A safe and robust formation control method for multiple unmanned surface vessels

Abstract

This invention relates to the field of cooperative control technology for marine robots, specifically to a safe and robust formation control method for multiple unmanned surface vessels (USVs). The method includes: establishing port Hamiltonian-form state equations for each USV; constructing a distributed leader-follower formation structure for multiple USVs, defining the relative positions and reference trajectories of each follower USV and calculating trajectory tracking errors; designing a preset performance boundary function to apply dynamic constraints and introducing a nonlinear differentiable mapping function; designing a closed-loop desired energy configuration function and constructing desired interconnected energy flows and desired dissipated energy flows; calculating the nonlinear differentiable mapping function, using an interconnected damping pairing method to solve for the desired momentum, and designing a controller to adjust the actual momentum in real time; designing a structure-preserving extended state observer to calculate the energy deviation between USVs, adjusting the uncertainty estimate in real time, and feeding it back to the control law in the form of a power compensation term. This invention improves the safety and robustness of multi-USV formation control.

Description

Technical Field

[0001] This invention relates to the field of collaborative control technology for marine robots, and in particular to a safe and robust formation control method for multiple unmanned surface vessels. Background Technology

[0002] With the development of intelligent marine equipment and autonomous navigation technology, unmanned surface vessels (USVs), as an important type of marine robot, have been gradually applied to mission scenarios such as marine surveying, environmental monitoring, resource exploration, maritime search and rescue, and collaborative patrols. Compared with single-vessel operations, multi-USV collaborative operations can expand the mission coverage, improve the efficiency of marine information acquisition, and enhance the ability to operate continuously under complex tasks. In multi-USV collaborative systems, formation control is a crucial foundation for achieving formation maintenance, path coordination, and task allocation. Its control effectiveness directly affects the motion stability, safety, and operational reliability of the multi-vessel system under complex sea conditions.

[0003] Existing multi-unmanned surface vessel (USV) formation control systems typically consist of a positioning and sensing unit, a communication unit, a control computing unit, and a propulsion execution unit. Each USV acquires its own position, heading, and speed through the positioning and sensing unit, and obtains the motion status of the lead USV or adjacent USVs through the communication unit. The control computing unit calculates the deviation between the following USVs and the desired position based on the preset formation, reference trajectory, and relative positions between USVs, and generates corresponding control commands. The propulsion execution unit adjusts the speed and heading of the USVs according to the control commands, ensuring that each USV moves along the reference trajectory in a set formation. Commonly used formation control methods include model predictive control (MMC) and backstepping. MMC typically relies on rolling optimization using the USV's nominal model, predicting the system state over a future period to obtain the control input. Backstepping methods often construct virtual control variables and actual control laws step-by-step based on the system dynamics model to achieve trajectory tracking and formation maintenance.

[0004] However, the marine environment is characterized by strong external disturbances such as wind, waves, and currents, significant changes in system parameters, and high nonlinearity in unmanned surface vessel (USV) dynamics. Model predictive control (MDI) in multi-USV cooperative scenarios involves large computational loads, requiring high model accuracy and real-time solution capabilities. When sea state changes rapidly, the actual effect of the control input can easily deviate from the predicted results. While backstepping can handle certain nonlinear problems, the control design process is complex and highly dependent on model parameters. The difficulty of controller design further increases when facing safety distance constraints and collision avoidance requirements among multiple USVs. Therefore, existing technologies still require a multi-USV formation control method that can balance formation maintenance accuracy, safety constraints, and disturbance resistance capabilities to improve the stability and engineering applicability of multi-USV cooperative operation in complex marine environments. Summary of the Invention

[0005] In view of this, the purpose of this invention is to propose a safe and robust formation control method for multiple unmanned surface vessels (USVs) to solve the problems of strong model dependence, high difficulty in real-time control, complex handling of safety constraints, and insufficient anti-interference capability in the formation control method for multiple USVs under complex sea conditions.

[0006] Based on the above objectives, the technical solution adopted by the present invention is: a safe and robust formation control method for multiple unmanned surface vessels, comprising the following steps:

[0007] S1. Based on port Hamiltonian theory, the kinematic and dynamic models of the multi-unmanned surface vessel system are restructured and the port Hamiltonian state equations of each unmanned surface vessel are established.

[0008] S2. Construct a distributed navigator-follower formation structure for multiple unmanned surface vessels and define the relative position and reference trajectory of each follower vessel;

[0009] S3. Calculate the trajectory tracking error of the following vessel based on the reference trajectory, design a preset performance boundary function to apply dynamic constraints to the trajectory tracking error, and introduce a nonlinear differentiable mapping function to convert the constrained error variable into an equivalent variable in the unconstrained space.

[0010] S4. Design the closed-loop desired energy configuration function for each unmanned surface vessel (USV), and construct the desired interconnected energy flow and desired dissipated energy flow under the Hamiltonian form state equation of the port of the USV.

[0011] S5. Calculate the nonlinear differentiable mapping function, solve for the desired momentum using the interconnected damping pairing method, and design a controller to adjust the actual momentum in real time.

[0012] S6. Design a structure to maintain an extended state observer. Based on the energy deviation between the expected momentum and the actual momentum of the unmanned surface vessel, adjust the uncertainty estimate in real time and feed it back to the control law in the form of a power compensation term to form an energy-consistent compensation mechanism.

[0013] Preferably, the port Hamiltonian state equation is:

[0014]

[0015] in, Indicates the first The actual trajectory of the unmanned surface vessel in the geodetic coordinate system. for The first derivative; These represent the magnitudes of the unmanned surface vessel's momentum, respectively. for The first derivative, The inertia matrix, This is the velocity vector in the hull coordinate system; The interconnection matrix represents the energy exchange relationships between different state variables within the system. is the damping matrix, representing the energy dissipation characteristics of the system; For the first The total energy function of an unmanned surface vessel. Indicates the first unmanned surface vessel port Hamiltonian state variables The gradient, i.e. , for Zero-dimensional matrix for 3D identity matrix For the first Control input for an unmanned surface vessel For the first The external environmental disturbances experienced by the unmanned surface vessel.

[0016] Preferably, the interconnection matrix Damping matrix ,in, for A 3D coordinate transformation matrix is ​​used to describe the mapping relationship between the hull coordinate system and the geodetic coordinate system. for transpose, for Vicoriolis force matrix for Dimensional hydrodynamic damping matrix.

[0017] Preferably, the multi-unmanned surface vessel distributed navigation-following formation structure is as follows: assuming the entire formation consists of... The formation consists of several unmanned surface vessels (USVs), with the first USV serving as the global leader, providing a global reference trajectory. The remaining USVs act as followers, tracking the preceding USV based on relative position information and communication topology, thus forming a multi-level interconnected distributed formation structure. The entire formation can be divided into... Each unmanned vessel is a local subsystem, consisting of a local lead vessel and a local follower vessel. Adjacent unmanned vessels exchange status information via a communication link.

[0018] Preferably, the relative positions of the following vessels are as follows: , ,in, For the first The expected distance between an unmanned surface vessel and its local pilot vessel. For the first The expected relative heading angle between an unmanned surface vessel and its local pilot vessel.

[0019] Preferably, the reference trajectory of each follower vessel is ,in, For the first The actual heading angle of the unmanned surface vessel Let be the coordinate transformation matrix determined by the actual heading angle of the local pilot vessel, used to transform the local formation offset from the local hull coordinate system to the geodetic coordinate system, and its formula can be expressed as follows: .

[0020] Preferably, the trajectory tracking error of the follower vessel is , among which, the The actual trajectory of the unmanned surface vessel can be represented as The reference trajectory can be represented as Therefore, its trajectory tracking error can be expanded as follows: , , and They represent the first An unmanned surface vessel is heading north East and heading angle Tracking error in direction.

[0021] Preferably, the preset performance boundary function is:

[0022]

[0023] in, Indicates the first Unmanned surface vessel Allowable range of initial error in direction. This indicates the upper bound of the steady-state error. Indicates the convergence rate. Indicates time.

[0024] Preferably, the dynamic constraint is , .

[0025] Preferably, the nonlinear differentiable mapping function is: .

[0026] The beneficial effects of this invention are as follows: Compared with the prior art, this invention restructures the kinematics and dynamics model of a multi-unmanned surface vessel (USV) system based on port Hamiltonian theory, and establishes port Hamiltonian-form state equations for each USV, enabling the multi-USV system to describe its pose, momentum, energy exchange, and energy dissipation relationships under a unified energy structure; by constructing a distributed leader-follower formation structure for multiple USVs and defining the relative positions and reference trajectories of each follower USV, the USVs can coordinate their movements according to a preset formation relationship; by calculating the trajectory tracking error based on the reference trajectory and applying dynamic constraints using a preset performance boundary function, Furthermore, by using a nonlinear differentiable mapping function to transform constrained error variables into equivalent variables in an unconstrained space, it is beneficial to handle error constraint problems during the control process. By designing a closed-loop desired energy configuration function, desired interconnected energy flow, and desired dissipated energy flow, and combining the interconnected damping pairing method to solve for the desired momentum and design the controller, the actual momentum can be adjusted in real time. By using a structure-preserving extended state observer to adjust the uncertainty estimate based on the energy deviation between the desired momentum and the actual momentum, and feeding it back to the control law as a power compensation term, an energy-consistent compensation mechanism can be formed, improving the safety and robustness of multi-unmanned surface vessel formation control. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the control method of the present invention;

[0029] Figure 2 This is a schematic diagram of the distributed navigation-following formation structure of multiple unmanned surface vessels according to the present invention;

[0030] Figure 3 This is a schematic diagram illustrating the trajectory tracking of multiple unmanned surface vessels in a formation according to the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains.

[0032] like Figure 1 As shown, a safe and robust formation control method for multiple unmanned surface vessels includes the following steps:

[0033] S1. Based on port Hamiltonian theory, the kinematic and dynamic models of the multi-unmanned surface vessel system are restructured and the port Hamiltonian state equations of each unmanned surface vessel are established.

[0034] Considering the time-varying and highly nonlinear characteristics of unmanned surface vessel (USV) dynamics models, directly using traditional equations of motion would be insufficient to clearly describe the physical intuition of energy flow within the system. Therefore, this step, based on port Hamiltonian theory, structurally reconstructs the kinematic and dynamic models of the multi-USV system, transforming the state evolution process of the USV system into an expression of energy interaction. This provides a unified energy modeling foundation for the subsequent design of the formation controller.

[0035] For the The Hamiltonian state equation for the port of an unmanned surface vessel can be expressed as:

[0036]

[0037] in, Indicates the first The actual trajectory of the unmanned surface vessel in the geodetic coordinate system. for The first derivative; These represent the magnitudes of the unmanned surface vessel's momentum, respectively. for The first derivative, The inertia matrix, This is the velocity vector in the hull coordinate system; The interconnection matrix represents the energy exchange relationships between different state variables within the system. is the damping matrix, representing the energy dissipation characteristics of the system; For the first The total energy function of an unmanned surface vessel. Indicates the first unmanned surface vessel port Hamiltonian state variables The gradient, i.e. , for Zero-dimensional matrix for 3D identity matrix For the first Control input for an unmanned surface vessel For the first The external environmental disturbances experienced by the unmanned surface vessel.

[0038] Furthermore, and They are constructed as follows:

[0039]

[0040]

[0041] in, for A 3D coordinate transformation matrix is ​​used to describe the mapping relationship between the hull coordinate system and the geodetic coordinate system. for transpose; for Vicoriolis force matrix; for The hydrodynamic damping matrix. Based on the above... and The structure can be used to characterize the energy transfer channels and energy dissipation mechanisms within the unmanned surface vessel system.

[0042] Based on the above modeling method, this step will focus on the multi-unmanned surface vessel system. and Unified inclusion into the Hamiltonian state space, with Based on this, a port Hamiltonian state equation with clear physical meaning is constructed. This equation not only accurately reflects the energy exchange, dissipation, and input interaction relationships of the unmanned surface vessel system, but also preserves the system's structural characteristics, providing a theoretical foundation for subsequent energy shaping, damping allocation, and disturbance compensation under safety constraints.

[0043] S2. Construct a distributed navigator-follower formation structure for multiple unmanned surface vessels and define the relative position and reference trajectory of each follower vessel.

[0044] The multi-unmanned surface vessel system adopts a distributed pilot-follow formation structure, such as Figure 2 As shown. Assume the entire formation consists of... The formation consists of several unmanned surface vessels (USVs), with the first USV serving as the global leader, providing a global reference trajectory. The remaining USVs act as followers, tracking the preceding USV based on relative position information and communication topology, thus forming a multi-level interconnected distributed formation structure. Therefore, the entire formation can be divided into... Each local subsystem consists of a local lead boat and a local follow boat. Adjacent unmanned boats transmit status information through communication links to maintain formation and coordinate movement.

[0045] In this formation, the first unmanned surface vessel (USV) serves as the overall navigator, and its actual trajectory can be represented as follows:

[0046]

[0047] in, and These represent the actual positions of the global navigation vessel in the geodetic coordinate system. This represents the actual heading angle of the global navigator. For the... A single unmanned surface vessel Its local pilot boat is defined as the first The first unmanned surface vessel, therefore The unmanned surface vessel needs to be based on the first The state information of each unmanned surface vessel (USV) constructs its own reference trajectory and tracks that reference trajectory. For intermediate-level USVs, i.e., the [missing information]... A single unmanned surface vessel It is both the first The unmanned surface vessel was a follower vessel, and at the same time served as the first The unmanned surface vessel (USV) serves as a partial lead vessel, thus forming a multi-level interconnected distributed lead-follow formation; the first The unmanned surface vessel (USV) acts as the last-stage follower, and its only task is to track the preceding USV.

[0048] To determine the overall formation, the relative positions of the lead boats and their corresponding follower boats are pre-defined. These relative positions are determined by the... The expected distance between an unmanned surface vessel and its local pilot vessel and expected relative heading angle Jointly determined. Further, to describe the first... The relative position of an unmanned surface vessel (USV) with respect to its local navigator is given by the formula:

[0049]

[0050] In the geodetic coordinate system, the first The reference trajectory of the unmanned surface vessel is and It can be represented as a joint determination:

[0051]

[0052] in, For the first The actual heading angle of the unmanned surface vessel The coordinate transformation matrix is ​​determined by the actual heading angle of the local pilot boat. It is used to transform the local formation offset from the local hull coordinate system to the geodetic coordinate system. The formula can be expressed as:

[0053]

[0054] In this way, each following vessel can determine the desired distance based on the real-time status information of its local lead vessel and a pre-set target distance. and expected relative heading angle It dynamically generates its own reference trajectory, thereby ensuring that each unmanned surface vessel maintains the predetermined formation configuration during the overall movement. This enables a global lead vessel to provide unified guidance for the entire formation's direction and path, and reduces the reliance of centralized control on communication bandwidth and computing resources through a distributed communication topology, thus improving the scalability, stability, and engineering feasibility of the multi-unmanned surface vessel formation system.

[0055] S3. Calculate the trajectory tracking error of the following vessel based on the reference trajectory, design a preset performance boundary function to apply dynamic constraints to the trajectory tracking error, and introduce a nonlinear differentiable mapping function to convert the constrained error variable into an equivalent variable in the unconstrained space.

[0056] After completing the distributed navigation-following formation structure and reference trajectory construction, in order to ensure that each unmanned surface vessel always meets the safe distance requirements during formation movement, this step applies dynamic constraints on the trajectory tracking error of each unmanned surface vessel based on the preset performance control theory.

[0057] For the For an unmanned surface vessel, the trajectory tracking error is defined in a geodetic coordinate system as:

[0058]

[0059] Among them, the The actual trajectory of the unmanned surface vessel can be represented as The reference trajectory can be represented as Therefore, its trajectory tracking error can be expanded as follows: , , and They represent the first An unmanned surface vessel is heading north East and heading angle Tracking error in direction.

[0060] To limit the evolution of the aforementioned trajectory tracking error within a preset safety domain, a preset performance boundary function that varies with time is introduced:

[0061]

[0062] in, Indicates the first Unmanned surface vessel Allowable range of initial error in direction. This indicates the upper bound of the steady-state error. Indicates the convergence rate. Indicates time. By setting different... , as well as The initial allowable range, steady-state accuracy, and convergence speed of errors in each direction can be adjusted according to the specific formation mission.

[0063] Based on the aforementioned preset performance boundary function, for the first... Tracking errors of unmanned surface vessels in all directions Apply the following dynamic constraints:

[0064]

[0065] Therefore, the trajectory tracking error in each direction Restricted to by Within the defined time-dependent dynamic boundary, the performance boundary gradually shrinks over time, causing the tracking error of the unmanned surface vessel (USV) to converge to the steady-state error range at a preset speed. This avoids formation instability or excessively close distances between USVs due to excessive errors during formation operations. Furthermore, the size of the safe domain is determined by the expected distance between USVs. minimum safe distance This is determined jointly. By reasonably selecting the parameters of the preset performance boundary function, the tracking error is always kept within the range of... Within a matching safety allowance range, this ensures that unmanned surface vessels meet minimum safety distance constraints during formation maneuvers, reducing the risk of collisions.

[0066] Since the aforementioned error constraints are inequality constraints, directly handling them within the port Hamiltonian energy framework is quite complex. Therefore, a nonlinear differentiable mapping function is introduced to transform the constrained error variables into equivalent variables in the unconstrained space. Specifically, for each Define the following transformation variables:

[0067]

[0068] Furthermore, This paper introduces the energy description of the port Hamiltonian model and performs structural embedding and reconstruction of the energy function based on this error transformation form. Specifically, by incorporating the energy term corresponding to the constraint error into the port Hamiltonian model function, the safety constraints participate in the subsequent energy shaping and damping allocation control process in the form of energy. Thus, without destroying the interconnection and dissipation structure of the port Hamiltonian model, a unified description of the unmanned surface vessel (USV) formation tracking error, safety distance constraints, and system energy evolution is achieved, providing a foundation for the subsequent construction of robust formation control laws that satisfy safety constraints.

[0069] S4. Design the closed-loop desired energy configuration function for each unmanned surface vessel (USV), and construct the desired interconnected energy flow and desired dissipated energy flow under the Hamiltonian state equations of the ports of the USV.

[0070] Within the framework of port Hamiltonian theory, to ensure stable tracking for each unmanned surface vessel (USV) while satisfying formation safety constraints, this step designs a closed-loop expected energy configuration function for each USV. and based on Construct the desired interconnected energy flow and desired dissipated energy flow under the Hamiltonian form of the state equations for the port of the unmanned surface vessel.

[0071] Specifically, energy configuration weights are selected based on different formation mission scenarios and control performance requirements. , , These are used to adjust the weight allocation of position error, momentum error, and constraint error in the desired energy structure, thereby obtaining the first... The desired port Hamiltonian energy structure of an unmanned surface vessel.

[0072] Furthermore, construct the expected interconnection matrix. With the expected damping matrix .in, Used to regulate the energy exchange channels in a closed-loop system and maintain the energy interconnection characteristics of the port Hamiltonian model; This is used to adjust the energy dissipation characteristics of the closed-loop system, causing the system energy to decay in a preset manner. Through the combined effect of the desired energy configuration, desired interconnection matrix, and desired damping matrix, a closed-loop Hamiltonian structure with expected stability is formed, providing a foundation for subsequent control law design.

[0073] S5. Calculate the nonlinear differentiable mapping function, solve for the desired momentum using the interconnected damping pairing method, and design a controller to adjust the actual momentum in real time.

[0074] Each unmanned surface vessel obtains its own current status in real time. And obtain information about its local pilot vessel through the communication network. Based on the aforementioned pilot-follower formation structure and the pre-set desired distance and desired heading angle, calculate the first... Reference trajectory of the following vessel .

[0075] Further, calculate the first Tracking error between the follower vessel and its reference trajectory , and will By mapping through preset performance constraints, we obtain the time-varying... This transforms the original error constraints into a control problem under unconstrained variables.

[0076] Based on this, the desired momentum that satisfies the safety constraints is solved using the interconnected damping pairing method. A controller was designed to adjust the actual momentum in real time, ensuring that the unmanned surface vessels (USVs) always track the desired trajectory within a safe range, thus achieving safe and coordinated operation of the entire formation. A specific schematic diagram of multi-USV formation trajectory tracking is shown below. Figure 3 As shown.

[0077] S6. Design a structure to maintain an extended state observer. Based on the energy deviation between the expected momentum and the actual momentum of the unmanned surface vessel, adjust the uncertainty estimate in real time and feed it back to the control law in the form of a power compensation term to form an energy-consistent compensation mechanism.

[0078] Addressing model uncertainties in unmanned surface vessels (USVs) in marine environments and external disturbances Based on the structural characteristics of the port Hamiltonian, a structure-preserving extended state observer is designed to estimate the unmodeled dynamic terms of the system and external disturbances in real time.

[0079] Specifically, the structure-preserving extended state observer bases its observation on the energy deviation between the actual and desired momentum of the unmanned surface vessel. The equivalent effects of external disturbances and parameter uncertainties on the system's energy distribution and momentum state are estimated, yielding the uncertainty estimator. This estimator is used to dynamically correct the actual energy state, ensuring that the observer estimation process remains consistent with the energy flow relationships of the port Hamiltonian system.

[0080] Furthermore, while maintaining the conservation of system energy flow and the invariance of the port Hamiltonian state equations, the observer output... Feedback to the control law in the form of power compensation terms This creates an energy consistency compensation mechanism. Through this mechanism, the impact of external disturbances and parameter uncertainties on the momentum and energy distribution of unmanned surface vessels (USVs) can be automatically weakened or offset, improving the dynamic response performance and robustness of USVs in formation control, and enabling multi-USV systems to maintain a stable and coordinated formation operation in complex sea conditions.

[0081] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.

[0082] This invention aims to cover all such substitutions, modifications, and variations that fall within the scope of protection. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A safe and robust formation control method for multiple unmanned surface vessels, characterized in that, Includes the following steps: S1. Based on port Hamiltonian theory, the kinematic and dynamic models of the multi-unmanned surface vessel system are restructured and the port Hamiltonian state equations of each unmanned surface vessel are established. S2. Construct a distributed navigator-follower formation structure for multiple unmanned surface vessels and define the relative position and reference trajectory of each follower vessel; S3. Calculate the trajectory tracking error of the following vessel based on the reference trajectory, design a preset performance boundary function to apply dynamic constraints to the trajectory tracking error, and introduce a nonlinear differentiable mapping function to convert the constrained error variable into an equivalent variable in the unconstrained space. S4. Design the closed-loop desired energy configuration function for each unmanned surface vessel (USV), and construct the desired interconnected energy flow and desired dissipated energy flow under the Hamiltonian form state equation of the port of the USV. S5. Calculate the nonlinear differentiable mapping function, solve for the desired momentum using the interconnected damping pairing method, and design a controller to adjust the actual momentum in real time. S6. Design a structure to maintain an extended state observer. Based on the energy deviation between the expected momentum and the actual momentum of the unmanned surface vessel, adjust the uncertainty estimate in real time and feed it back to the control law in the form of a power compensation term to form an energy-consistent compensation mechanism.

2. The method according to claim 1, characterized in that, The Hamiltonian state equation for the port is: in, Indicates the first The actual trajectory of the unmanned surface vessel in the geodetic coordinate system. for The first derivative; These represent the magnitudes of the unmanned surface vessel's momentum, respectively. for The first derivative, The inertia matrix, This is the velocity vector in the hull coordinate system; The interconnection matrix represents the energy exchange relationships between different state variables within the system. is the damping matrix, representing the energy dissipation characteristics of the system; For the first The total energy function of an unmanned surface vessel. Indicates the first unmanned surface vessel port Hamiltonian state variables The gradient, i.e. , for Zero-dimensional matrix for 3D identity matrix For the first Control input for an unmanned surface vessel For the first The external environmental disturbances experienced by the unmanned surface vessel.

3. The method according to claim 2, characterized in that, The interconnection matrix Damping matrix ,in, for A 3D coordinate transformation matrix is ​​used to describe the mapping relationship between the hull coordinate system and the geodetic coordinate system. for transpose, for Vicoriolis force matrix for Dimensional hydrodynamic damping matrix.

4. The method according to claim 1, characterized in that, The multi-unmanned surface vessel distributed navigation-following formation structure is as follows: Let the entire formation consist of… The formation consists of several unmanned surface vessels (USVs), with the first USV serving as the global leader, providing a global reference trajectory. The remaining USVs act as followers, tracking the preceding USV based on relative position information and communication topology, thus forming a multi-level interconnected distributed formation structure. The entire formation can be divided into... Each unmanned vessel is a local subsystem, consisting of a local lead vessel and a local follower vessel. Adjacent unmanned vessels exchange status information via a communication link.

5. The method according to claim 1, characterized in that, The relative positions of the following vessels are: , ,in, For the first The expected distance between an unmanned surface vessel and its local pilot vessel. For the first The expected relative heading angle between an unmanned surface vessel and its local pilot vessel.

6. The method according to claim 1, characterized in that, The reference trajectory of each follower vessel is as follows: ,in, For the first The actual heading angle of the unmanned surface vessel Let be the coordinate transformation matrix determined by the actual heading angle of the local pilot vessel, used to transform the local formation offset from the local hull coordinate system to the geodetic coordinate system, and its formula can be expressed as follows: .

7. The method according to claim 1, characterized in that, The trajectory tracking error of the following vessel is , among which, the The actual trajectory of the unmanned surface vessel can be represented as The reference trajectory can be represented as Therefore, its trajectory tracking error can be expanded as follows: , , and They represent the first An unmanned surface vessel is heading north East and heading angle Tracking error in direction.

8. The method according to claim 1, characterized in that, The preset performance boundary function is: in, Indicates the first Unmanned surface vessel Allowable range of initial error in direction. This indicates the upper bound of the steady-state error. Indicates the convergence rate. Indicates time.

9. The method according to claim 1, characterized in that, The dynamic constraint is , .

10. The method according to claim 1, characterized in that, The nonlinear differentiable mapping function is: .

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