Sight-line-based pursuit game decision-making method with capture radius

Abstract

The invention discloses a line-of-sight-based pursuit game decision-making method with a capture radius, and provides a framework of dynamic partitioning and optimal strategy combined solution based on a dynamic relative position relationship between a pursuit and an obstacle and between the pursuit and the obstacle and a dynamic relative position relationship between the pursuit and the obstacle and a dynamic relative position relationship between the pursuit and the obstacle and a dynamic relative position relationship between the escaper and the obstacle in a game scene of the pursuit and the escaper in a region in a complex obstacle environment. According to the method, a geometric method of a Cartesian ovoid is introduced, dominant area boundaries of pursuers and escapes in a pursuit game are constructed, and an optimal tracking path of the pursuers and an optimal escape direction of the escapes are analyzed, so that accurate description of game dynamics is realized; according to the zoning method, the pursuer can quickly adjust the strategy, and the escaper can also select the optimal path to avoid pursuing. The strategy decision-making efficiency of two game parties in a complex environment is remarkably improved, the method is particularly suitable for the field of high-dynamic military confrontation, the wide application potential is shown, and the method has great significance in promoting rapid development of related technologies.

Description

Technical Field

[0001] The present invention relates to the technical field of pursuit-evasion games and two-party decision-making, and particularly relates to a line-of-sight-based pursuit-evasion game decision-making method with a capture radius. Background Art

[0002] The line-of-sight-based pursuit-evasion game with a capture radius plays an important role in many fields. Especially in the context of the rise of vision robot systems, it is widely used in fields such as autonomous navigation, formation control, trajectory tracking, and urban surveillance. For example, in military, autonomous unmanned vehicles are used to detect and strike moving targets; in communication, unmanned vehicles maintain connections with mobile units; in nature conservation, underwater vehicles cross complex environments to monitor marine species. These scenarios can all be summarized as a superior agent pursuing an inferior agent while preventing the inferior agent from escaping the field of view. Such line-of-sight-based pursuit-evasion game problems are part of differential games. The methods for solving such problems usually rely on the Hamilton–Jacobi–Isaacs (HJI) equation to derive the value function and the optimal strategy. However, in scenarios involving multiple target terminals, solving the HJI equation becomes very challenging.

[0003] The most commonly used method currently is the geometric method: using Cartesian ovals to construct the reachable region of each escapee, that is, the escapee can reach any position inside the Cartesian oval, and the escapee will be captured by the pursuer on the Cartesian oval. However, most of the current methods based on Cartesian ovals are carried out in a scenario without obstacles, and there is a lack of application conditions for this method in scenarios with obstacles.

[0004] Most of the current pursuit-evasion game research is aimed at the pursuit-evasion problem without the influence of line of sight. When there is a blind spot during the pursuit process of a pursuer, the situation where the pursuer loses the target of the escapee will occur, and there will also be problems with strategies that cannot balance pursuit and maintain visibility. Summary of the Invention

[0005] The present invention aims to provide a line-of-sight-based pursuit-evasion game decision-making method with a capture radius, which can be applied to the fields of unmanned vehicles and high-dynamic military confrontations. In a complex environment with obstacles, while maintaining visibility of the escapee, it provides a more effective escape strategy for the escapee, enabling the pursuer to effectively complete the pursuit task.

[0006] To achieve the above object, the present invention provides the following technical solution: A line-of-sight-based pursuit-evasion game decision-making method with a capture radius, comprising the following steps:

[0007] S1. Set the game area, which includes a pursuer, an escapee, and possibly existing obstacles;

[0008] S2. Obtain the pursuer's field of view, star-shaped area, blind area, and the lines of sight formed with the vertices of the obstacles in the obstacle scenario;

[0009] S3. Obtain the capture radius of the pursuer, as well as the positions, speeds, and their speed ratio of the escapee and the pursuer;

[0010] S4. Decompose into two complementary areas, analyze the winning area and optimal strategy of the basic area where the pursuer is located, i.e., the star-shaped area, and construct a theoretical framework to support the strategy optimization and area analysis of the area outside the star-shaped area;

[0011] S5. In the star-shaped area, fix the position of the pursuer, use the relationship between the Cartesian oval and the vertices of the obstacles to construct the pursuer's strategy switching condition, and execute different strategies according to the condition to ensure that the pursuer completes the pursuit while maintaining visibility of the escapee;

[0012] S6. In the area outside the star-shaped area, fix the position of the pursuer, apply methods including but not limited to the Cartesian oval and the Hamilton–Jacobi–Isaacs (HJI) equation, divide the field of view into several areas, and determine the strategies of both sides according to the area where the escapee is located.

[0013] Specifically, the strategy switching condition of the star-shaped area is: determine a circle according to the positional relationship among the pursuer, the escapee, and the vertices of the obstacles, and judge whether the escapee is located inside the specific circle; if the escapee is located inside the circle, adopt a specific strategy, otherwise adopt another strategy.

[0014] Specifically, when the pursuer is located in the area outside the star-shaped area, obtain the positional relationship between the Cartesian oval formed by the pursuer and the escapee and the line of sight, use the geometric relationship between the Cartesian oval and its tangent line, as well as the kinematic equations of the escapee and the pursuer, and combine with the HJI equation to solve the optimal strategy, and determine the winning areas and corresponding strategies of the escapee and the pursuer.

[0015] Specifically, when the escapee is located in different areas divided by the geometric relationship and the HJI equation, adopt corresponding strategies, including but not limited to the direct pursuit strategy and the surveillance strategy, to ensure that the pursuer can complete the pursuit while maintaining visibility of the escapee.

[0016] Specifically, the use of the HJI equation for area division and strategy is as follows: define the transformation of the state space, obtain the Hamiltonian function and the first principal equation according to the trigonometric theorem and the kinematic formula, solve the first principal equation to obtain the optimal strategies of the escapee and the pursuer, substitute the optimal control strategy into the state equation to obtain the backward trajectory equation, and obtain the winning areas of the escapee and the pursuer according to the backward trajectory equation.

[0017] The principle and beneficial effects of this technical solution:

[0018] 1. The present invention provides a line-of-sight based pursuit-evasion game decision-making method with a capture radius in an obstacle area. A comprehensive solution is proposed for the scenario where there are obstacles in the area and attacks need to be carried out while maintaining visibility. The problem is decomposed into two complementary regions, each representing different game dynamics. By analyzing the winning region and optimal strategy of a basic region, i.e., the star-shaped region, a theoretical framework is constructed, which provides strong support and guidance for the strategy optimization and region analysis of the second region, i.e., the region outside the star-shaped region. This decomposition method significantly reduces the complexity of the problem and provides a clear theoretical basis for dynamic games in complex environments.

[0019] 2. The present invention provides a line-of-sight based pursuit-evasion game decision-making method with a capture radius in an obstacle area. Through explicit analysis, Cartesian ovals are introduced, and the specific conditions under which the direct attack strategy or the surveillance strategy has advantages during the pursuit process are clarified. Combining the geometric characteristics of Cartesian ovals, precise strategy expressions applicable to each scenario are derived, providing a reliable theoretical basis and practical guidance for game decision-making under different conditions. This analysis method provides a systematic decision-making basis for pursuit-evasion games in complex environments, making strategy selection more accurate and efficient.

[0020] 3. The present invention provides a line-of-sight based pursuit-evasion game decision-making method with a capture radius in an obstacle area. By applying the Hamilton-Jacobi-Isaacs (HJI) equation, an optimal balance is achieved between attacking and surveilling the target, and the winning regions and corresponding optimal strategies of the pursuer and the escapee are derived. Through this method, a comprehensive game solution framework is constructed, which is applicable to multi-target scenario environments with complex obstacles, significantly enhancing the theoretical depth and practical application value of pursuit-evasion games. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flowchart of the present invention;

[0022] Figure 2 is a schematic diagram of the first process of the line-of-sight based pursuit-evasion game of the present invention;

[0023] Figure 3 is a schematic diagram of the second process of the line-of-sight based pursuit-evasion game of the present invention;

[0024] Figure 4 is a schematic diagram of the third process of the line-of-sight based pursuit-evasion game of the present invention;

[0025] Figure 5 is a schematic diagram of the fourth process of the line-of-sight based pursuit-evasion game of the present invention;

[0026] Figure 6Schematic diagram V of the pursuit-evasion game process based on line of sight according to the present invention;

[0027] Figure 7 Schematic diagram VI of the pursuit-evasion game process based on line of sight according to the present invention;

[0028] Figure 8 Schematic diagram VII of the pursuit-evasion game process based on line of sight according to the present invention;

[0029] Figure 9 Schematic diagram VIII of the pursuit-evasion game process based on line of sight according to the present invention;

[0030] Figure 10 Schematic diagram IX of the pursuit-evasion game process based on line of sight according to the present invention. Detailed implementation manners

[0031] The present invention will be further described in detail below in conjunction with the accompanying drawings and implementation manners:

[0032] Embodiment:

[0033] As Figure 1 shown, a decision-making method for pursuit-evasion game based on line of sight in an obstacle area includes the following steps:

[0034] Step 1: Assume that there is a pursuer P and an evader E in the game area, and obtain the field of view F of the pursuer in the obstacle scenario P , star-shaped area S A , blind area O A , and the line of sight los A formed with the vertex A of the obstacle. Among them, when the evader crosses los A and enters O A , it indicates that the pursuer loses visibility of the evader. When the pursuer is located in S A , the pursuer can see the situations on both sides of the obstacle at the same time, and there is no los A and O A at this time. Fix the position of the pursuer. When the pursuer is located in S A , use the relationship between the Cartesian oval ω and the vertex A to construct the pursuer strategy switching condition. Eventually, the pursuer can definitely complete the pursuit of the evader while maintaining visibility of the evader; when the pursuer is located in other areas, divide the field of view F A into several areas according to the positional relationship formed by the vertex A, the line of sight los P and the Cartesian oval ω, and determine the strategies of both sides according to the area where the evader is located.

[0035] Specifically, as Figure 2 shown, represent the coordinates of points in the area with polar coordinates (r, θ), A is the pole, and one side O 1 of the obstacle is located at θ = π, and the star-shaped area S AFormed by extending the two sides of the obstacle in the reverse direction, O 1 , O 2 . x E (t) = (r e (t), θ e (t)) and x P (t) = (r p (t), θ p (t)) represent the positions of the escapee and the pursuer at time t respectively, v e and v p represent the speeds of the escapee and the pursuer respectively, and the ratio of their speeds is The difference in their polar angles θ ep = θ e - θ p . The capture radius of the pursuer is k, and the shortest distance between point M and x is expressed in the form of d(x, M), where x can be a point, a line, or a region. The mathematical model of the movement of the pursuer and the escapee in polar coordinates is:

[0036]

[0037] where, ψ p (t) and ψ e (t) are the control angles of the pursuer and the escapee, and are the speeds on the polar radius, and are the angular speeds.

[0038] The goal of the pursuer is to strike the escapee while maintaining surveillance, and the goal of the escapee is to avoid being struck by the pursuer and enter the blind area of the pursuer as soon as possible. This setting forms a complex game environment with multi-objective strategies and dynamic decision-making elements, aiming to study how the pursuer can effectively capture the escapee and how the escapee can adopt strategies to avoid being captured.

[0039] Based on this, the present invention can establish a pursuit-evasion game model based on the line of sight between an escapee and a pursuer under an obstacle, and use the Cartesian oval to construct the reachable region R E of the escapee. Among them, R E is expressed as:

[0040] R E = {X|d(X, E) ≤ α(d(X, P) - k)}

[0041] As Figure 3 shown, by setting the pursuit strategy of the pursuer, the pursuer will capture the escapee on or inside the Cartesian oval, and the escapee can reach any place inside the Cartesian oval without being captured by the pursuer. If the escapee chooses the control input ψ eWhen the fugitive tries to escape, the pursuer can adopt the following parallel strategies to ensure capturing the fugitive on or inside the Cartesian oval:

[0042]

[0043]

[0044] When the pursuer is located inside S A utilize the relationship between the Cartesian oval ω and the vertex A to construct the pursuer's strategy in the pursuit-evasion game. When the vertex A is not inside the Cartesian oval, the paths of the pursuer and the fugitive are not interfered by obstacles at this time, and the pursuer can directly adopt ψ p1 strategy to conduct the pursuit. On the contrary, when the vertex A is located inside the Cartesian oval, the coordinates of the fugitive are located inside the circle e 1 The expression within the circle e 1 region is as follows:

[0045] C e1 ={x E (r e , θ e )|r e ≤α(r p -k)}

[0046] At this time, the pursuer's strategy ψ p1 is affected by the obstacle, and by adopting the strategy ψ p2 =π, it is certain to drive the fugitive out of the circle e 1 , and then by adopting the strategy ψ p1 the pursuer can capture the fugitive. Therefore, when the pursuer is located inside S A , the pursuer can definitely capture the fugitive.

[0047] Step 2. When the pursuer is located in other regions, through the method of combining geometry and the HJI equation, the winning regions of the pursuer and the fugitive can be qualitatively analyzed, and the field of view F P of the pursuer can be quantitatively analyzed for region division, and there is a corresponding strategy for the fugitive in different regions.

[0048] Specifically, due to axial symmetry being a major feature of angular obstacles, studying the situation where the pursuer is located at θ p ∈(-π, 0) is sufficient to cover all situations under angular obstacles. Similarly, adopting ψ p1 needs to exclude the influence of obstacles. As shown in Figure 4 , T is a point on the ray PA, d(T, P)=k. When the Cartesian oval is tangent to los A , This theorem reveals the fixed-value relationship between Cartesian ovals and their tangents, providing theoretical support not only for the game problems described in this study but also for other game problems involving Cartesian ovals.

[0049] Combined with the previous conclusion, it can be seen that when the Cartesian oval does not intersect with los A the escaper is in region R P1 , and this region can be expressed as:

[0050]

[0051] where the pursuer can directly adopt strategy ψ p1 and finally capture the escaper.

[0052] When the escaper is outside region R p1 the pursuer can also eliminate the influence of obstacles through ψ p2 , that is, before the escaper enters the blind area O A the pursuer has reached vertex A to eliminate O A , and then the pursuer adopts ψ p1 to capture the escaper. During the process of the pursuer reaching A by adopting ψ p2 los A and O A remain unchanged, and the escaper can walk at most αr p , and during this period, the escaper cannot enter the pursuer's strike range. Under the combined action of these conditions, region R P2 is formed, and this region is expressed as:

[0053]

[0054] When the escaper is in R P2 , on the premise that the pursuer adopts ψ p2 , there are only two situations: when the pursuer reaches A, the escaper has not reached 0 A ; the pursuer has captured the escaper before reaching A. In either case, the pursuer can capture the escaper at the final moment. Strategies ψ p1 and ψ p2 are collectively referred to as the pursuit strategies.

[0055] For the remaining regions in F P except R p1 and R P2 , since the points in these regions are too close to O A , directly adopting the pursuit strategy may lead to the failure of capture, and at this time, the surveillance strategy should be adopted. As stated in step one, when the pursuer is at S AWhen the pursuer is at S, the pursuer will surely catch the escaper, and the pursuer will not lose sight of the escaper. Therefore, the core idea of the surveillance strategy is to first reach S while ensuring visibility of the escaper, A and then adopt the pursuit strategy. At this time, the line-of-sight-based pursuit-evasion game with a capture radius can be transformed into a game problem of maintaining visibility. A For the surveillance strategy, the method of region division is still used to formulate different strategies to achieve the purpose of keeping the escaper under surveillance.

[0056] Figures and respectively show the results of region division at and. Among them, the expression of R Figure 5 and Figure 6 respectively show and when the region division results. Among them, Figure 5 R P3 is:

[0057]

[0058] Figure 6 R P3 , R P4 and R P5 are respectively

[0059]

[0060] The corresponding strategies are respectively ψ P = π - θ p = ψ p4 and ψ P = π - θ p = ψ p5 . ψ p3 , ψ p4 and ψ p5 are collectively called the surveillance strategy. In and, a special region called R Figure 5 and Figure 6 is also marked. When the escaper is in this region, since the escaper is too close to vertex A, the pursuer cannot maintain visibility of the escaper only by adopting the surveillance strategy. When the escaper is in R Q . When the escaper is in R P3 , R P4 and R P5 , the pursuer can not only prevent the escaper from entering O A and R A before the pursuer reaches S Q , but also has a certain probability of entering R P1 or R P2 region, and the pursuer wins the game in the end.

[0061] When the escaper is in RQ When the escapee is too close to vertex A at this time, it doesn't necessarily mean that the escapee can definitely escape. Since the pursuer has a capture radius, there is a situation where the escapee is about to escape the pursuer's surveillance but is struck by the pursuer. At this time, both the pursuer and the escapee need to balance between direct capture or evasion and maintaining or disrupting the surveillance strategy. This can be well achieved by means of the HJI equation.

[0062] Define d(P, E) = R, and transform the state space from x = (x P , x E ) to x = (θ p , θ ep , m, R). According to the trigonometric theorem and the kinematic formula, the state equation is obtained as follows:

[0063]

[0064] Where, Let λ T = (λ p , λ θ , λ m , λ R ) represent the normal vector at the hypersurface point x = (θ p , θ ep , m, R). Let v p = 1 and v e = α, the Hamiltonian equation is:

[0065]

[0066] According to Isaacs' definition, the first principal equation is:

[0067]

[0068] By solving the first principal equation, the optimal strategies of the escapee and the pursuer are obtained as follows:

[0069]

[0070] Substitute the optimal strategy into the first principal equation, and the second principal equation can be written as:

[0071] αρ e - ρ p = 0

[0072] At any point on the hypersurface, there are two normal vectors pointing in opposite directions. In this work, the boundary normal direction pointing to the target set is selected. The optimal control strategy of each player at any point on the boundary is expressed as a function of the normal vector. Substitute the optimal control strategy into the state equation to obtain the backward trajectory equation:

[0073]

[0074] Among them, o represents the differentiation with respect to backward time. According to the conclusion of Step 1, when located within S A , the pursuer will surely win. Therefore, the pursuer has two goals: First, to achieve θ p > 0; second, to achieve R ≤ k. Therefore, the boundary of the target set is as follows:

[0075]

[0076] Boundary has a parametric form: θ p1 (0) = 0, θ ep1 (0) = π, λ m1 (0) = 0, λ R1 (0) = 0, m 1 (0), R 1 (0), λ p1 (0) and λ θ1 (0) are arbitrary. Boundary has a parametric form: θ ep2 (0) = π, R 2 (0) = k, λ p2 (0) = 0, λ m2 (0) = 0, θ p2 (0), m 2 (0), λ θ2 (0) and λ R2 (0) are arbitrary. These determine the parameters of the initial point of the backward trajectory equation. However, despite having derived the backward trajectory equation and its initial point parameters, the high dimensionality of the system and the complex coupling relationships between variables make it difficult to obtain an analytical expression. Therefore, numerical methods are used to solve it. By adjusting the initial parameters and applying the backward trajectory equation, different backward trajectories are obtained. Figure 7 and Figure 8 respectively show and when, for F P the complete region division. By fixing x P , finding the backward trajectory passing through x P , and recording the corresponding x E points. The obtained x E points are fitted to form and the corresponding boundary fences, and the intersection of the internal regions of the two obtained boundary fences forms the winning region W E of the evader, while the winning region of the pursuer is denoted as W P = F P \WE 。

[0077] When the escapee is at W P , the pursuer's goal is to attack the escapee in the shortest possible time, while the escapee tries to delay being targeted for as long as possible. Similarly, when the escapee is at W E , the escapee's goal is to get out of the pursuer's sight as soon as possible, while the pursuer tries to prolong the engagement time. Therefore, in the differential game, the duration of participation is used as the payoff function to analyze the optimal strategies of both sides. Regarding the winning time T ω as the payoff in the differential game, when the escapee is at W P , the payoff function is given by:

[0078]

[0079] At this time, the Hamiltonian equation can be written in the following form:

[0080]

[0081] When the escapee is at R P6 , the optimal control strategies of the pursuer and the escapee are the same as the optimal strategies of the escapee and the pursuer obtained when solving the first main equation, denoted as ψ p6 and ψ e6 . When the escapee is at W E , the optimal control angles of the pursuer and the escapee, denoted as and respectively, can be expressed as:

[0082]

[0083] By fixing the position of the pursuer and dividing the area of F P , there is a corresponding strategy for the escapee in each area, thus constructing a complete strategy system.

[0084] For example:

[0085] S1: Record the relative positions among the pursuer, the escapee and the obstacles, and judge whether the pursuer is at S A . If so, the pursuer can observe the situations on both sides of the obstacle and will not lose visibility of the escapee, and execute the pursuit strategy, see step S2; if not, divide the field of view F P of the pursuer into areas, and decide the strategy in real time according to the area where the escapee is located, see step S3;

[0086] S2: As Figure 9 , the pursuer is within S A . Judge whether the escapee is within the circle e1 If yes, then adopt strategy ψ P2 Force the escapee out of the circle 1 Then take ψ P1 If not, directly adopt strategy ψ P1 to hunt down the escapees;

[0087] S3: The pursuer is located in a location other than S A Other areas outside. Vision of the pursuer F P Divide the area and adopt different strategies according to the different areas where the escapees are located. Figure 10 , at the initial moment, the escapee is at R P6 The pursuer and the escaper adopt strategies ψ P6 and ψ e6 As time goes by, the escapees enter area R one by one. P3 and R P2 , prompting the pursuer to adjust its strategy accordingly to ψ P3 and ψ P2 , and finally captured the escapee.

[0088] In summary, the present invention provides a strategy for attacking while effectively maintaining visibility in scenarios where obstacles exist in the area, and specifically gives strategies for pursuers and escapees. Compared with traditional research based solely on geometric methods, the method of the present invention is not only applicable to single-target scenarios of intelligent agents, but can also handle the strategy equilibrium selection of multiple targets at the same time, which makes the method more versatile and can be applied in various fields involving multi-target strategies, such as military target tracking and attacking, communication network maintenance and connection, and ecological monitoring in complex environments.

[0089] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. For those skilled in the art, without departing from the technical solution of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A line-of-sight-based pursuit-and-escape game decision-making method with a capture radius, characterized in that: The following steps are involved: S1. Set up a game area, which includes a pursuer and a fleeer, as well as possible obstacles; S2, obtaining the pursuer's field of view, star-shaped area, blind area, and line of sight with the apex of the obstacle in the obstacle scene; S3, obtaining the capture radius of the pursuer, as well as the positions, speeds and speed ratios of the escaper and the pursuer; S4, decompose two complementary regions, analyze the winning region and optimal strategy of the star region, the basic region where the pursuer is located, and build a theoretical framework to provide support for strategy optimization and regional analysis of regions outside the star region; S5. In the star-shaped area, the pursuer's position is fixed, and the relationship between the Cartesian oval line and the obstacle vertex is used to construct the pursuer's strategy switching conditions. Different strategies are executed according to the conditions to ensure that the pursuer completes the pursuit while maintaining visibility of the escapee; S6. In the area outside the star-shaped area, fix the position of the pursuer, apply methods including but not limited to the Cartesian oval and the Hamilton–Jacobi–Isaacs (HJI) equation to divide the field of view into several areas, and determine the strategies of both parties based on the area where the escapee is located.

2. A line-of-sight-based pursuit-and-escape game decision-making method with a capture radius according to claim 1, characterized in that: The strategy switching condition of the star-shaped area is: determine the circle according to the positional relationship between the pursuer, the escaper and the vertices of the obstacle, and judge whether the escaper is located in a specific circle; if the escaper is in the circle, adopt a specific strategy, otherwise adopt another strategy.

3. The line-of-sight-based pursuit-and-escape game decision-making method with a capture radius according to claim 1 is characterized in that: When the pursuer is outside the star-shaped area, the positional relationship between the Cartesian oval formed by the pursuer and the escapee and the line of sight is obtained. The geometric relationship between the Cartesian oval and its tangent, as well as the kinematic equations of the escapee and the pursuer, are used to solve the optimal strategy in combination with the HJI equation to determine the winning areas and corresponding strategies of the escapee and the pursuer.

4. The line-of-sight-based pursuit-and-escape game decision-making method with a capture radius according to claim 3 is characterized in that: When the fugitive is located in different areas divided by geometric relationships and HJI equations, corresponding strategies are adopted, including but not limited to direct pursuit strategy and monitoring strategy, to ensure that the pursuer can complete the pursuit while maintaining visibility of the fugitive.

5. The line-of-sight-based pursuit-and-escape game decision-making method with a capture radius according to claim 4 is characterized in that: The HJI equation is used for area division and strategy: define the transformation of state space, and obtain the Hamiltonian function and the first principal equation according to the trigonometric theorem and kinematic formula. By solving the first principal equation, the optimal strategy of the escaper and the pursuer is obtained. Substituting the optimal control strategy into the state equation, the backward trajectory equation is obtained. According to the backward trajectory equation, the winning area of ​​the escaper and the winning area of ​​the pursuer are obtained.

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