Multi-aUV cooperative hunting control method based on virtual multi-target estimation center

Abstract

The application discloses a multi-AUV cooperative hunting control method based on a virtual multi-target estimation center, and comprises the following steps: S1, constructing an AUV kinematic model and initializing system states; S2, constructing a distributed cooperative multi-target virtual center estimator by using relative position information between the AUV and a target and relative position information between neighbor AUVs and the target; S3, constructing a multi-target hunting kinematic controller by using relative position information between the AUV and the neighbor and relative position information between the AUV and the estimated multi-target center; and S4, cooperatively controlling the AUV by using the kinematic controller constructed in step S3, so as to realize a hunting task on the multi-target virtual center. The application realizes distributed hunting control of multi-targets by using information of the AUV and the target in a local coordinate system and information of the target detected by the neighbor AUVs through multi-AUV cooperative estimation and control.

Description

Technical Field

[0001] This invention belongs to the field of distributed cooperative control technology for multiple AUVs, and specifically relates to a cooperative encirclement and control method for multiple AUVs based on a virtual multi-target estimation center. Background Technology

[0002] With the continuous advancement of intelligent agent technology, multi-agent systems have been widely applied in many fields such as security monitoring, satellite formation flying, environmental monitoring, and robot formation. In these fields, multi-agent systems need to complete complex tasks such as target localization, target tracking, and area coverage. Among these, the multi-target orbit control problem has significant practical implications. For example, in security monitoring tasks, multiple agents need to orbit around a target area to achieve continuous monitoring.

[0003] For underwater missions, the underwater environment is complex and changeable, with numerous uncertainties such as ocean currents, obstacles, and communication interference. These factors severely impact mission efficiency and reliability. A single AUV (Autonomous Underwater Vehicle) has limited detection range and mission capabilities; a malfunction can lead to mission failure. Multi-AUV systems, through collaborative operation, can significantly extend the detection range and improve mission reliability and efficiency. However, existing multi-AUV systems suffer from insufficient underwater positioning accuracy, limited measurement and communication distances, and susceptibility to target detection information failure. Furthermore, the formation of multiple targets orbiting each other is dynamic; targets may suddenly accelerate, turn, or even disappear and reappear, causing formation changes. This necessitates that AUV systems possess rapid response and real-time adjustment capabilities to ensure effective target tracking and encirclement. Summary of the Invention

[0004] The main objective of this invention is to overcome the shortcomings and deficiencies of existing technologies and propose a multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center. Through multi-AUV cooperative estimation and control, and by utilizing the information of AUVs and targets in the local coordinate system and the target information detected by neighboring AUVs, a distributed encirclement and control method for multiple targets can be achieved. This method is applicable to practical application scenarios such as underwater environment development, underwater environment confrontation, and disaster relief, and can significantly improve the task execution efficiency and reliability of multi-AUV systems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A multi-AUV cooperative encirclement and control method based on a virtual multi-object estimation center includes the following steps:

[0007] S1. Construct the AUV kinematic model and initialize the system state;

[0008] S2. Construct a distributed collaborative multi-target virtual center estimator by utilizing the relative position information between the AUV and the target, as well as the relative position information between neighboring AUVs and the target.

[0009] S3. Construct a multi-target encirclement kinematic controller by utilizing the relative position information between the AUV and its neighbors, as well as the relative position information between the AUV and the estimated multi-target center.

[0010] S4. Use the kinematic controller constructed in step S3 to perform coordinated control of the AUV to achieve the task of encircling and capturing multiple virtual targets.

[0011] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0012] 1. This invention adopts a distributed design, where all control and estimation processes rely only on local information, eliminating the need for global target information or centralized computation, thus reducing dependence on communication and computing resources. For situations where target information changes dynamically, such as when a target group is dispersed into several smaller subgroups, this invention utilizes a distributed multi-target virtual center estimator to adjust the AUV's estimation of the target center in real time, ensuring the system can still complete the encirclement task even in environments with insufficient information. Considering various influencing factors such as inaccurate underwater GPS positioning, limited detection range, and communication constraints, this invention designs a kinematic controller suitable for underwater operation, improving robustness and scalability.

[0013] 2. This invention designs a distributed multi-target virtual center estimator based on local information. It uses the estimated values ​​of the multi-target centers by neighboring AUVs and the target information detected by its own AUV to collaboratively estimate the virtual centers of multiple targets. This estimator is based on graph theory and consensus protocol, and is suitable for directed balanced graph ring topology. It can realize the distributed estimation of multi-target centers in communication-limited environments.

[0014] 3. Combining the relative position information between the AUV and its neighbors, as well as the relative position information between the AUV and the estimated center of multiple targets, this invention designs a kinematic controller. This controller drives the AUV to cooperate in encircling and capturing multiple targets around the virtual center of the target by adjusting the forward speed and head roll angular velocity of the AUV, while meeting the stability and convergence requirements of the encirclement and capture task. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method of the present invention;

[0016] Figure 2 This is a schematic diagram of multiple AUVs targeting multiple targets with a movement time of 0-200s in Example 1;

[0017] Figure 3This is a schematic diagram illustrating the estimation error of the virtual center position of multiple targets during the movement of multiple AUVs in Example 1;

[0018] Figure 4 This is a schematic diagram of multiple AUVs engaging multiple targets with a movement time of 200s-400s in Example 1;

[0019] Figure 5 This is a schematic diagram of the encirclement and capture of the target group by multiple AUVs in Example 2, which disperses the target group into two target subgroups;

[0020] Figure 6 This is a schematic diagram illustrating the estimation error of the center positions of the two target subgroups during the multi-AUV motion process in Example 2;

[0021] Figure 7 This is a schematic diagram of multiple AUVs encircling and capturing newly formed target subgroups when targets in a subgroup move, as shown in Example 2. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0023] This invention focuses on solving the problem of orbiting multiple targets using multiple AUVs. It utilizes only measurement information between AUVs and their neighbors, and among detectable targets—i.e., local information—to design a distributed multi-target virtual center estimation algorithm and an orbiting controller. An innovative framework is proposed, enabling each AUV to simultaneously measure the relative positions of targets and coordinate with other AUVs to estimate the target centers, then orbit around the virtual center of multiple targets. This invention considers the impact of dynamic changes in target information in underwater environments with weak communication. By utilizing its own relative position measurement information and neighbor information to collaboratively estimate the virtual center of multiple targets, it achieves multi-AUV encirclement and control of multiple targets based on local information, reducing reliance on global information and making it more suitable for underwater environments with limited information.

[0024] like Figure 1 As shown, the present invention provides a multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center, comprising the following steps:

[0025] S1. Construct the AUV kinematic model and initialize the system state; specifically:

[0026] The kinematic model of an AUV is represented as follows:

[0027]

[0028] Where the subscript i represents the i-th AUV, i = 1, 2, ..., n, and n is the number of AUVs; [x i y iis the coordinate of the i-th AUV in the inertial coordinate system, x i is the abscissa, y i is the ordinate; θ i is the heading angle of the i-th AUV in the inertial coordinate system; [u i ω i T is the input of the kinematic controller, u i , ω i represent the forward speed and the yaw angular velocity designed for the i-th AUV respectively.

[0029] S2. Use the relative position information between the AUV and the target and the relative position information between the neighboring AUV and the target to construct a distributed cooperative multi-target virtual center estimator; Step S2 includes:

[0030] S21. Define the cooperative pursuit task of the pursuit target and multiple targets; specifically:

[0031] For a team composed of n AUVs, the cooperative pursuit task of multiple targets is to cooperatively pursue the virtual center of m targets T j with an expected radius r i cooperatively, j = 1, 2,..., m, i = 1, 2,..., n, m ≤ n; if m < n, then some AUVs perform distributed pursuit for the same target;

[0032] Among them, one AUV can detect at most the relative position information j with one target T This relative position information is obtained in the local coordinate system of the AUV.

[0033] S22. Based on the neighbor relationship between multiple AUVs, construct a multi-AUV neighbor relationship topology graph; specifically:

[0034] Efficient data transmission is crucial for improving the exploration efficiency of multi-robots. However, common communication methods often carry a large amount of redundant information, resulting in a too high communication load. To address this problem, a front neighbor is specified for each AUV, where the front neighbor of the n-th AUV is the 1st AUV, thereby constructing a one-way circular neighbor relationship graph. The information interaction is a directed circular topology structure, so the amount of information transmitted can be effectively reduced. In this topology, each AUV (the (i + 1)-th) only needs to obtain the relative position estimation information about the multi-target virtual center from its neighbor AUV (the i-th); this way of information interaction has the fewest interaction channels in the multi-AUV system and is very suitable for scenarios with poor underwater communication environments. Only n interaction channels are required to meet the communication needs between n AUVs.

[0035] ​S23. Based on the neighbor relationships and the topology graph of the multi-AUV neighbor relationships, calculate the Laplace matrix of the communication graph. Specifically:

[0036] Let a directed graph G(V,E,A) be denoted by (V,E,A), where V is the set of nodes in the AUV, and E is the set of edges. A = [a] ij [] is the weighted adjacency matrix; the in-degree and out-degree of a node in a directed graph are defined as follows: and If the in-degree of each node in a graph equals its out-degree, then a directed graph G is balanced; an undirected graph is a special type of balanced graph, possessing a ji =a ij The property holds for all i and j;

[0037] If there exists a continuous sequence of edges from any node i to another node j in a graph, i ≠ j, then the directed graph G is said to be strongly connected.

[0038] Degree matrix Δ=[δ ij ] is a diagonal matrix, where δ ij =0 holds for all i ≠ j, and δ ii =deg out (v i This holds true for all i;

[0039] Calculate the Laplace matrix of the communication graph G among multiple AUVs based on their neighbor relationships. definition For a strongly connected graph, the rank of its Laplace matrix is ​​equal to n-1, where n is the Laplace matrix. Dimensions.

[0040] S24. Define the relative position between the i-th AUV and the j-th target in the local coordinate system. The expression is:

[0041]

[0042] in, For rotation matrix; [x j y j ] T Let x be the coordinates of the j-th target in the inertial coordinate system. j y is the x-axis. j The vertical axis is used as the coordinate.

[0043] S25. Define the relative position of the i-th AUV and the center of the multi-target system in the local coordinate system. The expression is:

[0044]

[0045] in, It is a rotation matrix; The coordinates of the virtual center of the multi-objective system in the inertial coordinate system. The x-axis is... The vertical axis is used as the coordinate.

[0046] S26. Construct a distributed collaborative multi-objective center estimator; specifically:

[0047] The distributed cooperative multi-objective center estimator is represented as:

[0048]

[0049] in, It is the estimated value of the multi-object virtual center calculated by the i-th AUV, i.e. The estimated value of λ; i These are the internal state variables of the central estimator for the i-th AUV, and γ1>0, γ2>0, and γ3>0 are the design parameters of the estimator; since and λ i+1 The update only requires information from neighboring AUVs, using a distributed protocol;

[0050] S27. Set the estimator parameters so that the distributed collaborative multi-objective center estimator tracks the relative positions of the multi-objective centers; specifically:

[0051] Set the estimator parameters γ1, γ2, and γ3 such that the input is time-varying. The output is The distributed collaborative multi-objective center estimator can track Furthermore, since the tracking error is bounded, the estimator parameters satisfy the following condition:

[0052] γ3>0 (6)

[0053]

[0054] Among them, a i and b i Represent the Laplace matrix respectively The real and imaginary parts of the i-th eigenvalue.

[0055] To ensure the convergence of the protocol, based on the gain condition mentioned above, the following steps are used to select the parameters γ1, γ2, and γ3 in the consensus protocol:

[0056] First, assign a positive number to γ3;

[0057] Calculate the lower bound of γ2: max{max(4γ3(b)} i 2 -a i 2 ),0}, and assign a value greater than the lower bound to γ2;

[0058] Finally, calculate the lower bound of γ1. And assign γ1 a value greater than this lower bound;

[0059] By selecting appropriate parameters, the estimation of the multi-objective virtual center eventually converges to a bounded region.

[0060] S3. Construct a multi-target encirclement kinematic controller using the relative position information between the AUV and its neighbors, as well as the relative position information between the AUV and the estimated multi-target center; including:

[0061] S31. Define the conditions that the target capture task must meet; specifically:

[0062]

[0063] Where i = 1, 2, ..., n, It is a constant. r i Let r1 = r2 = ... = r be the radius of the circular trajectory in the AUV target capture mission. n t is the motion time; defined And Ψ i Satisfy Ψ i ∈[0,2π), where the atan2 function is the arctangent function;

[0064] S32. Define the relative position between the i-th AUV and its neighboring (i+1)-th AUV in the local coordinate system. The expression; specifically:

[0065]

[0066] in, For rotation matrix; [x i+1 y i+1 ] T Let x be the coordinates of the (i+1)th neighboring AUV in the inertial coordinate system. i+1 y is the x-axis. i+1 The vertical axis is denoted by .

[0067] S33. Construct the kinematic controller for the multi-AUV system and set the kinematic controller inputs; the specific kinematic controller inputs for the multi-AUV system are:

[0068]

[0069] Where, k u >0,k w >0 represents the kinematic controller parameter; c is a constant with a value range of c∈(0,1);

[0070] S34. Define the state variable χ of the i-th AUV. i Specifically:

[0071] χ i =[y i ,ω i ,β i ] T (12)

[0072] Where, β i =θ i+1 -θ i The first differential of formula (12) is:

[0073]

[0074] when When, formula (13) is expressed as:

[0075]

[0076] The state variables of the entire AUV system are: In other words, when At that time, the unique equilibrium state of χ is:

[0077]

[0078] in,

[0079] S35, Design control parameter k u ,k w Specifically:

[0080] Design control parameter k u ,k w , so that:

[0081]

[0082] Therefore, k u ,k w The expression that needs to be satisfied is specifically:

[0083]

[0084] S4. Use the kinematic controller constructed in step S3 to perform coordinated control of the AUV to achieve the task of encircling and capturing multiple virtual targets.

[0085] In addition, when the target group begins to disperse and form multiple target subgroups, the distributed multi-target center estimator constructed in step S2 will re-estimate the virtual center of the multiple target subgroups, and then use the kinematic controller constructed in step S3 to drive multiple AUVs to surround the dispersed target subgroups.

[0086] To verify the effectiveness of the method of the present invention, the distributed cooperative multi-target virtual center estimator and multi-target encirclement kinematic controller obtained in steps S2 and S3 are applied to the encirclement control of multiple AUVs against multiple targets under the condition that the target information remains unchanged and the target is dispersed into multiple subgroups (taking 8 AUVs as an example).

[0087] To more effectively illustrate the effectiveness of the method of this invention, all parameter settings are consistent. The initialization of estimator parameters, controller parameters, and state parameters is shown in Table 1 below, where the initial positions of the 8 AUVs are set to random positions.

[0088]

[0089] Table 1

[0090] Example 1

[0091] This embodiment is a distributed multi-target encirclement and control system based on multiple AUVs when multiple targets are detected but not dispersed.

[0092] In this embodiment, each AUV is designed to detect at most one target, and the expected orbital radius r of each AUV is... i The distance is 15m, and the target's location is...

[0093] like Figure 2 The diagram shows multiple AUVs encircling and capturing multiple targets. Hollow triangles represent the initial positions of the AUVs, filled triangles represent their final positions, solid black lines represent the movement paths, and the solid origin represents the target's position. Figure 2 It can be seen that multiple AUVs can achieve the task of encircling and controlling multiple targets from any initial position. For example... Figure 3 The figure shows the curve of the estimation error of the multi-target virtual center estimator during AUV motion; from Figure 3 It can be seen that multiple AUVs eventually reached a consensus on the location estimation of the virtual center of multiple targets, and the estimation error was within a bounded range. Figure 2 and Figure 3 The movement time shown is 0-200s. To more intuitively demonstrate the effective implementation of the target capture mission, a schematic diagram of the multi-AUV movement trajectory from 200s to 400s is provided, as shown below. Figure 4As shown, multiple AUVs can simultaneously perform distributed estimation of the virtual center of multiple targets and complete the orbit of multiple targets, and the estimation error of the virtual center of multiple targets eventually converges to the bounded region.

[0094] Example 2

[0095] This embodiment describes the encirclement and control of multiple targets by multiple AUVs when the detected targets are dispersed into two subgroups.

[0096] To verify the effectiveness of this invention, without changing the control parameters, the target was dispersed into two subgroups, with the target's coordinates being... At this point, set the desired orbital radius r for each AUV. i It is 8m.

[0097] like Figure 5 As shown, this illustrates the motion trajectories of multiple AUVs surrounding two target subgroups when the target group disperses and forms two target subgroups. Figure 6 As shown, this represents the estimation error of the virtual centers of two target subgroups by a multi-AUV system. This demonstrates that the multi-target virtual center estimator can still estimate the centers of the subgroups, and the estimation error eventually converges to a bounded range, meeting the design requirements. Figure 7 As shown, when targets T5 and T8 occupy the same position, the multi-AUV system can still estimate the subgroup center through the multi-target virtual center estimator and simultaneously drive the AUVs through the controller to achieve the task of encircling and capturing multiple targets.

[0098] This invention provides a multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center. The information used by the multi-target virtual center estimator and controller depends only on the relative positions of the AUVs with their neighbors and with the targets in the local coordinate system. By dynamically estimating the virtual centers of the multiple targets and simultaneously driving the AUVs, a distributed target encirclement and control task is achieved, ensuring the stability of the system. This provides an effective solution for achieving the encirclement and control of multiple target groups in multi-AUV systems in underwater environments with weak communication.

[0099] It should also be noted that, in this specification, terms such as "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0100] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-AUV cooperative encirclement and control method based on a virtual multi-object estimation center, characterized in that, Includes the following steps: S1. Construct the AUV kinematic model and initialize the system state; S2. Utilizing the relative positional information between the AUV and the target, as well as the relative positional information between neighboring AUVs and the target, a distributed cooperative multi-target virtual center estimator is constructed; including: S21. Define the target of the encirclement and the collaborative encirclement task of multiple targets; S22. Based on the neighbor relationships among multiple AUVs, construct a multi-AUV neighbor relationship topology graph; S23. Based on the neighbor relationships and the topology graph of the multi-AUV neighbor relationships, calculate the Laplace matrix of the communication graph. ; S24. Define the relative position between the i-th AUV and the j-th target in the local coordinate system. The expression is: in, It is a rotation matrix; Let J be the coordinates of the j-th target in the inertial coordinate system. The x-axis is... The vertical axis is used as the coordinate. S25. Define the relative position of the i-th AUV and the center of the multi-target system in the local coordinate system. The expression is: in, It is a rotation matrix; The coordinates of the virtual center of the multi-objective system in the inertial coordinate system. The x-axis is... The vertical axis is used as the coordinate. S26. Construct a distributed collaborative multi-objective center estimator, specifically as follows: The distributed cooperative multi-objective center estimator is represented as: in, It is the estimated value of the multi-object virtual center calculated by the i-th AUV, i.e. The estimated value; It is the internal state variable of the central estimator of the i-th AUV. These are the design parameters of the estimator; because and The update only requires information from neighboring AUVs, using a distributed protocol; S27. Set the estimator parameters so that the distributed cooperative multi-objective center estimator tracks the relative positions of the multi-objective centers; S3. Construct a multi-target encirclement kinematic controller by utilizing the relative position information between the AUV and its neighbors, as well as the relative position information between the AUV and the estimated multi-target center. S4. Use the kinematic controller constructed in step S3 to perform coordinated control of the AUV to achieve the task of encircling and capturing multiple virtual targets.

2. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 1, characterized in that, Step S1 is as follows: Construct a kinematic model of the AUV, which is represented as follows: Where the subscript i represents the i-th AUV, i = 1, 2, ..., n, and n is the number of AUVs; Let i be the coordinates of the i-th AUV in the inertial coordinate system. The x-axis is... The vertical axis is used as the coordinate. Let be the heading angle of the i-th AUV in the inertial coordinate system; It is the kinematic controller input. These represent the forward speed and yaw rate of the i-th AUV design, respectively.

3. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 1, characterized in that, Step S21 is as follows: For a team consisting of n AUVs, a multi-target cooperative encirclement task involves targeting m targets. The virtual center with the desired radius Coordinated encirclement and capture, j=1,2,...,m, i=1,2,...,n. ;like Then, some AUVs will conduct distributed encirclement and capture of the same target; One AUV can detect at most one target. relative position information This relative position information is obtained in the local coordinate system of the AUV.

4. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 3, characterized in that, Step S22 is as follows: Each AUV is assigned a former neighbor, where the former neighbor of the nth AUV is the first AUV, thus constructing a unidirectional circular neighbor relationship graph. The information exchange is a directed circular topology, in which each AUV only needs to obtain relative position estimation information about the multi-objective virtual center from its neighboring AUVs. Step S23 is as follows: Let a directed graph G(V,E,A) be denoted by (V,E,A), where V is the set of nodes AUV and E is the set of edges, and E⊆V×V. It is a weighted adjacency matrix; the in-degree and out-degree of a node in a directed graph G are defined as follows: and If the in-degree of each node in the graph is equal to its out-degree, then the directed graph G is balanced. Undirected graphs are special types of equilibrium graphs, possessing... The property holds for all i and j; If in the graph, from any node i to another node... There exists a continuous sequence of edges in each case. If the directed graph G is strongly connected, then the graph G is called strongly connected. Degree matrix It is a diagonal matrix, where For all Established, and This holds true for all i; Calculate the Laplace matrix of the communication graph among multiple AUVs based on their neighbor relationships. ,definition ; For a strongly connected graph, the rank of its Laplacian matrix is ​​equal to... n is the Laplace matrix Dimensions.

5. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 1, characterized in that, Step S27 is as follows: Setting estimator parameters This makes the input time-varying. The output is The distributed collaborative multi-objective center estimator can track Furthermore, since the tracking error is bounded, the estimator parameters satisfy the following condition: in, and Represent the Laplace matrix respectively The real and imaginary parts of the i-th eigenvalue. ; To ensure the convergence of the protocol, based on the aforementioned gain condition, the following steps are used to select the parameters in the consensus protocol. : First give Assign a positive number; calculate The Lower World and give Assign a value greater than the lower bound; Finally, calculate The Lower World and give Assign a value greater than the lower bound; By selecting parameters, the estimation of the multi-objective virtual center eventually converges to the bounded region.

6. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 1, characterized in that, Step S3 includes: S31. Define the conditions that the target capture mission must meet; S32. Define the relative position between the i-th AUV and its neighboring (i+1)-th AUV in the local coordinate system. The expression; S33. Construct a kinematic controller for a multi-AUV system and set the input to the kinematic controller; S34. Define the state variables of the i-th AUV. ; S35, Design Control Parameters .

7. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 6, characterized in that, In step S31, the specific conditions that the target capture task needs to meet are as follows: Where i = 1, 2, ..., n, It is a constant. , Let be the radius of the circular trajectory in the AUV target capture mission. t is the motion time; defined ,and satisfy ,in, The function is the arctangent function; In step S32, the relative positions between the i-th AUV and its neighboring (i+1)-th AUV in the local coordinate system are determined. The specific expression is: in, It is a rotation matrix; Let be the coordinates of the (i+1)th neighboring AUV in the inertial coordinate system. The x-axis is... The vertical axis is denoted by .

8. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 6, characterized in that, In step S33, the kinematic controller input of the multi-AUV system is specifically as follows: in, Here are the parameters of the kinematic controller; c is a constant with a range of values. ; In step S34, the state variable of the i-th AUV Specifically: in, The first differential of formula (12) is: when When, formula (13) is expressed as: The state variables of the entire AUV system are: In other words, when hour, The only equilibrium state is: in, ; Step S35 is as follows: Design control parameters , so that: therefore, The expression that needs to be satisfied is specifically:

9. The multi-AUV cooperative encirclement and control method based on a virtual multi-target estimation center according to claim 1, characterized in that, When the target group begins to disperse and form multiple target subgroups, the distributed multi-target center estimator constructed in step S2 re-estimates the virtual center of the multiple target subgroups, and then uses the kinematic controller constructed in step S3 to drive multiple AUVs to surround the dispersed target subgroups.

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