A method for tracking and controlling maneuvering targets in an unmanned surface vessel swarm under complex dynamic environments

Abstract

This application discloses a method for tracking and controlling maneuvering targets in an unmanned surface vessel (USV) swarm under complex dynamic environments, belonging to the field of cooperative USV control. The method first equips each USV with an extended state observer to estimate the velocity and control input of an unknown maneuvering target online, and to compensate for external bounded disturbances. A distributed cooperative controller is designed, integrating target attraction, inter-vessel collision avoidance, environmental obstacle avoidance, and velocity coordination functions. This controller enables the USV swarm to autonomously form and dynamically adjust a stable tracking configuration around the target without pre-setting formation parameters. Simultaneously, a distributed event triggering mechanism deeply integrated with the controller is designed to dynamically determine communication timing based on local measurement errors and neighbor state deviations, significantly reducing the frequency of inter-vessel communication. This application effectively solves the challenge of cooperative tracking of USV swarms under multiple constraints such as unknown state, interference, intermittent communication, and obstacles in complex dynamic environments.

Description

Technical Field

[0001] This application relates to the field of unmanned surface vessel (USV) cooperative control, and in particular to a method for tracking and controlling a swarm of USV maneuvers in complex dynamic environments. Background Technology

[0002] Swarm cooperative control, due to its high efficiency and robustness in performing complex tasks, has become an important research direction in the field of intelligent unmanned systems. This technology shows broad application prospects in scenarios such as environmental monitoring, disaster relief, logistics distribution, and security patrol. Compared with manned platforms, unmanned surface vessels (USVs) have significant advantages such as small size, low cost, flexible deployment, and controllable risks, making them ideal platforms for performing tasks such as wide-area reconnaissance, target search and localization, moving target tracking, and cooperative interception and suppression. Among these, swarm cooperative tracking and control of USVs for maneuvering targets is particularly crucial.

[0003] Existing technologies typically face the following challenges: (1) Unknown target state: In actual tasks, targets are often non-cooperative, and their speed, acceleration and other state information are difficult to obtain; (2) Environmental interference and obstacles: External disturbances such as wind, waves and currents in the marine environment, as well as static / dynamic obstacles, seriously affect control accuracy and safety; (3) Limited communication resources: Continuous high-speed communication between cluster members will bring huge bandwidth pressure and energy consumption, especially in scenarios with poor communication conditions such as the open sea; (4) Strong dependence on formation: Traditional methods usually require the pre-set fixed geometric formation (such as circles and polygons), lacking the ability to adapt to target maneuvering and environmental changes.

[0004] While existing research has attempted to address some of these issues—for example, using disturbance observers to handle interference, employing artificial potential field (APF) methods for obstacle avoidance, and introducing event-triggered control (ETC) to reduce communication load—these methods are often isolated and fail to organically integrate state estimation, interference resistance, self-organized tracking, collision and obstacle avoidance, and intermittent communication optimization. In particular, there is a lack of a comprehensive control scheme that can break free from pre-defined formation dependence, spontaneously form tracking configurations through an intrinsic potential field mechanism, and deeply coordinate with event-triggered communication. Summary of the Invention

[0005] The purpose of this application is to provide a method for tracking and controlling the maneuvering target of an unmanned surface vessel swarm in a complex dynamic environment, so as to solve the problem of collaborative tracking under multiple complex constraints such as unknown target state, external interference, obstacles and communication limitations.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] This application provides a method for tracking and controlling maneuvering targets in an unmanned surface vessel (USV) swarm under complex dynamic environments, including:

[0008] S1. Configure an extended state observer and a sliding mode disturbance observer for each unmanned surface vessel in the cluster;

[0009] S2. Obtain the target's location information;

[0010] S3. Using the extended state observer and based on the target's position information, estimate the unknown velocity and control input of the target in real time to obtain the estimated value of the target velocity and the estimated value of the target control input;

[0011] S4. Using the sliding mode disturbance observer, estimate and compensate for the external bounded disturbances acting on the unmanned surface vessel in real time to obtain the estimated value of the disturbance by the unmanned surface vessel.

[0012] S5. Based on the estimated target velocity, the estimated target control input, and the estimated disturbance response of the unmanned surface vessel, design a distributed cooperative controller.

[0013] S6. Design a distributed event triggering mechanism, defining the state error of the unmanned surface vessel (USV) as the difference between its current speed and the speed broadcast to its neighbors at the most recent triggering time; when the norm of the USV's state error meets the preset triggering conditions, activate communication and broadcast the current speed information of the USV to its neighboring USVs; otherwise, keep communication silent.

[0014] S7. The speed information broadcast at the most recent trigger time in step S6 is used as the input of the distributed cooperative controller. The distributed cooperative controller is executed to drive the unmanned surface vessel cluster to autonomously form and maintain a stable tracking configuration around the target without the need for preset formation parameters, while avoiding collisions between vessels and environmental obstacles.

[0015] Optionally, the acquisition of the location information of the unknown target is specifically based on the target's location information obtained from the unmanned surface vessel's own sensors.

[0016] Optionally, the distributed cooperative controller includes a target attraction term, an inter-vessel collision avoidance term, an environmental obstacle avoidance term, and a velocity coordination term. The inter-vessel collision avoidance term and the environmental obstacle avoidance term are generated by the negative gradients of the collision avoidance potential field function and the obstacle avoidance potential field function, respectively. The velocity coordination term is used to drive all unmanned surface vessels to maintain the same speed as the target speed.

[0017] Optionally, the expression for the extended state observer is as follows:

[0018] ;

[0019] in, unmanned surface vessel The derivative of the target location estimate; For unmanned surface vessels An estimate of the target velocity; Indicates the measurable location of the target; For unmanned surface vessels An estimate of the target's location; unmanned surface vessel The derivative of the target velocity estimate; For unmanned surface vessels Estimates of the target control input; unmanned surface vessel The derivative of the target control input estimate, This is the gain for the extended state observer.

[0020] Optionally, the expression for the sliding mode disturbance observer is as follows:

[0021] ;

[0022] in, For unmanned surface vessels Estimates of the disturbance; , Indicates the gain of the perturbation observer. This indicates the sliding surface.

[0023] Optionally, the expression for the distributed collaborative controller is as follows:

[0024] ;

[0025] in, It is a distributed controller; To control the gain; unmanned surface vessel Location; express Unmanned surface vessel at the most recent trigger moment speed; Indicates the first Unmanned surface vessel; Represents the dynamic neighbor set of the unmanned surface vessel; express Unmanned surface vessels and Communication weights between unmanned surface vessels; express Unmanned surface vessel at the most recent trigger moment speed; For gradient operators; To avoid collisions, the potential field function; express Unmanned surface vessels and The relative distance between unmanned surface vessels; The obstacle avoidance potential field function; express obstacle; A set representing obstacles; express Unmanned surface vessels and The relative distance to the obstacles; express Triggering time; Indicates collaborative tracking control items; Represents velocity cooperation terms; Indicates obstacle avoidance items; For unmanned surface vessels Estimates of the disturbance.

[0026] Optionally, the expression for the collision avoidance potential field function is as follows:

[0027] ;

[0028] in, For gradient operators; To avoid collisions, the potential field function; , This is the collision avoidance constant; express Unmanned surface vessels and The relative distance between unmanned surface vessels To maintain a safe collision avoidance distance; The radius of the machine body; unmanned surface vessel Location; unmanned surface vessel The location.

[0029] Optionally, the expression for the obstacle avoidance potential field function is as follows:

[0030] ;

[0031] in, For gradient operators, This is the obstacle avoidance constant; express Unmanned surface vessels and The relative distance to the obstacles; For safe obstacle avoidance distance, for The radius of the obstacle; The radius of the machine body; unmanned surface vessel Location; express The location of the obstacle.

[0032] Optionally, the expression for the preset triggering condition is as follows:

[0033] ;

[0034] ;

[0035] in, express Triggering time; Indicates the current time; express Triggering time; Indicates the trigger function, Indicates state error, Indicates the parameters to be designed. express The cardinality of the neighbor set of unmanned surface vessels; express The velocity coordination term at the trigger moment.

[0036] According to the specific embodiments provided in this application, this application has the following technical effects:

[0037] This application provides a method for tracking and controlling maneuvering targets in an unmanned surface vessel (USV) swarm under complex dynamic environments, which has the following advantages compared to existing technologies:

[0038] Breaking free from formation dependence and achieving self-organized tracking: Through the potential field gradient driving mechanism, the cluster can spontaneously form a stable configuration around the target without any preset formation geometry parameters, which greatly improves the system's adaptability and robustness to target maneuverability and environmental changes.

[0039] Strong anti-interference and high-precision estimation: Through the joint design of extended state observer (ESO) and sliding mode disturbance observer (SMDO), it can effectively handle the two core challenges of unknown target state and external environmental disturbance, laying a solid foundation for high-precision tracking control;

[0040] Efficient utilization of communication resources: The proposed event-triggered mechanism can dynamically adjust the communication frequency according to the actual needs of the system, which significantly reduces the network communication load while ensuring control performance, and is particularly suitable for bandwidth-constrained marine application scenarios.

[0041] High safety: Through the design of collision avoidance potential fields and obstacle avoidance potential fields, it can simultaneously ensure collision avoidance between unmanned surface vessels and effective avoidance of obstacles in the environment, thus ensuring the safety of mission execution;

[0042] Theoretically sound and engineering-feasible: The stability and Zeno-free behavior of the system are proven through rigorous Lyapunov theory, providing a solid theoretical guarantee for the practical deployment of the algorithm. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a schematic diagram of a collaborative target tracking task in one embodiment of this application;

[0045] Figure 2 This is a schematic diagram of the target tracking and control framework of a multi-unmanned surface vessel system in one embodiment of this application;

[0046] Figure 3 This is a flowchart illustrating a method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment, according to one embodiment of this application.

[0047] Figure 4 This is a schematic diagram of the collision avoidance potential field according to an embodiment of this application;

[0048] Figure 5 This is a schematic diagram of the target velocity estimation error according to an embodiment of this application;

[0049] Figure 6 This is a schematic diagram of the target acceleration estimation error according to an embodiment of this application;

[0050] Figure 7 This is a schematic diagram of interference estimation error according to an embodiment of this application;

[0051] Figure 8 This is a schematic diagram of the unmanned surface vessel swarm tracking trajectory according to an embodiment of this application;

[0052] Figure 9 This is a schematic diagram of the spatial distribution of unmanned surface vessels at different times according to an embodiment of this application;

[0053] Figure 10 This is a schematic diagram illustrating tracking errors according to an embodiment of this application;

[0054] Figure 11 This is a schematic diagram illustrating the minimum inter-boat distance according to an embodiment of this application;

[0055] Figure 12 This is a schematic diagram illustrating the speed of an unmanned surface vessel according to an embodiment of this application;

[0056] Figure 13 This is a schematic diagram of trigger distribution according to an embodiment of this application;

[0057] Figure 14 This is a schematic diagram of the tracking trajectory of an unmanned surface vessel swarm in an obstacle environment according to an embodiment of this application;

[0058] Figure 15 This is a schematic diagram of the spatial distribution of unmanned surface vessels at different times under an obstacle environment according to an embodiment of this application;

[0059] Figure 16 This is a schematic diagram of tracking error in an obstacle environment according to an embodiment of this application;

[0060] Figure 17 This is a schematic diagram of the minimum inter-boat distance under an obstacle environment according to an embodiment of this application;

[0061] Figure 18 This is a schematic diagram of speed under an obstacle environment according to an embodiment of this application;

[0062] Figure 19 This is a schematic diagram of trigger distribution in an obstacle environment according to an embodiment of this application;

[0063] Figure 20 This is a schematic diagram of the trigger distribution of a prior art solution in an accessible environment according to an embodiment of this application;

[0064] Figure 21 This is a schematic diagram of the trigger distribution of a prior art solution in an obstacle environment according to an embodiment of this application. Detailed Implementation

[0065] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0066] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] Assume the unmanned surface vessel system moves in a two-dimensional space. Consider the following... A system consisting of one unmanned surface vessel and one target, the first The model of the unmanned surface vessel is as follows:

[0068] (1)

[0069] In the formula, unmanned surface vessel The derivative of the axis position, unmanned surface vessel The derivative of the axis position, The derivative of the unmanned surface vessel's velocity. The derivative of the heading angle, These represent the position vector and velocity vector of the unmanned surface vessel, respectively. Indicates the control inputs of the unmanned surface vessel. Indicates the heading angle. unmanned surface vessel The position of the axis unmanned surface vessel The position of the axis unmanned surface vessel The speed of the shaft, unmanned surface vessel The speed of the shaft, unmanned surface vessel Axis control input, unmanned surface vessel Axis control inputs.

[0070] To facilitate subsequent analysis, this application uses the dynamic feedback linearization method to transform equation (1) into a double integral model, which is the kinematic model of the unmanned surface vessel, and its expression is:

[0071] (2)

[0072] In the formula, The derivative representing the position of the unmanned surface vessel; The derivative representing the velocity of the unmanned surface vessel; Indicates the location of the unmanned surface vessel.

[0073] The unmanned surface vessel model in equation (1) can be rewritten as:

[0074] (3)

[0075] In the formula, The derivative representing the velocity of the unmanned surface vessel; This indicates the speed of the unmanned surface vessel.

[0076] Assumption 1: Unknown external disturbance Continuously differentiable and satisfying , , , To disturb the upper bound, This is the upper bound of the rate of change of the disturbance. This represents the rate of change of the disturbance.

[0077] Furthermore, since the motion pattern of non-cooperative targets is unknown, they can be modeled as follows:

[0078] (4)

[0079] in, The derivative representing the target position; The derivative representing the target velocity; Indicates the measurable location of the target. and This represents the target's unknown velocity and control input. Indicate target The position of the axis Indicate target The position of the axis Indicate target The speed of the shaft, Indicate target The speed of the shaft.

[0080] Assumption 2: Assume that the rate of change of the target control input is bounded, i.e. , To control the upper bound of the input rate of change, This represents the rate of change of the target control input.

[0081] In tracking and control problems, it is usually assumed that the target's motion state is fully known. This application considers the target's potential non-cooperative characteristics, assuming that its velocity and acceleration information are unknown, and only obtains the target's position information from sensors onboard the vessel.

[0082] Using diagrams To describe the information interaction between unmanned surface vessels, among which Let be the set of points in the graph, used to represent the set of unmanned surface vessels in the cluster. Let the edge set of the graph represent the interaction relationships between unmanned surface vessels. Let's consider the adjacency matrix. If the unmanned surface vessel... Capable of using unmanned surface vessels Receive information, then ;otherwise, Specifically, assuming .picture The degree matrix is ,in , unmanned surface vessel The in-degree, then the graph The Laplacian matrix is ​​defined as Define the dynamic neighbor set of the unmanned surface vessel as:

[0083] (5)

[0084] In the formula, For the dynamic neighbor set of the unmanned surface vessel; Indicates the first Unmanned surface vessel; Indicates the first Unmanned surface vessel; Indicates the relative distance between unmanned surface vessels. This indicates the sensing range of the unmanned surface vessel.

[0085] Compared to fixed topology, unmanned surface vessels (USVs) in dynamic network topology can detect the presence of neighboring USVs based on their own sensors, forming a fully distributed self-organizing communication architecture that better meets the needs of actual dynamic mission environments.

[0086] The core objective of this application is to design a distributed control protocol that enables a swarm of multiple unmanned surface vessels (USVs) to collaboratively track maneuvering targets with unknown state information in complex dynamic environments. For example... Figure 1 As shown, this tracking task requires the submarine to not only dynamically converge to the vicinity of the target, but also to autonomously form and maintain a stable configuration in an environment with obstacles and disturbances. To overcome challenges such as unknown target motion states (velocity, acceleration) and external disturbances, an online estimation mechanism needs to be established. Simultaneously, facing the constraints of intermittent communication and the urgent need for collision avoidance / obstacle avoidance, the protocol must significantly reduce the communication burden through a triggering mechanism and achieve an organic integration of potential field gradient-driven self-organizing configuration generation and collision avoidance / obstacle avoidance capabilities.

[0087] This application addresses environmental disturbances and unknown target motion by designing a disturbance observer and a state observer, respectively. The key innovation lies in utilizing a distributed cooperative controller based on collision avoidance and obstacle avoidance potential field gradients, which can autonomously form and maintain a stable tracking configuration around the target without pre-setting geometric parameters. Furthermore, it proposes an event-triggered mechanism deeply integrated with the controller, dynamically adjusting inter-UAV communication based on local measurement errors and neighbor state deviations, significantly reducing network load. Stability proofs based on Lyapunov guarantee the closed-loop system performance and eliminate Zeno behavior. The overall cooperative framework is as follows: Figure 2 As shown

[0088] In one exemplary embodiment, such as Figure 3 The diagram illustrates a flowchart of a method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment. This method is executed by a computer device, specifically a terminal or server, or both. In this embodiment, it includes steps S1 to S7. Wherein:

[0089] S1. Configure an extended state observer and a sliding mode disturbance observer for each unmanned surface vessel in the cluster.

[0090] S2. Obtain the target's location information.

[0091] S3. Using the extended state observer and based on the target's position information, estimate the unknown velocity and control input of the target in real time to obtain the estimated value of the target velocity and the estimated value of the target control input.

[0092] S4. Using the sliding mode disturbance observer, estimate and compensate for the external bounded disturbances acting on the unmanned surface vessel in real time, and obtain the estimated value of the disturbance by the unmanned surface vessel.

[0093] The extended state observer and the sliding mode perturbation observer are introduced below:

[0094] Extended State Observer

[0095] Considering that the target's position can be measured by sensors, and assuming that the target's velocity and control input are unknown, this application, based on the extended state observer theory, designs a separate state observer for each unmanned surface vessel (USV) to estimate the target's velocity and control input.

[0096] (6)

[0097] in, For observer gain; For unmanned surface vessels An estimate of the target's location; For unmanned surface vessels An estimate of the target velocity; For unmanned surface vessels Estimates of the target control input; unmanned surface vessel The derivative of the target location estimate, unmanned surface vessel The derivative of the target velocity estimate, unmanned surface vessel The derivative of the target control input estimate.

[0098] Before performing the tracking mission, the observer can be integrated into the onboard computer of the unmanned surface vessel. When the onboard sensors detect the target position, the speed and control input can be quickly calculated using equation (6).

[0099] Define position estimation error Speed ​​estimation error and control input estimation error for:

[0100] (7)

[0101] The dynamic equation for the estimation error is then:

[0102] (8)

[0103] in, unmanned surface vessel Error in target location estimation unmanned surface vessel Error in target velocity estimation unmanned surface vessel Error in estimating the target control input.

[0104] Define the estimation error vector The error dynamics can be expressed as

[0105] (9)

[0106] in, Error system matrix, For the error input matrix, The derivative of the target state estimation error. To control the rate of change of the target input, for 3D identity matrix , , All are gains.

[0107] Theorem 1: Consider the Lyapunov equation:

[0108] (10)

[0109] in, It is a positive definite symmetric matrix. , Let represent a symmetric matrix. Then, based on the observer (6), the target's velocity and control input can be estimated.

[0110] prove:

[0111] Candidate Lyapunov functions are defined as follows:

[0112] (11)

[0113] in, This represents the estimation error energy function. This represents the target state estimation error.

[0114] In order to make Choose the gain for the Hurwitz matrix (all eigenvalues ​​have negative real parts). Make the matrix The characteristic equation satisfies: The eigenvalues ​​are all located in the left half of the complex plane. The variables representing the characteristic equation, Represents the identity matrix.

[0115] Taking the derivative of the Lyapunov function, we get:

[0116] (12)

[0117] in, The derivative of the estimation error energy function is represented by... This represents the derivative of the target state estimation error.

[0118] According to the Lyapunov equation ,as well as We can obtain:

[0119] (13)

[0120] in, , This represents the upper bound of the rate of change of the control input.

[0121] make Using Young's inequality:

[0122] (14)

[0123] in, Denotes the upper bound of the norm. This represents the smallest eigenvalue.

[0124] Therefore, we can conclude that:

[0125] (15)

[0126] This indicates that the target state estimation error Ultimately uniformly bounded, and when When the target acceleration is constant, the estimation error converges exponentially to 0.

[0127] Sliding Mode Disturbance Observer Design (SMDO)

[0128] Define auxiliary state variables Its dynamic equation is:

[0129] (16)

[0130] In the formula, For sliding surface, For observer gain, Represents a distributed controller. unmanned surface vessel speed, This represents auxiliary state variables.

[0131] Based on (16), the disturbance observer is designed as follows:

[0132] (17)

[0133] For sliding surfaces Taking the derivative, we get:

[0134] (18)

[0135] in, express, This represents the derivative of the sliding surface.

[0136] Define the perturbation estimation error :

[0137] (19)

[0138] In the formula, For unmanned surface vessels An estimate of the disturbance. Further, we can obtain... .

[0139] Theorem 2: If Assumption 1 holds and the observer gain satisfies Then the system disturbance can be accurately estimated for the observer (17).

[0140] prove:

[0141] Candidate Lyapunov functions are defined as follows:

[0142] (20)

[0143] in, This represents the energy function related to the perturbation.

[0144] Differentiating (20), we get

[0145] (twenty one)

[0146] Considering, , Substituting into (19), we get...

[0147] (twenty two)

[0148] Furthermore, we can obtain This indicates that, The exponent converges to 0. According to the equivalent control principle on the sliding surface, once the system reaches and maintains its position on the sliding surface, it means... ,Right now .

[0149] S5. Based on the estimated target speed, the estimated target control input, and the estimated disturbance response of the unmanned surface vessel, design a distributed cooperative controller.

[0150] The self-organizing tracking controller designed in this application mainly includes four main modules: driving the unmanned surface vessel to approach the target. Achieving speed coordination between unmanned surface vessels Maintain distance between machines And autonomous obstacle avoidance Therefore, this application designs a controller with the following form:

[0151] (twenty three)

[0152] in, It is a distributed controller; To control the gain; unmanned surface vessel Location; express Unmanned surface vessel at the most recent trigger moment speed; Indicates the first Unmanned surface vessel; Represents the dynamic neighbor set of the unmanned surface vessel; express Unmanned surface vessels and Communication weights between unmanned surface vessels; express Unmanned surface vessel at the most recent trigger moment speed; For gradient operators; To avoid collisions, the potential field function; express Unmanned surface vessels and The relative distance between unmanned surface vessels; The obstacle avoidance potential field function; express obstacle; A set representing obstacles; express Unmanned surface vessels and The relative distance to the obstacles; express Triggering time; Indicates collaborative tracking control items; Represents velocity cooperation terms; Indicates obstacle avoidance items; For unmanned surface vessels Estimates of the disturbance.

[0153] design It has the following form:

[0154] (twenty four)

[0155] In the formula, , For the body radius, To maintain a safe collision avoidance distance, , Let be the collision avoidance constant. Further, we can obtain...

[0156] (25)

[0157] For obstacle avoidance potential field :

[0158] (26)

[0159] In the formula, , To avoid obstacles, the potential field is activated at a distance. For safe obstacle avoidance distance, for The radius of the obstacle Let be the obstacle avoidance constant. Taking its gradient, we get...

[0160] (27)

[0161] S6. Design a distributed event triggering mechanism, defining the state error of the unmanned surface vessel as the difference between its current speed and the speed broadcast to its neighbors at the most recent triggering time; when the norm of the state error of the unmanned surface vessel meets the preset triggering conditions, activate communication and broadcast the current speed information of the unmanned surface vessel to neighboring unmanned surface vessels; otherwise, keep communication silent.

[0162] S7. The speed information broadcast at the most recent trigger time in step S6 is used as the input of the distributed cooperative controller. The distributed cooperative controller is executed to drive the unmanned surface vessel cluster to autonomously form and maintain a stable tracking configuration around the target without the need for preset formation parameters, while avoiding collisions between vessels and environmental obstacles.

[0163] In traditional control strategies, information exchange between unmanned surface vessels (USVs) is continuous, i.e., data transmission is performed through fixed update steps. However, when the consistency error of the USV is in a relatively stable state, there is no need for controller calculation through state updates. To address this, this application proposes a tracking controller (23) based on an event-triggered mechanism. The design of the event-triggered rules is described below.

[0164] for Unmanned surface vessel, defining state error

[0165] (28)

[0166] When the following triggering conditions are met The unmanned surface vessel transmits its speed information to its neighbors via communication.

[0167] (29)

[0168] (30)

[0169] In the formula, For trigger function, For the parameters to be designed, express The cardinality of the neighbor set of unmanned surface vessels.

[0170] Theorem 3 Consider an unmanned surface vessel model with external disturbances that satisfies (3), if the parameters satisfy

[0171] , , ,

[0172] Under the action of the observers (6), (17) and the trigger controller (23), the unmanned surface vessel formation can track the target without any Zeno behavior.

[0173] Next, we will first demonstrate the formation tracking performance in an unobstructed environment.

[0174] Define relative position error and relative velocity error : , .

[0175] Define Lyapunov candidate functions as follows

[0176] (31)

[0177] in, Denotes Lyapunov candidate functions. Indicates the number of unmanned surface vessels. Indicates the first A single unmanned surface vessel Indicates control gain. express The relative positional error between the unmanned surface vessel and the target. express The relative speed error between the unmanned surface vessel and the target. Represents the dynamic neighbor set of the unmanned surface vessel. Indicates the first A single unmanned surface vessel express Unmanned surface vessels and Communication weights between unmanned surface vessels express Unmanned surface vessels and Distance difference between unmanned surface vessels;

[0178] Taking its derivative, we get,

[0179] (32)

[0180] in, Indicates the trigger time The relative speed error between the unmanned surface vessel and the target. Indicates the trigger time The relative speed error between the unmanned surface vessel and the target. Indicates control gain. Indicates control gain;

[0181] Combining (28), (32) can be further simplified to

[0182] (33)

[0183] in, , , express The state error of the unmanned surface vessel express The state error of the unmanned surface vessel express The relative speed error between the unmanned surface vessel and the target. express The relative speed error between the unmanned surface vessel and the target. Represents the state error vector. Indicates the constant value of the inequality. Represents the Laplace matrix, Represents a three-dimensional identity matrix. Let represent the velocity error vector. According to (29), we can obtain...

[0184] (34)

[0185] According to (30), we can obtain

[0186] (35)

[0187] in, This indicates the trigger parameter.

[0188] Depend on It can be seen that,

[0189] (36)

[0190] in, This represents the largest eigenvalue.

[0191] Then (34) can be transformed into

[0192] (37)

[0193] therefore, Combining Theorem 1 (30), it can be seen that the speed of the swarm system can converge to the target speed uniformly without collision. Furthermore, it can be seen that the unmanned surface vessel formation can autonomously form a stable configuration and track the target.

[0194] The following demonstrates that unmanned surface vessel formations can achieve autonomous obstacle avoidance.

[0195] Define Lyapunov functions

[0196] (38)

[0197] in, This represents a Lyapunov function. express Unmanned surface vessels and The difference in the position of the obstacle;

[0198] Differentiating (38), we get

[0199] (39)

[0200] in, This represents the derivative of the Lyapunov function.

[0201] Considering the unmanned surface vessel entering the obstacle activation area Time is limited, and besides Apart from that, all other state variables are bounded. According to the definition of the obstacle avoidance potential field function, ,like Then, when the unmanned surface vessel approaches the obstacle, the following inequality can be obtained:

[0202] (40)

[0203] Furthermore, it can be seen that, The following inequality holds.

[0204] (41)

[0205] Then by adjusting , can be obtained Therefore, based on the above theoretical analysis, it can be concluded that during the process of unmanned surface vessels forming a configuration and tracking, they can autonomously avoid obstacles.

[0206] We will now demonstrate that Zeno behavior does not exist in the system under the triggering strategy.

[0207] When state error Exceed When the next trigger time is activated, that is...

[0208] (42)

[0209] exist Inside, to Finding the derivative of Dini, we get

[0210] (43)

[0211] Furthermore, it can be seen that,

[0212] (44)

[0213] make , , This represents the upper bound of the rate of change of state error. Let represent the upper bound of the state error, then

[0214] (45)

[0215] At the triggering time, there is According to the principle of comparison, we can obtain

[0216] (46)

[0217] Furthermore, when At that time, it can be obtained

[0218] (47)

[0219] in, express The velocity coordination term at the trigger moment.

[0220] when At that time, obviously .like Then there is However, when the collaborative task is not completed, there are... This indicates Under triggering rules (29)-(30), the system does not have Zeno behavior.

[0221] By implementing steps S1 to S7 above, the collision avoidance and obstacle avoidance potential field gradients spontaneously drive the cluster to form a stable tracking configuration around the target. This intrinsic mechanism eliminates the need for any externally designed formation function, thereby enabling the multi-unmanned surface vessel system to obtain strong self-adjustment and adaptability. The emerging configuration can be dynamically adjusted according to the target's maneuverability and environmental obstacles, and can still maintain the integrity of the tracking structure when some members are missing.

[0222] Simulation and Analysis

[0223] This application verifies the algorithm through simulation experiments. First, the effectiveness of the Extended State Observer (ESO) and Sliding Mode Disturbance Observer (SMDO) is verified; second, the effectiveness of the controller is verified in both scenarios with and without obstacles; finally, the superiority of the proposed triggering mechanism is verified through comparative simulations.

[0224] The simulation parameters are set as follows. State observer gain: , , Perturbation observer gain: , Control gain: , , , Number of unmanned surface vessels: Potential field parameters: , , , Triggering parameters: , Upper bound of perturbation: Upper bound of acceleration: The control input for selecting the target is: .

[0225] Target state estimation and disturbance estimation

[0226] Simulation results of the two observers are as follows Figure 5-7 As shown. Figure 5 The results show that the target velocity estimation errors of each unmanned surface vessel converge to the zero neighborhood, indicating that the designed extended state observer can quickly track the unknown velocity of the target and satisfies the exponential convergence characteristic described in Theorem 1. Figure 6 The robust estimation capability of the extended state observer for time-varying control inputs was verified. Figure 7 This indicates that the disturbance estimation error remains stable within a small range, proving that the sliding mode disturbance observer can effectively compensate for time-varying disturbances.

[0227] Collaborative target tracking in accessible environments

[0228] Results of collaborative target tracking in an accessible environment, such as Figure 8-13 As shown. Figure 8 The diagram shows the trajectory of the target (dashed line) and the trajectory of the unmanned surface vessel swarm (solid line) in two-dimensional space. Figure 9 The spatial distribution at six time points demonstrates that, under the control of the controller, the unmanned surface vessel can self-organize into a stable cluster configuration without a predefined geometric formation function, while also verifying the self-adjusting capability of the collision avoidance potential field. Figure 10The cluster tracking error asymptotically converges to the zero neighborhood, proving that the proposed distributed controller can effectively achieve the expected goal. Figure 11 The minimum distance curve between intelligent agents is given, showing that the spacing between unmanned surface vessels always meets the collision avoidance constraint, which confirms the effectiveness of the potential field design. Figure 12 This indicates that the speed of all slave vessels can be synchronized to the target speed. Based on the above analysis, the unmanned surface vessel swarm has achieved effective and stable tracking of the target. Figure 13 The event-triggered communication distribution shown in Table 1 indicates that the communication frequency between unmanned surface vessels is significantly reduced compared to continuous communication, verifying that the event-triggered mechanism effectively reduces the communication burden while maintaining performance.

[0229] Table 1 Comparison of trigger counts in accessible environments

[0230]

[0231] Cooperative target tracking in obstacle environments

[0232] pass Figure 14-19 The effectiveness of the proposed control strategy in obstacle avoidance scenarios was verified. Figure 14 The image shows the target trajectory (dashed line) and the unmanned surface vessel (USV) trajectory (solid line) in a two-dimensional space containing a spherical obstacle (red area). It can be observed that when the swarm approaches the obstacle, the USV autonomously generates a smooth, collision-free bypass path by utilizing the obstacle avoidance potential field. Figure 15 The spatial distribution at six time points demonstrates that the unmanned surface vessel formation can successfully avoid obstacles and restore a stable configuration in complex environments, verifying its self-organizing capability without predefined geometric constraints. Figure 16 The tracking error showed transient fluctuations during obstacle avoidance, but eventually converged to an acceptable range, demonstrating the robustness of the controller to obstacle disturbances. Figure 17 The given minimum distance curve between unmanned surface vessels confirms the effectiveness of the collision avoidance potential field in obstacle environments. Figure 18 This indicates that the submarine experiences transient speed fluctuations due to evasive maneuvers, but ultimately maintains speed synchronization with the target, meeting the coordinated speed requirements. Figure 19 As shown in Table 2, the event-triggered communication distribution indicates that the communication frequencies of all unmanned surface vessels remained at a low level, and Zeno-like behavior was excluded.

[0233] Table 2 Comparison of trigger counts in obstacle environments

[0234]

[0235] Simulation comparison of different trigger functions

[0236] To further illustrate the superiority of the event-triggered control method designed in this paper, simulations were conducted under both obstacle-free and obstacle-containing conditions. Comparative simulations were performed using trigger functions from existing technologies [Yang, D.; Ren, W.; Liu, X. Decentralized event-triggered consensus for linear multi-agent systems under general directedgraphs. Automatica 2016, 69, 242-249.]. The simulation results are as follows: Figure 20-21 As shown in Tables 3 and 4.

[0237] Table 3 Comparison of trigger counts for different solutions in an accessible environment

[0238]

[0239] Table 4 Comparison of Trigger Counts for Different Schemes in Obstacle Environments

[0240]

[0241] Compared with the event-triggered control method designed in this application, the existing technology [Yang, D.; Ren, W.; Liu, X. Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs. Automatica 2016, 69, 242-249.] has a significantly higher number of event triggers. Simulation results show that the target tracking control algorithm based on event triggering can effectively reduce the number of communications, achieve intermittent communication, and realize target tracking.

[0242] In summary, this application proposes a distributed event-triggered control framework to address the cooperative tracking problem of multiple unmanned surface vessels (USVs) in dynamic and uncertain environments. Through observer design, dynamic estimation of the leader's unknown motion state and external disturbances is achieved. A self-organizing cooperative control architecture is proposed, which synchronously solves the problems of formation configuration generation, collision avoidance among USVs, and environmental obstacle avoidance through a potential field gradient-driven mechanism. An event-triggered strategy based on neighbor state errors is constructed to regulate communication behavior, significantly optimizing network load while ensuring system performance. The global asymptotic stability of the closed-loop system is rigorously proved using the Lyapunov method, and a strict positive lower bound is demonstrated for the trigger interval, fundamentally eliminating Zeno behavior. Future work will investigate complex formation tracking control under network attacks.

[0243] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0244] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment, characterized in that, The method for tracking and controlling maneuvering targets in a complex dynamic environment for unmanned surface vessels (USV) swarms includes: S1. Configure an extended state observer and a sliding mode disturbance observer for each unmanned surface vessel in the cluster; S2. Obtain the target's location information; S3. Using the extended state observer and based on the target's position information, estimate the unknown velocity and control input of the target in real time to obtain the estimated values ​​of the target velocity and the target control input. S4. Using the sliding mode disturbance observer, estimate and compensate for the external bounded disturbances acting on the unmanned surface vessel in real time to obtain the estimated value of the disturbance by the unmanned surface vessel. S5. Based on the estimated target velocity, the estimated target control input, and the estimated disturbance response of the unmanned surface vessel, design a distributed cooperative controller. S6. Design a distributed event triggering mechanism, defining the state error of the unmanned surface vessel (USV) as the difference between its current speed and the speed broadcast to its neighbors at the most recent triggering time; when the norm of the USV's state error meets the preset triggering conditions, activate communication and broadcast the current speed information of the USV to its neighboring USVs; otherwise, keep communication silent. S7. The speed information broadcast at the most recent trigger time in step S6 is used as the input of the distributed cooperative controller. The distributed cooperative controller is executed to drive the unmanned surface vessel cluster to autonomously form and maintain a stable tracking configuration around the target without the need for preset formation parameters, while avoiding collisions between vessels and environmental obstacles.

2. The method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment according to claim 1, characterized in that, The acquisition of the target's location information is specifically based on the target's location information obtained from the unmanned surface vessel's own sensors.

3. The method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment according to claim 1, characterized in that, The distributed cooperative controller includes a target attraction term, an inter-vessel collision avoidance term, an environmental obstacle avoidance term, and a velocity coordination term. The inter-vessel collision avoidance term and the environmental obstacle avoidance term are generated by the negative gradients of the collision avoidance potential field function and the obstacle avoidance potential field function, respectively. The velocity coordination term is used to drive all unmanned surface vessels to maintain the same speed as the target speed.

4. The method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment according to claim 1, characterized in that, The expression for the extended state observer is as follows: ； in, unmanned surface vessel The derivative of the target location estimate; For unmanned surface vessels An estimate of the target velocity; Indicates the measurable location of the target; For unmanned surface vessels An estimate of the target's location; unmanned surface vessel The derivative of the target velocity estimate; For unmanned surface vessels Estimates of the target control inputs; unmanned surface vessel The derivative of the target control input estimate, This is the gain for the extended state observer.

5. The method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment according to claim 1, characterized in that, The expression for the sliding mode perturbation observer is as follows: ； in, For unmanned surface vessels Estimates of the disturbance; , Indicates the gain of the perturbation observer. This indicates the sliding surface.

6. The method for tracking and controlling a swarm of unmanned surface vessels in a complex dynamic environment according to claim 4, characterized in that, The expression for the distributed collaborative controller is as follows: ； in, It is a distributed controller; To control the gain; unmanned surface vessel Location; express Unmanned surface vessel at the most recent trigger moment speed; Indicates the first Unmanned surface vessel; Represents the dynamic neighbor set of the unmanned surface vessel; express Unmanned surface vessels and Communication weights between unmanned surface vessels; express Unmanned surface vessel at the most recent trigger moment speed; For gradient operators; To avoid collisions, the potential field function; express Unmanned surface vessels and The relative distance between unmanned surface vessels; The obstacle avoidance potential field function; express obstacle; A set representing obstacles; express Unmanned surface vessels and The relative distance to the obstacles; express Triggering time; Indicates collaborative tracking control items; Represents velocity cooperation terms; Indicates obstacle avoidance items; For unmanned surface vessels Estimates of the disturbance.

7. The method for tracking and controlling a swarm of unmanned surface vessels (USVs) in a complex dynamic environment according to claim 3, characterized in that, The expression for the collision avoidance potential field function is as follows: ； in, For gradient operators; To avoid collisions, the potential field function; , This is the collision avoidance constant; express Unmanned surface vessels and The relative distance between unmanned surface vessels To maintain a safe collision avoidance distance; The radius of the machine body; unmanned surface vessel Location; unmanned surface vessel The location.

8. The method for tracking and controlling a swarm of unmanned surface vessels in a complex dynamic environment according to claim 7, characterized in that, The expression for the obstacle avoidance potential field function is as follows: ； in, For gradient operators, This is the obstacle avoidance constant; express Unmanned surface vessels and The relative distance to the obstacles; For safe obstacle avoidance distance, for The radius of the obstacle; The radius of the machine body; unmanned surface vessel Location; express The location of the obstacle; Let be the obstacle avoidance potential field function.

9. The method for tracking and controlling a swarm of unmanned surface vessels in a complex dynamic environment according to claim 1, characterized in that, The expression for the preset trigger condition is as follows: ； ； in, express Triggering time; Indicates the current moment; express Triggering time; Indicates the trigger function, Indicates state error, Indicates the parameters to be designed. express The cardinality of the neighbor set of unmanned surface vessels; express The velocity coordination term at the trigger moment.

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