Unified fixed time and preset time control method and system for USV-AUV cooperative trajectory tracking

Abstract

The invention provides a unified fixed time and preset time control method and system for USV-AUV cooperative trajectory tracking, and the method comprises the following steps: S1, task trajectory generation and modeling, S2, construction of a unified fixed time and preset time function, and giving of a stability condition, S3, state acquisition and time scaling error construction, and S4, state acquisition and time scaling error construction. The method comprises the steps of S1, establishing a first Lyapunov function and designing a virtual control law, S2, establishing a second Lyapunov function and designing a control law, and S6, establishing an overall Lyapunov function and analyzing preset time stability. According to the technical scheme, the control input can be always kept in an amplitude range which can be realized by a project, and unrealizable singular behaviors of the control gain at a specific moment are avoided, so that the main obstacle that a traditional preset time strategy is difficult to deploy in an actual system is overcome; and the engineering implementability of the method in an offshore operation scene is obviously improved.

Description

Technical Field

[0001] This invention relates to the field of trajectory tracking and control technology for unmanned systems, and in particular to a unified fixed-time and preset-time control method and system for cooperative trajectory tracking of USV-AUV. Background Technology

[0002] In missions such as ocean observation, seabed target detection, equipment inspection, and emergency search and rescue, heterogeneous collaborative systems composed of unmanned surface vessels (USVs) and underwater vehicles (AUVs) have become an important means to improve the efficiency of marine operations. USVs handle positioning and communication relay functions, while AUVs are responsible for underwater operations and detailed detection. The two achieve cross-domain division of labor and collaborative operations through coordinated trajectory tracking. However, under long-term environmental disturbances and complex ocean currents, the efficiency and stability of the system's collaborative control remain difficult to reliably guarantee.

[0003] In many maritime mission scenarios, the control performance of trajectory tracking depends not only on control accuracy but also significantly on time constraints. For example, in maritime search and rescue and rapid inspection missions, unmanned systems must reach the target state within a specified time; otherwise, mission delays or resource waste may occur. Therefore, time-indicating control methods that can achieve error convergence within a defined time range have received continuous attention, leading to the development of two main types of methods: fixed-time control and preset-time control. Fixed-time control allows the system state to converge within a time bound independent of initial conditions, but its practical application is limited in two ways: first, excessively large control inputs often occur in the initial stage, weakening the engineering feasibility of the method; second, the theoretical convergence time estimate is often conservative, making it difficult to guarantee compact time performance in practical engineering. Preset-time control further allows users to pre-specify the convergence time, giving the system higher time determinism. However, such methods generally rely on a gain structure that diverges as time approaches the preset time point, resulting in infinite gain in the control law near the convergence moment, making it difficult to implement in physical actuators. Furthermore, the control laws of many preset time control methods are only effective within a preset time interval and cannot continue to work after the interval is exceeded, thus limiting their application in actual engineering environments. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a unified fixed-time and preset-time control method and system for cooperative trajectory tracking of USV-AUVs. This method, within a unified control framework, suppresses the excessively large initial input of fixed-time control and avoids the gain divergence problem of preset-time control at preset points, thereby achieving a time-controllable and stable convergence process and ensuring that the control input remains within a reasonable range, thus improving the engineering practicality of the control strategy. Through the above design, the USV-AUV system can achieve time-controllable cooperative trajectory tracking performance while meeting engineering feasibility requirements.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking, comprising the following steps:

[0006] Step S1: Mission trajectory generation and modeling; First, based on the mission requirements, the desired trajectory of the USV-AUV cooperative trajectory tracking mission is generated at the shore-based end, and a three-degree-of-freedom USV nonlinear kinematics and dynamics model considering environmental interference and a four-degree-of-freedom AUV nonlinear kinematics and dynamics model considering environmental interference are constructed.

[0007] Step S2: Construct a unified fixed time and a preset time function and provide stability conditions;

[0008] Step S3: Obtain the current motion state of the unmanned surface vessel and the underwater vehicle through the sensors on the unmanned surface vessel and the underwater vehicle, compare it with the expected trajectory, construct the tracking error of the unmanned surface vessel and the underwater vehicle, and further construct the time scaling error based on the constructed unified fixed time and the preset time function.

[0009] Step S4: Construct the first Lyapunov function for the unmanned surface vessel and the underwater vehicle respectively, and obtain the corresponding virtual control law based on the backstepping method;

[0010] Step S5: Based on step S4, construct the second Lyapunov function for the unmanned surface vessel and the underwater vehicle respectively, and obtain the corresponding control law based on the backstepping method;

[0011] Step S6: Construct the Lyapunov function of the overall system for both the unmanned surface vessel and the underwater vehicle and conduct stability analysis, ensuring that the tracking error converges to the convergence domain within a preset time.

[0012] In a preferred embodiment, step 1 involves constructing a three-degree-of-freedom USV nonlinear kinematic and dynamic model that considers environmental disturbances, as shown in the following formula:

[0013]

[0014]

[0015] in, It is the actual trajectory vector composed of the unmanned surface vessel's position and bow angle information in the ground coordinate system, where, This indicates the actual position of the unmanned surface vessel in the inertial coordinate system. For the bow roll angle of the unmanned surface vessel, The first derivative of the actual trajectory vector, which is composed of the unmanned surface vessel's position and bow angle information in the ground coordinate system, is given. The sway velocity of the unmanned surface vessel in the attached coordinate system sway speed and bow roll rate The actual velocity vector formed It represents the first derivative of the actual velocity vector consisting of the pitch velocity, sway velocity, and yaw rate of the unmanned surface vessel in the attached coordinate system; Let represent the control input vector of the unmanned surface vessel, where For longitudinal force, It is a lateral force. This is the yaw moment; Let represent the unknown perturbation vector experienced by the unmanned surface vessel in the appendage coordinate system, where For longitudinal disturbances, This is a lateral disturbance. This is a yaw disturbance; It is a coordinate system transformation matrix based on unmanned surface vessels; It is based on the positive definite inertial matrix of the unmanned surface vessel; It is a Coriolis centripetal matrix based on unmanned surface vessels; It is based on the damping matrix of the unmanned surface vessel. Real number field;

[0016] A nonlinear kinematic and dynamic model of a four-degree-of-freedom AUV considering environmental disturbances is constructed, as shown in the following formula:

[0017]

[0018]

[0019] in, The actual trajectory vector is composed of the underwater vehicle's position and bow angle information in the terrestrial coordinate system, where... This indicates the actual position of the underwater vehicle in the inertial coordinate system. For the bow roll angle of the unmanned surface vessel; The first derivative of the actual trajectory vector composed of the position and bow angle information of the underwater vehicle in the terrestrial coordinate system; The sway velocity of the underwater vehicle based on the attached coordinate system sway speed Vertical velocity and bow roll rate The actual velocity vector formed; The first derivative of the actual velocity vector of an underwater vehicle based on the attached coordinate system, consisting of its pitch velocity, sway velocity, vertical velocity, and yaw rate. The control input vectors of the underwater vehicle are represented by the longitudinal torque. lateral moment Vertical moment and yaw moment ; Let represent the unknown disturbance vector experienced by the underwater vehicle in the appendage coordinate system, where Indicates longitudinal interference. Indicates lateral interference. Indicates vertical interference. Indicates yaw interference; It is a coordinate system transformation matrix based on underwater vehicles; It is based on the positive definite inertial matrix of the underwater vehicle; It is based on the Coriolis centripetal matrix of underwater vehicles; It is based on the damping matrix of underwater vehicles; The restoring force term is related to gravity and buoyancy, and T denotes transpose.

[0020] In a preferred embodiment, in step 2, a unified fixed time and a preset time function are constructed. As shown in the following formula:

[0021]

[0022] in, It is a time transformation function. t represents time. It is a preset time point and It is a preset time switching point; g is a finite positive integer representing the power.

[0023] If the Lyapunov function of the constructed system satisfy ,in, Represents Lyapunov functions If the first derivative of is given, then the system satisfies the preset time convergence, and the region of convergence is: ,in, , The coefficients are positive constants. It is a positive constant between 0 and 1; , It is a constant exponential parameter, and , , ;and It is a bounded positive constant used to characterize the upper bound of uncertainty and external disturbances in a system.

[0024] In a preferred embodiment, step 3 specifically includes:

[0025] First, the unmanned surface vessel trajectory tracking error and time scaling error are constructed as shown in the following formula:

[0026]

[0027]

[0028] in, and These represent the position error and velocity error of the unmanned surface vessel, respectively. and These represent the position-time scaling error and velocity-time scaling error of the unmanned surface vessel, respectively. This represents the virtual control law of the unmanned surface vessel. This represents the actual trajectory vector composed of the unmanned surface vessel's position and bow angle information in the ground coordinate system. This represents the desired trajectory of the unmanned surface vessel. This represents a unified fixed time and a preset time function. This represents the actual velocity vector consisting of the unmanned surface vessel's pitch velocity, sway velocity, and yaw rate in the attached coordinate system.

[0029] Next, the trajectory tracking error and time scaling error of the underwater vehicle are constructed as shown in the following formula:

[0030]

[0031] (9)

[0032] in, and These represent the position error and velocity error of the underwater vehicle, respectively. and These represent the position-time scaling error and velocity-time scaling error of the underwater vehicle, respectively. This represents the virtual control law for underwater vehicles. The actual trajectory vector is composed of the underwater vehicle's position and bow angle information in the terrestrial coordinate system. This represents the desired trajectory of the underwater vehicle. It is the actual velocity vector composed of the sway velocity, roll velocity, vertical velocity, and bow angular velocity of the underwater vehicle based on the attached coordinate system.

[0033] In a preferred embodiment, step 4 specifically includes:

[0034] For the first Lyapunov function used to construct the unmanned surface vessel :

[0035]

[0036] represent the position and time scaling error of the unmanned surface vessel, respectively, and T represents the transpose;

[0037] Based on the backstepping method and combined with the dynamics and kinematics model of the unmanned surface vessel (USV), the virtual control law of the USV is obtained:

[0038]

[0039] in, , , and It is a positive constant, among which ; This represents the inverse matrix of the coordinate system transformation matrix based on the unmanned surface vessel. The first derivative of a function with a uniform fixed time and a preset time is represented. This represents the inverse function of a function that represents a uniform fixed time versus a preset time. This indicates the positional error of the unmanned surface vessel. The first derivative of the desired trajectory of the unmanned surface vessel;

[0040] Construct the first Lyapunov function for an underwater vehicle :

[0041]

[0042] This indicates the position and time scaling error of an underwater vehicle.

[0043] Based on the backstepping method and combined with the dynamics and kinematics model of the underwater vehicle, the virtual control law of the underwater vehicle is obtained:

[0044]

[0045] in, , , and It is a positive constant, among which ; This represents the inverse matrix of the coordinate system transformation matrix based on the underwater vehicle. This indicates the positional error of the underwater vehicle. This represents the first derivative of the desired trajectory based on the underwater vehicle.

[0046] In a preferred embodiment, step 5 specifically includes:

[0047] First, construct a second Lyapunov function for the unmanned surface vessel. :

[0048]

[0049] represent the speed-time scaling error of the unmanned surface vessel, respectively, and T represents the transpose;

[0050] Based on the backstepping method and combined with the dynamics and kinematics model of the unmanned surface vessel, the control law of the unmanned surface vessel is obtained. :

[0051]

[0052] in, , , and It is a positive constant, among which ; This represents the positive definite inertial matrix based on the unmanned surface vessel. The first derivative of the function representing a uniform preset time and a fixed time is given. This represents the inverse function of a function that represents a uniform fixed time versus a preset time. Indicates the speed error of the unmanned surface vessel. This represents the predicted value of the unknown disturbance vector experienced by the unmanned surface vessel in the attached coordinate system. Represents the Coriolis centripetal matrix based on unmanned surface vessels; This represents the damping matrix based on the unmanned surface vessel. The virtual control law representing the unmanned surface vessel;

[0053] Next, we construct the second Lyapunov function for the underwater vehicle. :

[0054]

[0055] This indicates the speed-time scaling error of an underwater vehicle.

[0056] Based on the backstepping method and combined with the dynamics and kinematics model of the underwater vehicle, the control law of the underwater vehicle is obtained. :

[0057]

[0058] in, , , and It is a positive constant, among which ; This indicates the speed error of the underwater vehicle. This represents the predicted value of the unknown disturbance vector experienced by the underwater vehicle in the appendage coordinate system. This represents the Coriolis centripetal matrix based on the underwater vehicle. This represents the damping matrix based on the underwater vehicle. This represents the virtual control law of an underwater vehicle.

[0059] In a preferred embodiment, step 6 specifically includes:

[0060] First, construct the overall Lyapunov function for the unmanned surface vessel. :

[0061]

[0062] This represents the first Lyapunov function of the unmanned surface vessel. This represents the second Lyapunov function of the unmanned surface vessel;

[0063] Calculate the global Lyapunov function of the unmanned surface vessel. Regarding time first derivative Combining this with Young's inequality, we get:

[0064]

[0065] in, Let denote the first derivative of the first Lyapunov function of the unmanned surface vessel. Let denote the first derivative of the second Lyapunov function of the unmanned surface vessel. This represents a unified fixed time and a preset time function. It is a positive number; , is a bounded function term; For constant parameters and exponential parameters; , represents the bounded constant term, used to describe the upper bound of external disturbances and system uncertainties; ; Indicates the first The corresponding positive constant coefficients, i.e. and A unified representation; similarly, for and A unified representation; for and A unified representation; , ; It is the positive constant gain coefficient. express and The minimum value between; These are positive constant coefficients. express and The minimum value between; Represents the coordinate system transformation matrix based on the unmanned surface vessel; and These represent the position-time scaling error and velocity-time scaling error of the unmanned surface vessel, respectively, with T representing transpose;

[0066] Secondly, construct the overall Lyapunov function for the underwater vehicle. :

[0067]

[0068] This represents the first Lyapunov function of the underwater vehicle. This represents the second Lyapunov function for an underwater vehicle.

[0069] Calculate the global Lyapunov function of an underwater vehicle. Regarding time first derivative Combining this with Young's inequality, we can obtain:

[0070]

[0071] in, Let denote the first derivative of the first Lyapunov function of the underwater vehicle. Let represent the first derivative of the second Lyapunov function of the underwater vehicle. It is a positive number; , is a bounded function term; For constant parameters and exponential parameters; , represents the bounded constant term, used to describe the upper bound of external disturbances and system uncertainties; ; Indicates the first The corresponding positive constant coefficients, i.e. and A unified representation; similarly, for and A unified representation; for and A unified representation; , ; Positive gain coefficient, express and The minimum value between; These are positive constant coefficients. express and The minimum value between; This represents the coordinate system transformation matrix based on the underwater vehicle. and These represent the position-time scaling error and velocity-time scaling error of the underwater vehicle, respectively.

[0072] This invention also provides a unified fixed-time and preset-time control system for USV-AUV cooperative trajectory tracking, including a processor, a memory, and a bus. The memory stores machine-readable instructions executed by the processor. When the system is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the unified fixed-time and preset-time control method for USV-AUV cooperative trajectory tracking is as described above.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] 1. This invention provides a unified fixed-time and preset-time control method for USV-AUV cooperative trajectory tracking. A unified fixed-time and preset-time control framework is constructed, mitigating the problems of excessive control input and conservative estimated convergence time in the initial stage of traditional fixed-time control; and avoiding the problems of infinite gain and the control law being effective only within a preset interval in preset-time control. Under this control framework, the system tracking error can converge within a preset time, the control input amplitude can be kept within an achievable range, and the control law remains effective throughout the entire operating range.

[0075] 2. The control method proposed in this invention can keep the control input within the range of engineering-achievable amplitude, avoid the singular behavior of the control gain that cannot be achieved at a specific time, thereby overcoming the main obstacle that traditional preset time strategies are difficult to deploy in actual systems, and significantly improving the engineering feasibility of the method in marine operation scenarios. Attached Figure Description

[0076] Figure 1 This is a flowchart of a unified fixed-time and preset-time control method for USV-AUV cooperative trajectory tracking.

[0077] Figure 2 This is a schematic diagram of two-dimensional trajectory tracking.

[0078] Figure 3 This is a schematic diagram of three-dimensional trajectory tracking.

[0079] Figure 4 The USV trajectory tracking error is defined as follows: simulation duration is 300 seconds and preset convergence time is 15 seconds. This indicates the lateral position error of the unmanned surface vessel. This indicates the longitudinal position error of the unmanned surface vessel. This indicates the heading angle error of the unmanned vessel.

[0080] Figure 5 The simulation duration is 300 seconds and the preset convergence time is 15 seconds, where the AUV trajectory tracking error is... This indicates the lateral position error of the underwater vehicle. This indicates the longitudinal position error of the underwater vehicle. This indicates the vertical position error of the underwater vehicle. This indicates the heading angle error of an underwater vehicle.

[0081] Figure 6 The USV output torque is calculated for a simulation duration of 300 seconds and a preset convergence time of 15 seconds. For longitudinal torque, For lateral moment, This is the yaw moment.

[0082] Figure 7 The AUV output torque is calculated for a simulation duration of 300 seconds and a preset convergence time of 15 seconds. For longitudinal torque, For lateral moment, For vertical torque, This is the yaw moment.

[0083] Figure 8 The graph shows a comparison of the USV output torque of this method with that of fixed-time control / preset-time control when the simulation duration is 5 seconds and the preset convergence time is 5 seconds. For longitudinal torque, For lateral moment, This is the yaw moment.

[0084] Figure 9This is a comparison chart of the AUV output torque produced by this method and by fixed-time control / preset-time control when the simulation duration is 5 seconds and the preset convergence time is 5 seconds. The chart shows that... For longitudinal torque, For lateral moment, For vertical torque, This is the yaw moment. Detailed Implementation

[0085] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0086] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0087] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0088] like Figure 1-9 As shown, this invention provides a unified fixed-time and preset-time control method for USV-AUV cooperative trajectory tracking, specifically including the following steps:

[0089] Step S1: Mission Trajectory Generation and Modeling. First, based on the mission requirements, the desired trajectory for the USV-AUV cooperative trajectory tracking mission is generated at the shore-based end. Furthermore, nonlinear kinematic and dynamic models of a three-degree-of-freedom USV and a four-degree-of-freedom AUV considering environmental disturbances were constructed.

[0090] Step S1-1: First, construct a three-degree-of-freedom USV nonlinear kinematic and dynamic model considering environmental disturbances, as shown in the following formulas:

[0091]

[0092]

[0093] in, It is the actual trajectory vector composed of the unmanned surface vessel's position and bow roll angle information in the ground coordinate system; It is the actual velocity vector composed of the unmanned surface vessel's pitch velocity, sway velocity, and yaw rate in the attached coordinate system; This represents the control input vector of the unmanned surface vessel; This represents the unknown disturbance vector experienced by the unmanned surface vessel in the attached coordinate system; It is a coordinate system transformation matrix; It is a positive definite inertia matrix; It is a Coriolis centripetal matrix; It is the damping matrix.

[0094] Step S1-2: Construct a nonlinear kinematic and dynamic model of a four-degree-of-freedom AUV considering environmental disturbances, as shown in the following formulas:

[0095]

[0096]

[0097] in, It consists of the underwater vehicle's position and bow angle information in the ground coordinate system, and is used to describe the actual trajectory; The actual velocity vector is composed of the sway velocity, roll velocity, vertical velocity, and bow angular velocity of the underwater vehicle based on the attached coordinate system. This represents the control input vector of the underwater vehicle; This represents the unknown disturbance vector experienced by the underwater vehicle in the attached coordinate system; It is a coordinate system transformation matrix; It is a positive definite inertia matrix; It is a Coriolis centripetal matrix; It is the damping matrix; This is the restoring force term related to gravity and buoyancy.

[0098] Step S2: Construct a unified fixed time and a preset time function and provide stability conditions.

[0099] Step S2-1: First, construct a unified fixed time and a preset time function. As shown in the following formula:

[0100] (4)

[0101] in, , , It is a preset time point and It is a preset time switching point, and g is a finite positive integer representing the power.

[0102] Step S2-2: Further, if the Lyapunov function of the constructed system... satisfy Then the system satisfies the preset time convergence, and the region of convergence is: .in , , , , ,and It is a positive number.

[0103] Based on the above results, it can be seen that the present invention constructs a unified fixed time and preset time control framework, which is determined by the time segment in which the system is located: At that time, the system uses preset time control; At that time, the system uses fixed-time control; at the time... This enables the continuous connection of control laws, thereby achieving a smooth switch between the two types of time-constrained control modes.

[0104] Step S3: State Acquisition and Time Scale Error Construction. First, the current motion state of the UAV and underwater vehicle is obtained through sensors on the UAV and underwater vehicle, and compared with the expected trajectory to construct the tracking error of the UAV and underwater vehicle. Then, based on the constructed unified fixed time and preset time function, the time scale error is further constructed.

[0105] Step S3-1: First, construct the unmanned surface vessel trajectory tracking error and time scaling error, as shown in the following formula:

[0106] (6)

[0107] (7)

[0108] in, and These represent the position error and velocity error of the unmanned surface vessel, respectively. and These represent the position-time scaling error and velocity-time scaling error of the unmanned surface vessel, respectively. This represents the virtual control law of the unmanned surface vessel.

[0109] Step S3-2: Next, construct the trajectory tracking error and time scaling error of the underwater vehicle, as shown in the following formula:

[0110] (8)

[0111] (9)

[0112] in, and These represent the position error and velocity error of the underwater vehicle, respectively. and These represent the position-time scaling error and velocity-time scaling error of the underwater vehicle, respectively. This represents the virtual control law of an underwater vehicle.

[0113] Step S4: Construction of the first Lyapunov function and design of the virtual control law. The first Lyapunov function is constructed for both the unmanned surface vessel (USV) and the underwater vehicle (UV), and the corresponding virtual control law is obtained based on the backstepping method.

[0114] Step S4-1: First, construct the first Lyapunov function of the unmanned surface vessel:

[0115] (10)

[0116] Based on the backstepping method and combined with the dynamics and kinematics model of the unmanned surface vessel (USV), the virtual control law of the USV is obtained:

[0117] (11)

[0118] in, , , and It is a positive constant, among which .

[0119] Step S4-2: Next, construct the first Lyapunov function for the underwater vehicle:

[0120] (12)

[0121] Based on the backstepping method and combined with the dynamics and kinematics model of the underwater vehicle, the virtual control law of the underwater vehicle is obtained:

[0122] (13)

[0123] in, , , and It is a positive constant, among which .

[0124] Step S5: Construction of the second Lyapunov function and design of the control law. Based on step S4, a second Lyapunov function is constructed for both the unmanned surface vessel and the underwater vehicle, and the corresponding control law is obtained based on the backstepping method.

[0125] Step S5-1: First, construct a second Lyapunov function for the unmanned surface vessel:

[0126] (14)

[0127] Based on the backstepping method and combined with the dynamics and kinematics model of the unmanned surface vessel, the control law of the unmanned surface vessel is obtained:

[0128] (15)

[0129] in, To interfere with the observed values, and It is a normal number.

[0130] Step S5-2: Next, construct the second Lyapunov function for the underwater vehicle:

[0131] (16)

[0132] Based on the backstepping method and combined with the dynamics and kinematics model of the underwater vehicle, the control law of the underwater vehicle is obtained:

[0133] (17)

[0134] in, To interfere with the observed values, and It is a normal number.

[0135] Step S6: Overall Lyapunov Function Construction and Preset Time Stability Analysis. Based on the above steps, the overall Lyapunov functions for the unmanned surface vessel and the underwater vehicle are constructed and stability analysis is performed, ensuring that the tracking error converges to the convergence region within a preset time.

[0136] Step S6-1: First, construct the overall Lyapunov function for the unmanned surface vessel:

[0137] (18)

[0138] calculate Regarding time The first derivative of , combined with Young's inequality, yields:

[0139] (19)

[0140] in, , , , , .

[0141] As can be seen from step S2-2, the designed control law can make the tracking error of the unmanned surface vessel converge within a preset time.

[0142] Step S6-2: Next, construct the overall Lyapunov function for the underwater vehicle:

[0143] (20)

[0144] calculate Regarding time The first derivative of , combined with Young's inequality, yields:

[0145] (twenty one)

[0146] in, , , , , .

[0147] As can be seen from step S2-2, the designed control law can make the tracking error of the underwater vehicle converge within a preset time.

Claims

1. A unified fixed-time and preset-time control method for USV-AUV cooperative trajectory tracking, characterized in that, Includes the following steps: Step S1: Mission trajectory generation and modeling; First, based on the mission requirements, the desired trajectory of the USV-AUV cooperative trajectory tracking mission is generated at the shore-based end, and a three-degree-of-freedom USV nonlinear kinematics and dynamics model considering environmental interference and a four-degree-of-freedom AUV nonlinear kinematics and dynamics model considering environmental interference are constructed. Step S2: Construct a unified fixed time and a preset time function and provide stability conditions; Step S3: Obtain the current motion state of the unmanned surface vessel and the underwater vehicle through the sensors on the unmanned surface vessel and the underwater vehicle, compare it with the expected trajectory, construct the tracking error of the unmanned surface vessel and the underwater vehicle, and further construct the time scaling error based on the constructed unified fixed time and the preset time function. Step S4: Construct the first Lyapunov function for the unmanned surface vessel and the underwater vehicle respectively, and obtain the corresponding virtual control law based on the backstepping method; Step S5: Based on step S4, construct the second Lyapunov function for the unmanned surface vessel and the underwater vehicle respectively, and obtain the corresponding control law based on the backstepping method; Step S6: Construct the Lyapunov function of the overall system for both the unmanned surface vessel and the underwater vehicle and conduct stability analysis, ensuring that the tracking error converges to the convergence domain within a preset time.

2. The unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking according to claim 1, characterized in that, In step 1, a three-degree-of-freedom USV nonlinear kinematic and dynamic model considering environmental disturbances is constructed, as shown in the following formulas: in, It is the actual trajectory vector composed of the unmanned surface vessel's position and bow angle information in the ground coordinate system, where, This indicates the actual position of the unmanned surface vessel in the inertial coordinate system. For the bow roll angle of the unmanned surface vessel, The first derivative of the actual trajectory vector, which is composed of the unmanned surface vessel's position and bow angle information in the ground coordinate system, is given. The sway velocity of the unmanned surface vessel in the attached coordinate system sway speed and bow roll rate The actual velocity vector formed It represents the first derivative of the actual velocity vector consisting of the pitch velocity, sway velocity, and yaw rate of the unmanned surface vessel in the attached coordinate system; Let represent the control input vector of the unmanned surface vessel, where For longitudinal force, It is a lateral force. For yaw force; Let represent the unknown perturbation vector experienced by the unmanned surface vessel in the appendage coordinate system, where For longitudinal disturbances, This is a lateral disturbance. This is a yaw disturbance; It is a coordinate system transformation matrix based on unmanned surface vessels; It is based on the positive definite inertial matrix of the unmanned surface vessel; It is a Coriolis centripetal matrix based on unmanned surface vessels; It is based on the damping matrix of the unmanned surface vessel. Real number field; A nonlinear kinematic and dynamic model of a four-degree-of-freedom AUV considering environmental disturbances is constructed, as shown in the following formula: in, The actual trajectory vector is composed of the underwater vehicle's position and bow angle information in the terrestrial coordinate system, where... This indicates the actual position of the underwater vehicle in the inertial coordinate system. For the bow roll angle of the unmanned surface vessel; The first derivative of the actual trajectory vector composed of the position and bow angle information of the underwater vehicle in the terrestrial coordinate system; The sway velocity of the underwater vehicle based on the attached coordinate system sway speed Vertical velocity and bow roll rate The actual velocity vector formed; The first derivative of the actual velocity vector of an underwater vehicle based on the attached coordinate system, consisting of its pitch velocity, sway velocity, vertical velocity, and yaw rate. The control input vectors of the underwater vehicle are represented by the longitudinal torque. lateral moment Vertical moment and yaw moment ; Let represent the unknown disturbance vector experienced by the underwater vehicle in the appendage coordinate system, where Indicates longitudinal interference. Indicates lateral interference. Indicates vertical interference. Indicates yaw interference; It is a coordinate system transformation matrix based on underwater vehicles; It is based on the positive definite inertial matrix of the underwater vehicle; It is based on the Coriolis centripetal matrix of underwater vehicles; It is based on the damping matrix of underwater vehicles; The restoring force term is related to gravity and buoyancy, and T denotes transpose.

3. The unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking according to claim 1, characterized in that, In step 2, a unified fixed time and a preset time function are constructed. As shown in the following formula: in, It is a time transformation function. t represents time. It is a preset time point and It is a preset time switching point; g is a finite positive integer representing the power. If the Lyapunov function of the constructed system satisfy ,in, Represents Lyapunov functions If the first derivative of is given, then the system satisfies the preset time convergence, and the region of convergence is: ,in, , The coefficients are positive constants. It is a positive constant between 0 and 1; , It is a constant exponential parameter, and , , ;and It is a bounded positive constant used to characterize the upper bound of uncertainty and external disturbances in a system.

4. The unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking according to claim 1, characterized in that, Step 3 specifically includes: First, the unmanned surface vessel trajectory tracking error and time scaling error are constructed as shown in the following formula: in, and These represent the position error and velocity error of the unmanned surface vessel, respectively. and These represent the position-time scaling error and velocity-time scaling error of the unmanned surface vessel, respectively. This represents the virtual control law of the unmanned surface vessel. This represents the actual trajectory vector composed of the unmanned surface vessel's position and bow angle information in the ground coordinate system. This represents the desired trajectory of the unmanned surface vessel. This represents a unified fixed time and a preset time function. This represents the actual velocity vector consisting of the unmanned surface vessel's pitch velocity, sway velocity, and yaw rate in the attached coordinate system. Next, the trajectory tracking error and time scaling error of the underwater vehicle are constructed as shown in the following formula: in, and These represent the position error and velocity error of the underwater vehicle, respectively. and These represent the position-time scaling error and velocity-time scaling error of the underwater vehicle, respectively. This represents the virtual control law for underwater vehicles. The actual trajectory vector is composed of the underwater vehicle's position and bow angle information in the terrestrial coordinate system. This represents the desired trajectory of the underwater vehicle. It is the actual velocity vector composed of the sway velocity, roll velocity, vertical velocity, and bow angular velocity of the underwater vehicle based on the attached coordinate system.

5. The unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking according to claim 1, characterized in that, Step 4 specifically includes: For the first Lyapunov function used to construct the unmanned surface vessel : represent the position and time scaling error of the unmanned surface vessel, respectively, and T represents the transpose; Based on the backstepping method and combined with the dynamics and kinematics model of the unmanned surface vessel (USV), the virtual control law of the USV is obtained: in, , , and It is a positive constant, among which ; This represents the inverse matrix of the coordinate system transformation matrix based on the unmanned surface vessel. The first derivative of a function with a uniform fixed time and a preset time is represented. This represents the inverse function of a function that represents a uniform fixed time versus a preset time. This indicates the positional error of the unmanned surface vessel. The first derivative of the desired trajectory of the unmanned surface vessel; Construct the first Lyapunov function for an underwater vehicle : This indicates the position and time scaling error of an underwater vehicle. Based on the backstepping method and combined with the dynamics and kinematics model of the underwater vehicle, the virtual control law of the underwater vehicle is obtained: in, , , and It is a positive constant, among which ; This represents the inverse matrix of the coordinate system transformation matrix based on the underwater vehicle. This indicates the positional error of the underwater vehicle. This represents the first derivative of the desired trajectory based on the underwater vehicle.

6. The unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking according to claim 1, characterized in that, Step 5 specifically includes: First, construct a second Lyapunov function for the unmanned surface vessel. : represent the speed-time scaling error of the unmanned surface vessel, respectively, and T represents the transpose; Based on the backstepping method and combined with the dynamics and kinematics model of the unmanned surface vessel, the control law of the unmanned surface vessel is obtained. : in, , , and It is a positive constant, among which ; This represents the positive definite inertial matrix based on the unmanned surface vessel. The first derivative of the function representing a uniform preset time and a fixed time is given. This represents the inverse function of a function that represents a uniform fixed time versus a preset time. Indicates the speed error of the unmanned surface vessel. This represents the predicted value of the unknown disturbance vector experienced by the unmanned surface vessel in the attached coordinate system. Represents the Coriolis centripetal matrix based on unmanned surface vessels; This represents the damping matrix based on the unmanned surface vessel. This represents the virtual control law of the unmanned surface vessel. This represents the positive definite inertial matrix based on the unmanned surface vessel; Next, we construct the second Lyapunov function for the underwater vehicle. : This indicates the speed-time scaling error of an underwater vehicle. Based on the backstepping method and combined with the dynamics and kinematics model of the underwater vehicle, the control law of the underwater vehicle is obtained. : in, , , and It is a positive constant, among which ; This indicates the speed error of the underwater vehicle. This represents the predicted value of the unknown disturbance vector experienced by the underwater vehicle in the appendage coordinate system. This represents the Coriolis centripetal matrix based on the underwater vehicle. This represents the damping matrix based on the underwater vehicle. This represents the virtual control law for underwater vehicles. This represents the positive definite inertial matrix based on the underwater vehicle.

7. The unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking according to claim 1, characterized in that, Step 6 specifically includes: First, construct the overall Lyapunov function for the unmanned surface vessel. : This represents the first Lyapunov function of the unmanned surface vessel. This represents the second Lyapunov function of the unmanned surface vessel; Calculate the global Lyapunov function of the unmanned surface vessel. Regarding time first derivative Combining this with Young's inequality, we get: in, Let denote the first derivative of the first Lyapunov function of the unmanned surface vessel. Let denote the first derivative of the second Lyapunov function of the unmanned surface vessel. This represents a unified fixed time and a preset time function. It is a positive number; , is a bounded function term; For constant parameters and exponential parameters; , represents the bounded constant term, used to describe the upper bound of external disturbances and system uncertainties; ; Indicates the first The corresponding positive constant coefficients, i.e. and A unified representation; similarly, for and A unified representation; for and A unified representation; , ; It is the positive constant gain coefficient. express and The minimum value between; These are positive constant coefficients. express and The minimum value between; Represents the coordinate system transformation matrix based on the unmanned surface vessel; and These represent the position-time scaling error and velocity-time scaling error of the unmanned surface vessel, respectively, with T representing transpose; Secondly, construct the overall Lyapunov function for the underwater vehicle. : This represents the first Lyapunov function of the underwater vehicle. This represents the second Lyapunov function for an underwater vehicle. Calculate the global Lyapunov function of an underwater vehicle. Regarding time first derivative Combining this with Young's inequality, we can obtain: in, Let denote the first derivative of the first Lyapunov function of the underwater vehicle. Let represent the first derivative of the second Lyapunov function of the underwater vehicle. It is a positive number; , is a bounded function term; For constant parameters and exponential parameters; , represents the bounded constant term, used to describe the upper bound of external disturbances and system uncertainties; ; Indicates the first The corresponding positive constant coefficients, i.e. and A unified representation; similarly, for and A unified representation; for and A unified representation; , ; Positive gain coefficient, express and The minimum value between; These are positive constant coefficients. express and The minimum value between; This represents the coordinate system transformation matrix based on the underwater vehicle. and These represent the position-time scaling error and velocity-time scaling error of the underwater vehicle, respectively.

8. A unified fixed-time and preset-time control system for USV-AUV cooperative trajectory tracking, comprising a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executed by the processor; characterized in that, When the system is running, the processor and the memory communicate via a bus, and the machine-readable instructions are executed by the processor as described in any one of claims 1 to 7, which is a unified fixed time and preset time control method for USV-AUV cooperative trajectory tracking.

Images