Heterogeneous unmanned surface vehicle formation control method and system for specifying performance constraints and collision avoidance

Abstract

The application belongs to the technical field of unmanned vehicle formation control, and discloses a heterogeneous unmanned vehicle formation control method and system with specified performance constraints and collision avoidance. The application obtains a heterogeneous unmanned vehicle formation system model and sets a reference trajectory; generates a follower reference trajectory based on a leader-following framework; constructs a time domain mapping to convert a finite time domain control problem into an infinite time domain asymptotic convergence problem; defines a formation tracking error and sets an exponential convergence specified performance constraint; constructs an error conversion function to convert the constrained error into an unconstrained error and performs a time domain transformation; designs a virtual control law using a backstepping method, and approximates the derivative thereof using a dynamic surface filter; designs a system control law with adaptive disturbance based on the virtual control law; obtains a specified time controller through inverse mapping, so that the tracking error converges within a specified time and meets the performance constraint, and collision avoidance is achieved. The application integrates specified performance and collision avoidance constraints, and takes into account control accuracy and operation safety.

Description

Technical Field

[0001] This invention belongs to the field of unmanned surface vessel (USV) formation control technology, and particularly relates to a time-specific formation control, performance constraint and collision avoidance control technology for heterogeneous USVs, which can be applied to multi-USV collaborative mission scenarios such as marine exploration and collaborative operations. Background Technology

[0002] Unmanned surface vessels (USVs), with their intelligent, miniaturized, and lightweight characteristics, have become core equipment for marine operations such as ocean exploration and scientific research. While significant research has been conducted on basic control technologies for single USVs, such as trajectory tracking, path following, and disturbance suppression, single-vessel operations have inherent limitations in coverage, mission tolerance, and adaptability to complex environments. Multi-USV collaborative formation operations can overcome the limitations of single-vessel capabilities, better adapt to complex mission scenarios, and improve operational efficiency. Therefore, USV formation control technology has received widespread attention from academia and engineering. However, most existing research on USV formation control focuses on homogeneous systems, assuming that all USVs within the formation have identical model structures and dynamic parameters. In practical engineering applications, USVs within a formation typically exhibit differences in parameters such as mass, moment of inertia, and hydrodynamic coefficients. Heterogeneous USV formation control is more suitable for real-world application scenarios and has greater engineering value.

[0003] Regarding the safety performance of formation control, collision avoidance and specified performance constraints are prerequisites for stable formation operation. Existing research has achieved collision avoidance between vessels through methods such as specified performance constraints. In terms of control accuracy, specified performance constraints can constrain the transient and steady-state processes of formation errors, ensuring control accuracy. Currently, some studies have achieved collision avoidance between vessels through specified performance constraints, but in terms of time performance, it is difficult to meet the requirements of marine operational scenarios with strict time indicators.

[0004] Convergence time is one of the core indicators for evaluating control performance. With the increasing demands for timeliness in marine operations, control methods with explicit time constraints have gradually become a research hotspot. Finite-time control and fixed-time control have been applied to the field of unmanned surface vessel (USV) control, but both have inherent limitations. The convergence time of finite-time control is highly dependent on the initial state of the system; the larger the initial error, the longer the convergence time, making it impossible to guarantee the determinism of mission timeliness. While fixed-time control reduces the dependence of convergence time on the initial state, its designers cannot independently and flexibly pre-set the convergence time according to mission requirements. To overcome these technical bottlenecks, specified-time control theory has gradually matured. Among them, the time-domain mapping method, through coordinate transformation, can transform the convergence problem in the finite time domain into an asymptotic convergence problem in the infinite time domain, achieving independent pre-setting of the convergence time, which is independent of the system's initial conditions and control parameters. Currently, this technology has been gradually applied to scenarios such as single unmanned surface vessel trajectory tracking and stochastic nonlinear system stabilization. However, in the field of heterogeneous unmanned surface vessel formation control, there is still a lack of integrated control schemes that can simultaneously take into account convergence at a specified time, formation error performance constraints, and collision avoidance between vessels. It is difficult to meet the multiple requirements of timeliness, control accuracy, and operational safety in complex marine operations at the same time.

[0005] Most existing research on unmanned surface vessel (USV) swarm control focuses on homogeneous systems, assuming that all USVs within the swarm have identical model structures and dynamic parameters. However, in practical engineering applications, USVs within a swarm typically exhibit differences in parameters such as mass, moment of inertia, and hydrodynamic coefficients. Heterogeneous USV swarm control is more suitable for real-world application scenarios and has greater engineering value. Some current research has achieved collision avoidance between USVs by specifying performance constraints, but in terms of time performance, it is difficult to meet the stringent time requirements of marine operations. Finite-time control and fixed-time control have been applied to the field of USV control, but both have inherent limitations. The convergence time of finite-time control is highly dependent on the initial state of the system; the larger the initial error, the longer the convergence time, making it impossible to guarantee the determinism of mission timeliness. While fixed-time control reduces the dependence of convergence time on the initial state, its designers cannot independently and flexibly pre-set the convergence time according to mission requirements.

[0006] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: (1) Existing formation control schemes are mostly based on the assumption of isomorphic systems, which are not well adapted to actual engineering scenarios.

[0007] Most current research on unmanned surface vessel (USV) swarm control assumes that all USVs within a swarm have identical model structures and dynamic parameters. However, in actual marine operations, USVs within a swarm typically exhibit differences in parameters such as mass, moment of inertia, and hydrodynamic coefficients, making them typical heterogeneous systems. Directly applying homogeneous swarm control schemes to heterogeneous scenarios can lead to decreased swarm tracking accuracy and reduced system stability due to model mismatch, failing to fully meet the application requirements of practical engineering.

[0008] (2) Existing time-constrained control methods cannot achieve independent pre-setting of convergence time, resulting in insufficient determinism of task timeliness. Finite-time control and fixed-time control are currently widely used time-constrained control schemes, but both have inherent limitations. The convergence time of finite-time control is highly dependent on the initial state of the system; the larger the initial error, the longer the convergence time, and the determinism of timeliness cannot be guaranteed. Although fixed-time control reduces the dependence on the initial state, designers cannot independently and flexibly pre-set the convergence time according to task requirements, making it difficult to adapt to marine operation scenarios with strict requirements for time indicators.

[0009] (3) The field of heterogeneous unmanned surface vessel (USV) formation lacks a multi-performance integrated control scheme, making it difficult to simultaneously meet the requirements of timeliness, accuracy, and safety. Existing research on heterogeneous USV formation mainly focuses on optimizing collision avoidance capabilities, error performance constraints, or time convergence characteristics separately, and has not yet formed an integrated control framework that can simultaneously take into account specified time convergence, specified performance constraints of formation error, and collision avoidance between USVs. If multiple sets of control logic are superimposed to achieve multiple objectives, it is easy to cause control quantity conflicts and increase computational complexity, making it difficult to achieve stable and reliable collaborative control on heterogeneous USV systems. Summary of the Invention

[0010] To overcome the problems existing in related technologies, the present invention discloses an embodiment of a heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance, the technical solution of which is as follows: To address the time-bound formation control problem of unmanned surface vessels (USVs) with collision avoidance and specified performance constraints, this invention first transforms the time-bound control problem into an asymptotically convergent problem using time-domain mapping techniques. A performance function is designed to ensure the specified performance constraints on formation error, indirectly avoiding collisions between the lead USV and the follower USV. Then, a time-bound formation controller is designed using backstepping and dynamic surface control techniques. The designed controller can guarantee that the formation error of the USVs converges to a small neighborhood of zero within a specified time.

[0011] To achieve the above objectives, the present invention adopts the following technical solution: a heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance, comprising the following steps: S1, Obtain from The kinematics and dynamics models of each unmanned surface vessel (USV) in the leader-follower formation are used to set the reference trajectory of the first USV in the formation. S2. Based on the leader-follower formation framework, a reference trajectory for the following unmanned surface vessel is generated according to the actual trajectory of the leader unmanned surface vessel and its expected relative pose with respect to the following unmanned surface vessel. S3. Construct a time-domain mapping transformation to transform the original finite time domain... The time-specific formation control problem is mapped to an infinite time domain. The asymptotic convergence problem is solved, and the time-varying coefficients are calculated based on the time-domain mapping transformation. S4. Under the leader-follower formation framework, define the formation tracking error between the actual trajectory of the following unmanned surface vessel and the reference trajectory, and set a specified performance function to constrain the formation tracking error. The specified performance function has upper and lower bounds in the form of exponential convergence. S5. Construct an error transformation function based on the specified performance function to convert the constrained formation tracking error into an unconstrained transformation error, and perform a time-domain mapping transformation on the transformation error to obtain an infinite time-domain error. Transformation error under; S6. The virtual control law is designed using the backstepping method, and a first-order filter is introduced using dynamic surface control technology to approximate the derivative of the virtual control law, so as to avoid directly differentiating the virtual control law. S7. Design an infinite time domain based on the virtual control law. The system control law and adaptive law are used to estimate and compensate for unknown external environmental disturbances online; S8. Through the inverse transformation of the time-domain mapping transformation, the infinite time domain is transformed... Mapping the system control law and adaptive law back to the original finite time domain Obtain the formation controller and adaptive law at a specified time to drive the formation tracking error of each unmanned surface vessel within the specified time. The small neighborhood converges to zero, and the formation tracking error always satisfies the specified performance function constraint, thereby achieving collision avoidance between the lead unmanned surface vessel and the follower unmanned surface vessel.

[0012] Another object of the present invention is to provide a heterogeneous unmanned surface vessel (USV) formation control system with specified performance constraints and collision avoidance, the system being used to implement the aforementioned heterogeneous USV formation control method with specified performance constraints and collision avoidance, the system comprising: The data acquisition and model building module is used to acquire the kinematic and dynamic models of each unmanned surface vessel in a leader-follower formation consisting of N heterogeneous unmanned surface vessels, and to set the reference trajectory of the first unmanned surface vessel in the formation. The reference trajectory generation module is used to generate the reference trajectory of the following unmanned surface vessel (USV) based on the leader-follower formation framework, according to the actual trajectory of the leader USV and its expected relative pose with respect to the following USV. The time-domain mapping transformation module is used to construct time-domain mapping transformations, transforming the original finite-time domain... The time-specific formation control problem is mapped to an infinite time domain. The asymptotic convergence problem is solved, and the time-varying coefficients are calculated based on the time-domain mapping transformation. The specified performance constraint setting module is used to define the formation tracking error between the actual trajectory and the reference trajectory of the following unmanned surface vessel under the leader-follower formation framework, and to set a specified performance function to constrain the formation tracking error. The specified performance function has upper and lower bounds in the form of exponential convergence. The error transformation module is used to construct an error transformation function based on the specified performance function, convert the constrained formation tracking error into an unconstrained transformed error, and perform a time-domain mapping transformation on the transformed error to obtain an infinite time domain error. Transformation error under; The virtual control law design module is used to design virtual control laws using the backstepping method, and to use dynamic surface control technology to introduce a first-order filter to approximate the derivative of the virtual control law, so as to avoid directly differentiating the virtual control law. The control law and adaptive law design module is used to design infinite time domain based on the virtual control law. The system control law and adaptive law are used to estimate and compensate for unknown external environmental disturbances online; The time-domain inverse mapping and controller output module is used to transform the infinite time domain through the inverse transformation of the time-domain mapping transformation. Mapping the system control law and adaptive law back to the original finite time domain Obtain the formation controller and adaptive law at a specified time to drive the formation tracking error of each unmanned surface vessel within the specified time. A small neighborhood that converges to zero; The control input / output interface module is connected to the output terminal of the time-domain inverse mapping and controller output module, and is used to transmit the control signals output by the specified time formation controller and adaptive law to the actuators of each unmanned surface vessel, driving each unmanned surface vessel to move according to the formation control command.

[0013] Combining all the above technical solutions, the beneficial effects of this invention are as follows: First, this invention studies the time-bound formation control problem of unmanned surface vessels (USVs) with collision avoidance constraints and specified performance requirements. To solve the core challenge of time-bound control, this invention uses time-domain mapping technology to transform the time-bound convergence problem into an asymptotic convergence problem; combining backstepping and dynamic surface control techniques, a time-bound formation controller is designed; by constructing a suitable performance function, specified performance constraints are imposed on the formation error, thereby ensuring the collision avoidance requirements between the lead USV and the following USVs; based on Lyapunov stability theory, the designed controller can ensure that the USV formation error converges to a small neighborhood of zero within a specified time, providing a solid theoretical foundation for the practical application of time-bound formation control of USVs. According to the subsequent numerical simulation of three heterogeneous USVs, the simulation results show that the USV formation can achieve time-bound stability, and the trajectory diagram reflects collision avoidance between USVs, demonstrating that the formation error can achieve the specified performance constraints.

[0014] Secondly, it adapts to heterogeneous unmanned surface vessel (USV) systems, fitting practical engineering application scenarios. This invention is designed for heterogeneous scenarios where USVs within a formation differ in mass, moment of inertia, and hydrodynamic coefficients. It breaks through the traditional formation control scheme's assumption of identical isomorphic ideals for all vessel models, effectively avoiding problems such as decreased formation tracking accuracy and deteriorated system stability caused by model mismatch. This better aligns with real-world marine operations, possessing stronger practical value and scenario adaptability. Convergence time can be independently preset, ensuring strong task timeliness. This invention employs time-domain mapping technology, transforming the formation convergence problem within a finite time domain into an asymptotic convergence problem in an infinite time domain through variable transformation in the time domain. This allows the convergence time of formation tracking errors to be independently preset by the designer according to task requirements, and the convergence duration is independent of the system's initial state and control parameters. Compared to finite-time control and fixed-time control, this method completely eliminates the constraints of initial errors and control parameters on the convergence time, strictly matching marine operation scenarios with strict time requirements and ensuring the timeliness of formation task execution.

[0015] Third, the integrated design of specified performance and collision avoidance constraints balances control accuracy and operational safety. This invention integrates specified performance constraints and safety distance design into a unified control framework. By applying transient and steady-state performance boundary constraints to formation errors, it strictly ensures the control accuracy of formation tracking. Simultaneously, through the matching design of error boundary thresholds and safety distances, collision avoidance between unmanned surface vessels (USVs) is achieved. This integrated design achieves multiple objectives of control accuracy and operational safety while ensuring convergence within a specified time. It avoids control conflicts caused by the superposition of multiple independent control logics, improving the coordination and reliability of system operation. On the engineering side, formations can be directly assembled using heterogeneous USVs, reducing deployment and modification costs; the convergence time can be independently preset, ensuring the deterministic execution of time-sensitive tasks; the integrated design balances control accuracy and collision avoidance safety, avoiding control conflicts and accident risks caused by the superposition of multiple logics. Attached Figure Description

[0016] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the disclosure of this invention and, together with the description, serve to explain the principles of the disclosure of this invention. Figure 1 This is a flowchart of a heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance provided in an embodiment of the present invention. Figure 2 This is a leader-follower formation control framework diagram provided in an embodiment of the present invention; Figure 3 The position variable provided in the embodiments of the present invention Line graph; Figure 4 This is the formation error provided in the embodiments of the present invention. Line graph; Figure 5 This is the formation error provided in the embodiments of the present invention. Line graph; Figure 6 This is the formation error provided in the embodiments of the present invention. Line graph; Figure 7 The control input provided in the embodiments of the present invention Line graph; Figure 8 The control input provided in the embodiments of the present invention Line graph; Figure 9 The control input provided in the embodiments of the present invention Line graph. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0018] The innovation of this invention lies in: 1. This invention designs a formation controller for heterogeneous unmanned surface vessels (USVs), which can be directly adapted to mixed-operation scenarios of USVs of different models and parameters. This better aligns with the actual engineering practices of real-world marine operations, significantly improving the applicability and practical value of the formation control scheme. Furthermore, the invention introduces dynamic surface control technology into the controller design, avoiding repeated differentiation of the virtual control law in traditional backstepping designs through a first-order filtering mechanism. This greatly reduces the controller's computational complexity and hardware computing power requirements, making it more compatible with embedded control platforms for USVs and lowering the difficulty of engineering implementation.

[0019] 2. This invention applies specified performance constraints to the formation tracking error, enabling strict control over the convergence speed and steady-state accuracy of the error throughout the entire process, thus ensuring formation control accuracy from the root. Simultaneously, based on the transient boundary characteristics of the position error, a matching safety distance threshold is designed, utilizing the boundary characteristics of the error constraints to achieve collision avoidance between the following and lead vessels. This eliminates the need for an additional independent collision avoidance algorithm module, simultaneously achieving the dual goals of formation control accuracy and inter-vessel operational safety within a unified control framework, thereby improving the coordination and reliability of system operation.

[0020] 3. This invention employs a time-domain mapping method, transforming the formation control problem within a finite time domain into an asymptotic convergence problem in an infinite time domain through variable transformation in the time domain. Theoretically, this ensures that the system convergence time is completely independent of the system initial conditions and controller design parameters. The convergence duration can be flexibly and independently preset according to task requirements, significantly improving the time determinism and scenario adaptability of formation tasks, and providing reliable control technology support for high-time-efficiency marine operations.

[0021] Example 1 illustrates that this invention can be applied to two typical engineering scenarios: collaborative search and rescue at sea and timed regional marine mapping. It clarifies the specific application background of mixed-formation unmanned surface vessels (USVs) with different models and dynamic parameters performing missions. This invention ensures that the formation converges within a specified time, with tracking errors not exceeding the specified performance boundaries throughout the entire process. Simultaneously, it achieves collision avoidance between vessels, solving the practical engineering problems of poor adaptability, uncontrollable convergence time, and easy conflict due to multiple constraints in traditional isomorphic solutions.

[0022] like Figure 1As shown, the heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance provided in this embodiment of the invention includes the following steps: S1, Obtain from The kinematics and dynamics models of each unmanned surface vessel (USV) in the leader-follower formation are used to set the reference trajectory of the first USV in the formation. S2. Based on the leader-follower formation framework, a reference trajectory for the following unmanned surface vessel is generated according to the actual trajectory of the leader unmanned surface vessel and its expected relative pose with respect to the following unmanned surface vessel. S3. Construct a time-domain mapping transformation to transform the original finite time domain... The time-specific formation control problem is mapped to an infinite time domain. The asymptotic convergence problem is solved, and the time-varying coefficients are calculated based on the time-domain mapping transformation. S4. Under the leader-follower formation framework, define the formation tracking error between the actual trajectory of the following unmanned surface vessel and the reference trajectory, and set a specified performance function to constrain the formation tracking error. The specified performance function has upper and lower bounds in the form of exponential convergence. S5. Construct an error transformation function based on the specified performance function to convert the constrained formation tracking error into an unconstrained transformation error, and perform a time-domain mapping transformation on the transformation error to obtain an infinite time-domain error. Transformation error under; S6. The virtual control law is designed using the backstepping method, and a first-order filter is introduced using dynamic surface control technology to approximate the derivative of the virtual control law, so as to avoid directly differentiating the virtual control law. S7. Design an infinite time domain based on the virtual control law. The system control law and adaptive law are used to estimate and compensate for unknown external environmental disturbances online; S8. Through the inverse transformation of the time-domain mapping transformation, the infinite time domain is transformed... Mapping the system control law and adaptive law back to the original finite time domain Obtain the formation controller and adaptive law at a specified time to drive the formation tracking error of each unmanned surface vessel within the specified time. The small neighborhood converges to zero, and the formation tracking error always satisfies the specified performance function constraint, thereby achieving collision avoidance between the lead unmanned surface vessel and the follower unmanned surface vessel.

[0023] To enable those skilled in the art to fully understand and implement this invention, the technical details involved in each step are explained in detail below, in conjunction with specific mathematical models and derivation processes.

[0024] A. Description of the unmanned surface vessel system; The heterogeneous unmanned surface vessel (USV) formation described in this invention refers to a formation in which the dynamic parameters of each USV within the formation, such as mass, moment of inertia, and hydrodynamic coefficient, vary individually; subscripts are used. Parameters (inertia matrix) Coriolis matrix Damping matrix (etc.) respectively correspond to the first Each unmanned surface vessel (USV) has its own independent parameter set, and the parameter values ​​may differ between different USVs. Considering the USV formation... Composed of 10 unmanned surface vessels, the first The kinematic and dynamic equations of an unmanned surface vessel can be expressed by the following expression: ; ; In the formula, Let be a rotation matrix. Rotation matrix The expression is: ; In the formula, , This refers to the location in the geodetic coordinate system. For heading angle; , For oscillation speed, The drift speed, To bypass The bow roll rate of the shaft; The inertia matrix, The Coriolis centripetal force matrix, Here is the damping parameter matrix; This is the control input vector for the unmanned surface vessel. These are the pitch thrust, drift thrust, and yaw moment of the unmanned surface vessel. This is the vector of external environmental disturbances caused by wind, waves, and ocean currents; Assuming the mass of the unmanned surface vessel is uniformly distributed, then the matrix... , and The expression is: ; ; ; In the formula, , , , , For unknown parameters; For the quality of unmanned surface vessels, The distance from the center of gravity of the unmanned surface vessel to the origin of the hull coordinate system. For the bow roll moment of inertia, , and These are hydrodynamic parameters; Assumption 1: Consider that the unknown environmental disturbances are bounded, that is: ; in, It is an unknown positive number. .

[0025] B. Leader-follower formation control framework; Consider by A leader-follower formation framework consisting of unmanned surface vessels, such as Figure 2 As shown, Using the geodetic coordinate system, Let be the ship's coordinate system. The reference trajectory of the first unmanned surface vessel is... Connectivity between each unmanned surface vessel is maintained, considering the first... Unmanned surface vessel tracking the first The unmanned surface vessel's reference trajectory is designed as follows: ; in, , Representing the The trajectory of the unmanned surface vessel , , and These are design parameters.

[0026] Since there is no need to consider the first unmanned surface vessel and the reference trajectory The invention is designed to avoid collisions. , and when It can be designed For appropriate values. In actual formation tasks, , and It is designed to be a time-varying value or a constant value to meet the needs of different tasks.

[0027] Assumption 2: Reference Trajectory and its derivative It is bounded.

[0028] C. Time-domain mapping technology; Define the following time-domain mapping: ; In the formula, For a specified time, Constrained in a finite time domain Establish a finite time domain and infinite time domain Mapping relationship between them: ; In the formula, To define symbols, This is a time-scale transformation function. interval Mapped to ; interval Mapped to In controller design, it is desirable to incorporate the time domain... The problem of specified time control is transformed into the time domain. The asymptotic convergence problem on the time domain. Therefore, by using equation (2) to transform the infinite time domain variables. The derivative introduces a time-varying coefficient: ; In the formula, is the time-varying coefficient.

[0029] Formulas (1) and (2) define a time-domain mapping transformation to transform the time domain... Transform to the time domain Transforming the specified time control problem into an asymptotic convergence problem is the core technology for achieving specified time control. Based on the definitions of time-domain mapping transformation in formulas (1) and (2), formula (3) introduces time-varying coefficients, which is the key to time-domain transformation and plays an important role in the indirect design of specified time controllers.

[0030] D. Specify performance constraints and collision avoidance; Within the leader-follower formation framework, the formation error is defined as follows: ; ; ; In the formula, For about Orientational formation error, For about Orientational formation error, For formation error with respect to rudder angle direction, These represent the system status of the unmanned surface vessel. These are the desired states for the system state design; To ensure the specified performance constraints on formation error, consider the following inequality: ; In the formula, For formation error, and These are the upper and lower bounds of the time-varying formation error, respectively. The upper and lower bounds of the formation error are designed as exponentially convergent functions as follows: ; ; In the formula, , , , and Positive parameter, constant and Indicates that when the condition is met and The maximum allowable steady-state tracking error at that time .

[0031] According to equation (4), the position error is expressed as: ; In the formula, This represents the actual position error; Set position error constraints: ; In the formula, The desired distance between unmanned surface vessels. To maintain a safe distance between the following unmanned surface vessel (USV) and the lead USV, .

[0032] Formula (5) defines the specified performance constraints of the formation error and gives the upper and lower bounds of the formation error constraints. Through the designed formation control framework, Formula (8) links the collision avoidance problem with the performance constraint problem, and realizes the collision avoidance between unmanned surface vessels through the specified performance constraints of the error.

[0033] E. Design of a time-specific formation controller; A smooth and strictly monotonically increasing error transformation function is introduced. This function guarantees that the system satisfies the constraint inequality (5), as expressed below: ; In the formula, , For an intrinsically bounded function space, This is the conversion error; The error transformation function Defined as: ; In the formula, for of Power of 1 for of Power of 1 for of Power; Define the following equation: ; Substituting equation (10) into equation (11), we get: ; In order to obtain The derivative of , taking the logarithm of both sides of equation (12): ; In the formula, and These are the upper and lower bounds of the time-varying formation error, respectively.

[0034] According to equations (4) and (13), for time The derivative is: ; ; ; in: ; ; According to equations (11) and (15), we obtain .

[0035] when By multiplying equations (3) and (14), the state variables are obtained. For variables The derivative: ; ; ; By using time-domain mapping techniques, the original control problem is transformed into a problem defined in the time domain. The asymptotic convergence problem on the equation. This is because there are time-varying coefficients in equation (16). In the subsequent controller design, this invention introduces a gain term. To compensate for the efficiency loss caused by the time-varying coefficient.

[0036] Step 1: Define the following transformation: ; ; ; ; ; In the formula, for transformation, For filtering error, for transformation, These are the filtered virtual control vector and virtual controller vector. for Transformation; Let V be the velocity vector of the unmanned surface vessel. Consider the following Lyapunov function: ; The virtual controller is designed as follows: ; ; ; In the formula, As an intermediate variable, for about The derivative of for of Power; in: ; ; In the formula, For system parameters, For the corresponding parameters with respect to time The derivative; ; According to formula (19) of the virtual controller, we get: ; in: ; In the backstepping control framework, the controller design requires incorporating the derivative of formula (19) of the virtual controller. However, the derivative of the virtual controller includes the acceleration of the pilot unmanned surface vessel, which is difficult to measure in practical engineering. To address this challenge, this invention employs dynamic surface control technology to avoid the need for differentiation in the virtual control.

[0037] Introduce the following filter: ; In the formula, The filtering time constant is , , .

[0038] Through the filter formula (22). For variables The derivative can be obtained. Among them, Represented as the filtering time constant, , , .

[0039] According to equations (17) and (22), we obtain For variables The derivative: ; in, , , According to equation (19), , , It is a continuous function.

[0040] Consider the following Lyapunov function: ; in, , , Indicates to The estimate, To estimate the error, .

[0041] Apply equation (24) to the variables Differentiate: ; Design Time Domain The controller and adaptive law are as follows: ; ; definition for: ; In the formula, Represents the hyperbolic tangent function. , , These are design parameters. .

[0042] Based on the above analysis, the time domain is obtained. The formation controller on the top. Through time-domain mapping transformation of equations (1) to (3), we obtain The specified time array controller and adaptive law are as follows: ; ; ; ; ; in, ; and , .

[0043] for In order to ensure the control target, select The corresponding formation controller is as follows: ; ; ; Equations (19), (26), and (27) are used to design the time domain. The virtual controller, control law, and adaptive law under the given conditions achieve asymptotic convergence of the formation. The time-domain data is indirectly obtained through time-domain mapping transformation. The specified time formation controller and adaptive law are given by formulas (28), (29) and (30). The controller is designed to ensure that the formation error of the unmanned surface vessel converges to a small neighborhood of zero within a specified time, and to achieve specified performance constraints on the error and collision avoidance between unmanned surface vessels.

[0044] F. Stability analysis; Theorem 1: Based on Assumptions 1 and 2, consider the following... The leader-follower formation framework, consisting of 10 unmanned surface vessels (USVs), under the control of the controller and the adaptive law, ensures that the formation tracking error converges to a small neighborhood of zero within a specified time. All signals in the closed-loop system are bounded, guaranteeing the specified performance constraints of the formation error and avoiding collisions between the leader and follower USVs.

[0045] Proof: Based on Assumption 1 and Young's inequality, we can obtain the following inequality: ; ; Furthermore, due to the properties of the hyperbolic tangent function, we can obtain: ; ;

[0046] According to Yang's inequality, we can obtain: ; ; in, .

[0047] Based on equations (33) and (34), substituting equations (26) and (27) into equation (25), we can obtain: ; in, ; ; In the formula, and These represent the minimum and maximum values ​​of the corresponding matrix eigenvalues, respectively.

[0048] According to equation (35), for : ; in, , .

[0049] when According to equations (24) and (36), we can obtain: ; ; ; ; According to equation (37), by appropriately adjusting the parameters It can guarantee The exponent converges to a small neighborhood of zero. Because... Boundedness, It is also bounded, and more so than The convergence is faster. The formation error can be deduced using equations (9) and (11). The exponential convergence to a small neighborhood of zero is achieved. The tracking error is determined through the time-domain mapping relationships (1)-(3). Can be done at a specified time The small neighborhood converges to zero. Based on the above analysis, the error variable can be derived using equation (37). , , and It is bounded. According to equation (4), the state of the unmanned surface vessel... It is bounded. and The boundedness guarantees and The boundedness of and in equation (17) Boundedness. Through The boundedness of [the property] can guarantee [the property]. and The boundedness of the signal. Therefore, the formation controller is bounded, meaning that all signals in the closed-loop system are bounded.

[0050] according to The boundedness of, assuming ,in From equations (10) and (11), we can obtain: ; in, The lower bound is The upper boundary is .

[0051] consider right Taking the derivative, we get: ; get and This ensures that the specified performance constraints are met. Therefore, it can be inferred that ,or According to equation (6), we obtain , And it has: ; in, , By selecting appropriate design parameters and It can satisfy: ; Therefore, it is satisfied. This means that collision avoidance is achieved between the lead unmanned surface vessel (USV) and the following USV.

[0052] This invention studies the time-limited formation control problem of heterogeneous unmanned surface vessels (USVs) with collision avoidance constraints and specified performance requirements. To solve the core challenge of time-limited control, a time-domain mapping technique is used to transform the time-limited convergence problem into an asymptotic convergence problem. Combining backstepping and dynamic surface control techniques, a time-limited formation controller is designed. Simultaneously, by constructing a suitable performance function, specified performance constraints are imposed on the formation error, thereby indirectly ensuring the collision avoidance requirements between USVs. Based on Lyapunov stability theory, the designed controller ensures that the USV formation error converges to a small neighborhood of zero within a specified time, providing a solid theoretical foundation for the practical application of time-limited formation control of heterogeneous USVs.

[0053] Example 2, the heterogeneous unmanned surface vessel (USV) formation control system with specified performance constraints and collision avoidance provided in this embodiment of the invention includes: The data acquisition and model building module is used to acquire the kinematic and dynamic models of each unmanned surface vessel in a leader-follower formation consisting of N heterogeneous unmanned surface vessels, and to set the reference trajectory of the first unmanned surface vessel in the formation. The reference trajectory generation module is used to generate the reference trajectory of the following unmanned surface vessel (USV) based on the leader-follower formation framework, according to the actual trajectory of the leader USV and its expected relative pose with respect to the following USV. The time-domain mapping transformation module is used to construct time-domain mapping transformations, transforming the original finite-time domain... The time-specific formation control problem is mapped to an infinite time domain. The asymptotic convergence problem is solved, and the time-varying coefficients are calculated based on the time-domain mapping transformation. The specified performance constraint setting module is used to define the formation tracking error between the actual trajectory and the reference trajectory of the following unmanned surface vessel under the leader-follower formation framework, and to set a specified performance function to constrain the formation tracking error. The specified performance function has upper and lower bounds in the form of exponential convergence. The error transformation module is used to construct an error transformation function based on the specified performance function, convert the constrained formation tracking error into an unconstrained transformed error, and perform a time-domain mapping transformation on the transformed error to obtain an infinite time domain error. Transformation error under; The virtual control law design module is used to design virtual control laws using the backstepping method, and to use dynamic surface control technology to introduce a first-order filter to approximate the derivative of the virtual control law, so as to avoid directly differentiating the virtual control law. The control law and adaptive law design module is used to design infinite time domain based on the virtual control law. The system control law and adaptive law are used to estimate and compensate for unknown external environmental disturbances online; The time-domain inverse mapping and controller output module is used to transform the infinite time domain through the inverse transformation of the time-domain mapping transformation. Mapping the system control law and adaptive law back to the original finite time domain Obtain the formation controller and adaptive law at a specified time to drive the formation tracking error of each unmanned surface vessel within the specified time. A small neighborhood that converges to zero; The control input / output interface module is connected to the output terminal of the time-domain inverse mapping and controller output module. It is used to transmit the control signals output by the specified time formation controller and adaptive law to the actuators of each unmanned surface vessel (USV), driving each USV to move according to the formation control command. In theory, time-domain mapping technology can be used to achieve time-specific formation control of unmanned surface vessels (USVs). Compared with fixed-time and finite-time control, the convergence time of the proposed controller is independent of the initial state of the system and is not affected by design parameters. At the same time, by designing performance functions, specified performance constraints on formation errors are achieved, which indirectly avoids collisions between USVs.

[0054] To demonstrate the effectiveness of the time-specific formation controller, this invention considers a leader-follower formation control framework consisting of three heterogeneous unmanned surface vessels (USVs). The mass parameters of the USVs are as follows: , , , , , , , , , , , The length of the unmanned surface vessel is The damping term is defined as: , , , , Unknown environmental interference is , , .

[0055] The specified performance constraint function is designed as follows: , , , , Choose a safe distance. , , , , , Reference trajectory .

[0056] The controller design parameters are as follows: , , , , , The initial conditions are set as follows: , , , , Specified time Second.

[0057] The dynamic parameters, such as mass and damping, are taken from the typical hydrodynamic characteristics of small unmanned surface vessels (USVs), conforming to the conventional parameter range for USV modeling in the field of marine engineering. Control parameters and specified convergence time are also included. Key parameters such as safety distance are carefully selected. First, the positive definiteness of the relevant conditions of Lyapunov's theorem in the theoretical derivation must be ensured. Simultaneously, following the principles of marine engineering control design, a balance must be struck between convergence time accuracy and environmental disturbance robustness. The control gain needs to be sufficient to drive the formation error to converge within a specified time, while avoiding excessive gain that would amplify the impact of environmental disturbances. The safety distance is set at 1.2m to match the initial state of the hull size, and the initial formation distance is selected to take into account transient response characteristics.

[0058] Depend on Figure 3 It can be seen that the three unmanned surface vessels (USVs) follow the reference trajectory designed for them, and that the lead USV and the follower USV avoid collisions. Figures 4-6 Formation error , and The curve graph, by Figures 4-6 It can be seen that the formation error is constrained within the specified range. Figures 7-9 These represent the control inputs of the three unmanned surface vessels. , and The curve graph. Figure 2 For the leader-follower formation control framework, Figure 3 For position variable curves, Figure 4 for Formation error curves in direction, Figure 5 for Formation error curves in direction, Figure 6 The formation error curve is shown in the rudder angle direction. Figure 7 The curve for the first component of the control input for the three unmanned surface vessels. Figure 8 The curve for the second component of the control input for the three unmanned surface vessels. Figure 9The curves for the third component of the control input for the three unmanned surface vessels are shown. Before the switch, the control input is equation (29), and after the switch, it is equation (31). That is, after the system stabilizes at a specified time through time-domain mapping technology, equation (31) ensures the stable state of the system thereafter. From the above results, it can be seen that the formation error can converge to a small neighborhood of zero within a specified time, and all signals in the system are bounded.

[0059] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for controlling heterogeneous unmanned surface vessels (USVs) formations with specified performance constraints and collision avoidance, characterized in that, The method includes the following steps: S1, Obtain from The kinematics and dynamics models of each unmanned surface vessel (USV) in the leader-follower formation are used to set the reference trajectory of the first USV in the formation. S2. Based on the leader-follower formation framework, a reference trajectory for the following unmanned surface vessel is generated according to the actual trajectory of the leader unmanned surface vessel and its expected relative pose with respect to the following unmanned surface vessel. S3. Construct a time-domain mapping transformation to transform the original finite time domain... The time-specific formation control problem is mapped to an infinite time domain. The asymptotic convergence problem is solved, and the time-varying coefficients are calculated based on the time-domain mapping transformation. S4. Under the leader-follower formation framework, define the formation tracking error between the actual trajectory of the following unmanned surface vessel and the reference trajectory, and set a specified performance function to constrain the formation tracking error. The specified performance function has upper and lower bounds in the form of exponential convergence. S5. Construct an error transformation function based on the specified performance function to convert the constrained formation tracking error into an unconstrained transformation error, and perform a time-domain mapping transformation on the transformation error to obtain an infinite time-domain error. Transformation error under; S6. The virtual control law is designed using the backstepping method, and a first-order filter is introduced using dynamic surface control technology to approximate the derivative of the virtual control law, so as to avoid directly differentiating the virtual control law. S7. Design an infinite time domain based on the virtual control law. The system control law and adaptive law are used to estimate and compensate for unknown external environmental disturbances online; S8. Through the inverse transformation of the time-domain mapping transformation, the infinite time domain is transformed... Mapping the system control law and adaptive law back to the original finite time domain Obtain the formation controller and adaptive law at a specified time to drive the formation tracking error of each unmanned surface vessel within the specified time. The small neighborhood converges to zero, and the formation tracking error always satisfies the specified performance function constraint, thereby achieving collision avoidance between the lead unmanned surface vessel and the follower unmanned surface vessel.

2. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 1, characterized in that, In step S3, the construction of the time-domain mapping transformation includes: Establishing a finite time domain and infinite time domain Mapping relationship between them: ； In the formula, For a specified time, Constrained in a finite time domain ; ； In the formula, To define symbols, This is a time-scale transformation function. interval Mapped to ; In controller design, it is desirable to utilize the finite time domain. The problem of controlling a specified time on a given time domain is transformed into an infinite time domain problem. asymptotic convergence problem; For the infinite time domain of the transformed variables The derivative introduces a time-varying coefficient: ； In the formula, is the time-varying coefficient.

3. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 1, characterized in that, In step S4, the formation tracking error is defined as: ； ； ； In the formula, For about Orientational formation error, For about Orientational formation error, For formation error with respect to rudder angle direction, These represent the system status of the unmanned surface vessel. These are the desired states for the system state design; The specified performance function is set to the following inequality constraint form: ； In the formula, For formation error, and These are the upper and lower bounds of the time-varying formation error, respectively. The upper and lower bounds of the formation error are designed as exponentially convergent functions as follows: ； ； In the formula, , , , and Positive parameter, constant and Indicates that the condition is met and The maximum allowable steady-state tracking error at that time .

4. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 3, characterized in that, In step S8, collision avoidance between the lead unmanned surface vessel (USV) and the follower USV is achieved in the following manner: Define the actual position error between the following unmanned surface vessel (USV) and the lead USV: ； In the formula, This represents the actual position error; Set position error constraints: ； In the formula, The desired distance between unmanned surface vessels. To maintain a safe distance between the following unmanned surface vessel (USV) and the lead USV, .

5. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 4, characterized in that, In step S5, the error transformation function is a smooth and strictly monotonically increasing function. It meets the following conditions: ； In the formula, , For an intrinsically bounded function space, This is the conversion error; The error transformation function Defined as: ； In the formula, for of Power of 1 for of Power of 1 for of Power; The relationship between formation tracking error and conversion error is as follows: ； Conversion error Solve using the following algebraic equation: ； In the formula, and These are the upper and lower bounds of the time-varying formation error, respectively.

6. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 5, characterized in that, In step S6, the virtual control law is in the infinite time domain. The following design is as follows: Define the following transformation: ； ； ； ； ； In the formula, for transformation, For filtering error, for transformation, These are the filtered virtual control vector and virtual controller vector. for Transformation; Let V be the velocity vector of the unmanned surface vessel. ； ； ； In the formula, As an intermediate variable, for about The derivative of for of Power; The intermediate variable is: ； ； In the formula, For system parameters, For the corresponding parameters with respect to time The derivative; ; The first-order filter introduced in dynamic surface control technology in the infinite time domain The following design is as follows: ； In the formula, The filtering time constant is , , .

7. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 6, characterized in that, In step S7, the infinite time domain The system control law is designed as follows: ； ； ； The infinite time domain The adaptive law design is as follows: ； In the formula, For design parameters, for The absolute value, ; definition for: ； In the formula, , , For design parameters, .

8. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 7, characterized in that, In step S8, the infinite time domain is... Mapping the system control law and adaptive law back to the original finite time domain Obtaining the formation controller and adaptive law at a specified time includes: ； ； ； ； definition for: ； In the formula, , ; for ,Pick The corresponding formation controller is switched to: 。 9. The heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance according to claim 8, characterized in that, In step S1, obtain from The kinematic and dynamic models of each unmanned surface vessel (USV) in a leader-follower formation composed of heterogeneous USVs are as follows: ； ； In the formula, Let be a rotation matrix. Rotation matrix The expression is: ； In the formula, , This refers to the location in the geodetic coordinate system. For heading angle; , For oscillation speed, The drift speed, To bypass The bow roll rate of the shaft; The inertia matrix, The Coriolis centripetal force matrix, Here is the damping parameter matrix; This is the control input vector for the unmanned surface vessel. These are the pitch thrust, drift thrust, and yaw moment of the unmanned surface vessel. This is the vector of external environmental disturbances caused by wind, waves, and ocean currents; Assuming the mass of the unmanned surface vessel is uniformly distributed, then the matrix... , and The expression is: ； ； ； In the formula, , , , , For unknown parameters; For the quality of unmanned surface vessels, The distance is the distance from the center of gravity of the unmanned surface vessel to the origin of the vessel's coordinate system. For the bow roll moment of inertia, , and These are hydrodynamic parameters; External environmental disturbance vector The following boundedness conditions must be met: ； In the formula, For an unknown positive number, ; The reference trajectory of the first unmanned surface vessel was If the first Unmanned surface vessel tracking the first The reference trajectory for each unmanned surface vessel (USV) is generated using the following formula: ； In the formula, , For the first The trajectory of the unmanned surface vessel , , and Design parameters; reference trajectory and its derivative It is bounded.

10. A heterogeneous unmanned surface vessel (USV) formation control system with specified performance constraints and collision avoidance, characterized in that, This system is used to implement the heterogeneous unmanned surface vessel (USV) formation control method with specified performance constraints and collision avoidance as described in any one of claims 1 to 9, and the system includes: The data acquisition and model building module is used to acquire the kinematic and dynamic models of each unmanned surface vessel in a leader-follower formation consisting of N heterogeneous unmanned surface vessels, and to set the reference trajectory of the first unmanned surface vessel in the formation. The reference trajectory generation module is used to generate the reference trajectory of the following unmanned surface vessel (USV) based on the leader-follower formation framework, according to the actual trajectory of the leader USV and its expected relative pose with respect to the following USV. The time-domain mapping transformation module is used to construct time-domain mapping transformations, transforming the original finite-time domain... The time-specific formation control problem is mapped to an infinite time domain. The asymptotic convergence problem is solved, and the time-varying coefficients are calculated based on the time-domain mapping transformation. The specified performance constraint setting module is used to define the formation tracking error between the actual trajectory and the reference trajectory of the following unmanned surface vessel under the leader-follower formation framework, and to set a specified performance function to constrain the formation tracking error. The specified performance function has upper and lower bounds in the form of exponential convergence. The error transformation module is used to construct an error transformation function based on the specified performance function, convert the constrained formation tracking error into an unconstrained transformed error, and perform a time-domain mapping transformation on the transformed error to obtain an infinite time domain error. Transformation error under; The virtual control law design module is used to design virtual control laws using the backstepping method, and to use dynamic surface control technology to introduce a first-order filter to approximate the derivative of the virtual control law, so as to avoid directly differentiating the virtual control law. The control law and adaptive law design module is used to design infinite time domain based on the virtual control law. The system control law and adaptive law are used to estimate and compensate for unknown external environmental disturbances online; The time-domain inverse mapping and controller output module is used to transform the infinite time domain through the inverse transformation of the time-domain mapping transformation. Mapping the system control law and adaptive law back to the original finite time domain Obtain the formation controller and adaptive law at a specified time to drive the formation tracking error of each unmanned surface vessel within the specified time. A small neighborhood that converges to zero; The control input / output interface module is connected to the output terminal of the time-domain inverse mapping and controller output module, and is used to transmit the control signals output by the specified time formation controller and adaptive law to the actuators of each unmanned surface vessel, driving each unmanned surface vessel to move according to the formation control command.

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