from the pursuit action set while selected from the escape action set;

[0031] Since there are m types of pursuit actions and n types of escape actions, after two rounds of pulse pursuit and escape between the pursuer and the escapee, the relative distance solutions of strategy combinations can be calculated.

[0032] Furthermore, the minmax game tree search method is as follows:

[0033] First, predict the two-round game between the pursuer and the escapee, and obtain the root nodes of all strategy combinations. Then, conduct the search of the min layer. Since there are m types of pursuit actions in the pursuit action set, there are m choices when selecting the second pulse of the pursuit satellite; divide the root nodes into portions according to the sorting, with m nodes in each portion. Select the minimum value among the m nodes as the child nodes of the min layer, and thus obtain child nodes;

[0034] When conducting the max layer search, since there are n types of escape actions in the escape action set, there are n choices when selecting the second pulse of the escape satellite; divide the child nodes obtained from the min layer into portions according to the sorting, with n nodes in each portion. Select the maximum value among the n nodes as the child nodes of the max layer, and obtain the solution of the pursuit and escape game tree after the last two rounds of pulses, and output the obtained pursuit and escape strategies and the corresponding relative distances.

[0035] Furthermore, the calculation method of the relative distance of all orientations under the optimal strategy is as follows:

[0036] Taking the initial position of the escaping spacecraft as the origin, make a plane circle with a radius of The pursuit spacecraft starts at this circle, and then the pursuer and the escapee conduct a pursuit and escape game based on game tree search to calculate the relative distance after two rounds of both sides.

[0037] Furthermore, the solution process of the optimal pursuit start orientation is as follows:

[0038] Divide the entire circle evenly into N parts, starting from Gradually increase to obtain the angle of each part, that is , perform the calculation of the final relative distance to obtain the final relative distances corresponding to N parts , and then take the minimum value among the N parts , and the corresponding azimuth is the optimal pursuit azimuth angle.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] The present invention provides an analysis method for the optimal pursuit start azimuth of orbital pursuit and escape based on pulse maneuver conditions. The optimal pursuit and escape strategy is searched by using a game tree, and then the optimal pursuit start azimuth is calculated through numerical verification, providing an optimal pursuit azimuth for the pursuit spacecraft in orbital pursuit and escape. At the same time, it also enables the escaping spacecraft to avoid being occupied by the pursuit spacecraft in a suitable pursuit direction for pursuit and escape. The present invention considers the limited action set of the pursuit and escape spacecraft and the influence of the natural evolution of the spacecraft, resulting in different final relative distances obtained by different start azimuths of the pursuit spacecraft. By comparing the final relative distances of different azimuths, the optimal pursuit start azimuth under the same orbital plane is obtained, which is helpful for the subsequent research on the initial position selection in orbital pursuit and escape. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0042] Figure 1 is a flowchart of the analysis method for the optimal pursuit start azimuth of orbital pursuit and escape based on pulse maneuver conditions of the present invention.

[0043] Figure 2 is an orbital coordinate system diagram established with the initial position of the escaping spacecraft of the present invention.

[0044] Figure 3 is a schematic diagram of the trajectories of the natural evolution of the pursuit and escape parties of the present invention.

[0045] Figure 4 is a schematic diagram of the final relative distances of different azimuths of the present invention.

[0046] Figure 5 is a schematic diagram of the final relative distances of different transfer times of the present invention.

[0047] Figure 6 is a schematic diagram of the pursuit and escape game tree of two rounds of the present invention.

[0048] Figure 7 Schematic diagram of the pursuit-evasion game tree for two rounds in Embodiment 1 of the present invention. Detailed implementation manners

[0049] The following describes exemplary embodiments of the present application with reference to the accompanying drawings. Various details of the embodiments of the present application are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present application. Similarly, for clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0050] Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts fall within the scope of protection of the present application.

[0051] In addition, the term "and / or" herein is merely a description of the association relationship of associated objects, indicating that three relationships can exist. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " herein generally represents an "or" relationship between the associated objects before and after.

[0052] The present invention will be further described in detail below with reference to the accompanying drawings:

[0053] See Figure 1 , the present invention provides a method for analyzing the optimal pursuit start azimuth based on impulsive maneuver conditions in orbit pursuit-evasion, discussing which azimuth the pursuit spacecraft should pursue the escaping spacecraft in the pursuit-evasion problem between non-cooperative satellites is optimal, specifically including the following steps:

[0054] S1, assume that the pursuer and the evader conduct pursuit-evasion in the same orbital plane, input the initial relative distance r between the escaping spacecraft and the pursuing spacecraft, input the orbital altitude a, and establish an orbital coordinate system with the initial position of the escaping spacecraft as the origin. The X-axis points from the center of the earth to the direction of the escaping spacecraft, and the Y-axis is the direction of the velocity in the orbital plane where the escaping spacecraft is located, as Figure 2 shown. Assume the initial state of the escaping spacecraft is ;

[0055] S2, let be the angle between the line connecting the pursuing spacecraft and the escaping spacecraft and the Y-axis, and obtain the initial state of the pursuing spacecraft as ;

[0056] S3, the pursuer and evader spacecraft adopt a pulse pursuit-evasion game strategy solution method based on game tree search, and the specific steps are as follows:

[0057] S3.1. Design the finite action sets for both the pursuer and the evader;

[0058] First, set the existing pursuit action set of the pursuing satellite P and the escaping satellite E and the escaping action set , where m is the total number of existing action sets of the pursuing satellite and n is the total number of existing action sets of the escaping satellite.

[0059] Assume that both the pursuer and the evader implement pursuit actions and escaping actions simultaneously, and after time, they reach the corresponding positions and . The orbital transfer of the spacecraft here is all carried out in a single-pulse manner, and the equations are as follows:

[0060]

[0061] Among them,

[0062]

[0063] Meanwhile

[0064]

[0065]

[0066] Substitute the state of the pursuing or escaping satellite and the pulse increment corresponding to the pursuing or escaping action into the above formula, and the state of the pursuing or escaping satellite after one round can be obtained.

[0067] S3.2. Taking the relative distance between the pursuer and the evader after two rounds of pulses as the optimization objective, calculate the root nodes obtained from all combinations of pursuer-evader strategies in two rounds;

[0068] Taking the relative distance between the pursuer and the evader after two rounds of pulses as the optimization objective, calculate the relative distances obtained from all combinations of pursuer-evader actions in two rounds.

[0069] Optimization objective can be expressed as:

[0070]

[0071] Among them,

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] Selected from the pursuit action set while selected from the escape action set.

[0078] Since there are m kinds of pursuit actions and n kinds of escape actions, after two rounds of pulse pursuit and escape by both the pursuer and the escapee, the relative distance solutions of strategy combinations can be calculated.

[0079] S3.3. According to the above root node, establish a game tree, and use the minmax game tree search method to search the min layer starting from the root node to obtain the corresponding child nodes. Then perform a max search on the corresponding child nodes, and thus perform one minmax search;

[0080] S3.4. According to the corresponding number of rounds, perform two minmax game tree searches to obtain the optimal strategies of both the pursuer and the escapee in each round, as well as the relative distance after two rounds of pulses;

[0081] Establish a two-round pursuit and escape game tree, as shown in Figure 6 .

[0082] Since the pursuing satellite hopes that the relative distance after two rounds of pulses is as small as possible, while the escaping satellite hopes that the relative distance after two rounds of pulses is as large as possible. Therefore, adopt the minmax game tree search method to find the pursuit and escape game strategies that meet the search method from the root nodes, and obtain the corresponding relative distance solutions.

[0083] The minmax game tree search method is as follows: First, predict the two-round game of both the pursuer and the escapee, and all the root nodes obtained by the strategy combinations. Then perform the search of the min layer. Since there are m kinds of actions in the pursuit action set , when choosing the second pulse of the pursuing satellite, there are m choices. Divide the root nodes into parts according to the sorting, with m nodes in each part, and select the minimum value among the m nodes as the child nodes of the min layer, so that child nodes can be obtained. When performing the max layer search, since there are n kinds of actions in the escape action set , when choosing the second pulse of the escaping satellite, there are n choices. Divide the child nodes obtained in the min layer into There are n nodes in each share. Select the maximum value among the n nodes as the child node of the max layer. Similarly, for the node selection of the min layer and the max layer, the solution of the pursuit-evasion game tree for the last two rounds is obtained. Output the obtained pursuit-evasion strategy and the corresponding relative distance.

[0084] S4. The pursuit spacecraft starts to pursue from different starting azimuths respectively, compares the relative distances of all azimuths under the optimal strategy, and obtains the optimal pursuit starting azimuth under this initial condition.

[0085] S4.1. Since the pursuit spacecraft and the escaping spacecraft conduct pursuit-evasion in the same orbital plane, only consider the pursuit-evasion of the pursuit spacecraft at different azimuths of 360° in the plane, as Figure 3 shown. Taking the initial position of the escaping spacecraft as the origin and with a radius of make a plane circle. The starting position of the pursuit spacecraft is on this circle, and then both the pursuer and the evader conduct a pursuit-evasion game based on game tree search, and calculate the relative distance after two rounds of both sides.

[0086] S4.2. Divide the whole circle into N equal shares, starting from and gradually increasing, obtain the angle of each share, that is , and conduct the calculation of the final relative distance to obtain the final relative distances corresponding to N shares .

[0087] S4.3. Then take the minimum value among the N shares, and the corresponding azimuth is the optimal pursuit azimuth angle.

[0088] S4.4. Change the magnitude of the transfer time, and repeat the steps of S3 and S4 to obtain the optimal pursuit starting azimuth under different transfer times.

[0089] Example 1:

[0090] Suppose the escaping satellite E is on a circular orbit with an orbital altitude of 42000 km. Establish a relative coordinate system with the initial position of the escaping spacecraft as the origin. The initial state of the escaping spacecraft is shown in Table 1.

[0091] Table 1 Initial relative position and velocity of the escaping spacecraft E (km, km / s)

[0092]

[0093] The following are the specific implementation steps of Example 1 of the present invention:

[0094] S1. Set that both the pursuer and the evader conduct pursuit-evasion in the same orbital plane, and input the orbital altitude Taking the initial position of the escaping spacecraft as the origin, an orbital coordinate system is established. The X-axis points from the center of the earth to the direction of the escaping spacecraft, and the Y-axis points to the velocity direction within the orbital plane where the escaping spacecraft is located, as Figure 2 shown. Set the initial state of the escaping spacecraft as ;

[0095] S2, input the initial relative distance between the escaping spacecraft and the pursuing spacecraft ;

[0096] S3, let be the angle between the line connecting the pursuing spacecraft and the escaping spacecraft and the Y-axis, and obtain the initial state of the pursuing spacecraft as ;

[0097] S4, the pursuit-evasion game strategy solution method based on game tree search is adopted for the pursuit and evasion spacecraft, and the specific steps are as follows:

[0098] S4.1, design the existing pursuit action set of the pursuing satellite P and the escaping action set of the escaping satellite E, where the pursuit action set respectively represents:

[0099] Action : Pulse dv in the negative X-axis direction

[0100]

[0101] Action : Pulse dv in the positive X-axis direction

[0102]

[0103] Action : Pulse dv in the negative Y-axis direction

[0104]

[0105] Action : Pulse dv in the positive Y-axis direction

[0106]

[0107] Action : No maneuver

[0108]

[0109] The escaping action set respectively represents:

[0110] Action : Pulse 0.5dv in the negative X-axis direction

[0111]

[0112] Action : Pulse of 0.5dv in the positive X-axis direction

[0113]

[0114] Action : Pulse of 0.5dv in the negative Y-axis direction

[0115]

[0116] Action : Pulse of 0.5dv in the positive Y-axis direction

[0117]

[0118] Action : No maneuver

[0119]

[0120] Assume that both the pursuer and the evader implement pursuit actions and evasion actions , and both reach the corresponding positions after time. The orbit transfer of the spacecraft here is all carried out in a single-pulse manner, and the equation is as follows: and . Here, the orbit transfer of the spacecraft is all carried out in a single-pulse manner, and the equation is as follows:

[0121]

[0122] Where

[0123]

[0124] At the same time

[0125]

[0126]

[0127] Substitute the state of the pursuing or evading satellite and the pulse increment corresponding to the pursuing or evading action into the above formula, and the state of the pursuing or evading satellite after one round can be obtained.

[0128] S4.2. Taking the relative distance between the pursuer and the evader after two rounds of pulses as the optimization objective, calculate the relative distances obtained by all combinations of pursuing and evading actions in two rounds.

[0129] Optimization objective Can be expressed as:

[0130]

[0131] Where

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] Selected from the pursuit action set while Selected from the escape action set.

[0138] Since there are 5 pursuit actions and 5 escape actions, and the pursuer and the escapee go through two rounds of pulsed pursuit and escape, 625 relative distance solutions of strategy combinations can be calculated.

[0139] S4.3, S4.4, Establish a two-round pursuit and escape game tree, as Figure 7 shown.

[0140] Since the pursuing satellite hopes that the relative distance after two rounds of pulses is as small as possible, while the escaping satellite hopes that the relative distance after two rounds of pulses is as large as possible. Therefore, the minmax game tree search method is adopted to find the pursuit and escape game strategies that meet the search method from 625 root nodes, and the corresponding relative distance solutions are obtained.

[0141] The minmax game tree search method is as follows: First, predict the two-round game between the pursuer and the escapee, and all 625 root nodes obtained from the strategy combinations. Then perform the search of the min layer. Since there are 5 pursuit strategies , when choosing the second pulse of the pursuing satellite, there are 5 choices. Sort the root nodes into 125 parts, each part has 5 nodes, and select the minimum value among the 5 nodes as the child node of the min layer, so that 125 child nodes can be obtained. When performing the max layer search, since there are 5 escape strategies , when choosing the second pulse of the escaping satellite, there are 5 choices. Sort the 125 child nodes obtained from the min layer into 25 parts, each part has 5 nodes, and select the maximum value among the 5 nodes as the child node of the max layer. Similarly, select the nodes of the min layer and the max layer to obtain the solution of the final two-round pursuit and escape game tree. Output the obtained pursuit and escape strategies and the corresponding relative distances.

[0142] In S5, the pursuit spacecraft starts to pursue from different starting orientations, compares the relative distances of all orientations under the optimal strategy, and obtains the optimal pursuit starting orientation under this initial condition.

[0143] S5.1. Since the pursuit spacecraft and the escaping spacecraft perform pursuit and escape in the same orbital plane, only the different orientations of the pursuit spacecraft in the 360° plane are considered for pursuit and escape, as Figure 3 shown. Therefore, a plane circle is made with the initial position of the escaping spacecraft as the center and a radius of . The starting position of the pursuit spacecraft is on this circle, and then both the pursuer and the escapee conduct a pursuit and escape game based on game tree search to calculate the relative distance after two rounds of both sides.

[0144] S5.2. The entire circle is evenly divided into 36,000 parts. Starting from and gradually increasing, the angle of each part is obtained, that is, , and the final relative distance is calculated to obtain the final relative distances corresponding to 36,000 parts . A relative distance graph corresponding to each orientation is made, as shown in Figure 4 below.

[0145] S5.3. Then, the minimum value among the 36,000 parts is taken, and the corresponding orientation is the optimal pursuit azimuth angle.

[0146] S5.4. Change the magnitude of the transfer time, and repeat the steps of S4 and S5 to obtain relative distance graphs under different transfer times, as shown in Figure 5 below. It is obtained that the optimal pursuit starting direction is related to the transfer time, but there is no specific rule.

[0147] The above is only the preferred embodiment of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. Method for analyzing the optimal pursuit start azimuth under the condition of impulsive maneuver, characterized in that, Including: Set the pursuer and the fugitive to pursue and escape on the same orbital plane. Based on the orbital altitude and the initial relative distance between the escaping spacecraft and the pursuing spacecraft, establish an orbital coordinate system with the initial position of the escaping spacecraft as the origin, and determine the initial states of the escaping spacecraft and the pursuing spacecraft. Based on the initial states of the escaping spacecraft and the pursuing spacecraft, adopt a pulse pursuit and escape game strategy solution method based on game tree search to obtain the relative distance under the optimal strategy. The pursuing spacecraft starts to pursue from different starting azimuths, compares the relative distances of all azimuths under the optimal strategy, and obtains the optimal pursuit starting azimuth under this initial condition.

2. The method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition according to claim 1, characterized in that The X-axis of the orbital coordinate system points from the center of the earth to the direction of the escaping spacecraft, and the Y-axis is the direction of the velocity pointing within the orbital plane where the escaping spacecraft is located.

3. The method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition according to claim 1, wherein The initial state of the escaping spacecraft is 。 4. The method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition according to claim 1, wherein The initial state of the pursuing spacecraft is where r represents the initial relative distance between the escaping spacecraft and the pursuing spacecraft, represents the angle between the line connecting the pursuing spacecraft and the escaping spacecraft and the Y-axis.

5. The method for analyzing the optimal pursuit start azimuth based on the pulse maneuver condition according to claim 1, characterized in that The solution process of the pulse pursuit and escape game strategy based on game tree search includes: Determine the finite action sets of the pursuer and the fugitive. According to the finite action sets, with the relative distance between the pursuer and the fugitive after two rounds of pulses as the optimization target, calculate the root nodes obtained from all pursuit and escape strategy combinations in two rounds. Establish a game tree based on the root nodes, adopt the minmax game tree search method, start searching from the root nodes for the min layer to obtain the corresponding child nodes, and then conduct a max search on the corresponding child nodes, so as to conduct one minmax game tree search. According to the corresponding number of rounds, conduct two minmax game tree searches to obtain the optimal strategies for each round of the pursuer and the fugitive, as well as the relative distance after two rounds of pulses.

6. The method for analyzing the optimal pursuit start azimuth of orbital pursuit and escape based on pulse maneuver conditions according to claim 5, wherein The finite action sets of the two parties in the pursuit and escape include the existing pursuit action set of the pursuit satellite P and the existing escape action set of the escape satellite E , where m is the total number of existing action sets of the pursuit satellite, and n is the total number of existing action sets of the escape satellite.

7. The method for analyzing the optimal pursuit start azimuth of orbital pursuit and escape based on pulse maneuver conditions according to claim 5, characterized in that, The optimization target is: Wherein, Select from the pursuit action set while select from the escape actions ; Since there are m types of pursuit actions and n types of escape actions, after two rounds of pulse pursuit and escape by both the pursuer and the escapee, the relative distance solutions of strategy combinations can be calculated.

8. The method for analyzing the optimal pursuit start azimuth of orbital pursuit and escape based on pulse maneuver conditions according to claim 5, characterized in that The minmax game tree search method is: First, predict the two-round game between the pursuer and the evader. All the root nodes obtained from the strategy combinations are then subjected to the search of the min layer. Since there are m types of pursuit actions, there are m choices when selecting the second pulse of the pursuing satellite. The root nodes are sorted and divided into parts, with m nodes in each part. The minimum value among the m nodes is selected as the child node of the min layer, thus obtaining child nodes. When performing the max-layer search, due to the escape action set having n types, there are n choices when selecting the second pulse of the escaping satellite; divide the sub-nodes obtained from the min layer into parts according to sorting, with n nodes in each part. Select the maximum value among the n nodes as the sub-node of the max layer, obtain the solution of the pursuit-evasion game tree after the last two rounds of pulses, and output the obtained pursuit-evasion strategy and the corresponding relative distance.

9. The method for analyzing the optimal pursuit start azimuth of orbit pursuit and escape based on pulse maneuver conditions according to claim 1, characterized in that, The calculation method of the relative distance of all azimuths under the optimal strategy is: Taking the initial position of the escaping spacecraft as the origin and with a radius of make a planar circle. The starting position of the pursuing spacecraft is on this circle, and then the pursuer and the escapee conduct a pursuit-evasion game based on game tree search to calculate the relative distance between the two sides after two rounds.

10. The method for analyzing the optimal pursuit start azimuth based on pulse maneuver conditions according to claim 1, wherein The solution process of the optimal pursuit starting azimuth is: Divide the whole circle evenly into N parts. Starting from gradually increasing, obtain the angle of each part, that is , perform the calculation of the final relative distance, and obtain the final relative distances corresponding to the N parts , then take the minimum value among the N parts , and the corresponding azimuth is the optimal pursuit azimuth angle.

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