An open formation hunting method based on multi-agent pursuit-evasion game with field of view interaction

Abstract

The present application relates to an open formation hunting method based on multi-agent pursuit and evasion game with field of view interaction, first, a new open formation layout of pursuers hunting evaders is proposed, and a new interactive dynamics model is established to describe the influence of pursuers on evaders; next, a mathematical model of field of view interaction is introduced, and the field of view interaction is equipped to each pursuer; then, a hunting method is proposed, which realizes effective capture by gradually changing the size and shape of formation geometric layout. The following problems are solved: (1) a new hunting method is proposed to reduce the cost required for hunting. (2) the mathematical model of field of view interaction is applied in the hunting method.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of multi-agent pursuit-evasion, and relates to an open formation pursuit method based on multi-agent pursuit-evasion game with field of view interaction. BACKGROUND

[0002] In recent years, pursuit-evasion game and pursuit strategy have been a hot topic in many research fields such as game theory, optimal control, behavioral biology, etc. This topic has wide attraction for military and civil applications, such as missile interception, aircraft control, search and rescue operations, etc. However, most of the pursuit strategy researches are limited to linear motion or have strict requirements on the initial relative position. In addition, most of the current pursuit methods try to build a closed formation to capture the target. In practice, a closed formation requires more agents to participate in order to complete the task, resulting in more cost. In addition, after the closed formation is destroyed, the pursuers need to reorganize and capture the evader. Therefore, it is of great practical significance to study an open formation layout.

[0003] Field of view is often used as a mathematical model that can perceive the surrounding environment, and the corresponding perception sensor has good practical effect. However, the mathematical model of field of view interaction has not been well applied in the research of pursuit-evasion game and pursuit strategy. SUMMARY

[0004] Technical problems to be solved

[0005] In order to avoid the shortcomings of the prior art, the application provides an open formation pursuit method based on multi-agent pursuit-evasion game with field of view interaction, which mainly solves the following problems: (1) a new pursuit method is proposed to reduce the cost required for pursuit; (2) the mathematical model of field of view interaction is applied in the pursuit method.

[0006] Technical scheme

[0007] An open formation pursuit method based on multi-agent pursuit-evasion game with field of view interaction, characterized in that: it comprises n pursuers and one evader; the pursuit steps are as follows:

[0008] Step 1: (1) a coordinate system with the center pursuer as the origin is established, and the evader moves along the x-axis, and a geometric model layout of the pursuer and the evader is established as:

[0009] The n pursuers are uniformly distributed on a circle with a radius R, the center of the circle is located on the x-axis, and the distance between the center of the circle and the evader is l;

[0010] The central chaser is defined as level 0, the chasers on both sides form level 1, the chasers adjacent to level 1 form level 2, and so on, with each side having m = (n-1) / 2 levels of chasers. The last level is located on the same straight line parallel to the y-axis as the center.

[0011] (2) Dynamic equations of the pursuer and the escapee:

[0012] The pursuers maintain a constant speed v, and the layout of n pursuers is maintained, moving along the x-axis towards the escapee; let ξ p (t)=[x p (t),y p (t)] and ξ e (t)=[x e (t),y e Let (t) represent the positions of a pursuer and an escapee at time t, respectively. and Let represent the dynamics of a pursuer and an escapee at time t, respectively.

[0013] Step 2: Construct a mathematical model of the pursuer's field of view, extending the escapee's motion along the x-axis to a complete two-dimensional environment;

[0014] The field-of-view mathematical model uses an isosceles triangle geometry to represent the perception ability of any pursuer i, denoted as: Through distributed control laws, the escapee is positioned within the field of view triangle of each pursuer. Inside, the pursuer adjusts its direction based on the angle and direction of the fleeing person;

[0015] The The three points are and Define a direction θ relative to the pursuer i angular offset ε i ;

[0016] Define distance and These represent the escapee's destinations on the three sides of the triangle. and The distance;

[0017] Step 3: Based on the geometric model established in Step 1 and the field-of-view model provided for the pursuer in Step 2, the encirclement method is as follows:

[0018] The evader moves along the x-axis according to the dynamics of the evader, and the n pursuers maintain the layout of step 1 according to the dynamics of the i-th level pursuer, and move along the x-axis to the evader; when the front pursuer, i.e. the m-th level pursuer, moves to the same x-axis coordinate as the evader, the front pursuer, i.e. the m-th level pursuer, stops moving in the x-axis direction, i.e. the speed of the front pursuer, i.e. the m-th level pursuer, in the x-axis is 0, i.e.

[0019] The front pursuer moves along the x-axis in the direction perpendicular to the x-axis, and the evader is tackled, i.e. Since the radius of the circle is equal to the distance of the front pursuer to the x-axis, i.e. Therefore, the radius of the circle decreases as decreases; at this time, the other pursuers adaptively adjust their positions on the circle so that they are still on the circle.

[0020] Finally, when the front pursuer moves to , the pursuer successfully captures the evader.

[0021] In the layout of the geometric model, the coordinate position of each pursuer in the formation relative to the center pursuer is:

[0022]

[0023] where i={0,1,…,m}, the i-th level pursuer on both sides is located at

[0024] The distance between the i-th level pursuer above the first level and the evader in the x-axis is:

[0025]

[0026] The total distance between the i-th level pursuer above the first level and the evader is:

[0027]

[0028] The total distance between the 0-th level center pursuer and the evader is:

[0029]

[0030] where

[0031] The dynamics of the i-th level pursuer is represented by a continuous and monotonically decreasing function σ i :

[0032]

[0033] where, where the specific behavior parameters α and β.

[0034] The parameters a and b together define the degree to which the evader tries to escape as the distance to the pursuer decreases, a = 1.5, b = 0.15.

[0035] The dynamics of the evader are:

[0036]

[0037] where s = 0.5, and 0 is the dynamics of the 0th pursuer.

[0038] In the field of view mathematical model, the relative distance between the pursuer and the evader is converted into x and y axis components, position, angle and distance are as follows:

[0039]

[0040]

[0041] where R (e i ) represents the rotation matrix corresponding to the angle e i , and The transfer vector is represented as:

[0042]

[0043] where g i represents half of the top angle of the isosceles triangle.

[0044] The arbitrary pursuer i is equipped with a limited field of view sensor, which can perceive the angle and direction of the evader within the field of view.

[0045] An electronic device, characterized by comprising a processor and a memory, the processor is used to execute the computer program stored in the memory to realize the steps of the open formation encirclement method based on multi-agent pursuit and evasion game with field of view interaction.

[0046] A readable storage medium, characterized by, the readable storage medium stores a computer program, the computer program is executed by the processor to realize the steps of the open formation encirclement method based on multi-agent pursuit and evasion game with field of view interaction.

[0047] A computer program product, characterized by comprising computer executable instructions, the instructions are executed to realize the steps of the open formation encirclement method based on multi-agent pursuit and evasion game with field of view interaction.

[0048] Advantages

[0049] The application provides an open formation hunting method based on multi-agent pursuit and evasion game with field of view interaction.

[0050] The application has the following beneficial effects:

[0051] The application can be applied to a multi-agent pursuit and evasion hunting model, and realizes the capture of the pursuer on the evader within a limited time.

[0052] (1) On the basis of the general dynamic model studied at present, a new interactive dynamic model is established to describe the influence of the pursuer on the evader, and the open formation capture strategy is promoted in theory.

[0053] (2) A new open formation layout is proposed for cooperative hunting of the evader.

[0054] (3) By introducing the mathematical model of the field of view interaction, the limitation of the fixed initial position of the agent is eliminated, and the strategy proposed by the method of the application is expanded from single-axis motion to the whole two-dimensional environment.

[0055] (4) After the field of view interaction model is equipped for each pursuer, the motion ability of the evader is also expanded. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 is a schematic diagram of the hunting strategy of the application, and is a schematic diagram of the hunting strategy when n=5 in the embodiment

[0057] Figure 2 is a schematic diagram of the mathematical model of the field of view interaction of the application, and is a schematic diagram of the mathematical model of the field of view interaction when n=5 in the embodiment

[0058] Figure 3 is a schematic diagram of the motion of the open formation equipped with the field of view model to capture the evader, and is a schematic diagram of the motion of the open formation equipped with the field of view model to capture the evader when n=5 in the embodiment. DETAILED DESCRIPTION

[0059] The application will be further described in combination with the embodiments and the drawings:

[0060] Step 1: (1) Establish a coordinate system with the central pursuer as the origin, and the evader moves along the x-axis. The geometric model layout of the pursuer and the evader is as follows:

[0061] 5 pursuers are evenly distributed on a circle with a radius of R = 3, and the center of the circle is located on the x-axis. The distance between the center of the circle and the evader is l = 2;

[0062] The central pursuer is defined as the 0th level, the two adjacent pursuers on both sides constitute the 1st level, the pursuers adjacent to the 1st level are the 2nd level, and the order is arranged as follows: there are 2 levels of pursuers on each side, and the last level is located on the same straight line as the center parallel to the y-axis;

[0063] In the geometric model layout, the coordinate position of each pursuer in the formation relative to the central pursuer is as follows:

[0064]

[0065] where i = {0, 1, 2}, the i-level pursuer on both sides is located at

[0066] The distance between any i-level pursuer above the 1st level and the evader on the x-axis is:

[0067]

[0068] The total distance between any i-level pursuer above the 1st level and the evader is:

[0069]

[0070] The total distance between the 0th level central pursuer and the evader is:

[0071]

[0072] where

[0073] (2) The dynamic equation of the pursuer and the evader:

[0074] The pursuer maintains a constant speed v, maintains the layout of 5 pursuers, and moves along the x-axis towards the evader. Let ξ p (t) = [x p (t), y p (t)] and ξ e (t) = [x e (t), y e (t)] represent the positions of a certain pursuer and evader at time t, respectively, then and represent the dynamics of a certain pursuer and evader at time t, respectively.

[0075] In this method, the dynamics of the escapee are influenced by the pursuer.

[0076] This method defines the dynamics of the escapee as being influenced by a pursuer of a characteristic at level i, by a continuously monotonically decreasing function σ. i express

[0077]

[0078] Among them, specific behavioral parameters α and β, which together define the degree to which the escapee tries to escape as the distance to the pursuer decreases, α = 1.5, β = 0.15;

[0079] The dynamics of the escapee are:

[0080]

[0081] Where, σ 0 It is the dynamics of the level 0 pursuer.

[0082] Step 2: Construct a mathematical model of the pursuer's field of view, extending the escapee's motion along the x-axis to a complete two-dimensional environment;

[0083] The field-of-view mathematical model uses an isosceles triangle geometry to represent the perception ability of any pursuer i, denoted as: Through distributed control laws, the escapee is positioned within the field of view triangle of each pursuer. Inside, the pursuer adjusts its direction based on the angle and direction of the fleeing person;

[0084] The The three points are and Define a direction θ relative to the pursuer i angular offset ε i ;

[0085] The model equips the pursuer with a limited field-of-view sensor, enabling it to perceive the angle and direction of the escapee within the field of view.

[0086] In the field-of-view mathematical model, the pursuer calibrates its direction based on the angle and direction of the escapee.

[0087] The relative distance between the pursuer and the fleeing person is converted into x-axis and y-axis components, with the position, angle, and distance as follows:

[0088]

[0089] Where R(ε) i ) represents the angle ε i The rotation matrix, and The transfer vector is represented as:

[0090]

[0091] where γ i represents half of the top angle of the isosceles triangle.

[0092] By a distributed control law, the evader is within the field of view triangle of each pursuer.

[0093] In addition, the distance and respectively represent the distance of the evader to the three edges of the triangle and , as shown in Figure 2 .

[0094] Step 3: Based on the geometric model established in step 1 and the field of view model equipped for the pursuer in step 2, the trapping method is:

[0095] The evader moves along the x-axis according to the dynamics of the evader, and the five pursuers maintain the layout of step 1 and move along the x-axis according to the dynamics of the i-th level pursuer; when the front pursuer, i.e. the second level pursuer, moves to the same x-axis coordinate as the evader, the front pursuer, i.e. the second level pursuer, stops moving in the x-axis direction, i.e. the speed of the front pursuer, i.e. the second level pursuer, in the x-axis is 0, i.e.

[0096] The front pursuer moves along the x-axis perpendicular to the x-axis to implement the encircling of the evader, i.e. Since the radius of the circle is equal to the distance of the front pursuer to the x-axis, i.e. Therefore, the radius of the circle decreases with the decrease of ; at this time, the other pursuers adaptively adjust their positions on the circle ring so that they are still on the circle ring.

[0097] Finally, when the front pursuer moves to , the pursuer successfully captures the evader.

[0098] Therefore, the present application mainly solves the following problems:

[0099] (1) A new trapping method is proposed to reduce the cost required for trapping.

[0100] (2) The mathematical model of field of view interaction is applied to the trapping method.

Claims

1. An open formation hunting method based on multi-agent pursuit-evasion game with field of view interaction, characterized in that: The game includes n pursuers and one evader; the hunting steps are as follows: Step 1: (1) a coordinate system with the center pursuer as the origin is established, the evader moves along the x-axis, and a geometric model layout of the pursuer and the evader is established: n pursuers are uniformly distributed on a circle with a radius R, the center of the circle is on the x-axis, and the distance between the center and the evader is l; The center pursuer is defined as the 0th level, the two adjacent pursuers form the 1st level, the adjacent 1st level is the 2nd level, and the order is sequentially sorted as each side exists m = (n-1) / 2 levels of pursuers, and the last level is located on the same straight line as the center parallel to the y-axis; (2) the dynamics equation of the pursuer and the evader: The pursuers keep constant speed v, keep the layout of n pursuers, and move along the x axis to the evader; let ξ p (t) = [x p (t), y p (t)] and ξ e (t) = [x e (t), y e (t)] respectively represent the position of a certain pursuer and evader at time t, then and respectively represent the dynamics of a certain pursuer and evader at time t; Step 2: the field of view mathematical model of the pursuer is constructed, and the movement of the evader along the x-axis is extended to a complete two-dimensional environment; The field of view mathematical model: represents the perception ability of any pursuer i in a geometric structure of an isosceles triangle, represented as By the distributed control law, the evader is within the field of view triangle of each pursuer The pursuer calibrates its direction according to the angle and direction of the evader. The three points are and define an angular offset ε i relative to the direction θ i of the pursuer. Define distances and denote the distances of the evader to the three sides of the triangle and respectively; Step 3: based on the geometric model established in step 1 and the field of view model of the pursuer in step 2, the hunting method is: The evader moves along the x-axis according to the dynamics of the evader, and n pursuers maintain the layout of step 1, and move along the x-axis to the evader according to the dynamics of the ith level pursuer; when the front chaser, i.e., the mth level chaser, moves to the same x-axis coordinate as the evader, the front chaser, i.e., the mth level chaser, stops the movement in the x-axis direction, i.e., the speed of the front chaser, i.e., the mth level chaser, in the x-axis is 0, i.e., The front chaser moves along the x-axis in a direction perpendicular to the x-direction, and performs a tackle on the evader, i.e. Since the radius of the circle is equal to the distance of the front chaser to the x-axis, i.e. Therefore, the radius of the circle decreases as the distance of the front chaser to the x-axis decreases; at this time, the other chasers adaptively adjust their positions on the circle ring so that they are still on the circle ring. Therefore, the radius of the circle decreases as the distance of the front chaser to the x-axis decreases; at this time, the other chasers adaptively adjust their positions on the circle ring so that they are still on the circle ring. Finally, when the front chaser moves to the chaser successfully captures the evader.

2. The method of claim 1, wherein the method is based on a multi-agent pursuit-evasion game with field-of-view interaction. In the geometric model layout, the coordinate position of each pursuer in the formation relative to the center pursuer is: where i = {0, 1,..., m}, the i-th pursuer on both sides is located at The distance between any ith level pursuer above the 1st level and the evader on the x-axis is: The total distance between any ith level pursuer above the 1st level and the evader is: The total distance between the 0th level center pursuer and the evader is: wherein 3. The method of claim 1, wherein the method further comprises: The dynamics of the i-th pursuer is given by the continuous monotone decreasing function σ i denotes: Wherein, wherein the specific behavior parameters α and β.

4. The method of claim 3, wherein the method further comprises: The parameters α and β together define the degree of the evader's effort to escape as the distance to the pursuer decreases, α = 1.5, β = 0.

15.

5. The method of claim 1, wherein the method further comprises: The dynamics of the evader is: where σ 0 is the dynamics of the 0th chaser.

6. The method of claim 1, wherein the method further comprises: In the field of view mathematical model, the relative distance between the pursuer and the evader is converted into x-axis and y-axis components, the position, angle and distance are as follows: where R(ε i ) denotes the rotation matrix corresponding to the angle ε i , and denotes the transfer vector is represented as: where γ i represents half of the angle of the top corner of the isosceles triangle.

7. The method of claim 1, wherein: The arbitrary pursuer i is equipped with a limited field of view sensor, which can sense the angle and direction of the evader in the field of view.

8. An electronic device, comprising: The processor is used to execute the computer program stored in the memory to realize the steps of the open formation hunting method based on multi-agent pursuit-escape game with field of view interaction according to any one of claims 1 to 7.

9. A readable storage medium, characterized by, The computer program stored on the readable storage medium is executed by the processor to realize the steps of the open formation hunting method based on multi-agent pursuit-escape game with field of view interaction according to any one of claims 1 to 7.

10. A computer program product, characterised in that The computer executable instructions are used to realize the steps of the open formation hunting method based on multi-agent pursuit-escape game with field of view interaction according to any one of claims 1 to 7 when executed.

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