A designated performance adaptive formation control method for a water unmanned surface vehicle

Abstract

The application relates to the technical field of water surface unmanned ship control, in particular to a specified performance adaptive formation control method for a water surface unmanned ship, which comprises the following steps: establishing an unmanned ship dynamics model, decomposing environmental disturbance into an unknown deterministic component and a Gaussian random component and substituting the components into the model to obtain an Ito type random differential equation; constructing formation tracking error according to the states of a leading unmanned ship and a following unmanned ship and a preset formation relative position, and setting a specified performance function which changes with time; performing constraint error transformation on the formation tracking error based on the specified performance function, constructing virtual control and actual control input by using transformation error and speed error, and introducing unknown deterministic disturbance, dynamics model parameters and Gaussian random disturbance into adaptive estimation; and constructing a comprehensive random Lyapunov function to perform stability analysis; the application realizes quantitative performance constraint of unmanned ship formation tracking error under random ocean disturbance, collision-free between ships and stable convergence with probability.

Description

Technical Field

[0001] This invention relates to the field of unmanned surface vessel (USV) control technology, and in particular to a method for adaptive formation control of USVs with specified performance. Background Technology

[0002] Unmanned surface vessels (USVs) possess advantages such as autonomous operation, compact configuration, and high operational flexibility, and are widely used in maritime scenarios such as maritime patrol, marine environmental monitoring, and maritime security reconnaissance. Compared to single-vessel operations, multi-USV swarm operations can significantly improve the execution efficiency and scenario adaptability of complex maritime missions. Existing technologies have proposed various solutions, including swarm control methods based on sliding mode control and inverse optimal swarm control strategies under a leader-follower architecture. These technologies also introduce specified performance control techniques to impose preset constraints on swarm tracking errors, achieving quantitative assurance of control accuracy. Simultaneously, collision avoidance between vessels is achieved through connectivity maintenance and safe distance maintenance strategies.

[0003] However, in real marine environments, wind, waves, and ocean currents typically couple and act on the hull. The formation mechanism stems from the superposition of numerous independent, minute, random turbulent factors, causing environmental disturbances to exhibit both long-term constant average effects and irregular high-frequency random oscillations, exhibiting strong randomness and uncertainty. Existing formation control schemes generally simplify marine environmental disturbances into negligible quantities or deterministic disturbances with known boundaries. This idealized assumption is severely inconsistent with actual sea conditions, leading to distorted and overly conservative control modeling, which easily triggers control jitter or even formation instability under random sea conditions. Furthermore, traditional formation control can only achieve asymptotic stability and cannot explicitly constrain the convergence range of tracking errors and transient overshoot. Existing high-precision formation control schemes require independent collision avoidance judgment and constraint switching modules, resulting in complex architectures and high computational demands. Therefore, a performance-specific adaptive formation control method for surface unmanned surface vessels is currently needed. Summary of the Invention

[0004] To address the technical problem that existing unmanned surface vessel (USV) formation control methods struggle to simultaneously guarantee specified performance constraints on formation tracking error and safe collision avoidance between vessels under random marine environmental disturbances, this invention provides a specified performance adaptive formation control method for USVs.

[0005] This invention provides a method for adaptive formation control of unmanned surface vessels with specified performance, employing the following technical solution: An adaptive formation control method for surface unmanned surface vessels with specified performance includes: S1. Establish a dynamic model of the unmanned surface vessel (USV), obtain the operating status of the leading USV and the following USV, and decompose the environmental disturbances caused by wind, waves and ocean currents into mean deterministic components and zero-mean random components. S2. Based on the status of the leader unmanned surface vessel (USV) and the follower USV and the preset relative positions of the formation, construct the formation tracking error of the follower USV and set a specified performance function for the formation tracking error that varies with time. S3. Based on the specified performance function, constrain the formation tracking error to transform the formation tracking error with boundary constraints into an unbounded transformation error, and obtain an infinite generator operator expression with the transformation error vector as the weight. S4. Using the transformation error and the unmanned surface vessel speed error, construct virtual control variables and actual control inputs, and perform adaptive online estimation of the deterministic disturbance parameters corresponding to the mean deterministic components, the unknown hydrodynamic parameters in the dynamic model, and the random disturbance covariance parameters corresponding to the zero-mean random components. S5. Construct a stochastic Lyapunov function based on the transformation error, velocity error, and estimation errors of each parameter, and perform stability analysis. Adjust the virtual control quantity and actual control input through an adaptive law. S6. The adaptively adjusted actual control input is sent to the propulsion actuators of each following unmanned surface vessel (USV), so that each USV tracks the lead USV and maintains the preset formation distance under random environmental disturbances.

[0006] Furthermore, the establishment of the dynamic model of the unmanned surface vessel includes establishing a geodetic inertial coordinate system and a hull-fixed motion coordinate system, obtaining the position, heading vector, and velocity vector of each unmanned surface vessel, and establishing the kinematic mapping relationship between the two coordinate systems through a coordinate rotation matrix; A dynamic model of the unmanned surface vessel (USV) is established based on kinematic mapping relationships and the rigid body momentum theorem. The dynamic model includes the USV's inertia matrix, added mass inertia matrix, Coriolis and centripetal force matrices, fluid damping matrix, unknown nonlinear hydrodynamic terms, wind disturbance torque, wave disturbance torque, and control input thrust.

[0007] Furthermore, the environmental disturbance is decomposed into a mean deterministic component and a zero-mean random component, including a binary decomposition of the ocean current velocity, wind disturbance moment, and wave disturbance moment into mean deterministic and zero-mean random components, respectively. The mean deterministic component is used to characterize the persistent shift caused by the environmental disturbance, and the zero-mean random component is used to characterize the random fluctuations caused by the environmental disturbance. The binary decomposition expression is as follows: , in, For wind disturbance torque, For the mean deterministic component of the wind disturbance torque, For the zero-mean random component of the wind disturbance torque, For wave disturbance torque, For the mean deterministic component of the wave disturbance torque, The zero-mean random component of the wave disturbance torque. Let the ocean current velocity vector be... The mean deterministic component of the ocean current velocity vector. The zero-mean random component of the ocean current velocity vector. The time derivative of the ocean current velocity vector. The time derivative of the deterministic component of the mean ocean current velocity. Let be the time derivative of the zero-mean random component of the ocean current velocity.

[0008] Further, step S1 also includes substituting the deterministic mean component and the zero-mean random component into the dynamic model to obtain deterministic parameter terms and random disturbance terms, aggregating the deterministic parameter terms and random disturbance terms respectively, and converting the aggregated dynamic model into an Iton-type stochastic differential equation. The expression of the Iton-type stochastic differential equation is as follows: , in, Let be the velocity of the i-th unmanned surface vessel. For the increment of the Wiener process, Let i be the nominal dynamics term of the i-th unmanned surface vessel. For the regression matrix of deterministic environmental disturbance parameters, For deterministic environmental disturbance parameter vectors, Let be the inverse of the nominal inertia matrix of the i-th unmanned surface vessel. The regression matrix for unknown hydrodynamic parameters. The position and attitude of the unmanned surface vessel. For the unknown hydrodynamic parameters vector of the unmanned surface vessel, The control input is the normalized nominal inertia matrix. is the covariance parameter for random perturbation.

[0009] Further, step S2 includes determining the desired pose of the following unmanned surface vessel (USV) based on the pose of the leader USV, the pose of the following USV, and the preset relative position of the formation, and comparing the actual pose of the following USV with the desired pose to obtain the formation tracking error. For each error channel of the formation tracking error, a specified upper boundary function and a specified lower boundary function that vary with time are set, so that the formation tracking error is constrained between the specified upper boundary function and the specified lower boundary function throughout the entire process. The expression of the specified performance function is: , in, , These are the specified upper and lower boundary functions for the performance of the j-th error channel, respectively. , These are the initial values ​​for the upper and lower boundaries, used to limit the maximum allowable transient range of formation tracking error. , These are the steady-state values ​​of the upper and lower boundaries, used to limit the steady-state accuracy of formation tracking error. , A positive attenuation coefficient. It is a time variable.

[0010] Further, step S3 includes constructing a smooth mapping that is strictly monotonically increasing with respect to the transformation error, mapping the ratio of the formation tracking error to a specified performance upper boundary function to an unconstrained space; Inverting the smooth mapping yields the unbounded transformation error for each error channel, and the unbounded transformation error forms the transformation error vector. Based on the transformation error vector, a positive definite first-layer stochastic Lyapunov function is constructed, and a stochastic system infinite generator operator is applied to the first-layer stochastic Lyapunov function to obtain an expression for the infinite generator operator with the transformation error vector as the weight and containing a positive definite scaling matrix and a time-varying boundary compensation vector.

[0011] Further, step S4 includes constructing a virtual control quantity based on the no-boundary transformation error, and subtracting the actual body velocity of the following unmanned surface vessel from the virtual control quantity to obtain the velocity tracking error. Based on the velocity tracking error, the actual control input is calculated using the random backstepping method. The expression for the actual control input is: , in, This is the actual control input vector. For speed tracking error, The time derivative of the virtual control quantity. The total equivalent inertia matrix is... The velocity feedback gain matrix is ​​positive definite. For the nominal kinetic term, For the regression matrix of deterministic environmental disturbance parameters, The regression matrix for unknown hydrodynamic parameters. , , These are the online estimates of deterministic perturbation parameters, unknown hydrodynamic parameters, and the combined scalar of random perturbation covariance, respectively. This is the position-velocity coupling cross term matrix. Let be the positive constants for Young's inequality.

[0012] Further, step S4 also includes designing adaptive update laws consisting of an identification term and a decay correction term driven by the velocity tracking error for the deterministic disturbance parameters, the unknown hydrodynamic parameters, and the random disturbance covariance parameters, respectively, and feeding back each online estimate to the actual control input. The expression of the adaptive update law is: , in, , It is a positive definite adaptive gain matrix. A positive adaptive gain scalar. , , A positive attenuation correction factor. , and They are respectively , , The time derivative.

[0013] Further, step S5 includes incorporating the boundless transformation error, velocity tracking error, estimation error of deterministic disturbance parameters, estimation error of unknown hydrodynamic parameters, and estimation error of random disturbance covariance parameters into the same positive definite function to construct a comprehensive stochastic Lyapunov function for determining the stability of unmanned surface vessel formation control. The expression of the comprehensive stochastic Lyapunov function is as follows: , in, To synthesize stochastic Lyapunov functions, For the first layer of random Lyapunov functions, For speed tracking error term, , and These represent the estimation errors for deterministic environmental disturbance parameters, unknown hydrodynamic parameters, and random disturbance covariance parameters, respectively. It is a positive definite adaptive gain matrix. It is a positive adaptive gain scalar.

[0014] Further, step S5 includes applying the stochastic system infinite generation operator to the synthetic stochastic Lyapunov function, and scaling the position-velocity coupling cross term and the random perturbation term using Young's inequality to obtain the exponentially decaying upper bound of the synthetic stochastic Lyapunov function. The convergence residual set of the formation tracking error is determined based on the upper bound of exponential decay, and the feedback gain of the actual control input and the adaptive gain of the adaptive update law are tuned according to the convergence residual set. The upper bound of exponential decay satisfies: , in, For mathematical expectation, At the initial moment, The positive convergence rate coefficient is determined by the feedback gain and the adaptive gain. The residual is a positive bounded constant. It is a time variable.

[0015] In summary, the present invention has the following beneficial technical effects: 1. This invention sets a specified performance function that varies with time for the formation tracking error, and performs a constrained error transformation on the formation tracking error based on the specified performance function. After converting the formation tracking error with boundary constraints into a boundaryless transformation error, it performs stabilization control, realizing explicit quantitative constraints on the maximum overshoot, convergence speed and steady-state accuracy of the formation tracking error. This solves the problem that traditional formation control can only achieve asymptotic stability and the control accuracy is not adjustable, thereby improving the precision operation capability of unmanned surface vessel formations in complex sea conditions.

[0016] 2. This invention decomposes environmental disturbances caused by wind, waves and ocean currents into unknown deterministic components and Gaussian random components, and introduces the unknown deterministic disturbances, dynamic model parameters and Gaussian random disturbances into the adaptive estimation process, enabling the controller to identify and counteract the constant offset effect of environmental disturbances online. At the same time, by constraining the influence of random oscillations by control gain, the control strategy is adapted to the real ocean random environment, effectively reducing control jitter.

[0017] 3. This invention indirectly constrains the relative distance between the following unmanned surface vessel (USV) and the leader USV by designing parameters that specify the boundary of the performance function. It can ensure that the formation meets the safety distance requirements between the USVs throughout the entire process without the need to add a separate collision avoidance judgment and constraint switching module. This achieves integrated control of high-precision tracking and safe collision avoidance, simplifies the control architecture, reduces the amount of computation, and avoids control oscillations and logic conflicts caused by switching between multiple modules.

[0018] 4. This invention constructs a comprehensive stochastic Lyapunov function based on the transformation error, velocity error, and estimation errors of each parameter, and performs stochastic stability analysis. This makes all signals of the closed-loop system probabilistically bounded, and the formation tracking error probabilistically converge to the residual set. Moreover, the entire control process does not depend on the precise hull model and prior sea state information, and can adaptively adapt to different hull types and time-varying sea states. This enables the engineering application of the control method in different unmanned surface vessel formation operation scenarios. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process of a performance-specific adaptive formation control method for unmanned surface vessels in an embodiment of the present invention; Figure 2 This is a schematic diagram of a leader-follower formation structure provided in an embodiment of the present invention; Figure 3 This is a diagram showing the motion trajectories of three unmanned surface vessels under random environmental disturbances in an embodiment of the present invention; Figure 4 The eastward position of the three unmanned surface vessels in this embodiment of the invention. The response curve; Figure 5 The northward position of the three unmanned surface vessels in this embodiment of the invention. The response curve; Figure 6 The heading angles of the three unmanned surface vessels in this embodiment of the invention. The response curve; Figure 7 For the eastward formation tracking error in the embodiments of the present invention and the curves showing the changes in its specified performance function; Figure 8 The northbound formation tracking error in this embodiment of the invention and the curves showing the changes in its specified performance function; Figure 9 For example, the heading formation tracking error in this embodiment of the invention. and the curves showing the changes in its specified performance function; Figure 10 In this embodiment of the invention, the longitudinal thrust component is controlled. The change curve; Figure 11 In this embodiment of the invention, the lateral force component of the control input is... The change curve; Figure 12 In this embodiment of the invention, the control input bow roll torque component is... The change curve; Figure 13 The northbound formation tracking error in this embodiment of the invention A comparison curve chart; Figure 14 For the eastward formation tracking error in the embodiments of the present invention A comparison curve chart; Figure 15 For example, the heading formation tracking error in this embodiment of the invention. A comparison curve chart; Figure 16 In this embodiment of the invention, the longitudinal thrust component is controlled. The comparison curve. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the accompanying drawings.

[0021] Example 1 Reference Figure 1This embodiment of an adaptive formation control method for a specified performance of an unmanned surface vessel includes: S1. Establish a dynamic model of the unmanned surface vessel (USV), obtain the operating status of the leading USV and the following USV, and decompose the environmental disturbances caused by wind, waves and ocean currents into unknown deterministic components and Gaussian random components. S2. Based on the status of the leader unmanned surface vessel (USV) and the follower USV and the preset relative positions of the formation, construct the formation tracking error of the follower USV and set a specified performance function for the formation tracking error that varies with time. S3. Perform constrained error transformation on the formation tracking error based on the specified performance function, and convert the formation tracking error with boundary constraints into a boundless transformation error; S4. Using the transformation error and the unmanned surface vessel speed error, construct virtual control quantities and actual control inputs, and introduce unknown deterministic disturbances, dynamic model parameters and Gaussian random disturbances into the adaptive estimation process; S5. Construct a stochastic Lyapunov function based on the transformation error, velocity error, and estimation errors of each parameter, and perform stability analysis. Adjust the virtual control quantity and actual control input through an adaptive law. S6. The adaptively adjusted actual control input is sent to the propulsion actuators of each following unmanned surface vessel (USV), so that each USV tracks the lead USV and maintains the preset formation distance under random environmental disturbances.

[0022] Specifically, a method for adaptive formation control of unmanned surface vessels with specified performance includes the following: like Figure 1 , Figure 2 As shown in Figure S1, this embodiment takes a leader-follower formation consisting of N unmanned surface vessels as the object, i=1,2,…,N, where the first vessel is the leader unmanned surface vessel and the rest are follower unmanned surface vessels.

[0023] Establish a geodetic inertial coordinate system Fixed coordinate system with hull Two standard ship coordinate systems are used: a geodetic inertial coordinate system with its origin fixed at the sea surface, used to describe the global position and heading of the unmanned surface vessel (USV); and a hull-fixed moving coordinate system with its origin at the center of gravity, used to describe the relative velocity of the USV. The position and heading vector of the i-th USV in the geodetic inertial coordinate system are obtained through onboard navigation and sensing equipment. ,in The location is facing east. The location is north. The bow angle is obtained; simultaneously, its velocity vector in the fixed-moving coordinate system of the hull is acquired. ,in, Forward and backward speed, The lateral drift speed, The bow roll angular velocity is determined by a coordinate rotation matrix between the two coordinate systems. Establish kinematic mapping relationships: (1-1) in, Let be the first derivative of the position and heading vector of the i-th unmanned surface vessel in the geodetic inertial coordinate system with respect to time. The above kinetic mapping relationship only describes the mapping relationship from velocity to global position and does not include external force. It constitutes the kinematic layer of the unmanned surface vessel system. The position, heading and body velocity states of the leader and follower unmanned surface vessels are obtained in the above way, providing the state basis for the construction of subsequent formation tracking errors.

[0024] Based on the aforementioned kinematic mapping relationships, and using the rigid body momentum theorem, Coriolis force, fluid damping, added mass inertia, unknown nonlinear hydrodynamics, environmental disturbances, and control inputs are uniformly incorporated into the force balance equations. Furthermore, the relative velocity of the unmanned surface vessel (USV) relative to the ocean current is considered. By incorporating ocean current velocity into the dynamic model, a dynamic model of the unmanned surface vessel is established: (1-2) in, Let be the relative velocity vector of the i-th unmanned surface vessel relative to the ocean current. Let be the velocity vector of the i-th unmanned surface vessel in the fixed-movement coordinate system of the hull. Let the ocean current velocity vector be... The inertia matrix of a rigid body is expressed as follows: , To add the mass inertia matrix, The expression for the Coriolis and centripetal force matrices is: , The fluid damping matrix is ​​expressed as follows: , The regression matrix for the unknown nonlinear hydrodynamic term is expressed as: , For the unknown hydrodynamic parameters vector of the unmanned surface vessel, , These are the disturbance torque vectors caused by wind and waves, respectively. To control the input thrust and torque vector, In the above matrix representation, The equivalent mass element for the longitudinal forward and backward channels. , The equivalent mass element for the lateral drift channel. , This is the coupled inertial element for the lateral drift and bow roll channels. , The equivalent moment of inertia element for the bow rocker channel. in, For the quality of unmanned surface vessels, The vertical coordinate of the centroid For the bow roll moment of inertia, , , , The hydrodynamic derivatives can all be obtained through system identification. For coupling elements, , The hydrodynamic damping coefficient, obtained through system identification, includes a linear damping term and a velocity quadratic damping term. Let be the bow roll rate of the i-th unmanned surface vessel.

[0025] Traditional unmanned surface vessel (USV) modeling only considers still water conditions or treats disturbances as deterministic disturbances with known boundaries, which does not match the real ocean environment. Considering that wind, waves, and ocean currents in the real ocean environment are composed of a large number of independent, minute, random turbulent factors, and according to the central limit theorem, their time-varying fluctuations asymptotically follow a Gaussian distribution, while wind, waves, and ocean currents exert a constant average force over a long period, this embodiment considers the ocean current velocity... Wind disturbance torque and wave disturbance torque A uniform binary decomposition is performed between the deterministic component with the mean and the random component with the zero mean: (1-3) in, For wind disturbance torque, For the mean deterministic component of the wind disturbance torque, For the zero-mean random component of the wind disturbance torque, For wave disturbance torque, For the mean deterministic component of the wave disturbance torque, The zero-mean random component of the wave disturbance torque. Let the ocean current velocity vector be... The mean deterministic component of the ocean current velocity vector. The zero-mean random component of the ocean current velocity vector. The time derivative of the ocean current velocity vector. The time derivative of the deterministic component of the mean ocean current velocity. The time derivative of the zero-mean random component of the ocean current velocity; The mean deterministic components of each physical quantity characterize the persistent offset effect caused by environmental disturbances. This component continuously causes steady-state offsets in formation tracking errors and is an unknown constant to be estimated online. It can be identified and completely canceled online through subsequent adaptive update laws. The zero-mean random components of the physical quantities characterize the random fluctuation effect caused by environmental disturbances. This component is an irregular high-frequency oscillation that cannot be completely eliminated by adaptive estimation. It is necessary to use stochastic Lyapunov theory to prove that the formation tracking error is probabilistically bounded under its influence.

[0026] Substituting the results of the binary decomposition into the dynamic model (1-2): First, the relative velocity... Substituting its derivative into the fluid damping term and the additional mass inertia term; then... , The decomposition is directly substituted into the external force summation term; then, all terms containing both deterministic components with mean and random components with zero mean are combined into a single term, and all deterministic constant combination terms are grouped into deterministic parameter terms. All zero-mean random combination terms are aggregated into random perturbation terms (diffusion terms) containing Wiener processes. The definition of each combination quantity in the aggregation process is: , (1-4) in, It is the total equivalent inertia matrix (i.e., the nominal inertia matrix). The nominal dynamics term characterizes the deterministic dynamic properties of the hull itself, resulting from the Coriolis force and fluid damping. For the regression matrix of deterministic environmental disturbance parameters, To concatenate line by line, It is a third-order identity matrix. For deterministic environmental disturbance parameter vectors, To splice by column, The control input is the normalized nominal inertia matrix. , Let be the covariance matrix corresponding to the zero-mean random components. For covariance calculation, the two together constitute the random perturbation covariance parameter. .

[0027] Substitute the definitions of each combination quantity in the aggregation process into the dynamic model (1-2), and multiply both sides of the equation by the inverse of the nominal inertia matrix. After completing variable aggregation and random term standardization, the aggregated dynamic model is transformed into an Iton-type stochastic differential equation: (1-5) in, Let be the random derivative of the velocity of the i-th unmanned surface vessel. For the increment of the Wiener process, The position and attitude of the unmanned surface vessel. For the unknown hydrodynamic parameter vector of the unmanned surface vessel, the above processing integrates the dispersed multi-source random environmental disturbances into deterministic parameter terms. and single diffusion term Standard Itoh form: In the deterministic parameter term and All of them are unknown constants, which can be used as online estimation objects for subsequent adaptive update laws to completely offset steady-state offset errors; the single diffusion term strictly matches the operational framework of the infinite generation operator of the stochastic nonlinear system, and the theoretical proof of the probability-bounded closed-loop system can be directly applied by the stochastic stability lemma, thus forming a dynamic model of the fully driven unmanned surface vessel with random disturbances and parameter uncertainties.

[0028] S2. Based on the established Iton-type stochastic differential dynamics model, complete the construction of the formation tracking error and set the specified performance function.

[0029] In a leader-follower formation, the desired pose (reference trajectory) of the i-th follower UAV is calculated based on the poses of the leader UAV, the poses of the follower UAVs, and the preset relative positions of the formation. Using the position of the leader unmanned surface vessel as a reference point, the desired formation spacing is determined according to the preset relative positions of the formation. Expected observation angle and relative heading angle Determine the desired geometric relationship between the following unmanned surface vessel (USV) and the leader USV to obtain the desired pose. and its time derivative Among them, the expected formation spacing Greater than the preset minimum safe collision distance .

[0030] Will follow the actual position of the unmanned surface vessel With desired pose The difference is calculated to obtain the pose tracking error (i.e., the formation tracking error). : (2-1) in, , These represent the tracking errors for eastward and northward directions, respectively. For heading tracking error, the three correspond to respectively Three error channels, , and The actual pose components of the i-th following unmanned surface vessel at time t are used to construct the actual pose vector. , , Let be the expected pose component of the i-th following unmanned surface vessel at time t, and let be the position synthesis error between the following unmanned surface vessel and its leader unmanned surface vessel: This characterizes the deviation in straight-line distance between boats.

[0031] To ensure that the transient overshoot, convergence speed, and steady-state accuracy of formation tracking errors can be explicitly and quantitatively constrained, a specified performance function that varies with time is set for the formation tracking error of each error channel. This specified performance function includes a specified upper boundary function and a specified lower boundary function, both of which are exponential time-varying functions. (2-2) in, , These are the specified upper and lower boundary functions for the performance of the j-th error channel, respectively. , These are the initial values ​​for the upper and lower boundaries, used to limit the maximum allowable transient range of formation tracking error. , These are the steady-state values ​​at the upper and lower boundaries, used to limit the steady-state accuracy of the formation tracking error, and satisfying the following conditions: , ; , A positive attenuation coefficient is used to define the convergence rate of the boundaries. The upper and lower boundary functions are strictly monotonically decreasing and convergent with respect to time, ensuring that the formation tracking error satisfies the following conditions throughout the entire process. This allows for the explicit quantitative design of three performance indicators in formation tracking error: maximum overshoot, convergence speed, and steady-state accuracy, through boundary parameters.

[0032] It should be noted that this boundary design also serves as a collision avoidance mechanism between vessels: by selecting initial boundary values ​​that satisfy... This ensures that the position synthesis error meets the requirements throughout the entire process. This means that the actual distance between the boats is always greater than the minimum safe collision avoidance distance, and the formation can operate without collisions throughout without the need for additional collision avoidance modules. The preset minimum safe collision avoidance distance, Let i be the expected formation spacing between the i-th following unmanned surface vessel and its leader unmanned surface vessel. , These are the initial values ​​of the performance upper boundary functions for the eastward and northward error channels, respectively, i.e., the boundary values ​​at time t=0.

[0033] S3. Since the formation tracking error is subject to a bilateral time-varying constraint of an exponential time-varying function, it is a constrained variable and cannot be directly used in controller design. In this embodiment, a parameter is constructed for the preset performance transformation error. Strictly monotonically increasing smooth mapping Map the ratio of formation tracking error to its specified performance upper bound to an unconstrained space: (3-1) in, The preset performance transformation error for the j-th channel is... To specify the ratio of the upper and lower limits of performance, since about The transformation is strictly monotonically increasing, and its inverse function exists and is unique. The transformation error can be obtained by inverting equation (3-1). When formation tracking error When approaching the specified performance boundary, Approaching infinity, therefore Boundedness and Equivalent without touching the boundary The monotonicity of the mapping indicates that the transformation error... There are upper and lower limits, that is , It is a positive constant; By substituting the upper and lower limits, the formation tracking error can be derived. The original constraint interval. Therefore, as long as you remain calm... By making it bounded, we can guarantee... The entire process avoids touching the specified performance boundaries, thus transforming the formation tracking error with boundary constraints into a boundaryless transformation error. The controller only needs to stabilize the new variables after the transformation to automatically ensure that the error does not exceed the limit. The transformation error vector is composed of the transformation errors of each channel. .

[0034] Construct the first layer of stochastic Lyapunov functions using a preset performance transformation error: (3-2) in, For the first layer of random Lyapunov functions, To predetermine the norm of the performance transformation error vector, The reason for taking the fourth power form of the positive definite scalar function is that the infinite generation operator of the stochastic system involves the second derivative operation with respect to the diffusion term, and the fourth-order Lyapunov function is convenient for trace scaling of the stochastic diffusion term, thus fitting the stability analysis framework of Iton-type stochastic differential equations.

[0035] Since the model established in step S1 is an Itō-type stochastic differential equation, the ordinary time derivative is no longer applicable. Therefore, for Applying an infinite generation operator to a random system ,get: (3-3) in, For an infinite number of operators that generate random systems, For the first layer of random Lyapunov functions, The positive definite scaling matrix derived from the smooth mapping is denoted as: , Let be the first derivative of the actual pose of the i-th unmanned surface vessel with respect to time. Let the first derivative of the desired pose (reference trajectory) with respect to time be _____. For time-varying boundary compensation vectors, For pose change rate tracking error, This is the positive definite scaling factor for the eastward position channel. This is the positive definite scaling factor for the northbound position channel. The positive definite scaling factor for the bow channel is given by equation (3-3), which serves as the design objective for the virtual control variable. Subsequently, the virtual control variable is designed to achieve... By forming a negative definite convergence term and eliminating the recursive design of the position-velocity coupling cross term that cannot be eliminated within the pose subsystem, the transformation error can be guaranteed to converge to the residual set in a probabilistic manner, thereby indirectly ensuring that the formation tracking error meets the specified performance constraints throughout the entire process.

[0036] After constraint error transformation, the derivative of the mapping will derive transformation error nonlinear terms within the pose subsystem. These terms are composed of the transformation error vector, the positive definite scaling matrix, and the desired pose derivative. The transformation error nonlinear terms and time-varying boundary compensation terms can be eliminated by compensation from the S4 virtual control quantity. Through the above processing, on the one hand, the specified performance function realizes the designability and reproducibility of three performance indicators: maximum overshoot, convergence speed, and steady-state accuracy. On the other hand, the smooth mapping transformation eliminates the need to handle boundary constraints in the controller design and indirectly achieves inter-vessel collision avoidance through boundary initial value design, eliminating the need for a separate collision avoidance module.

[0037] S4. Define speed tracking error ,in To track the actual speed of the unmanned surface vessel, This is the virtual control quantity (virtual speed command) to be designed. This characterizes the deviation between the actual speed and the desired formation speed. The design logic lies in: unmanned surface vessel kinematic mapping. Since pose and velocity are directly correlated, and control input cannot be directly applied to the pose channel, the velocity is... As an intermediate virtual command, we first ensure the convergence of pose error, and then design the real thrust tracking in the next step.

[0038] Based on the first-layer stochastic Lyapunov function and its infinite generation operator objective formula constructed in step S3, the virtual control quantity is designed to consist of reference trajectory feedforward, transformation error negative feedback, and time-varying boundary compensation: (4-1) in, , These are virtual speed commands for longitudinal forward / reverse and lateral drift channels, respectively, both measured via the bow angle. The function decomposition maps the desired motion in the geodetic coordinate system to the hull coordinate system. This is the virtual angular velocity command for the bow rocker channel. , These are the synthesized control quantities for the eastward and northward error channels, respectively. The position convergence gain of the bow channel is a positive number. This is the preset performance transformation error for the bow channel. The heading angular velocity of the reference trajectory. For the boundary compensation term of the heading passage, This is the positive definite scaling factor for the heading channel.

[0039] Substituting equation (4-1) into equation (3-3) in step S3, the boundary compensation term in the virtual control quantity of equation (4-1) and the time-varying boundary compensation vector within parentheses in equation (3-3) The negative feedback term cancels out and is scaled by a positive definite matrix. The effect of this is to form a negative definite convergence term, thereby eliminating the transformation error nonlinearity and time-varying boundary compensation term within the pose subsystem; wherein, the transformation error nonlinearity is formed by the positive definite scaling matrix. Transformation error vector and the derivative of the desired pose Composed of various elements, and at the same time, due to the actual body speed With virtual control quantity There is a speed tracking error This deviation is mapped into the pose subsystem via kinematics, forming a position-velocity coupled cross term, which, after simplification, yields: (4-2) in, For the first layer of random Lyapunov functions The infinite generation operator of the random system, Let be the positive definite feedback gain matrix, where , and These represent the position convergence gains for the eastbound, northbound, and bow-head channels, respectively; all are positive constants. The first term... For a purely negative term, when the speed tracking error After convergence, The expression is negative definite, thus ensuring that the pose error after the preset performance transformation converges exponentially to the residual set. The second term For position-velocity coupling cross terms, The term is the coupling cross-term matrix, which is the connecting term between the two steps of the backstepping method. It will be eliminated in the design of the second-level Lyapunov function. Through the above substitution and elimination process, the stabilization problem of the pose subsystem is transformed into a convergence problem dominated by pure negative definite terms. It is only necessary to complete the elimination of coupling cross-terms in the velocity channel to ensure that the formation tracking error meets the specified performance constraints throughout the entire process. Based on the virtual control quantity, the speed tracking error is... The second step of the backstepping method is introduced, and the estimation errors of deterministic environmental disturbance parameters, unknown hydrodynamic parameters of the dynamic model, and the estimation errors of the Gaussian random disturbance covariance combination quantity and velocity tracking error are uniformly incorporated into the recursive process. Using Young's inequality, the coupling cross-terms and the random diffusion terms of the velocity channel left over from equation (4-2) are uniformly scaled, and the cross-coupling terms are decomposed into convergent negative terms and bounded constant terms, ensuring that the upper bound of the infinite generating operator decays exponentially. Based on this, the actual control input is designed, which consists of hull dynamics compensation, virtual control differential feedforward, velocity tracking error negative feedback, adaptive disturbance compensation, and scaling compensation. (4-3) in, The actual control inputs are the thrust and torque vectors. The total equivalent inertia matrix is... The velocity feedback gain matrix is ​​positive definite. This is a negative feedback term for speed error, used to suppress speed oscillation. The time derivative of the virtual control quantity serves as the virtual control differential feedforward term, used to compensate for the lag caused by the time-varying desired velocity. For the nominal dynamic compensation term, For deterministic disturbance compensation terms, For deterministic environmental disturbance parameter vectors The online estimate, To model the nonlinear hydrodynamic compensation term, unknown hydrodynamic parameter vector The online estimate, with the last term being the scaling compensation term, wherein, Let the positive constants be bounded for Young's inequality. For the coupling cross terms left over from online cancellation (4-2), Used to suppress the effects of random diffusion terms online. For the scalar of covariance combination of random perturbations The online estimate.

[0040] To ensure that the online estimates in equation (4-3) converge in real time and remain bounded throughout the process, unknown deterministic perturbations, dynamic model parameters, and Gaussian random perturbations are introduced into the adaptive estimation process. Modified adaptive update laws are designed for the deterministic environmental perturbation parameter vector, the unknown hydrodynamic parameter vector, and the covariance parameter of the Gaussian random perturbation, respectively: (4-4) in, , It is a positive definite adaptive gain matrix. A positive adaptive gain scalar. , , The decay correction coefficient is positive. All three adaptive update laws employ a correction structure, each consisting of two parts: one is the error-driven update term (e.g., ...). The larger the speed tracking error, the greater the parameter correction magnitude, and parameter identification is driven dynamically and in real time by the system; the second is the attenuation suppression term (i.e. , , This is used to prevent the estimated parameters from drifting infinitely under unexcited conditions and to ensure that all estimated values ​​are globally bounded. Each online estimated value is fed back to the actual control input of equation (4-3) in real time.

[0041] S5. The transformation error obtained in step S3, the velocity tracking error obtained in step S4, and the estimation errors of each parameter are all incorporated into the same positive definite function to construct a comprehensive stochastic Lyapunov function to determine the integrated stability of all error variables. The expression of the comprehensive stochastic Lyapunov function is as follows: (5-1) in, To synthesize stochastic Lyapunov functions, The first layer of random Lyapunov functions constructed in step S3, For speed tracking error term, , and These represent the estimation errors for deterministic environmental disturbance parameters, unknown hydrodynamic parameters, and random disturbance covariance parameters, respectively. It is a positive definite adaptive gain matrix. The positive adaptive gain scalar has its inverse or reciprocal used as the weight of the corresponding estimation error term. This function unifies the estimation of pose, velocity, and three types of unknown parameters into the same positive definite framework, essentially achieving synchronous stability of position tracking, velocity tracking, and unknown parameter estimation.

[0042] Applying the stochastic system infinite generation operator to equation (5-1), substituting it into the actual control input equation (4-3) and the adaptive update law equation (4-4) from step S4, and using Young's inequality to uniformly scale the cross-coupling terms between position-velocity coupling, velocity error, and stochastic diffusion, all cross-coupling terms are decomposed into convergent negative terms and bounded constant terms, resulting in: (5-2) in, Represents the smallest eigenvalue of the matrix; by selecting the gain, In equation (5-2), the first five terms on the right-hand side are all negative definite convergence terms, corresponding to the convergence of velocity tracking error, transformation error, and the three types of estimation errors, respectively; the last four terms are bounded constant terms, consisting of the true values ​​of the unknown parameters and the scaling constant. Equation (5-2) can be rearranged into an exponentially decaying upper bound form. ,in, The positive convergence rate coefficient is determined by the feedback gain and the adaptive gain. Since the residuals are positive and bounded constants, we can obtain: (5-3) in, For mathematical expectation, At the initial moment, The positive convergence rate coefficient is determined by the feedback gain and the adaptive gain. The residual is a positive bounded constant. As a time variable, when At that time, the exponent term , Eventually stabilized .

[0043] Based on equations (5-1) to (5-3), the closed-loop unmanned surface vessel leader-follower formation system satisfies the following four performance conclusions: First, the formation tracking error converges probabilistically to the residual set. Because... It is positively correlated with the fourth power of the transformation error and the velocity tracking error, as can be obtained from equation (5-3): (5-4) That is, both the transformation error and the velocity tracking error converge probabilistically to the value of... , The determined small residual set, and the size of the residual set can be compressed by increasing the gain parameter.

[0044] Secondly, all signals in the closed-loop system are bounded by probability. This can be seen from equation (5-3). There is always an upper limit, that is According to the bounded probability; and because The error consists of five positive definite terms: transformation error, velocity tracking error, disturbance estimation error, hull parameter estimation error, and noise estimation error. Since the positive definite function is bounded, each term itself is probabilistically bounded. Bounded, and therefore each online estimate Bounded, the actual control input is bounded, and all signals in the closed-loop system remain bounded.

[0045] Third, the formation tracking error meets the specified performance constraints. From step S3, it can be seen that the mapping... about Strictly monotonically increasing, and There are upper and lower limits Substituting this into the mapping equation (3-1) allows us to deduce that the formation tracking error lies entirely within the original constraint range between the specified upper and lower boundary functions of the performance, without touching the boundary.

[0046] Fourth, there was no collision between each following unmanned surface vessel and its leader unmanned surface vessel throughout the entire process. This is because the position synthesis error meets the requirements. And the initial boundary values ​​in step S2 are as follows Design, therefore For any As always, the actual distance between the boats is always greater than the minimum safe collision avoidance distance.

[0047] S6. Within each control cycle, the control unit of each following unmanned surface vessel executes the following closed-loop calculation process: First, it obtains the position, heading, and velocity status of itself and the leader unmanned surface vessel; then, it calculates the desired pose and constructs the formation tracking error according to step S2; finally, it substitutes the error into the specified performance function to complete the constraint error transformation and obtain the transformed error vector. Secondly, calculate the virtual control quantity according to step S4. The speed tracking error is obtained by subtracting the actual volume velocity from the virtual control quantity. It also reads the online estimates of the outputs of three sets of adaptive update laws. Then, substitute the above quantities into equation (4-3) to calculate the actual control input. ,in, The longitudinal thrust component is converted into thrust commands for the unmanned surface vessel's longitudinal propellers via the drive mechanism. The lateral force component is converted into a thrust command for the lateral thruster via the drive mechanism. The thrust and torque components are converted into torque commands for the bow-turning actuator via the drive mechanism. Finally, the thrust and torque commands are sent to the propulsion actuator of the vessel for execution. Simultaneously, the online estimates are dynamically updated in real time according to equation (4-4) for use in the next control cycle. Each following unmanned surface vessel executes the above process independently and in parallel, and the control input is adjusted in real time according to the adaptive estimation process.

[0048] The adaptively adjusted actual control input drives the propulsion actuators of each following unmanned surface vessel (USV), enabling each USV to track the lead USV and maintain a preset formation distance under the aforementioned random environmental disturbances. The specific operational process is as follows: In terms of tracking performance, the formation tracking error is constrained to the upper and lower boundary functions of the specified performance throughout the entire process after the constraint error transformation. Its transient overshoot, convergence speed and steady-state accuracy all meet the performance indicators preset by the specified performance function, realizing the specification and reproducibility of formation control performance. Regarding operational safety, since the initial values ​​of the specified performance boundaries are based on... The design ensures that the actual distance between boats is always greater than the minimum safe collision avoidance distance. The formation did not collide at all during the entire process; In terms of disturbance suppression, the deterministic components in environmental disturbances are identified online by the adaptive estimation process and offset by the adaptive disturbance compensation term in the actual control input. The Gaussian random components in environmental disturbances cannot be completely eliminated, and their influence is constrained by the scaling compensation term in the actual control input. The formation tracking error converges to a small residual set in a probabilistic manner, thereby ensuring the continuous and stable operation of the formation under random sea conditions.

[0049] Example 2 The difference between this embodiment and Embodiment 1 is that this embodiment provides a simulation experiment of a specified performance adaptive formation control method for unmanned surface vessels; Simulation objects and formation structure like Figure 2 As shown, this embodiment adopts a leader-follower formation structure, with the formation consisting of three unmanned surface vessels (N=3), where the first vessel is the leader unmanned surface vessel, and the second and third are the follower unmanned surface vessels. Each follower unmanned surface vessel calculates its desired pose based on the pose of its leader unmanned surface vessel, its own pose, and the preset relative position of the formation.

[0050] Simulation condition settings The simulation parameters are set as follows: The rigid body inertia matrix elements of the three unmanned surface vessels are defined as follows: , The external mass inertia matrix is The damping terms of the fluid damping matrix are: , in, Let be the rigid body inertial matrix of the i-th unmanned surface vessel. matrix elements, The three unmanned surface vessels have different mass parameters to verify the adaptive capability of the method of the present invention to different hulls; the additional mass inertia matrix is ​​the value of its main diagonal elements, and the unit is consistent with the inertia of the corresponding degree of freedom; , , , , For fluid damping matrix The damping terms are all composed of the superposition of the first-order velocity term and the second-square velocity term, reflecting the characteristic that fluid damping increases nonlinearly with velocity. These represent the longitudinal forward and backward speeds, lateral drift speeds, and bow roll speeds of the i-th unmanned surface vessel, respectively.

[0051] Formation configuration parameters are set as follows: desired formation spacing Expected observation angle Relative heading angle , Minimum safe collision avoidance distance The initial condition is that the initial velocity of each boat is zero, i.e. The specified performance constraint for output tracking error is set as follows: ; ; ;

[0052] The covariance matrix of the random perturbation is set as follows The average value of environmental disturbances is set to The controller design parameters are set as follows: , .

[0053] Simulation Results and Analysis The simulation results related to the adaptive formation control designed in this invention are as follows: Figures 2-11 As shown.

[0054] like Figure 3 As shown, under random environmental disturbances, all three unmanned surface vessels (USVs) successfully tracked their respective predefined reference trajectories, thereby establishing and maintaining the preset formation configuration. Furthermore, within the designed formation framework, each leader USV and its followers achieved collision-free operation, verifying the effectiveness of indirectly achieving inter-vessel collision avoidance through the design of specified performance boundary parameters.

[0055] like Figures 4-6 As shown, the three unmanned surface vessels are positioned to the east. Northward position and bow angle The response curves of each vessel smoothly converge to their respective expected values, indicating that each vessel maintains good attitude tracking performance under random disturbances.

[0056] like Figures 7-9 As shown, the formation tracking error for each channel Throughout the process, the data remained between the corresponding upper and lower boundary functions of the specified performance, without touching the boundaries, and eventually converged to a smaller value. This verifies the quantitative guarantee capability of the specified performance constraints for the transient overshoot, convergence speed, and steady-state accuracy of formation tracking errors.

[0057] like Figures 10-12 As shown, control input Since the entire process is bounded and the changes are executable, in order to verify the superiority of the proposed random performance formation control method, the method of the present invention is compared with the specified performance formation control method under deterministic environmental disturbances through simulation.

[0058] like Figures 13-15 As shown, the northbound, eastbound, and heading formation error curves for the specified performance control method under deterministic environmental disturbances are presented respectively. Figures 13-15 and Figures 7-9 The comparison shows that the formation tracking error converges faster and has smaller steady-state oscillations in the method of the present invention, with sufficient safety margin throughout the process, and is less likely to touch the preset error boundary; the proposed controller not only effectively ensures control accuracy, but also enables the formation error to converge to a small neighborhood of zero at a faster speed.

[0059] like Figure 16 As shown, Figure 16 The first component of the control input for three unmanned surface vessels is given under two control frameworks. The comparison curves, where the dashed line represents the control input under the deterministic framework. Figure 16 As can be seen, the control input curve of the formation control framework proposed in this embodiment is smoother, with less violent thrust fluctuation and lower energy consumption. At the same time, since the disturbance modeling of this invention fits the characteristics of random wind and waves in the real ocean, the formation spacing is more stable under random sea conditions, and the collision avoidance robustness is significantly better than the comparative scheme under the deterministic framework.

[0060] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for adaptive formation control of unmanned surface vessels with specified performance, characterized in that, include: S1. Establish a dynamic model of the unmanned surface vessel (USV), obtain the operating status of the leading USV and the following USV, and decompose the environmental disturbances caused by wind, waves and ocean currents into mean deterministic components and zero-mean random components. S2. Based on the status of the leader unmanned surface vessel (USV) and the follower USV and the preset relative positions of the formation, construct the formation tracking error of the follower USV and set a specified performance function for the formation tracking error that varies with time. S3. Based on the specified performance function, constrain the formation tracking error to transform the formation tracking error with boundary constraints into an unbounded transformation error, and obtain an infinite generator operator expression with the transformation error vector as the weight. S4. Using the transformation error and the unmanned surface vessel speed error, construct virtual control variables and actual control inputs, and perform adaptive online estimation of the deterministic disturbance parameters corresponding to the mean deterministic components, the unknown hydrodynamic parameters in the dynamic model, and the random disturbance covariance parameters corresponding to the zero-mean random components. S5. Construct a stochastic Lyapunov function based on the transformation error, velocity error, and estimation errors of each parameter, and perform stability analysis. Adjust the virtual control quantity and actual control input through an adaptive law. S6. The adaptively adjusted actual control input is sent to the propulsion actuators of each following unmanned surface vessel (USV), so that each USV tracks the lead USV and maintains the preset formation distance under random environmental disturbances.

2. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 1, characterized in that, The establishment of the dynamic model of the unmanned surface vessel includes establishing a geodetic inertial coordinate system and a hull-fixed moving coordinate system, obtaining the position, heading vector and velocity vector of each unmanned surface vessel, and establishing the kinematic mapping relationship between the two coordinate systems through a coordinate rotation matrix. A dynamic model of the unmanned surface vessel (USV) is established based on kinematic mapping relationships and the rigid body momentum theorem. The dynamic model includes the USV's inertia matrix, added mass inertia matrix, Coriolis and centripetal force matrices, fluid damping matrix, unknown nonlinear hydrodynamic terms, wind disturbance torque, wave disturbance torque, and control input thrust.

3. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 2, characterized in that, Environmental disturbances are decomposed into deterministic components with mean and random components with zero mean. This includes performing binary decomposition of ocean current velocity, wind disturbance moment, and wave disturbance moment into deterministic and random components with mean and zero mean, respectively. The deterministic components with mean are used to characterize the persistent shift caused by the environmental disturbance, and the random components with zero mean are used to characterize the random fluctuations caused by the environmental disturbance. The binary decomposition expression is as follows: ， in, For wind disturbance torque, For the mean deterministic component of the wind disturbance torque, For the zero-mean random component of the wind disturbance torque, For wave disturbance torque, For the mean deterministic component of the wave disturbance torque, The zero-mean random component of the wave disturbance torque. Let the ocean current velocity vector be... The mean deterministic component of the ocean current velocity vector. The zero-mean random component of the ocean current velocity vector. The time derivative of the ocean current velocity vector. The time derivative of the deterministic component of the mean ocean current velocity. Let be the time derivative of the zero-mean random component of the ocean current velocity.

4. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 3, characterized in that, Step S1 further includes substituting the deterministic mean component and the zero-mean random component into the dynamic model to obtain deterministic parameter terms and random disturbance terms, aggregating the deterministic parameter terms and random disturbance terms respectively, and converting the aggregated dynamic model into an Itō-type stochastic differential equation. The expression of the Itō-type stochastic differential equation is as follows: ， in, Let be the velocity of the i-th unmanned surface vessel. For the increment of the Wiener process, Let i be the nominal dynamics term of the i-th unmanned surface vessel. For the regression matrix of deterministic environmental disturbance parameters, For deterministic environmental disturbance parameter vectors, Let be the inverse of the nominal inertia matrix of the i-th unmanned surface vessel. The regression matrix for unknown hydrodynamic parameters. The position and attitude of the unmanned surface vessel. For the unknown hydrodynamic parameters vector of the unmanned surface vessel, The control input is the normalized nominal inertia matrix. is the covariance parameter for random perturbation.

5. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 1, characterized in that, Step S2 includes determining the desired pose of the following unmanned surface vessel (USV) based on the pose of the leader USV, the pose of the following USV, and the preset relative position of the formation, and comparing the actual pose of the following USV with the desired pose to obtain the formation tracking error. For each error channel of the formation tracking error, a specified upper boundary function and a specified lower boundary function that vary with time are set, so that the formation tracking error is constrained between the specified upper boundary function and the specified lower boundary function throughout the entire process. The expression of the specified performance function is: ， in, , These are the specified upper and lower boundary functions for the performance of the j-th error channel, respectively. , These are the initial values ​​for the upper and lower boundaries, used to limit the maximum allowable transient range of formation tracking error. , These are the steady-state values ​​of the upper and lower boundaries, used to limit the steady-state accuracy of formation tracking error. , A positive attenuation coefficient. It is a time variable.

6. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 5, characterized in that, Step S3 includes constructing a smooth mapping that is strictly monotonically increasing with respect to the transformation error, mapping the ratio of the formation tracking error to the specified performance upper boundary function to an unconstrained space; Inverting the smooth mapping yields the unbounded transformation error for each error channel, and the unbounded transformation error forms the transformation error vector. Based on the transformation error vector, a positive definite first-layer stochastic Lyapunov function is constructed, and a stochastic system infinite generator operator is applied to the first-layer stochastic Lyapunov function to obtain an expression for the infinite generator operator with the transformation error vector as the weight and containing a positive definite scaling matrix and a time-varying boundary compensation vector.

7. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 4, characterized in that, Step S4 includes constructing a virtual control quantity based on the no-boundary transformation error, and subtracting the actual body velocity of the following unmanned surface vessel from the virtual control quantity to obtain the velocity tracking error. Based on the velocity tracking error, the actual control input is calculated using the random backstepping method. The expression for the actual control input is: ， in, This is the actual control input vector. For speed tracking error, The time derivative of the virtual control quantity. The total equivalent inertia matrix is... The velocity feedback gain matrix is ​​positive definite. For the nominal kinetic term, For the regression matrix of deterministic environmental disturbance parameters, The regression matrix for unknown hydrodynamic parameters. , , These are the online estimates of deterministic perturbation parameters, unknown hydrodynamic parameters, and the combined scalar of random perturbation covariance, respectively. This is the position-velocity coupling cross term matrix. Let be the positive constants for Young's inequality.

8. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 7, characterized in that, Step S4 further includes designing adaptive update laws consisting of an identification term and a decay correction term driven by the velocity tracking error for deterministic disturbance parameters, unknown hydrodynamic parameters, and random disturbance covariance parameters, respectively, and feeding back each online estimate to the actual control input. The expression of the adaptive update law is: ， in, , It is a positive definite adaptive gain matrix. A positive adaptive gain scalar. , , A positive attenuation correction factor. , and They are respectively , , The time derivative.

9. A method for adaptive formation control of unmanned surface vessels with specified performance according to claim 8, characterized in that, Step S5 involves incorporating the boundless transformation error, velocity tracking error, estimation error of deterministic disturbance parameters, estimation error of unknown hydrodynamic parameters, and estimation error of random disturbance covariance parameters into the same positive definite function to construct a comprehensive stochastic Lyapunov function for determining the stability of unmanned surface vessel formation control. The expression of the comprehensive stochastic Lyapunov function is as follows: ， in, To synthesize stochastic Lyapunov functions, For the first layer of random Lyapunov functions, For speed tracking error term, , and These represent the estimation errors for deterministic environmental disturbance parameters, unknown hydrodynamic parameters, and random disturbance covariance parameters, respectively. It is a positive definite adaptive gain matrix. It is a positive adaptive gain scalar.

10. The method for adaptive formation control of unmanned surface vessels with specified performance according to claim 9, characterized in that, Step S5 includes applying the stochastic system infinite generation operator to the synthetic stochastic Lyapunov function, and scaling the position-velocity coupling cross term and the random perturbation term using Young's inequality to obtain the exponentially decaying upper bound of the synthetic stochastic Lyapunov function. The convergence residual set of the formation tracking error is determined based on the upper bound of exponential decay, and the feedback gain of the actual control input and the adaptive gain of the adaptive update law are tuned according to the convergence residual set. The upper bound of exponential decay satisfies: ， in, For mathematical expectation, At the initial moment, The positive convergence rate coefficient is determined by the feedback gain and the adaptive gain. The residual is a positive bounded constant. It is a time variable.

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