A method for cooperative hunting of fast escapees

Abstract

The application discloses a kind of fast escapee cooperative hunting method, belong to multi-agent cooperative control field.The application implementation method is: according to the state observation information of escapee and the state information of pursuer oneself determines opposite azimuth, task allocation and communication topology transformation are carried out to pursuer, and pursuer is divided into a hunter and two groups of besiegers;Based on the speed ratio of pursuit and escape and parallel guidance law, hunter hunting strategy is formulated for the hunter, so that the hunter quickly approaches the escapee while trying to keep the azimuth angle unchanged with the escapee;According to the state information of escapee and adjacent pursuer, besieger hunting strategy is formulated for the besieger, to ensure that the Apollo circle between adjacent pursuers does not produce escape gap as far as possible while reducing the distance between the escapee and the Apollo circle, and balance the relationship between the two;Based on the hunter hunting strategy and the besieger hunting strategy, the cooperative hunting of the fast escapee is realized.The application improves the success rate and hunting efficiency of the fast escapee hunting.

Description

A method for the coordinated capture of fast escapees Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control and relates to a method for multiple pursuing agents to cooperate in capturing a fast-escaping agent. Background Technology

[0002] In recent years, multi-agent cooperative control has become a prominent research area. Cooperative encirclement, as an important application of multi-agent cooperative control, has received widespread attention due to its enormous potential in target defense, disaster relief, and hostile strikes.

[0003] The cooperative encirclement problem is a typical multi-agent cooperative control problem, mainly referring to the process by which multiple pursuing agents approach and surround one or more escaping agents, restricting their activity range and ultimately capturing them. Encirclement strategies have wide applications in daily life and the military, such as intelligent lifeboats rescuing people from drowning, frigates escorting main ships, and destroyers encircling enemy vessels.

[0004] Based on the speed relationship between the pursuer and the escapee, the pursuit problem can be divided into two types: (1) The pursuer's speed is higher than the escapee's speed. In this case, the escapee will inevitably be captured within a finite time, and the outcome of the pursuit game is predictable; therefore, the time required to complete the pursuit and the final location distribution of the pursuers are the main concerns. (2) The pursuer's speed is equal to or slower than the escapee's speed. In this case, the final outcome of the pursuit game is related to many factors, such as the speed ratio between the pursuer and the escapee, the initial location distribution of the pursuers, and the number of pursuers, which is more significant for research.

[0005] Currently, scholars both domestically and internationally have conducted extensive research on the problem of encircling and capturing slow or constant-speed escapees. Dynamic encirclement point allocation, model predictive control, and Veno plotting can all effectively solve this type of problem. The Apollonius circle theory can better reflect the ability of the pursuer to constrain fast-moving escapees. Multi-agent cooperative encirclement strategies can be designed based on the dynamic changes of the overlap angle, occupancy angle, and escape angle of adjacent Apollonius circles. There are two main problems in current related research: (1) the pursuer and the escapee are usually considered to be able to move freely without considering angular velocity constraints; (2) the real-time state information of the escapee is not fully utilized to allocate tasks to the pursuer, so as to formulate more targeted encirclement methods.

[0006] The patent, "A Multi-Unmanned Vessel Swarm Encirclement Method Based on Improved LSTM Network Trajectory Prediction," uses an improved LSTM algorithm to predict the target's trajectory, allowing pursuing vessels to ambush the target vessel's path in advance. It also combines centralized, hybrid, and Hungarian algorithm-based approaches from the virtual structure method in cooperative control to assign tasks to the pursuing vessels, generating a U-shaped array along the target vessel's trajectory and encircling it based on this array. This method relies on the target vessel lacking strong intelligent perception and escape capabilities; that is, the target vessel's speed is slower than the pursuing vessels, and its perception domain is smaller. Therefore, its application scenarios are somewhat limited. If the target vessel's speed is faster than the pursuing vessels, this method will struggle to complete the encirclement mission.

[0007] The patent "A Cluster Encirclement Method, System, and Execution Device" discloses a cluster encirclement method based on Apollonius Circle theory. It determines the total occupancy angle for encirclement and classifies the encirclement stage based on this angle, mainly into an encirclement formation stage and an encirclement maintenance stage. The optimal encirclement speed is determined based on the speed ratio between the pursuing and escaping parties during the encirclement stage. However, this method does not consider speed and angular velocity constraints, making its application in real-world projects difficult. The escapee's motion design is overly simplistic; once the escapee detects a loophole and possesses intelligent escape techniques, they can easily break out of the encirclement. Furthermore, each participant in the encirclement needs to know global information, placing significant pressure on formation communication and making practical application challenging. Summary of the Invention

[0008] The purpose of this invention is to provide a method for the coordinated encirclement and capture of fast-escaping individuals. Based on the escapee's state observation information and the pursuer's own state information, the relative azimuth angle is determined. Task allocation and communication topology transformation are performed on the pursuers, dividing them into one hunter and two groups of surroundrs. Based on the speed ratio between the pursuer and escapee and the parallel guidance law, a hunter pursuit strategy is formulated for the hunter, enabling the hunter to quickly approach the escapee while maintaining a relatively constant azimuth angle. Based on the escapee's and adjacent pursuers' state information, an surroundr pursuit strategy is formulated for the surroundrs, ensuring that no escape gaps are created between adjacent pursuers' Apollonius circles while minimizing the distance between them and the escapee, and balancing the relationship between the two. The coordinated encirclement and capture of fast-escaping individuals is achieved based on the hunter and surroundr pursuit strategies. This invention can successfully encircle and capture fast-moving intelligent escapees, improving the success rate and efficiency of the encirclement. The term "fast-escaping individual" refers to an escapee whose movement speed is faster than that of the pursuer.

[0009] The objective of this invention is achieved through the following technical solution:

[0010] The present invention discloses a method for the coordinated capture of a rapidly escaping individual, comprising the following steps:

[0011] Step 1: Based on the Apollonius Circle theory, determine the minimum number of pursuers and the initial optimal location distribution.

[0012] To capture a faster escapee, two conditions must be met:

[0013] ① There are enough pursuers to surround the escapee;

[0014] ②The pursuer can continuously close the distance with the escapee until the escapee is captured.

[0015] Because the escapee is faster than the pursuer, if the escapee moves to the opposite side when the pursuer is on the same side, the escapee can escape. Therefore, the pursuer can only capture the escapee when the escapee is surrounded by multiple pursuers.

[0016] The motion model of the intelligent agent is constructed as shown in equation (1):

[0017]

[0018] The agents include a pursuing agent and an escaping agent, both of which use the same motion model, i∈{P,e}, P={p1,…,p N} is a set of N pursuers, where e represents the escapee. [x i ,y i ]∈R 2 V represents the position of the i-th agent. The N pursuers are homogeneous, possessing the same mobility. i =V p , V p and V e V represents the speed of the pursuer and the escapee, respectively. p <V e ; ψ i Represents the heading angle, u i This represents the control input for the i-th agent. In this case, the constraints on the control input make the agent's motion model a nonholonomic model, resulting in the agent being subject to a minimum turning radius constraint. The control input constraints for each agent are as follows:

[0019] u min ≤u i ≤u max (2)

[0020] Among them, u min u max These are the minimum and maximum values ​​for controlling the input, respectively.

[0021] Preset the initial positions of the pursuer and the escapee, R i ,i∈[1,N] represents the distance between the i-th pursuer and the escapee. σ i,i+1 i∈[1,N] represents two adjacent pursuers p i and p i+1 The phase angle relative to the escapee e.

[0022] Each pursuer has a positive capture radius. When the escapee enters any pursuer's capture area, the escapee will be successfully captured, and the capture mission will be successful. The termination condition of the pursuit game is:

[0023]

[0024] By introducing the Apollonius Circle theory, the relative motion capabilities of the pursuer and the escapee can be described more accurately. Points A and B are the intersections of the two tangents passing through the escapee e with the Apollonius Circle, respectively. The angle ζ formed by the two tangents eA and eB represents the ability of the pursuer p to restrict the escapee e at the current moment. ζ is called the occupancy angle of the pursuer p relative to the escapee e.

[0025] The expressions for the center Q and radius r of the Apollonius circle are as follows:

[0026]

[0027]

[0028] Where λ represents the speed ratio between the pursuer and the pursuer, satisfying the expression: λ=(V p / V e ).

[0029] According to formulas (4) and (5), the occupancy angle ζ is expressed as:

[0030]

[0031] in, It is the angle between the line pe connecting the pursuer p and the escapee e and the tangent eA or eB.

[0032] For any two adjacent trackers p i and p i+1 If the neighboring tracker p i and p i+1 If the Apollonius circles intersect, then the occupancy angles will also intersect, forming a larger occupancy angle called the overlapping occupancy angle ζ. i,i+1 The expression for the overlapping occupancy angle is as follows:

[0033] ζ i,i+1 =2ζ-θ i,i+1 (7)

[0034] Where, θ i,i+1 It is the angle of overlap between the Apollonius circles.

[0035] If the overlap angle θ i,i+1 If θ ≥ 0, it indicates that the pursuer has complete control over the escapee. i,i+1 <0 indicates that the neighboring tracker p i and p i+1 An escape gap has appeared, giving the escapee a chance to jump out of the encirclement. Therefore, θ should be avoided as much as possible. i,i+1 The condition <0 occurs. The process of multiple pursuers encircling a fast-escaping individual can be broken down into several separate encirclement processes by adjacent pursuers. Therefore, the initial positional distribution of the pursuers must avoid gaps. Adjacent pursuers p i and p i+1 The angle σ relative to the escapee e i,i+1 The following conditions must be met:

[0036]

[0037] When there are a total of N pursuers, according to formula (8), the number of pursuers must satisfy the following relationship:

[0038]

[0039] To avoid θ as much as possible i,i+1 The occurrence of a <0 case indicates that the initial positions of the pursuers are evenly distributed, that is:

[0040]

[0041] Step 2: Obtain status observation information of the escapee and adjacent pursuers; the observation information includes position information and heading angle information.

[0042] Step 3: Based on the state observation information of the escapee and adjacent pursuers obtained in Step 2, determine the relative azimuth angle according to the escapee's state observation information and the pursuer's own state information. Perform task allocation and communication topology transformation based on the relative azimuth angle to obtain the task allocation result, that is, divide the pursuers into one hunter and two groups of surroundrs.

[0043] Based on the state observation information of the escapee and adjacent pursuers obtained in step two, the relative motion between the pursuers and the escapee is determined. ξ i Representative of the pursuers pi heading angle ψ i Relative to the line p i The angle between e and φ i The heading angle ψ of the escapee e e Relative to the line p i The angle between e and e.

[0044] To reduce the probability of escapees breaking through, while considering the escapee's angular velocity constraint, greater emphasis is placed on the tightness of the defense in the direction directly opposite the escapee's heading. Based on the escapee's real-time heading angle and the positional distribution between the pursuer and the escapee, the pursuers are divided into two roles: hunters and surroundrs. Specifically, the pursuers are divided into one hunter and two groups of surroundrs, as follows:

[0045] |φ i The pursuer corresponding to the minimum value is set as the hunter. Among the remaining pursuers, 0 < φ is selected. i The pursuers with a value ≤π form the first group of surroundrs, G1, and the remaining surroundrs form the second group, G2. Then, within surroundrs G1 and G2, the pursuit proceeds according to |φ. i The pursuers' actions are prioritized in ascending order to form a new communication topology. The hunter's primary task is to quickly approach the escapee and shorten the distance; the surroundr's primary task is to assist the hunter in the encirclement, avoiding any escape gaps between themselves and adjacent pursuers, while simultaneously getting as close to the escapee as possible.

[0046] The hunters' task allocation changes dynamically with the escapee's heading angle. Through task allocation, the hunters' pursuit strategies become more targeted, enabling them to respond more quickly to changes in the escapee's heading angle and thus capture the escapee more safely and rapidly.

[0047] Step Four: Based on the task allocation results obtained in Step Three, design capture strategies for both the hunter and the surroundr. Specifically, formulate a hunter pursuit strategy for the hunter and an surroundr pursuit strategy for the surroundr. Based on the speed ratio between the pursuer and the escapee and the parallel guidance law, formulate a hunter pursuit strategy for the hunter, enabling the hunter to quickly approach the escapee while maintaining a relatively constant azimuth angle with the escapee. Based on the state information of the escapee and adjacent pursuers, formulate an surroundr pursuit strategy for the surroundr, ensuring that no escape gaps are created between adjacent pursuers' Apollonius circles while minimizing the distance between the pursuer and the escapee, and balancing the relationship between the two.

[0048] Step 4.1: Based on the task allocation results obtained in Step 3, design encirclement strategies for the hunter and the encircler respectively through Step 4.2 and Step 4.3.

[0049] Step 4.2: In order to shorten the distance between the hunter and the escapee, the hunter uses a parallel guidance law to ensure that the hunter's azimuth angle relative to the escapee remains unchanged, while reducing the distance between the hunter and the escapee.

[0050] Based on geometric analysis using the parallel guidance law, V is obtained. e sinφ i =V p sinξ * i After formula transformation, the pursuer p can be obtained. i Optimal heading angle ψ * i Relative to the line p i The included angle of e is shown in equation (11):

[0051]

[0052] Therefore, based on the speed ratio between the pursuer and the pursuer and the parallel guidance law, a hunter pursuit strategy is formulated to ensure that the hunter's optimal heading angle satisfies equation (12):

[0053]

[0054] That is, to construct a hunter pursuit strategy based on the hunter's optimal heading angle, so that the hunter can quickly approach the escapee while keeping the heading angle between the hunter and the escapee as constant as possible.

[0055] Step 4.3: To ensure that all adjacent Apollonius circles intersect and can quickly approach the escapee, the strategy design of the surroundr is transformed into solving an optimal control problem. The objective function is constructed as follows:

[0056]

[0057] Among them, E angle =(σ i,i+1 -Δσ) 2 Δσ is the expected value of the phase angle between two adjacent pursuers relative to the escapee, i.e., Δσ = 2π / N; and It is the phase angle σ between adjacent pursuers i,i+1 The distance between the pursuing and fugitive parties is R i The change in α and β is a weighting factor, where α∈(0,1) and β>0. The adjacency relationship of the pursuers is determined by the communication topology.

[0058] Based on geometric analysis, the distance R between the pursuing and fleeing parties is... i Change Satisfying equation (14):

[0059]

[0060] The weighting factor α is a binary variable, and its value is determined by σ. i,i+1 The determination is made using the following formula:

[0061]

[0062] Solving the optimal problem described by formula (13-15), we obtain the pursuer p. i Optimal heading angle ψ * i Relative to the line p i The angle ξ between e and e * i Therefore, the formula for calculating the optimal heading angle for the encircler is as follows:

[0063]

[0064] That is, to construct the pursuer strategy based on the optimal heading angle of the pursuer, to ensure that no escape gap is generated between the pursuer and the Apollonius circle of the adjacent pursuer, while reducing the distance between the pursuer and the escapee, and balancing the relationship between the two.

[0065] Step 5: Discretize the agent motion model constructed in Step 1 with a sampling time of T to obtain a discretized agent motion model. Update the pursuer's state based on the discretized agent motion model.

[0066] Based on the agent motion model (1), the agent motion model is discretized with a sampling time of T, and the expression is as follows:

[0067]

[0068] Update the status of the pursuer according to formula (17).

[0069] Step Six: Based on the location distribution of the pursuers and the escapees, and in conjunction with the criteria for determining the success or failure of the encirclement, determine the encirclement phase. If the encirclement is still ongoing, redistribute tasks and formulate strategies; if the conditions for success or failure of the encirclement have been met, the encirclement mission ends.

[0070] The conditions for determining whether the encirclement or capture was successful or unsuccessful correspond to conditions 1 and 2, respectively:

[0071] Condition 1: If satisfy The encirclement mission was successful; record the current time t.

[0072] Condition 2: If there exists a straight line ax + by = c that completely separates the escapee from the pursuer, it is determined that the escapee has broken out of the pursuer's encirclement, and the capture mission fails.

[0073] If neither of the above two conditions is met, let t:=t+1, jump to step 2, and continue the encirclement and capture mission until the encirclement and capture mission is completed.

[0074] Beneficial effects:

[0075] 1. This invention discloses a rapid collaborative encirclement method for escapees. It allocates tasks to pursuers based on the escapee's instantaneous heading angle. The relative azimuth angle is determined according to the escapee's state observation information and the pursuer's own state information. Then, task allocation and communication topology transformation are performed to obtain the task allocation result, dividing the pursuers into one hunter and two groups of surroundrs. Compared to existing methods that treat pursuers as a unified whole or as several identical independent individuals, the proposed pursuer task allocation method fully considers the escapee's real-time movement state and allocates tasks (role assignments) based on the pursuers' positional distribution relative to the escapee. This facilitates the development of more targeted pursuit strategies, improving encirclement efficiency and success rate. It is important to note that the task allocation is dynamic throughout the encirclement process, capable of handling various intelligent escape behaviors of the escapee, such as rapid turns, sudden stops, and misdirection.

[0076] 2. This invention discloses a method for the rapid coordinated capture of escapees, which divides all pursuers into two camps, G1 and G2, using the escapee's real-time heading as the dividing line. Then, within the pursuer groups G1 and G2, according to |φ i The actions of the surroundrs are prioritized in ascending order of their azimuth relative to the escapee, thus forming a new communication topology. The surroundrs act sequentially according to their azimuth relative to the escapee, increasing the tightness of the defense and reducing the probability of escape gaps between adjacent Apollonius circles.

[0077] 3. This invention discloses a rapid collaborative encirclement method for catching escapees, employing a hunter pursuit strategy based on the parallel guidance law. Based on the speed ratio between the pursuer and the escapee and the parallel guidance law, the hunter's instantaneous optimal heading angle is obtained through geometric analysis. The parallel guidance law helps the hunter approach the escapee while maintaining a relatively stable heading angle, thus maintaining the encirclement formation, avoiding significant formation changes that could create escape gaps, and improving the success rate of the encirclement.

[0078] 4. This invention discloses a rapid escapee cooperative encirclement method, employing an encircler pursuit strategy based on optimal control. It comprehensively considers factors such as the overlap angle between the encircler and adjacent pursuers, the rate of change of the overlap angle, and the rate of change of the distance to the escapee. The encircler pursuit strategy design is transformed into solving an optimal control problem, obtaining the instantaneous optimal heading angle of the encircler. The encircler pursuit strategy based on optimal control disclosed in this invention can ensure that no escape gaps occur between adjacent Apollonius circles, while simultaneously getting as close as possible to the escapee and balancing the relationship between them, thereby improving the success rate and efficiency of the encirclement. Attached Figure Description

[0079] Figure 1 is an overall flowchart of the implementation method of the collaborative encirclement and capture method for fast-escaping individuals in a collaborative encirclement and capture mission;

[0080] Figure 2 is a schematic diagram of the invalid distribution of the initial positions of the pursuers in a coordinated encirclement mission;

[0081] Figure 3 is a schematic diagram of the effective distribution of the initial positions of the pursuers in a coordinated encirclement mission;

[0082] Figure 4 is a geometrical diagram showing the effective distribution of the initial positions of the pursuers in a coordinated encirclement mission;

[0083] Figure 5 is a schematic diagram of the Apollonius circle formed by a single pursuer and a single escapee in a coordinated encirclement mission.

[0084] Figure 6 is a schematic diagram of the overlapping occupancy angle formed by overlapping Apollonius circles in a coordinated encirclement mission;

[0085] Figure 7 is a schematic diagram of the escape angle formed by non-overlapping Apollonius circles in a coordinated encirclement mission;

[0086] Figure 8 is a schematic diagram of the relative motion between the pursuers and the escapee in a coordinated encirclement and capture mission;

[0087] Figure 9 is a schematic diagram of the task allocation for pursuers in a coordinated encirclement and capture mission.

[0088] Figure 10 is a schematic diagram of the instantaneous communication topology of the pursuers in a coordinated encirclement and capture mission;

[0089] Figure 11 is a schematic diagram of the parallel guidance law of the hunter in a coordinated encirclement mission;

[0090] Figure 12 is a schematic diagram of the optimal escape direction for escapees in a coordinated capture mission.

[0091] Figure 13 shows the motion trajectories of each agent in the collaborative encirclement example;

[0092] Figure 14 shows the entire encirclement process in the collaborative encirclement example. Figure 14(a) shows the initial position distribution of the pursuing agents in the collaborative encirclement example. Figures 14(b) and (c) show the position distribution of the pursuing agents at different stages of the collaborative encirclement example. Figure 14(d) shows the position distribution of the pursuing agents when the encirclement is successful in the collaborative encirclement example.

[0093] Figure 15 shows the task allocation diagram at different times in the collaborative encirclement example. Figure 15(a) is a schematic diagram of the task allocation of the pursuers in the case shown in Figure 14(b), and Figure 15(b) is a schematic diagram of the task allocation of the pursuers in the case shown in Figure 14(c).

[0094] Figure 16 shows the distance changes between the pursuers and the escapee in a coordinated encirclement and capture example.

[0095] Figure 17 shows the change in the overlap angle between adjacent pursuers in a collaborative encirclement example. Detailed Implementation

[0096] To better illustrate the purpose and advantages of this invention, the following description, in conjunction with the accompanying drawings and examples, further explains the invention. Addressing the issue that existing cooperative capture methods do not consider the angular velocity constraints of escapees or the task allocation for pursuers, this invention discloses a highly efficient and rapid cooperative capture method for escapees. By analyzing the real-time state of the escapee, it allocates tasks to pursuers and performs communication topology transformations, thereby designing more targeted capture strategies, improving the success rate of cooperative capture, and shortening the capture time. The overall flowchart of the implementation method is shown in Figure 1.

[0097] The following examples demonstrate the effectiveness of the method proposed in this invention under some typical conditions. Both the pursuer and the escapee move at a constant speed, and the total time required to complete the encirclement mission is used as a performance indicator to evaluate the effectiveness of the encirclement. The longer the encirclement takes, the higher the reward for the escapee, and vice versa for the pursuer.

[0098] The speed of the escapee V e =1m / s, λ=V p / V e =0.9, control input Capture radius R c =2m, sampling time T =0.1s. Initially, the distance R between the pursuer and the escapee is... i =40m, i∈P. The following implementation is carried out in MATLAB, and its purpose is to realize the cooperative capture of a fast-escaping agent by multiple pursuing agents.

[0099] As shown in Figure 1, the specific implementation steps of the collaborative capture method for rapid escapees disclosed in this embodiment are as follows:

[0100] Step 1: Based on the Apollonius Circle theory, determine the minimum number of pursuers and the initial optimal location distribution.

[0101] Since the speed ratio of the pursuer and the fugitive is λ = 0.9, the fugitive's speed is faster than the pursuer's. When the pursuer is on the same side as the fugitive, if the fugitive moves to the opposite side, they can escape, as shown in Figure 2. Therefore, the pursuers can only capture the fugitive when they are surrounded by multiple pursuers, as shown in Figure 3.

[0102] The motion model of the intelligent agent is constructed as shown in equation (18):

[0103]

[0104] The agents include a pursuing agent and an escaping agent, both of which use the same motion model, i∈{P,e}, P={p1,…,p N} is a set of N pursuers, where e represents the escapee. [x i ,y i ]∈R 2 V represents the position of the i-th agent. The N pursuers are homogeneous, possessing the same mobility. i =V p =0.9m / s, V p and V e V represents the speed of the pursuer and the escapee, respectively. e =1m / s; ψ i Represents the heading angle, u i This represents the control input for the i-th agent. In this case, the constraints on the control input make the agent's motion model a nonholonomic model, resulting in the agent being subject to a minimum turning radius constraint. The control input constraints for each agent are as follows:

[0105] u min ≤u i ≤u max (19)

[0106] Among them, u min u max These are the minimum and maximum values ​​of the control input, u min =-π / 6, u max =π / 6.

[0107] The initial location distribution of the pursuers and the escapees is shown in Figure 4. i ,i∈[1,N] represents the distance between the i-th pursuer and the escapee. σ i,i+1i∈[1,N] represents two adjacent pursuers p i and p i+1 The phase angle relative to the escapee e.

[0108] Each pursuer has a positive capture radius. When the escapee enters any pursuer's capture area, the escapee will be successfully captured, and the capture mission will be successful. The termination condition of the pursuit game is:

[0109]

[0110] Among them, R c R represents the capture radius of the pursuer. c =2m.

[0111] By introducing the Apollonius Circle theory, the relative motion capabilities of the pursuer and the escapee are described more accurately. The Apollonius circle Q of the pursuer p relative to the escapee e is shown in Figure 5. Points A and B are the intersections of the two tangents passing through the escapee e and the Apollonius circle, respectively. The angle ζ formed by the two tangents eA and eB represents the ability of the pursuer p to restrict the escapee e at the current moment, and ζ is called the occupancy angle of the pursuer p relative to the escapee e.

[0112] The expressions for the center Q and radius r of the Apollonius circle are as follows:

[0113]

[0114]

[0115] Where λ represents the speed ratio between the pursuer and the pursuer, satisfying the expression: λ=(V p / V e = 0.9.

[0116] According to formulas (21) and (22) and Figure 5, the occupancy angle ζ is expressed as:

[0117]

[0118] in, It is the angle between the line pe connecting the pursuer p and the escapee e and the tangent eA or eB.

[0119] For any two adjacent trackers p i and p i+1 If the neighboring tracker p i and p i+1If the Apollonius circles intersect, then the occupancy angles will also intersect, forming a larger occupancy angle called the overlapping occupancy angle ζ. i,i+1 As shown in Figure 6, the expression for the overlapping occupancy angle is as follows:

[0120] ζ i,i+1 =2ζ-θ i,i+1 (twenty four)

[0121] Where, θ i,i+1 It is the angle of overlap between the Apollonius circles.

[0122] If the overlap angle θ i,i+1 If θ ≥ 0, it indicates that the pursuer has complete control over the escapee. i,i+1 <0 indicates that the neighboring tracker p i and p i+1 An escape gap has appeared, as shown in Figure 7. At this point, the escapee has the opportunity to jump out of the encirclement through the escape gap; therefore, it is crucial to avoid θ as much as possible. i,i+1 The condition <0 occurs. The process of multiple pursuers encircling a fast-escaping individual can be broken down into several encirclement processes of adjacent pursuers. Therefore, the initial positional distribution of the pursuers must avoid gaps. Adjacent pursuers p i and p i+1 The angle σ relative to the escapee e i,i+1 The following conditions must be met:

[0123]

[0124] Based on formula (25) and the Apollonius Circle theory, the number of pursuers must satisfy the following:

[0125]

[0126] In this example, N=4, meaning there are 4 pursuers and 1 escapee participating in the coordinated capture mission. To minimize the risk of θ... i,i+1 The occurrence of a condition <0 indicates that the initial positions of the pursuers are evenly distributed, i.e., satisfying the condition.

[0127]

[0128] Based on this, the initial positions of the agents are set as e(0,0), p1(40,0), p2(0,40), p3(-40,0), and p4(0,-40), in meters (m). The initial heading angles of the agents are ψ. e =0, ψ p,1 =π / 2, ψ p,2 =π, ψp,2 =-π / 2, ψ p,4 = -π. The positional distribution of each agent is shown in Figure 14(a).

[0129] Step 2: Obtain status observation information of the escapee and adjacent pursuers; the observation information includes position information and heading angle information.

[0130] Step 3: Based on the state observation information of the escapee and the adjacent pursuers obtained in Step 2, determine the relative azimuth angle according to the state observation information of the escapee and the state information of the pursuer. Based on the relative azimuth angle, perform task allocation and communication topology transformation for the pursuers to obtain the task allocation result, that is, divide the pursuers into one hunter and two groups of surroundrs.

[0131] Based on the state observation information of the escapee and adjacent pursuers obtained in step two, the relative motion between the pursuers and the escapee is determined, as shown in Figure 8. ξ i Representative of the pursuers p i heading angle ψ i Relative to the line p i The angle between e and φ i The heading angle ψ of the escapee e e Relative to the line p i The angle between e and e.

[0132] The pursuers base their task allocation and communication topology changes on the following:

[0133] |φ i The pursuer corresponding to the minimum value is set as the hunter. Among the remaining pursuers, 0 < φ is selected. i The pursuers with a value ≤π form the first group of surroundrs, G1, and the remaining surroundrs form the second group, G2. Then, within surroundrs G1 and G2, the pursuit proceeds according to |φ. i The actions of the pursuers are prioritized in ascending order to form a new communication topology. Referring to Figure 9, the pursuer p1 has the smallest |φ1|, so p1 is designated as the hunter, and the Apollonius Circle corresponding to p1 is marked in red in Figure 9. The pursuer p2 has φ2∈(0,π], designated as the first group of surroundrs G1, i.e., G1={p2}. The pursuers p3, p4, p5 have φ3, φ4, φ4∈[-π,0), designated as the second group of surroundrs G2, i.e., G2={p3,p4,p5}. Then, within each group, actions are prioritized according to |φ1|. i Perform a communication topology transformation, as shown in Figure 10.

[0134] It is important to note that the hunters' task allocation changes dynamically with the escapee's heading angle. This task allocation allows the hunters to employ more targeted pursuit strategies, responding more quickly to changes in the escapee's heading angle, and ultimately capturing the escapee more safely and rapidly.

[0135] In the case shown in Figure 14(b), the task allocation result is shown in Figure 15(a). Here, p4 is the hunter, (p1, p2, p3) are the surroundrs, G1 = {p1, p2}, and G2 = {p3}. The formation communication topology can be described as: p4 → p3, p4 → p1 → p2.

[0136] In the scenario shown in Figure 14(c), the task allocation for the pursuers is shown in Figure 15(b). Here, p2 is the hunter, (p3, p4, p1) is the surroundr, G1 = {p1}, and G2 = {p3, p4}. The formation communication topology can be described as: p2 → p1, p2 → p3 → p4.

[0137] Step Four: Based on the task allocation results obtained in Step Three, design capture strategies for both the hunter and the surroundr. Specifically, formulate a hunter pursuit strategy for the hunter and an surroundr pursuit strategy for the surroundr. Based on the speed ratio between the pursuer and the escapee and the parallel guidance law, formulate a hunter pursuit strategy for the hunter, enabling the hunter to quickly approach the escapee while maintaining a relatively constant azimuth angle with the escapee. Based on the state information of the escapee and adjacent pursuers, formulate an surroundr pursuit strategy for the surroundr, ensuring that no escape gaps are created between adjacent pursuers' Apollonius circles while minimizing the distance between the pursuer and the escapee, and balancing the relationship between the two.

[0138] Step 4.1: Based on the task allocation results obtained in Step 3, design encirclement strategies for the hunter and the encircler respectively through Step 4.2 and Step 4.3.

[0139] Step 4.2: In order to shorten the distance between the hunter and the escapee, the hunter uses a parallel guidance law to ensure that the hunter's azimuth angle relative to the escapee remains unchanged, while reducing the distance between the hunter and the escapee, as shown in Figure 11.

[0140] Based on geometric analysis using the parallel guidance law, V is obtained. e sinφ i =V p sinξ * i After formula transformation, the pursuer p can be obtained. i Optimal heading angle ψ * i Relative to the line p i The included angle of e is shown in equation (28):

[0141]

[0142] Therefore, based on the speed ratio between the pursuer and the pursuer and the parallel guidance law, a hunter pursuit strategy is formulated to ensure that the hunter's optimal heading angle satisfies equation (29):

[0143]

[0144] That is, to construct a hunter pursuit strategy based on the hunter's optimal heading angle, so that the hunter can quickly approach the escapee while keeping the heading angle between the hunter and the escapee as constant as possible.

[0145] Step 4.3: To ensure that all adjacent Apollonius circles intersect and can quickly approach the escapee, the strategy design of the surroundr is transformed into solving an optimal control problem. The objective function is constructed as follows:

[0146]

[0147] Among them, E angle =(σ i,i+1 -Δσ) 2 Δσ is the expected value of the phase angle between two adjacent pursuers relative to the escapee, i.e., Δσ = 2π / N; and It is the phase angle σ between adjacent pursuers i,i+1 The distance between the pursuing and fugitive parties is R i The change in α and β is a weighting factor, where α∈(0,1) and β>0. The adjacency relationship of the pursuers is determined by the communication topology.

[0148] Based on the geometric analysis in Figure 8, the distance R between the pursuing and fleeing parties is... i Change Satisfying equation (31):

[0149]

[0150] The weighting factor α is a binary variable, and its value is determined by σ. i,i+1 The determination is made using the following formula:

[0151]

[0152] Step 5: To verify the effectiveness of the capture method disclosed in this invention, we also developed an intelligent escape strategy for the escapee, as shown below:

[0153] For escapees with intelligent breakout strategies, the goal is to create a gap in the encirclement formation, allowing the escapee to break free. The escapee's strategy is to select the adjacent pursuer with the smallest overlap angle and move in the direction where the overlap angle decreases most rapidly. Since the initial formation is symmetrical, all overlap angles are the same, and the escapee randomly selects two adjacent pursuers.

[0154] Based on the geometric analysis in Figure 8, the phase angle σ between adjacent pursuers and the escapee is obtained. i,i+1 rate of change The following relationship must be satisfied:

[0155]

[0156] According to formula (33), in ξ i and ξ i+1 If it remains unchanged, satisfy The escapee chooses to move in direction χ, so that... The minimum value is shown in Figure 12. The mathematical expression is as follows:

[0157] φ i,i+1 =χ-σ i,i+1 (34)

[0158]

[0159] According to formula (35), solve the equation f(χ) * When ) = 0, the instantaneous optimal escape direction of the escapee is obtained. This is when the distance R between the escapee and any pursuer is... i ≤3R c , In order to avoid entering the capture area of ​​the pursuers, they choose the second-best escape direction to escape and prolong the time before being captured.

[0160] The formula for calculating the optimal heading angle for the escapee is as follows:

[0161]

[0162] Step Six: Update the states of the pursuer and the escapee. According to formula (1), the agent motion model is discretized with a sampling time of T, as shown in the following expression:

[0163]

[0164] Update the status of the pursuer and the escapee according to formula (37).

[0165] Step Seven: Based on the location distribution of the pursuers and the escapees, and in conjunction with the criteria for success or failure of the encirclement, determine the encirclement phase. If the encirclement is still ongoing, redistribute tasks and formulate strategies; if the criteria for success or failure have been met, the encirclement mission ends.

[0166] The conditions for determining whether the encirclement or capture was successful or unsuccessful correspond to conditions 1 and 2, respectively:

[0167] Condition 1: If satisfy The encirclement mission was successful; record the current time t.

[0168] Condition 2: If there exists a straight line ax + by = c that completely separates the escapee from the pursuer, it means that the escapee has escaped the pursuer's encirclement and the capture mission has failed.

[0169] If neither of the above two conditions is met, let t:=t+1, jump to step 2, and continue the encirclement and capture mission until the encirclement and capture mission is completed.

[0170] The entire cooperative encirclement process is illustrated in Figures 13 and 14. Figure 13 shows the trajectories of four pursuers and one escapee. An asterisk marks the initial positions of the agents, and a hexagram marks their final positions. A red circle represents the capture area for the pursuers. The escapee is successfully captured when any pursuer is located within or on the boundary of the circle. To more comprehensively demonstrate the effectiveness of the proposed method, Figure 14 shows the different stages of the cooperative encirclement. Figure 16 shows the distance between the pursuers and the escapee, with the pursuers continuously closing the distance. Finally, at t = 53.4 seconds, the escapee is captured. Figure 17 shows the overlap angle between adjacent Apollonius circles. Throughout the encirclement process, the minimum overlap angle is 0.17 rad, indicating no escape gaps between adjacent Apollonius circles.

[0171] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for the coordinated capture of a rapidly escaping individual, characterized in that: The process includes the following steps: Step 1: Determine the minimum number of pursuers and the initial optimal location distribution based on the Apollonius Circle theory; Step 2: Obtain the state observation information of the escapee and adjacent pursuers. The observation information includes position information and heading angle information; Step 3: Based on the state observation information of the escapee and adjacent pursuers obtained in Step 2, determine the relative azimuth angle according to the escapee's state observation information and the pursuer's own state information; perform task allocation and communication topology transformation for the pursuers based on the relative azimuth angle to obtain the task allocation result, that is, divide the pursuers into one hunter and two groups of surroundrs; The implementation method of Step 3 is to determine the relative motion between the pursuers and the escapee based on the state observation information of the escapee and adjacent pursuers obtained in Step 2; ξ i Representative of the pursuers p i heading angle ψ i Relative to the line p i The angle between e and φ i The heading angle ψ of the escapee e e Relative to the line p i The angle e; based on the escapee's real-time heading angle and the positional distribution between the pursuer and the escapee, the pursuers are divided into two roles: hunters and surroundrs, that is, the pursuers are divided into one hunter and two groups of surroundrs, specifically based on the following: |φ i The pursuer corresponding to the minimum value is set as the hunter. Among the remaining pursuers, 0 < φ is selected. i The pursuers with a value ≤π form the first group of surroundrs G1, and the remaining surroundrs form the second group of surroundrs G2; then, within surroundrs G1 and G2, according to |φ i The pursuitrs' actions are prioritized in ascending order to form a new communication topology. The hunter's task is to quickly approach the escapee and shorten the distance. The surroundr's task is to assist the hunter in the encirclement, avoiding escape gaps with adjacent pursuers while getting as close to the escapee as possible. The hunter's task allocation dynamically changes with the escapee's heading angle. Through task allocation, the hunter's pursuit strategy becomes more targeted and can respond more quickly to changes in the escapee's heading angle. Step four: Based on the task allocation results obtained in step three, encirclement strategies are designed for both the hunter and surroundr, i.e., a hunter pursuit strategy is developed for the hunter, and an surroundr pursuit strategy is developed for the surroundr. Based on the speed ratio of the pursuers and the parallel guidance law, a hunter pursuit strategy is developed for the hunter, enabling the hunter to... The process involves rapidly approaching the escapee while maintaining a similar azimuth angle. Based on the state information of the escapee and adjacent pursuers, a pursuit strategy is developed to minimize escape gaps between the Apollonius circles of adjacent pursuers, reduce the distance to the escapee, and balance the relationship between them. Step five: The agent's motion model is discretized over a sampling time of T, resulting in a discretized model. The pursuer's state is then updated based on this discretized model. Step six: The pursuit phase is determined based on the positional distribution of the pursuers and the escapee, combined with the criteria for successful or failed encirclement. If the encirclement is still ongoing, tasks are reassigned and strategies are developed. If the conditions for successful or failed encirclement are met, the encirclement task ends.

2. The method for coordinated capture of a rapidly escaping individual as described in claim 1, characterized in that: The first step is to capture the faster escapee, which requires two conditions: ① There are enough pursuers to surround the escapee; ② The pursuers can continuously close the distance with the escapee until they capture the escapee; Since the escapee is faster than the pursuers, when the pursuers are on the same side as the escapee, if the escapee moves to the opposite side, the escape is achieved. Therefore, only when the escapee is surrounded by multiple pursuers can the pursuers possibly capture the escapee; the agent motion model is constructed as shown in equation (1): The agents include a pursuing agent and an escaping agent, both of which use the same motion model, i∈{P,e}, P={p1,…,p N } is a set of N pursuers, where e represents the escapee; [x i ,y i ]∈R 2 V represents the position of the i-th agent; the N pursuers are homogeneous, possessing the same mobility, and V... i =V p , V p and V e V represents the speed of the pursuer and the escapee, respectively. p <V e ; ψ i Represents the heading angle, u i Let u represent the control input of the i-th agent. In this case, the constraints on the control input make the agent's motion model a nonholonomic model, resulting in the agent being subject to a minimum turning radius constraint. The control input constraints for each agent are as follows: u min ≤u i ≤u max (2) Where, u min u max These are the minimum and maximum values ​​of the control input; and the preset initial positions of the pursuer and the escapee, R. i ,i∈[1,N] represents the distance between the i-th pursuer and the escapee; σ i,i+1 i∈[1,N] represents two adjacent pursuers p i and p i+1 The phase angle relative to the escapee e; each pursuer has a positive capture radius. When the escapee enters any pursuer's capture area, the escapee will be successfully captured, and the encirclement mission will be successful; the termination condition of the pursuit game is: By introducing the Apollonius Circle theory, the relative motion capabilities of the pursuer and the escapee are described more accurately. Points A and B are the intersections of the two tangents passing through the escapee e with the Apollonius Circle, respectively. The angle ζ formed by the two tangents eA and eB represents the ability of the pursuer p to restrict the escapee e at the current moment, and ζ is called the occupancy angle of the pursuer p relative to the escapee e. The expressions for the center Q and radius r of the Apollonius Circle are as follows: Where λ represents the speed ratio between the pursuer and the pursuer, satisfying the expression: λ=(V p / V e According to formulas (4) and (5), the occupancy angle ζ is expressed as: in, It is the angle between the line pe connecting the pursuer p and the escapee e and the tangent eA or eB; for any two adjacent pursuers p i and p i+1 If the neighboring tracker p i and p i+1 If the Apollonius circles intersect, then the occupancy angles will also intersect, forming a larger occupancy angle called the overlapping occupancy angle ζ. i,i+1 The expression for the overlapping occupancy angle is as follows, ζ i,i+1 =2ζ-θ i,i+1 (7) Where, θ i,i+1 It is the angle of overlap between the Apollonius circles; if the angle of overlap θ i,i+1 If θ ≥ 0, it indicates that the pursuer has complete control over the escapee; if θ i,i+1 <0 indicates that the neighboring tracker p i and p i+1 An escape gap has appeared, giving the escapee a chance to jump out of the encirclement. Therefore, θ should be avoided as much as possible. i,i+1 <0 occurs; the process of multiple pursuers encircling a fast-escaping individual can be broken down into several adjacent pursuers encircling the fast-escaping individual, therefore the initial positional distribution of the pursuers must avoid gaps; adjacent pursuers p i and p i+1 The angle σ relative to the escapee e i,i+1 The following conditions must be met: When there are a total of N pursuers, according to formula (8), the number of pursuers must satisfy the following relationship: To avoid θ as much as possible i,i+1 The occurrence of a <0 case indicates that the initial positions of the pursuers are evenly distributed, that is:

3. The method for coordinated capture of a rapidly escaping individual as described in claim 1, characterized in that: Step 4 is implemented as follows: Step 4.1: Based on the task allocation results obtained in Step 3, design encirclement strategies for the hunter and the surroundr respectively through Steps 4.2 and 4.3; Step 4.2: In order to shorten the distance with the escapee, the hunter uses the parallel guidance law to ensure that the hunter's azimuth angle relative to the escapee remains unchanged, while reducing the distance with the escapee; based on the parallel guidance law, geometric analysis is performed to obtain V. e sinφ i =V p sinξ * i After formula transformation, the pursuer p can be obtained. i Optimal heading angle ψ * i Relative to the line p i The included angle of e is shown in equation (11): Therefore, based on the speed ratio between the pursuer and the pursuer and the parallel guidance law, a hunter pursuit strategy is formulated to ensure that the hunter's optimal heading angle satisfies equation (12): That is, construct a hunter pursuit strategy based on the hunter's optimal heading angle, so that the hunter can quickly approach the escapee while maintaining the same azimuth angle with the escapee as much as possible; Step 4.3: In order to ensure that all adjacent Apollonius circles intersect and can quickly approach the escapee, the strategy design of the surroundr is transformed into solving an optimal control problem, and the objective function is constructed as follows: Among them, E angle =(σ i,i+1 -Δσ) 2 Δσ is the expected value of the phase angle between two adjacent pursuers relative to the escapee, i.e., Δσ = 2π / N; and It is the phase angle σ between adjacent pursuers i,i+1 The distance between the pursuing and fugitive parties is R i The change in α and β are both weighting factors, where α∈(0,1) and β>0; the adjacency relationship between the pursuers is determined by the communication topology; according to geometric analysis, the distance R between the pursuers and the pursuers is... i Change Satisfying equation (14): The weighting factor α is a binary variable, and its value is determined by σ. i,i+1 The determination is made using the following formula: Solving the optimal problem described by formula (13-15), we obtain the pursuer p. i Optimal heading angle ψ * i Relative to the line p i The angle ξ between e and e * i Therefore, the formula for calculating the optimal heading angle of the encircler is as follows: That is, to construct a pursuit strategy for the surroundr based on the surroundr's optimal heading angle, ensuring that no escape gap is generated between the surroundr and the Apollonius circle of the adjacent pursuer, while reducing the distance between the surroundr and the escapee, and balancing the relationship between the two.

4. The method for coordinated capture of a rapidly escaping individual as described in claim 3, characterized in that: Step 5 is implemented by discretizing the agent motion model (1) at a sampling time of T, as shown in the following expression: Update the status of the pursuer according to formula (17).

5. The method for coordinated capture of a rapidly escaping individual as described in claim 4, characterized in that: In step six, the conditions for determining whether the encirclement is successful or unsuccessful correspond to conditions 1 and 2 respectively: Condition 1: If satisfy The capture mission is successful, and the current time t is recorded. Condition 2: If there exists a straight line ax + by = c that completely separates the escapee and the pursuer, it is determined that the escapee has broken out of the pursuer's encirclement, and the capture mission fails. If neither of the above two conditions is met, let t:=t+1, jump to step 2, and continue the encirclement and capture mission until the encirclement and capture mission is completed.

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