Unmanned surface vehicle path following control method based on variable gain fixed time observer

Abstract

The application discloses a kind of based on variable gain fixed time observer's unmanned ship path tracking control method, the present application relates to ship motion control technical field, especially based on variable gain fixed time state observer's unmanned ship path tracking control method, include the following steps: step (1): establish unmanned ship geodetic coordinate system reconstruction mathematical model;Step (2): design dynamic error envelope and adaptive time scaling factor;Step (3): construct the variable gain fixed time extended state observer of same quality;Step (4): design backstepping path tracking controller based on dynamic surface technology;Step (5): simulation verification.The present application wants to solve the problem that unmanned ship is low in tracking accuracy under complex sea conditions and "fast tracking" and "noise suppression" is difficult to take into account, by introducing error dynamic envelope and adaptive gain adjustment mechanism, to improve the transient convergence speed and steady-state noise performance of path tracking.

Description

Technical Field

[0001] This invention relates to the field of ship motion control technology, and in particular to a path tracking control method for unmanned surface vessels based on a variable gain fixed-time state observer. Background Technology

[0002] With the deepening of ocean development, unmanned surface vehicles (USVs) are widely used in marine surveying, environmental monitoring, and military reconnaissance due to their small size, low cost, and high autonomy. High-precision trajectory tracking control is fundamental to achieving autonomous navigation of these USVs. However, USVs face severe challenges when navigating at sea: on the one hand, the marine environment is extremely complex, with external disturbances such as wind, waves, and currents being unknown, time-varying, and sudden; on the other hand, the USV's own model parameters (such as hydrodynamic coefficients) are difficult to obtain accurately, resulting in model uncertainty. To address these issues, active disturbance rejection control technology based on Extended State Observer (ESO) is widely used. ESO can treat model uncertainty and external disturbances as "lumped disturbances" for real-time estimation and compensation.

[0003] However, traditional fixed-gain ESOs have significant limitations in practical applications. There is a trade-off between "speed" and "stability": increasing the observer bandwidth to improve the estimation speed of sudden disturbances introduces a large amount of high-frequency sensor measurement noise, leading to severe jitter in the control servo and wear on the actuators; conversely, reducing the bandwidth to suppress noise results in significant lag in the observer's tracking of sudden disturbances. This invention proposes an unmanned surface vessel path tracking control method based on a variable-gain fixed-time state observer. By introducing a dynamic error envelope and an adaptive gain adjustment mechanism, it achieves adaptive adjustment of the observer gain while ensuring fixed-time convergence, thus balancing disturbance rejection performance and noise suppression capabilities. Summary of the Invention

[0004] The present invention discloses an unmanned surface vessel path tracking control method based on a variable gain fixed-time state observer, which has high tracking accuracy, strong anti-disturbance capability and can effectively suppress servo motor jitter.

[0005] The following are the specific steps for implementing this invention:

[0006] The path tracking control method for unmanned surface vessels based on a variable-gain fixed-time state observer includes the following steps:

[0007] Step (1): Establishing a reconstructed mathematical model of the unmanned surface vessel in a geodetic coordinate system: Studying the motion of the underactuated unmanned surface vessel in the horizontal plane, establishing its three-degree-of-freedom (swell, roll, and yaw) dynamic model in the horizontal plane; through coordinate transformation, converting the model established in the hull coordinate system into a second-order integral cascade system in the geodetic coordinate system, and unifying the nonlinear coupling terms, hydrodynamic parameter uncertainties, and external environmental disturbances in the model into a lumped disturbance term, and extending it to the third state of the system, establishing a third-order state-space model of position-velocity-disturbance:

[0008]

[0009] In the above formula, , , These represent the geodetic coordinates, velocity, and lumped disturbance of the unmanned surface vessel, respectively. The control input items are known; The rate of change of the unknown disturbance.

[0010] Step (2): Design dynamic error envelope and adaptive time scaling factor: Based on the actual observation position error, design dynamic error envelope variables. This variable can be updated based on the instantaneous trend of error changes: it decays exponentially when the error decreases, and follows the error peak at a faster rate when the error surges due to sudden disturbances. Based on Constructing an adaptive gain adjustment factor (i.e., time scaling factor), using a smooth bounded function to ensure This enables adaptive adjustment of the internal time flow rate of the observer.

[0011] Step (3): Construct a variable-gain fixed-time extended state observer based on Lyapunov stability: Based on the third-order model reconstructed in step (1), introduce the adaptive gain adjustment factor from step (2). A nonlinear correction term with a recursive double power structure is designed; the variable gain term is transformed into a coupling term of the system state by introducing a scaling transformation, and the observer linear gain matrix is ​​designed using the linear matrix inequality (LMI) to provide positive damping; under the bandwidth time-varying rate constraint, where the real-time bandwidth is determined by the base observation bandwidth... With adaptive gain adjustment factor The definition of the product, i.e. By scaling the nonlinear correction term using the Hardy-Littlewood-Polya (HLP) inequality, the observer energy function is ensured to satisfy a fixed-time convergence form, thereby achieving global fixed-time convergence in physical time and estimating the position, velocity, and lumped disturbance of the unmanned surface vessel in real time.

[0012] Step (4): Design a backstepping path tracking controller based on dynamic surface technology: Use the state estimate and disturbance estimate output in step (3) to design a virtual control law; introduce a first-order low-pass filter to process the virtual control signal to obtain its derivative, avoiding the "differential explosion" problem in the backstepping method; combine feedforward disturbance compensation to design the final control force and torque, and drive the unmanned surface vessel propulsion system to achieve tracking of the desired path.

[0013] Step (5): Simulation verification: The unmanned surface vessel path tracking controller based on the variable gain fixed time extended state observer designed in steps (1) to (4) is simulated on the unmanned surface vessel model.

[0014] The present invention has the following beneficial effects:

[0015] 1. The method described in this invention solves the trade-off between "noise suppression" and "fast tracking" in traditional fixed-gain observers by introducing a dynamic error envelope and an adaptive gain adjustment mechanism. It automatically reduces bandwidth in steady state to filter sea wave noise and automatically increases bandwidth for rapid compensation when subjected to sudden disturbances, significantly improving the adaptability of unmanned surface vessels in complex sea conditions.

[0016] 2. This invention uses fixed-time convergence theory to design the observer correction term, ensuring that the observation error converges to a bounded region near the origin within a fixed time, and the convergence time is independent of the initial state, thus exhibiting superior transient performance compared to asymptotic convergence and finite-time convergence. Attached Figure Description

[0017] Figure 1 This is a flowchart of the steps described in this invention;

[0018] Figure 2 This is a structural diagram of the unmanned surface vessel path tracking control system of the present invention;

[0019] Figure 3 The diagram shows the planar path curve of the unmanned surface vessel under the method of this invention.

[0020] Figure 4 This is a graph showing the relationship between position estimation error and adaptive bandwidth variation under the method of this invention.

[0021] Figure 5 This is a comparison diagram between the method of the present invention and the fixed gain control input;

[0022] Figure 6 A comparison of the position estimation error norm under the invented method and the fixed gain method;

[0023] Figure 7 Verification diagram of the fixed-time convergence characteristics of the observer under the invented method; Detailed Implementation

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described below with reference to the accompanying drawings:

[0025] Implementation Case 1

[0026] like Figure 1 The path tracking method for unmanned surface vessels based on a variable gain fixed-time observer includes the following steps:

[0027] Step (1): Establishing and reconstructing the mathematical model of the unmanned surface vessel's motion: Establishing a three-degree-of-freedom dynamic model of the unmanned surface vessel in the hull coordinate system:

[0028]

[0029] In the above formula The inertia matrix includes the added mass. For velocity vector, For Coriolis matrix, Here is the damping matrix. To control the input, External environmental interference. This is addressed through coordinate transformation. ,in This maps the system to a geodetic coordinate system. State variables are defined. , , Assume the derivative of the lumped perturbation is bounded, i.e. Construct the following third-order extended state-space model:

[0030]

[0031] in, Given the control gain matrix, The rate of change of the unknown disturbance.

[0032] Step (2): Design the dynamic error envelope and adaptive time scaling factor: In order to balance noise suppression and fast tracking, a dynamic error envelope is designed. and its driven adaptive gain Define the observation position error. Design dynamic error envelope variables. The update law is as follows:

[0033]

[0034] in, For decay rate, This represents the growth rate due to abrupt disturbances. Based on... Design an adaptive gain adjustment factor :

[0035]

[0036] In the above formula, This is the maximum gain ratio. To adjust sensitivity, This is the switching threshold.

[0037] Step (3): Construct a variable-gain fixed-time extended state observer and prove its stability: Based on the third-order model reconstructed in step (1), combined with real-time bandwidth Construct the following observer:

[0038]

[0039] in, Based on bandwidth, . This is a nonlinear double-power term responsible for fixed-time convergence.

[0040] Proof of observer stability:

[0041] Define observation error And introduce scaling error variable ,in , , , The system is then organized into a compact matrix form:

[0042]

[0043] in Let be the coupling matrix introduced due to the time-varying bandwidth. The Lyapunov function is constructed as follows:

[0044]

[0045] right Differentiating and substituting into the error dynamics equation, we get:

[0046]

[0047] In the above formula, Design constraints using linear matrix inequalities (LMI) and Rayleigh's business nature Further scaling of the derivative term:

[0048]

[0049] Assumption ,make .

[0050] The bandwidth filtering constraint designed in step (2) This ensures the negative definiteness of the quadratic term coefficient. The effective linear decay rate is defined as... For the nonlinear double-power correction term Continuous scaling is performed using the Hardy-Littlewood-Polya (HLP) inequality:

[0051]

[0052] in, , Let be a very small positive constant. The above inequality can be simplified to the standard fixed-time convergent differential inequality form:

[0053]

[0054] The design parameters satisfy:

[0055]

[0056] According to the finite-time / fixed-time stability lemma, the error variable... Will be independent of the initial state The residual set converges to near the origin in physical time. Its upper bound on convergence time satisfy:

[0057]

[0058] Step (4): Design a backstepping path tracking controller based on dynamic surface technology:

[0059] Using the system state estimate obtained in step (3) , and lumped disturbance estimate A controller is designed by combining backstepping and dynamic surface control techniques. The specific process is as follows:

[0060] Step 1: Define the position tracking error vector The actual location of the unmanned surface vessel With the expected path Difference:

[0061]

[0062] Taking its derivative, we get:

[0063]

[0064] Step 2: Design the virtual control law Stable position error Choose a positive definite gain matrix. ,design as follows:

[0065]

[0066] To handle the cause Differentiation leads to a "differential explosion" term as the system order increases. A first-order low-pass filter is introduced to filter the virtual control signal. The signal is processed to obtain the filtered virtual control signal. and its derivative :

[0067]

[0068] in, The time constant of the filter, This is the tracking command for the velocity subsystem. The initial conditions of the filter are set to... .

[0069] Step 3: Define the speed tracking error The actual speed and the expected speed after filtering Difference:

[0070]

[0071] Based on the model in step (1), the dynamic equations of the velocity subsystem are:

[0072]

[0073] right Find the derivative and substitute it into the system model:

[0074]

[0075] To stabilize speed errors and compensate for external disturbances, the final control force and torque inputs were designed. Here we introduce the lumped disturbance estimate output from step (3). Perform feedforward compensation:

[0076]

[0077] In the above formula, Here is the positive definite gain matrix of the velocity subsystem; This is the disturbance compensation term output by the observer, used to offset model uncertainties and environmental disturbances; Based on Lyapunov stability design, the coupling effect between the position subsystem and the velocity subsystem is eliminated.

[0078] Step (5): Simulation verification:

[0079] The unmanned surface vessel path tracking controller based on the variable gain fixed-time extended state observer designed in steps (1) to (5) is simulated as follows: the desired path is set to the northward radius. Eastward radius The elliptical trajectory; the total simulation time is The sampling step size is To simulate the measurement uncertainties of real sensors, zero-mean Gaussian white noise was added to the position and heading angle feedback. The noise standard deviation is set to Measurement noise corresponding to the north, east, and heading angles, respectively. During the simulation... Time-varying ocean wave disturbances, simulated by superposition of multi-frequency sine waves, are introduced to simulate real complex sea conditions. Among them, interference frequency Evenly distributed in Within the interval, phase exist Internal random distribution, amplitude Randomization is applied based on the baseline strength. The initial state of the unmanned surface vessel is set to... The positional deviation from the expected trajectory starting point is significant and is used to test the convergence performance of the system.

[0080] Figure 3 The planar path tracking curves of the unmanned surface vessel (USV) under the method of this invention are shown. The solid black line in the figure represents the actual trajectory of the USV, and the circled points represent the desired reference path. Simulation results show that despite a large initial positional deviation, the USV can quickly adjust its course and converge to the desired elliptical trajectory under the control of the controller. The actual trajectory and the reference trajectory highly overlap during the steady-state phase. Especially... After encountering sudden ocean wave interference, the trajectory did not show significant deviation or oscillation, demonstrating that the control strategy of this invention has excellent transient response speed and anti-interference robustness. Figure 4 The curves showing the variation of the position estimation error norm and adaptive bandwidth under the method of this invention are presented. The results reveal the core adjustment mechanism of VB-FTESO: in the early stage of simulation or at the moment of disturbance, when the estimation error is large, the observer bandwidth can adaptively increase to improve the state tracking speed and quickly eliminate the error; in the steady state stage, as the error decreases, the bandwidth automatically decreases to suppress the influence of high-frequency measurement noise from the sensor on the system. This mechanism effectively solves the contradiction between fast response and noise suppression in traditional fixed-gain observers. Figure 5The control input curves of the method of this invention and the high-gain control method were compared. The results show that, compared with the severe chattering generated by high-gain control, the control torque calculated by the method of this invention is smooth and continuous. Figure 6 The curves showing the position estimation error norms of the method of this invention and the traditional fixed-gain method are presented. Figure 7 The fixed-time convergence property of the observer was verified. Three different initial estimation errors were set ( , , Simulation results show that, regardless of the initial error magnitude, the observation error can converge to a small neighborhood near the origin within a preset fixed time.

[0081] This invention introduces a variable gain fixed-time extended state observer and designs a path tracking controller based on observer compensation. It solves the problems of low tracking accuracy of unmanned surface vessels under external environmental interference and the difficulty in balancing "fast tracking" and "noise suppression". The designed control method can significantly improve the transient convergence speed and steady-state noise immunity of path tracking.

[0082] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A path tracking control method for unmanned surface vessels based on a variable-gain fixed-time state observer, characterized in that: It includes the following steps: Step (1): Establish a second-order integrator reconstruction model of the unmanned surface vessel in the geodetic coordinate system: study the motion of the underactuated unmanned surface vessel in the horizontal plane and establish its three-degree-of-freedom dynamic model; through coordinate transformation, the model established in the hull coordinate system is converted into a second-order integral cascade system in the geodetic coordinate system, and the nonlinear coupling terms, hydrodynamic parameter uncertainties and external environmental disturbances in the model are uniformly summarized into lumped disturbance terms, and extended to the third state of the system, and a third-order extended state space model including position, velocity and lumped disturbance is established. Step (2): Design dynamic error envelope and adaptive time scaling factor: Based on the actual observation position error, design dynamic error envelope variables. ; This variable can be updated based on the instantaneous trend of error changes: it decays exponentially when the error decreases, and follows the error peak at a faster rate when the error surges due to sudden disturbances; based on Constructing an adaptive gain adjustment factor Using a smooth bounded function to ensure This enables adaptive adjustment of the internal time elapsed rate of the observer; Step (3): Construct a variable-gain fixed-time extended state observer based on Lyapunov stability: Based on the third-order model reconstructed in step (1), introduce the adaptive gain adjustment factor from step (2). Design a nonlinear correction term with a recursive double power structure; By introducing a scaling transformation, the variable gain term is converted into a coupling term of the system state, and the linear matrix inequality (LMI) is used to design the observer's linear gain matrix to provide positive damping; under the bandwidth time-varying rate constraint, where the real-time bandwidth is determined by the base observation bandwidth... With adaptive gain adjustment factor The definition of the product, i.e. By scaling the nonlinear correction term using the Hardy-Littlewood-Polya (HLP) inequality, the observer energy function is ensured to satisfy a fixed-time convergence form, thereby achieving global fixed-time convergence in physical time and estimating the position, velocity, and lumped disturbance of the unmanned surface vessel in real time. Step (4): Design a backstepping path tracking controller based on dynamic surface technology: Use the state estimate and disturbance estimate output in step (3) to design a virtual control law; introduce a first-order low-pass filter to process the virtual control signal to obtain its derivative, avoiding the "differential explosion" problem in the backstepping method; combine feedforward disturbance compensation to design the final control force and torque, drive the unmanned surface vessel propulsion system to achieve tracking of the desired path; Step (5): Simulation verification: The unmanned surface vessel path tracking controller based on the variable gain fixed time extended state observer designed in steps (1) to (4) is simulated and verified on the unmanned surface vessel model.

2. The unmanned surface vessel path tracking control method based on a variable gain fixed-time extended state observer according to claim 1, characterized in that: The specific process of model reconstruction described in step (1) is as follows: The dynamic model of the unmanned surface vessel in the hull coordinate system is as follows: Through coordinate transformation The system is reconstructed into a third-order extended state-space model in the geodetic coordinate system: In the above formula, The pose is in the geodetic coordinate system. For the velocity in the geodetic coordinate system, For lumped disturbance terms; The inertia matrix, For velocity vector, To control the input, External interference; Given the control gain matrix, The rate of change of the unknown disturbance. In the above formula, The inertia matrix, For the velocity in the ship's coordinate system, The pose is in the geodetic coordinate system. Let be a rotation matrix. For antisymmetric matrices, To control the input, External interference To control the input matrix.

3. The unmanned surface vessel path tracking control method based on a variable gain fixed-time extended state observer according to claim 1, characterized in that: The observer design described in steps (2) and (3) is as follows: Dynamic error envelope The renewal law: in, For observation position error, For decay rate, This represents the growth rate caused by the mutational perturbation. Adaptive gain adjustment factor : in, This is the maximum gain ratio. To adjust sensitivity, This is the switching threshold. The state equation of the variable-gain fixed-time extended state observer is designed as follows: in, , , These are estimates of position, velocity, and lumped disturbance. For observation position error, The baseline observation bandwidth. A nonlinear correction function used to achieve fixed-time convergence. Designed as follows: ， In the above formula, , , Positive gain coefficients that ensure the stability of the corresponding characteristic polynomial Hurwitz. Low power. satisfy ,in ;Higher power satisfy ,in .

4. The unmanned surface vessel path tracking control method based on a variable gain fixed-time extended state observer according to claim 1, characterized in that: The specific design steps of the backstepping path tracking controller mentioned in step (4) are as follows: Step 1: Based on the desired path and observer to estimate position Define position error : Step 2: Design the virtual control law: Design the virtual control vector Stabilization position error subsystem: in, It is a positive definite gain matrix. Step 3: Dynamic Surface Filtering: Let the virtual control vector... Through a time constant A first-order low-pass filter is used to obtain the filtered virtual control signal. and its derivative : Step 4: Design the dynamic control law: Define the speed tracking error And introduce the disturbance estimate from the observer output. Perform feedforward compensation and design the final control law. .

Images