Unmanned ship path tracking control method based on 13-point adaptive PID anti-noise

Abstract

The application discloses an unmanned ship path tracking control method based on 13-point adaptive PID anti-noise, relates to the path tracking technical field, and comprises the following steps: S1, a three-degree-of-freedom model of unmanned ship movement is constructed; S2, according to the three-degree-of-freedom model of unmanned ship movement, the speed of the unmanned ship machine is adjusted and the state is updated by using an adaptive PID controller and a 13P-ADAZND model constructed by 13-point ZTD format. The application adopts the 13-point ZTD format, the truncation error can reach seven orders, the numerical phase time delay is greatly reduced, compared with the low-order method, the application can reduce the deviation in high-precision operations such as turning and berthing, and higher path tracking precision is realized.

Description

Unmanned surface vessel path tracking control method based on 13-point adaptive PID noise reduction Technical Field

[0001] This invention relates to the field of path tracking technology, and specifically to a path tracking control method for unmanned vessels based on 13-point adaptive PID noise reduction. Background Technology

[0002] With the continuous development of global trade and ocean exploration, autonomous tracking and control of unmanned surface vessels (USVs) in complex sea conditions has gradually become an important technology for improving shipping efficiency, reducing human resources, and ensuring shipping safety. In actual sea areas, the motion of USVs is inevitably affected by multiple sources of disturbance such as wind, waves, and currents. Simultaneously, sensors experience time delays due to random noise. These factors cause the kinematics of USVs to exhibit strong nonlinearity, time-varying characteristics, and uncertainty. Any degradation in control performance can lead to excessive energy consumption, trajectory deviation, or even collision risks. Therefore, achieving high-precision, noise-resistant, and real-time trajectory tracking and control of USVs in complex sea environments is one of the major challenges in the field of intelligent shipping and marine engineering.

[0003] To address this challenge, academia and industry have conducted extensive research. Traditional control models, such as sliding mode control, backstepping, and model predictive control, while theoretically stable, often rely on precise mathematical modeling and parameter requirements, resulting in high computational complexity and difficulty in meeting the high-frequency real-time requirements of unmanned vessel tracking control. In recent years, deep learning, due to its end-to-end learning methods and nonlinear fitting capabilities, has demonstrated strong adaptability in simulations and has been widely applied to unmanned vessel heading control. However, its reliance on high-quality large-scale real-ship data, its black-box nature, and insufficient generalization ability under unknown sea conditions make it difficult to directly apply to shipping scenarios.

[0004] Against this backdrop, neural dynamics (ND) has gained widespread recognition due to its superior computational and parallel capabilities. Among these, zero-form neural dynamics (ZND), as a novel method for solving dynamic optimization and time-varying problems, has gradually attracted attention. It constructs an error function to allow the system to approximate the desired solution within a finite time. Compared to traditional gradient descent ND, ZND exhibits better real-time performance and stability. However, most of these basic models employ fixed gain parameters, resulting in poor adaptability and limited noise immunity when facing dynamically changing ocean noise. Subsequent improvements, such as integral ZND or some simple adaptive ZND, while enhancing disturbance immunity to some extent, either fail to completely solve the problem of fixed parameters or have simple adaptive laws that are difficult to handle complex disturbances in real-world ocean environments. Therefore, the limitations of solving the heading problem of unmanned vessels in real-world ocean environments can be summarized as follows:

[0005] 1) Poor real-time performance. Existing traditional control methods, when used for guidance and control in actual sea areas, often lead to increased computational loads due to model-dependent matrix inversion or online optimization, failing to meet the high-frequency real-time requirements of unmanned surface vessels (USVs). While deep learning methods possess modeling capabilities for real-time control, data such as weather and sea conditions are difficult to obtain in complex sea areas, making it challenging to achieve precise control of the vessel's tracking path when encountering unknown situations.

[0006] 2) Weak noise resistance. In real sea areas, disturbances such as wind, waves and currents often occur in combination. Although existing control methods can achieve basic control of unmanned vessels under weak noise conditions, they lack effective control mechanisms when facing complex disturbances, which can easily cause track deviations and thus affect the tracking path and navigation safety.

[0007] 3) Low accuracy. Common low-order discrete schemes are prone to causing time delays in numerical values. This makes the control commands and the actual response of the unmanned vessel asynchronous. In situations requiring high precision, such as turning and berthing, the error increases significantly, making it difficult to meet the unmanned vessel's requirements for high-precision and low-latency path tracking. Summary of the Invention

[0008] To address the above problems, this invention proposes a path tracking control method for unmanned vessels based on 13-point adaptive PID noise reduction.

[0009] The technical solution of this invention is: a path tracking control method for unmanned vessels based on 13-point adaptive PID noise reduction, comprising the following steps:

[0010] S1. Construct a three-degree-of-freedom model of the motion of the unmanned vessel;

[0011] S2. Based on the three-degree-of-freedom model of the unmanned vessel's motion, the speed of the unmanned vessel is adjusted and its state is updated using an adaptive PID controller and a 13P-ADAZND model constructed in the 13-point ZTD format.

[0012] Furthermore, S1 includes the following sub-steps:

[0013] S11. Determine the attitude transformation matrix, control input vector, external disturbances, and uncontrolled dynamic characteristics of the unmanned vessel during actual navigation.

[0014] S12. Based on the attitude transformation matrix, control input vector, external disturbance, and uncontrolled dynamic characteristics of the unmanned vessel during actual navigation, construct a three-degree-of-freedom model of the unmanned vessel's motion.

[0015] Furthermore, in S11, the attitude transformation matrix The expression is:

[0016] ;

[0017] in, Let be a matrix relating to the bow roll angle. Let be the state vector of the unmanned vessel. For time variables, To raise the bow angle;

[0018] When the state variables change, the bow angle in the state variables... Changes occur, which in turn cause changes in the attitude transformation matrix.

[0019] In S11, the control input vector The expression is:

[0020] ;

[0021] in, For the longitudinal velocity command in the coordinate system of the unmanned vessel, The lateral velocity command in the coordinate system of the unmanned vessel. For bow roll rate command, Transpose of a vector;

[0022] Control input vector It is composed of state vectors The result is that The three velocities in the vector , and They will all follow the input state vector The attitude transformation matrix changes accordingly. With control input vector Combined, What is presented is the velocity in the unmanned surface vessel coordinate system through the angle transformation in the attitude transformation matrix, that is... The three speeds inside , and How to apply it to state variables.

[0023] In S11, external disturbances The expression is:

[0024] ;

[0025] in, Environmental factors cause longitudinal velocity noise interference to unmanned surface vessels in the navigation coordinate system. To address the interference of environmental factors on the lateral velocity noise of unmanned surface vessels in the navigation coordinate system. Environmental factors cause noise interference to the bow roll rate of unmanned vessels in the navigation coordinate system;

[0026] Environmental factors refer to wind and waves, etc.

[0027] In S11, the uncontrolled dynamic characteristics of the unmanned vessel during actual navigation. The expression is:

[0028] ;

[0029] in, Let x be the velocity of the unmanned surface vessel along the x-axis of the navigation coordinate system without any control input. Let y be the velocity of the unmanned surface vessel along the y-axis of the navigation coordinate system without any control input. This is the angular velocity of the bow roll angle of the unmanned vessel without any control input.

[0030] The x-axis points north, and the y-axis points east.

[0031] Furthermore, in S12, the three-degree-of-freedom mathematical model of the unmanned vessel's motion... The expression is:

[0032] ;

[0033] in, This refers to the uncontrolled dynamic characteristics of unmanned vessels during actual navigation. Here is the attitude transformation matrix. To control the input vector, External disturbances For time variables, Let be the state vector of the unmanned vessel.

[0034] Furthermore, S2 includes the following sub-steps:

[0035] S21. Construct an error function and calculate the error between the expected trajectory and the actual trajectory of the unmanned vessel.

[0036] S22. Based on the error between the expected trajectory and the actual trajectory of the unmanned vessel, construct an adaptive integral error function and an adaptive ZND model, and obtain the dynamic evolution process of the error function.

[0037] S23. Based on the dynamic evolution process of the error function, a PID controller is obtained, and the longitudinal speed, lateral speed and bow roll rate of the unmanned vessel are adjusted.

[0038] S24. Based on the three-degree-of-freedom model of unmanned vessel motion, construct the 13P-ADAZND model;

[0039] S25. Update the state of the unmanned vessel using the 13P-ADAZND model.

[0040] An adaptive integral error function and an adaptive ZND model are constructed, and the combination of the two improves noise resistance and real-time response capabilities.

[0041] Furthermore, the adaptive integral error function The expression is:

[0042] ;

[0043] ;

[0044] ;

[0045] in, To dynamically adjust the adaptive law, For weighted adaptive laws, Let be the error function. It is at a certain time in the interval 0-t. The error, For a certain moment in the time interval 0-t, The coefficients of the weighted adaptive law are... To dynamically adjust the coefficients of the adaptive law, For time variables, Let L be the L2 norm of the function. It is an exponential function. The value of the weighted adaptive law is the value of a certain moment in the time interval 0-t.

[0046] Furthermore, in S22, the expression for the 13P-ADAZND model is:

[0047]

[0048]

[0049] ;

[0050] ;

[0051] in, This is the predicted state quantity for the next sampling point. This is the weighted accumulation of error up to the next sampling point. This is the state variable of the current sampling point. This is the weighted accumulation of errors up to the current sampling point. This refers to the state variables of the previous sampling point. This is the weighted accumulation of error up to the previous sampling point. This refers to the state variables of the second and first sampling points. This is the weighted cumulative error up to the first two sampling points. This refers to the state variables of the first three sampling points. This is the weighted cumulative error up to the first three sampling points. This refers to the state variables of the first four sampling points. This is the weighted cumulative error up to the first four sampling points. This refers to the state variables of the first five sampling points. This is the weighted cumulative error up to the first five sampling points. This refers to the state variables of the first six sampling points. This is the weighted cumulative error up to the first six sampling points. This refers to the state variables of the first seven sampling points. This is the weighted cumulative error up to the first seven sampling points. This refers to the state variables of the first eight sampling points. This is the weighted cumulative error up to the first eight sampling points. This refers to the state variables of the first nine sampling points. This is the weighted cumulative error up to the first nine sampling points. For the state variables up to the first ten sampling points, This is the weighted cumulative error up to the first ten sampling points. This refers to the state variables of the first eleventh sampling point. This is the weighted cumulative error up to the eleventh sampling point. This is a partial formula used to calculate the rate of change of the state variable at the current sampling point. For the current sampling point's state variable, The derivative of the expected output at the current sampling point. The current sampling point is affected by external noise. To dynamically adjust the adaptive law, For weighted adaptive laws, Let be the state vector of the unmanned vessel. For time variables, Let be the desired output state at any time within the time interval 0-t. For a certain moment in the time interval 0-t, To output the desired trajectory, The actual output of the current sampling point State variables of the current sampling point The inverse of the Jacobian matrix obtained after differentiation, This represents the actual output value at the current sampling point. The value of the weighted adaptive law corresponding to the current sampling point. For the actual output, Let be the value of the weighted adaptive law at a certain moment within the time interval 0-t. Let be the expected output value corresponding to a certain moment in the time interval 0-t. The sampling interval is between 0 and 1. The expected output for the current sampling point. To output the desired trajectory, For in 0- At a certain moment in time The actual output, Indicates 0- The system state quantity at any given moment within a given time period.

[0052] The beneficial effects of this invention are:

[0053] (1) Based on nullification neurodynamics, this invention introduces a dynamic adjustment adaptive law into the ZND model to obtain an adaptive ZND model, which improves the real-time response capability of the unmanned vessel. At the same time, in order to resist noise interference, a new adaptive integral error function is constructed. By combining the weighted adaptive law with the integral, the steady-state deviation caused by time-varying ocean currents and the jitter caused by waves are mitigated, thereby suppressing marine environmental noise and further enhancing its real-time dynamic response capability.

[0054] (2) The present invention constructs a dynamic evolution function of error function in zero-dimensional neural dynamics, derives a generalized adaptive PID controller, and explicitly introduces it into a model of an unmanned vessel with noise, thereby achieving noise suppression and speed regulation of the unmanned vessel under various marine environmental noise conditions.

[0055] (3) The present invention adopts the 13-point ZTD format, the truncation error can reach the seventh order, and the numerical phase delay is greatly reduced. Compared with the low-order method, the present invention can reduce the deviation in high-precision operations such as turning and berthing, and achieve higher track tracking accuracy. Attached Figure Description

[0056] Figure 1 is a flowchart of the unmanned vessel path tracking control method package based on 13-point adaptive PID noise reduction;

[0057] Figure 2 is a schematic diagram of the coordinate system;

[0058] Figure 3 is a schematic diagram of a PID controller;

[0059] Figure 4 shows a three-dimensional flight path diagram;

[0060] Figure 5 shows the tracking curves for the three components.

[0061] Figure 6 is a schematic diagram of random noise interfering with unmanned ships. Detailed Implementation

[0062] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0063] As shown in Figure 1, this invention provides a path tracking control method for unmanned surface vessels based on 13-point adaptive PID noise reduction, comprising the following steps:

[0064] S1. Construct a three-degree-of-freedom model of the motion of the unmanned vessel;

[0065] S2. Based on the three-degree-of-freedom model of the unmanned vessel's motion, the speed of the unmanned vessel is adjusted and its state is updated using an adaptive PID controller and a 13P-ADAZND model constructed in the 13-point ZTD format.

[0066] In unmanned surface vessel (USV) tracking control, the six degrees of freedom are forward, drift, yaw, heave, roll, and pitch. Since this invention primarily focuses on whether the USV can accurately track the desired trajectory, the heave, roll, and pitch degrees of freedom are not addressed. This invention only concerns whether accurate trajectory tracking can be achieved at the USV's current position. The 13P-ADAZND model of this invention predicts the state vector of the next sampling point using the state vectors of the previous 12 sampling points, and so on for subsequent unknown sampling points. The state vector is... ,in, This indicates the instantaneous position of the unmanned vessel in the northward direction (first degree of freedom - forward) of the navigation coordinate system. The first degree of freedom (DOF) represents the instantaneous position of the unmanned vessel in the eastward direction of the navigation coordinate system (the second degree of freedom – yaw). The third degree of freedom (Yaw) represents a motion pattern determined by both the Yaw angle and the Yaw velocity. Originally, it represented the bow angle, which is the angle between the unmanned vessel's direction of motion and the north axis of the navigation coordinate system. The other angular velocity r that determines the bow angle appears in the 13P-ADAZND model controller. The three-degree-of-freedom features established in this invention appear in the state vector and controller of the 13P-ADAZND model, respectively.

[0067] This invention proposes a noise-resistant discrete-time neural dynamics model based on a 13-point adaptive proportional-integral-derivative (PID) model (13P-ADAZND). This model enhances the real-time response and rapid adjustment of the unmanned surface vessel (USV) tracking trajectory by designing two adaptive laws. An adaptive PID controller is designed to improve the USV's noise suppression capability and reduce the impact of disturbances such as those from the marine environment. Furthermore, a 13-point Zhang time-discrete (ZTD) scheme is proposed to improve the model's accuracy. This invention demonstrates excellent performance in terms of noise resistance, high accuracy, and real-time performance, providing reliable support for the autonomous tracking control of USVs.

[0068] The operating mechanism of this invention can be understood as follows: Within each sampling period, the system first calculates the deviation between the unmanned vessel and the desired trajectory using an error function. Then, two adaptive PID modules adjust the control law according to the error magnitude to achieve fine-tuning of the longitudinal velocity, lateral velocity, and yaw rate. Finally, the state is predicted and updated using a 13-point discrete iterative formula to ensure that the unmanned vessel can move stably along the desired trajectory. This process is equivalent to equipping the unmanned vessel with predictive and self-adjusting capabilities, enabling it to correct yaw in a timely manner under noise and avoid trajectory drift.

[0069] In this embodiment of the invention, S1 includes the following sub-steps:

[0070] S11. Determine the attitude transformation matrix, control input vector, external disturbances, and uncontrolled dynamic characteristics of the unmanned vessel during actual navigation.

[0071] S12. Based on the attitude transformation matrix, control input vector, external disturbance, and uncontrolled dynamic characteristics of the unmanned vessel during actual navigation, construct a three-degree-of-freedom model of the unmanned vessel's motion.

[0072] Figure 2 shows the geometric relationship and symbol definition between the navigation coordinate system and the unmanned vessel coordinate system.

[0073] Figure 2: Symbol Definitions and Relationship Interpretations Let the origin of the navigation coordinate system be... The (N) axis is used to represent the north direction (N). The (E) axis indicates eastward (E). (D) indicates the direction pointing towards the center of the earth. Let be the origin of the unmanned surface vessel's coordinate system, that is, to regard the unmanned surface vessel as the origin, and the direction of the unmanned surface vessel's movement as the vertical axis of the unmanned surface vessel's coordinate system, denoted as . Its vertical velocity is u, and the horizontal axis of the unmanned surface vessel coordinate system is... Its horizontal velocity is denoted as v. The ship circles... The speed of shaft rotation is denoted as the angular velocity of the bow roll, and the angular velocity of the bow roll is... Let V be the angle between the northward direction of the navigation coordinate system and the direction of the ship's movement. In the unmanned vessel coordinate system, the resultant velocity of the unmanned vessel's longitudinal and lateral velocities is the water flow velocity V.

[0074] When unmanned surface vessels (USVs) navigate in real-world ocean environments, they are affected by multi-source noise disturbances such as wind, waves, and currents, resulting in motions that are highly nonlinear, strongly coupled, and time-varying. To describe the motion of USVs, this invention employs a three-degree-of-freedom (DOF) dynamic model, a mathematical model describing the motion of USVs under regular wave conditions, including surge, sway, yaw, heave, roll, and pitch. The first three degrees of freedom are translational motions, while the latter three are rotational motions. In most trajectory tracking and path control problems, the three degrees of freedom on the horizontal plane (surge, sway, yaw) are typically the focus, as they directly determine the USV's position changes and heading attitude in the ocean, forming the core of control design.

[0075] In this embodiment of the invention, in S11, the relationship between the input and the state derivative is transformed by the attitude transformation matrix. The expression is:

[0076] ;

[0077] in, Let be a matrix relating to the bow roll angle. Let be the state vector of the unmanned vessel. For time variables, To raise the bow angle;

[0078] When the state variables change, the bow angle in the state variables... Changes occur, which in turn cause changes in the attitude transformation matrix.

[0079] In S11, to ensure the unmanned vessel navigates precisely along the desired trajectory, a control input vector is introduced. The expression is:

[0080] ;

[0081] in, For the longitudinal velocity command in the coordinate system of the unmanned vessel, The lateral velocity command in the coordinate system of the unmanned vessel. For bow roll rate command, Transpose of a vector;

[0082] Control input vector It is composed of state vectors The result is that The three velocities in the vector , and They will all follow the input state vector The attitude transformation matrix changes accordingly. With control input vector Combined, What is presented is the velocity in the unmanned surface vessel coordinate system through the angle transformation in the attitude transformation matrix, that is... The three speeds inside , and How to apply it to state variables.

[0083] The longitudinal speed command represents the desired forward speed in the longitudinal direction of the hull, the lateral speed command represents the lateral drift speed of the hull, and the bow roll rate command represents the turning angular velocity of the unmanned vessel.

[0084] In S11, external disturbances The expression is:

[0085] ;

[0086] in, Environmental factors cause longitudinal velocity noise interference to unmanned surface vessels in the navigation coordinate system. To address the interference of environmental factors on the lateral velocity noise of unmanned surface vessels in the navigation coordinate system. Environmental factors cause noise interference to the bow roll rate of unmanned vessels in the navigation coordinate system;

[0087] Environmental factors refer to wind and waves, etc.

[0088] In S11, the uncontrolled dynamic characteristics of the unmanned vessel during actual navigation. The expression is:

[0089] ;

[0090] in, Let x be the velocity of the unmanned surface vessel along the x-axis of the navigation coordinate system without any control input. Let y be the velocity of the unmanned surface vessel along the y-axis of the navigation coordinate system without any control input. This is the angular velocity of the bow roll angle of the unmanned vessel without any control input.

[0091] The x-axis points north, and the y-axis points east.

[0092] In this embodiment of the invention, S12 is a three-degree-of-freedom mathematical model of the motion of the unmanned vessel. The expression is:

[0093] ;

[0094] in, This refers to the uncontrolled dynamic characteristics of unmanned vessels during actual navigation. Here is the attitude transformation matrix. To control the input vector, External disturbances For time variables, Let be the state vector of the unmanned vessel.

[0095] That is, the speed change of an unmanned surface vessel when there is no control input. With state vector The bow angle is related to the various velocities presented in the unmanned vessel's coordinate system (i.e., middle , and How the longitudinal, lateral, and yaw velocities (represented by the angular velocities) affect the state variables. This is the state vector of the unmanned vessel in the navigation coordinate system, used to represent its instantaneous position. It includes the coordinates of the vertical and horizontal axes in the navigation coordinate system, as well as the angle by which the unmanned vessel deviates from the north direction of the navigation coordinate system.

[0096] In this embodiment of the invention, S2 includes the following sub-steps:

[0097] S21. Construct an error function and calculate the error between the expected trajectory and the actual trajectory of the unmanned vessel.

[0098] S22. Based on the error between the expected trajectory and the actual trajectory of the unmanned vessel, construct an adaptive integral error function and an adaptive ZND model, and obtain the dynamic evolution process of the error function.

[0099] S23. Based on the dynamic evolution process of the error function, a PID controller is obtained, and the longitudinal speed, lateral speed and bow roll rate of the unmanned vessel are adjusted.

[0100] S24. Based on the three-degree-of-freedom model of unmanned vessel motion, construct the 13P-ADAZND model;

[0101] S25. Update the state of the unmanned vessel using the 13P-ADAZND model.

[0102] An adaptive integral error function and an adaptive ZND model are constructed, and the combination of the two improves noise resistance and real-time response capabilities.

[0103] To enhance the noise immunity of unmanned surface vessels (USVs) in complex sea conditions, this invention incorporates the classic PID control concept into the ZND structure. However, unlike traditional fixed-gain PID controllers, this PID controller is an adaptive controller. It constructs two adaptive laws by dynamically combining nonlinear functions with the error, enabling the USV to track its trajectory in real time. Furthermore, the PID controller in this invention is derived from a newly proposed adaptive integral error dynamic evolution process. It includes an integral term related to the error and combines this integral term with a weighted adaptive law, enhancing the model's noise immunity. On one hand, it can suppress deviations caused by ocean currents and low-frequency waves, eliminating steady-state errors. On the other hand, it can also suppress high-frequency random noise in real time, ensuring that the USV maintains a stable trajectory even under adverse conditions such as waves and crosswinds.

[0104] In this embodiment of the invention, in step S21, to better solve the tracking and control problem of unmanned vessels, the invention first compares the desired trajectory of the unmanned vessel with its actual trajectory to obtain the error between its position and desired orientation. To avoid the problem of a single error converging too slowly or too quickly in a dynamic and complex environment, an adaptive law is introduced. The error is adjusted in real time by adjusting the magnitude and rate of change, ensuring that the error decays rapidly under different noise intensities. A new adaptive integral error function is then implemented. Set as .

[0105] To further improve the trajectory tracking capability of unmanned surface vessels, this invention proposes to use... Replacing the fixed coefficients in traditional ZND, the derivative of the new adaptive integral error function is obtained. Adaptive integral error function The expression is:

[0106] ;

[0107] ;

[0108] ;

[0109] in, To dynamically adjust the adaptive law, For weighted adaptive laws, Let be the error function. It is at a certain time in the interval 0-t. The error, For a certain moment in the time interval 0-t, The coefficients of the weighted adaptive law are... To dynamically adjust the coefficients of the adaptive law, For time variables, Let L be the L2 norm of the function. It is an exponential function. The value of the weighted adaptive law is the value of a certain moment in the time interval 0-t. .

[0110] Used to dynamically adjust the system's response speed based on the magnitude of the current error. Used to adaptively adjust the weights in the integral term based on the magnitude of the error. It reflects the error between the expected trajectory and the actual trajectory.

[0111] In this embodiment of the invention, in S22, the present invention, for the first time, employs a 13-point ZTD scheme to iteratively solve the error dynamics. Compared with traditional low-order Euler or fourth-order Runge-Kutta methods, this scheme has seventh-order truncation accuracy, which can reduce phase delay and accumulated error, enabling the unmanned surface vessel to maintain high-precision path tracking during long-distance navigation and complex maneuvers. Based on the above design, the 13P-ADAZND model of the present invention is obtained. After 13-point discretization, it can achieve high-precision, real-time, and noise-resistant tracking control of the unmanned surface vessel trajectory in complex noise environments.

[0112] The expression for the 13P-ADAZND model is:

[0113]

[0114]

[0115] ;

[0116] ;

[0117] in, This is the predicted state quantity for the next sampling point. This is the weighted accumulation of error up to the next sampling point. This is the state variable of the current sampling point. This is the weighted accumulation of errors up to the current sampling point. This refers to the state variables of the previous sampling point. This is the weighted accumulation of error up to the previous sampling point. This refers to the state variables of the second and first sampling points. This is the weighted cumulative error up to the first two sampling points. This refers to the state variables of the first three sampling points. This is the weighted cumulative error up to the first three sampling points. This refers to the state variables of the first four sampling points. This is the weighted cumulative error up to the first four sampling points. This refers to the state variables of the first five sampling points. This is the weighted cumulative error up to the first five sampling points. This refers to the state variables of the first six sampling points. This is the weighted cumulative error up to the first six sampling points. This refers to the state variables of the first seven sampling points. This is the weighted cumulative error up to the first seven sampling points. This refers to the state variables of the first eight sampling points. This is the weighted cumulative error up to the first eight sampling points. This refers to the state variables of the first nine sampling points. This is the weighted cumulative error up to the first nine sampling points. For the state variables up to the first ten sampling points, This is the weighted cumulative error up to the first ten sampling points. This refers to the state variables of the first eleventh sampling point. This is the weighted cumulative error up to the eleventh sampling point. This is a partial formula used to calculate the rate of change of the state variable at the current sampling point. For the current sampling point's state variable, The derivative of the expected output at the current sampling point. The current sampling point is affected by external noise. To dynamically adjust the adaptive law, For weighted adaptive laws, Let be the state vector of the unmanned vessel. For time variables, Let be the desired output state at any time within the time interval 0-t. For a certain moment in the time interval 0-t, To output the desired trajectory, The actual output of the current sampling point State variables of the current sampling point The inverse of the Jacobian matrix obtained after differentiation, This represents the actual output value at the current sampling point. The value of the weighted adaptive law corresponding to the current sampling point. For the actual output, Let be the value of the weighted adaptive law at a certain moment within the time interval 0-t. Let be the expected output value corresponding to a certain moment in the time interval 0-t. The sampling interval is between 0 and 1. The expected output for the current sampling point. To output the desired trajectory, For in 0- At a certain moment in time The actual output, Indicates 0- The system state quantity at any given moment within a given time period.

[0118] That is, the expected rate of change of the output over time.

[0119] The following description is based on an example.

[0120] As shown in Figure 3, based on the given expected trajectory Based on the actual output D(x(t)), the error function e(t) = D(x(t)) - For the desired trajectory The error function is integrated and applied to the desired trajectory after being controlled by the sum of the weighted adaptive law and the dynamic adjustment adaptive law, respectively. Taking the derivative, we obtain the entire sequence of terms. A generalized PID controller with proportional, integral, and derivative functions is used. The entire process is regulated by an adaptive PID controller, involving two adaptive laws. To improve the model's noise resistance, noise interference p(t) is added to the model, allowing it to resist the noise. Next, to find the law of change of the state variable x(t), the derivative with respect to the error e(t) is taken. The inverse of the Jacobian matrix is ​​obtained by taking the partial derivative of the actual output vector D(x(t)) with respect to the state vector x(t). Finally, combining the first 12 known points with the rate of change of the state vector x(t), a 13-point discretization is performed to obtain the next predicted state vector, which is then output. Finally, the output value is fed back to the original system and the desired trajectory. Subtracting the values ​​gives the error, and so on, to achieve prediction of each future value.

[0121] Let x(t) be the desired trajectory, D(x(t)) be the state variable, e(t) be the actual output, p(t) be the error function, and p(t) be the noise. For Jacobian matrices, (t) is the weighted adaptive law. To dynamically adjust the adaptive law, Summation symbol.

[0122] In this experiment, we studied the trajectory tracking problem of an unmanned surface vessel (USV) under zero noise and random noise conditions. In the 3D trajectory diagram shown in Figure 4, the USV's tracking path converges rapidly to the desired trajectory. The x-axis represents the USV's position in the north-south direction, and the y-axis represents its position in the east-west direction. The x-axis represents the bow angle of the ship in the horizontal plane, i.e., the angle between the bow and the north axis of the navigation coordinate system. Simulation results show that, under zero noise, the actual trajectory highly overlaps with the desired trajectory in a short time, exhibiting fast convergence speed and high accuracy. The maximum error during steady-state convergence reaches 8.1055e-13, which is almost negligible, verifying that the algorithm possesses extremely high control accuracy and convergence characteristics under ideal conditions. From the x-axis, y-axis, and... (Figure 5 shows...) The tracking curves for the three axes further demonstrate that the outputs of all three degrees of freedom quickly approach the desired value, with no significant oscillations or delays during tracking. This indicates that the proposed 13P-ADAZND model can achieve high-precision and stable trajectory tracking under zero-noise conditions. Figure 6 introduces random noise to interfere with the unmanned surface vessel. The results show that even under complex noise conditions, the actual trajectory still follows the desired trajectory well. The 3D track diagram shows that the actual trajectory is basically consistent with the desired trajectory, with only minor jitter, but the overall trend and convergence effect are good. The corresponding error curves show that the error fluctuates somewhat under random noise, but remains within a very small range, exhibiting rapid decay and stability. This indicates that the algorithm has good robustness and noise resistance, effectively resisting the impact of random noise and external disturbances on trajectory tracking accuracy.

[0123] This invention proposes a novel 13-point adaptive PID noise-resistant discrete nullable neurodynamic model (13P-ADAZND) for high-precision control of unmanned surface vessel (USV) trajectory tracking. By designing two adaptive laws and incorporating them into the nullable neurodynamics and PID controller, the interference of various noises on the system is effectively suppressed, achieving fast real-time response. Furthermore, a 13-point iterative scheme is introduced to improve the model's numerical accuracy and long-term tracking performance. Compared with existing techniques, this method exhibits higher accuracy and stronger noise resistance in noisy environments, effectively solving the trajectory tracking control problem of USVs in complex sea areas. Finally, simulation experiments under zero noise and random noise conditions further demonstrate the effectiveness of this method. Experiments show that the proposed model can not only achieve accurate tracking in ideal environments but also maintain good real-time performance and high accuracy under random noise interference, significantly improving the safety and reliability of USVs during trajectory tracking. This research provides a new approach for precise path control of USVs in complex marine environments and has broad application prospects.

[0124] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A path tracking control method for unmanned surface vessels based on 13-point adaptive PID noise reduction, characterized in that, Includes the following steps: S1. Construct a three-degree-of-freedom model of the unmanned surface vessel's (USV) motion; S2. Based on the three-degree-of-freedom model of USV motion, use an adaptive PID controller and a 13P-ADAZND model constructed in 13-point ZTD format to adjust the USV's speed and update its state; S1 includes the following sub-steps: S11. Determine the attitude transformation matrix, control input vector, external disturbance, and uncontrolled dynamic characteristics of the USV during actual navigation; S12. Based on the attitude transformation matrix, control input vector, external disturbance, and uncontrolled dynamic characteristics of the USV during actual navigation, construct a three-degree-of-freedom model of the USV's motion; S2 includes the following sub-steps: S2 1. Construct an error function to calculate the error between the desired trajectory and the actual trajectory of the unmanned surface vessel (USV); S22. Based on the error between the desired and actual trajectories, construct an adaptive integral error function and an adaptive ZND model, and obtain the dynamic evolution process of the error function; S23. Based on the dynamic evolution process of the error function, obtain a PID controller and adjust the longitudinal velocity, lateral velocity, and yaw rate of the USV; S24. Based on the three-degree-of-freedom model of the USV's motion, construct a 13P-ADAZND model; S25. Update the state of the USV using the 13P-ADAZND model; In S22, the adaptive integral error function... The expression is: ； ； ;in, To dynamically adjust the adaptive law, For weighted adaptive laws, Let be the error function. It is at a certain time in the interval 0-t. The error, For a certain moment in the time interval 0-t, The coefficients of the weighted adaptive law are... To dynamically adjust the coefficients of the adaptive law, For time variables, Let L be the L2 norm of the function. It is an exponential function. The value of the weighted adaptive law is the value of a certain moment in the time interval 0-t.

2. The unmanned vessel path tracking control method based on 13-point adaptive PID noise reduction as described in claim 1, characterized in that, In S11, the attitude transformation matrix The expression is: ;in, Let be a matrix relating to the bow roll angle. Let be the state vector of the unmanned vessel. For time variables, The bow roll angle; in S11, the control input vector The expression is: ;in, For the longitudinal velocity command in the coordinate system of the unmanned vessel, The lateral velocity command in the coordinate system of the unmanned vessel. For bow roll rate command, It is a vector transpose; in S11, the external disturbance The expression is: ;in, Environmental factors cause longitudinal velocity noise interference to unmanned surface vessels in the navigation coordinate system. To address the interference of environmental factors on the lateral velocity noise of unmanned surface vessels in the navigation coordinate system. The noise interference on the bow roll rate of the unmanned vessel caused by environmental factors in the navigation coordinate system; in S11, the uncontrolled dynamic characteristics of the unmanned vessel during actual navigation. The expression is: ;in, Let x be the velocity of the unmanned surface vessel along the x-axis of the navigation coordinate system without any control input. Let y be the velocity of the unmanned surface vessel along the y-axis of the navigation coordinate system without any control input. This is the angular velocity of the bow roll angle of the unmanned vessel without any control input.

3. The unmanned surface vessel path tracking control method based on 13-point adaptive PID noise reduction as described in claim 1, characterized in that, In S12, the three-degree-of-freedom mathematical model of the unmanned vessel's motion. The expression is: ;in, This refers to the uncontrolled dynamic characteristics of unmanned vessels during actual navigation. Here is the attitude transformation matrix. To control the input vector, External disturbances For time variables, Let be the state vector of the unmanned vessel.

4. The unmanned vessel path tracking control method based on 13-point adaptive PID noise reduction as described in claim 1, characterized in that, In S24, the expression for the 13P-ADAZND model is: ； ;in, This is the predicted state quantity for the next sampling point. This is the weighted accumulation of error up to the next sampling point. This is the state variable of the current sampling point. This is the weighted accumulation of errors up to the current sampling point. This refers to the state variables of the previous sampling point. This is the weighted accumulation of error up to the previous sampling point. This refers to the state variables of the second and first sampling points. This is the weighted cumulative error up to the second and third sampling points. This refers to the state variables of the first three sampling points. This is the weighted cumulative error up to the first three sampling points. This refers to the state variables of the first four sampling points. This is the weighted cumulative error up to the first four sampling points. This refers to the state variables of the first five sampling points. This is the weighted cumulative error up to the first five sampling points. This refers to the state variables of the first six sampling points. This is the weighted cumulative error up to the first six sampling points. This refers to the state variables of the first seven sampling points. This is the weighted cumulative error up to the first seven sampling points. This refers to the state variables of the first eight sampling points. This is the weighted cumulative error up to the first eight sampling points. This refers to the state variables of the first nine sampling points. This is the weighted cumulative error up to the first nine sampling points. For the state variables up to the first ten sampling points, This is the weighted cumulative error up to the first ten sampling points. This refers to the state variables of the first eleventh sampling point. This is the weighted cumulative error up to the eleventh sampling point. This is a partial formula used to calculate the rate of change of the state variable at the current sampling point. For the current sampling point's state variable, The derivative of the expected output at the current sampling point. The current sampling point is affected by external noise. To dynamically adjust the adaptive law, For weighted adaptive laws, Let be the state vector of the unmanned vessel. For time variables, Let be the desired output state at any time within the time interval 0-t. For a certain moment in the time interval 0-t, To output the desired trajectory, The actual output of the current sampling point State variables of the current sampling point The inverse of the Jacobian matrix obtained after differentiation, This represents the actual output value at the current sampling point. The value of the weighted adaptive law corresponding to the current sampling point. For the actual output, Let be the value of the weighted adaptive law at a certain moment within the time interval 0-t. Let be the expected output value corresponding to a certain moment in the time interval 0-t. The sampling interval is between 0 and 1. The desired output for the current sampling point. To output the desired trajectory, For in 0- At a certain moment in time The actual output, Indicates 0- The system state quantity at any given moment within a given time period.

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