Unmanned ship model-free adaptive trajectory tracking control method in packet loss environment

Abstract

The application provides a model-free adaptive trajectory tracking control method for unmanned ships in a packet loss environment, which comprises the following steps: establishing an underactuated unmanned ship kinematics model, designing a data packet loss prediction sequence compensation mechanism, and outputting actual pose and actual speed; building a double closed-loop control framework with a proportional differential controller in the outer loop and a model-free adaptive controller combined with a discrete extended state observer in the inner loop; designing an outer loop proportional differential controller, taking the pose error between the reference pose and the actual pose as the input, and outputting the expected speed; designing an inner loop model-free adaptive controller, taking the speed error between the expected speed and the actual speed as the input, and outputting the control input before compensation; and designing an inner loop discrete extended state observer, outputting the disturbance estimation value as the disturbance compensation signal, and generating the compensated control input. The application realizes the robust control and collaborative compensation mechanism under the condition of data packet loss and disturbance superposition, so as to guarantee the safe and reliable operation of the unmanned ship trajectory tracking control.

Description

Technical Field

[0001] This invention relates to the technical field of autonomous driving for unmanned vessels, and in particular to a model-free adaptive trajectory tracking control method for unmanned vessels in a packet loss environment. Background Technology

[0002] Unmanned surface vessels (USVs) are widely used in maritime transport, environmental monitoring, hydrological surveying, ocean observation, and safety inspection. Trajectory tracking control, as a fundamental capability for autonomous navigation, is crucial for ensuring accurate motion response, operational safety, and reliable mission execution. However, existing trajectory tracking control technologies still face numerous challenges in real-world networked control environments and complex sea conditions.

[0003] I. Control Challenges Arising from Network Communication Constraints and Data Packet Loss

[0004] On the one hand, networked sensing and control architectures are increasingly widely used in real-world marine systems. However, these architectures are often affected by radio interference, communication blockages, or bandwidth limitations, easily leading to problems such as data packet loss, communication delays, and intermittent signal interruptions. Under data packet loss conditions, discontinuous feedback signals can cause inaccurate tracking error calculations, unreliable controller updates, and sudden fluctuations in control inputs. At the instant network communication recovers from packet loss, traditional numerical differentiation can generate artificially large derivative spikes in response to abrupt signal changes, easily disrupting the closed-loop system stability of downstream proportional-derivative and predictive control modules.

[0005] On the other hand, to reduce reliance on precise mathematical models, existing technologies have proposed methods such as model-free adaptive control and data-driven predictive control. However, most existing data-driven control methods are designed under the assumption that effective feedback data can be continuously provided, which often fails to meet the requirements in networked unmanned surface vessels where packet loss exists. Although some technologies have studied data-driven control for networked nonlinear systems to address communication delays and packet loss, there is still a lack of sufficient consideration and suppression of feedback discontinuities caused by packet loss and derivative spikes caused by signal recovery periods.

[0006] II. Control Challenges Arising from Nonlinear Dynamics and Lumped Disturbances

[0007] Unmanned vessels in real water environments not only have nonlinear and strongly coupled dynamic models, but are also highly susceptible to time-varying external disturbances, hydrodynamic uncertainties, and lumped disturbances such as unmodeled dynamics, which can reduce trajectory tracking accuracy.

[0008] To address these issues, existing technologies typically employ model-based control, adaptive control, disturbance observer-based control, and predictive control to improve trajectory tracking accuracy and robustness against environmental disturbances. Furthermore, extended state observers are used to estimate unknown disturbances online and provide compensation for controllers in data-driven or unmanned surface vessel control systems. However, these existing control methods often rely on partially accurate model information or continuously reliable measurement signals, limiting their direct application under data loss conditions.

[0009] In general, existing technologies primarily focus on single adaptive control, networked data-driven approaches, or disturbance observation compensation. However, under complex conditions of data loss and lumped disturbances, they still suffer from insufficient transient error suppression capabilities and control instability during the recovery period. Currently, no technology fully integrates predictive control based on model-free adaptive control and disturbance suppression based on extended state observers into a unified dual-closed-loop unmanned surface vessel (USV) tracking framework. Therefore, it is urgent to design robust control and collaborative compensation mechanisms for data loss and disturbance superposition conditions to ensure the safe and reliable operation of USV trajectory tracking control. Summary of the Invention

[0010] To address the technical problems of insufficient transient error suppression capability, easy instability of control during recovery period, and low trajectory tracking accuracy under complex conditions of data packet loss and lumped disturbance superposition, this invention proposes a model-free adaptive trajectory tracking control method for unmanned vessels under packet loss environment. It realizes robust control and collaborative compensation mechanism for the superposition of data packet loss and disturbance conditions to ensure the safe and reliable operation of unmanned vessel trajectory tracking control.

[0011] To achieve the above objectives, the technical solution of the present invention is implemented as follows: a model-free adaptive trajectory tracking control method for unmanned surface vessels under packet loss conditions, comprising the following steps:

[0012] S1: Establish an underactuated unmanned surface vessel kinematic model, design a data packet loss prediction sequence compensation mechanism, and output the actual pose and actual velocity.

[0013] S2: Generate reference pose based on preset reference trajectory, and build a dual closed-loop control framework that combines an outer loop of proportional-derivative controller and an inner loop of model-free adaptive controller with discrete extended state observer;

[0014] S3: Design an outer loop proportional-derivative controller, taking the pose error between the reference pose and the actual pose as input, and outputting the desired velocity;

[0015] S4: Design an inner-loop model-free adaptive controller, taking the speed error between the desired speed and the actual speed as input, and outputting the control input before compensation;

[0016] S5: Design an inner-loop discrete extended state observer, output the extended state disturbance estimate as a disturbance compensation signal, and subtract it from the control input before compensation to generate the control input after compensation.

[0017] The method for outputting the actual pose and actual velocity in the designed data packet loss prediction sequence compensation mechanism is as follows:

[0018] At each normal sampling time Using the current effective measurement state as the initial condition, construct the prediction sequence. , of which Predicting nodes for:

[0019] ;

[0020] in, , To predict sequence length, , , These represent the pose state, velocity state, and control input of the unmanned vessel at sampling time k, respectively.

[0021] When data packet loss occurs, let the time of the last successful communication be... Calculate the current sampling time With the last successful communication time Time difference between directly from the predicted sequence Extract the first Each prediction node serves as an information transmission node;

[0022] Actual pose Actual speed and actual control input The switching logic is determined by the following:

[0023] ;

[0024] in, For data to be successfully transmitted, For data packet loss, , , These represent the pose, velocity, and control input of the unmanned surface vessel at sampling time k. , , The unmanned ship was at the moment of its last successful communication. Predicted pose, velocity, and control inputs.

[0025] The outer-loop proportional-differential controller is designed to output the desired velocity using the pose error between the reference pose and the actual pose as input.

[0026] The pose error in the inertial coordinate system is transformed by coordinate rotation to obtain the actual pose tracking error in the body coordinate system. A first-order low-pass filter is designed to smooth the difference term of the actual pose tracking error. The smoothed actual pose tracking error is used to generate the desired velocity by the outer loop proportional-differential controller, which serves as the reference input for the inner loop model-free adaptive controller.

[0027] The coordinate rotation transformation and the design method of the first-order low-pass filter are as follows:

[0028] The coordinate rotation transformation is as follows:

[0029] ;

[0030] ;

[0031] in, , , These represent the longitudinal reference position, lateral reference position, and reference yaw angle of the unmanned surface vessel at sampling time k, respectively. , These represent the actual longitudinal tracking error and the actual yaw angle tracking error of the unmanned surface vessel at sampling time k, respectively. , , These represent the actual longitudinal position, actual lateral position, and actual yaw angle of the unmanned vessel at sampling time k;

[0032] Based on the actual longitudinal tracking error and the actual yaw angle tracking error, the original discrete difference term is designed. Set the differential term to zero the instant packet loss is recovered:

[0033] ;

[0034] ;

[0035] in, Data packet loss occurred at the previous sampling time. For sampling time k, data was successfully transmitted. Actual longitudinal tracking error Original discrete difference term, Actual yaw angle tracking error Original discrete difference term, , These represent the actual longitudinal tracking error and the actual yaw angle tracking error of the unmanned vessel at the previous sampling time, respectively.

[0036] The smoothing derivative term is obtained using a filter update law:

[0037] ;

[0038] ;

[0039] in, These are the filter coefficients. Sampling time, The filter time constant is This is the derivative of the smoothed actual longitudinal error. This is the derivative of the smoothed actual yaw angle error.

[0040] The desired speed is:

[0041] ;

[0042] ;

[0043] in, , Let be the longitudinal expected velocity and the turning expected velocity of the unmanned vessel at sampling time k, respectively. , These represent the feedforward longitudinal velocity and feedforward yaw rate of the unmanned surface vessel at sampling time k, corresponding to the reference trajectory. The actual lateral tracking error of the unmanned surface vessel at sampling time k. , , This is the proportional positive gain parameter. , All are differential positive gain parameters; For distance constraint terms, , This is the distance threshold.

[0044] The method for designing the inner-loop model-free adaptive controller, using the speed error between the desired speed and the actual speed as input, and outputting the control input before compensation, is as follows:

[0045] Establish a discrete control system and derive the system dynamic linearization; design an inner-loop model-free adaptive controller based on the system dynamic linearization, and output the control input before compensation.

[0046] The method for establishing a discrete control system and deriving the dynamic linearization of the system is as follows:

[0047] Discrete control systems are:

[0048] ;

[0049] in, Let V be the velocity vector of the unmanned vessel at the next sampling time. For unmanned ships at the sampling time The velocity vector, , These represent the longitudinal velocity and turning velocity of the unmanned vessel at sampling time k, respectively. This is the control input for the unmanned surface vessel at sampling time k. , These represent the longitudinal thrust and yaw control torque of the unmanned surface vessel at sampling time k, respectively. , They are two unknown positive integers;

[0050] for There exists a time-varying pseudopartial derivative matrix. The dynamic linearized input-output increment relationship of the system is obtained as follows:

[0051] ;

[0052] in, This represents the velocity increment of the unmanned vessel at the next sampling time. For unmanned ships at the sampling time The control input increment, For residual set items;

[0053] The prediction model for obtaining the velocity vector is:

[0054] .

[0055] The method for designing an inner-loop model-free adaptive controller based on system dynamic linearization, and outputting the control input before compensation, is as follows:

[0056] Design the loss function for the inner-loop model-free adaptive controller control law:

[0057] ;

[0058] in, Let the unmanned vessel's expected velocity be at the next sampling time. It is a positive weighting coefficient;

[0059] Differentiating the loss function and setting it to zero yields the control input increment. for:

[0060] ;

[0061] in, To control the step size;

[0062] Control inputs before compensation:

[0063] ;

[0064] in, , These represent the longitudinal thrust and yaw control torque of the unmanned surface vessel before compensation at sampling time k, respectively. , These are the control step sizes for the longitudinal channel and the steering channel, respectively. , These are the positive weighting coefficients for the longitudinal channel and the turning channel, respectively. , The unmanned boat at the sampling time The pseudo-partial derivatives of longitudinal velocity and steering velocity;

[0065] Design pseudopartial derivative estimate Loss function:

[0066] ;

[0067] pseudo-partial derivative estimate The update law is:

[0068] ;

[0069] in, To control the step size, It is a positive weighting coefficient. This is the incremental control input for the unmanned vessel at the previous sampling time.

[0070] The method for designing the inner-loop discrete extended state observer is as follows:

[0071] Introducing an expansion state:

[0072] ;

[0073] ;

[0074] in, , The unmanned boat at the sampling time The longitudinal expansion state and the directional expansion state, , These represent the longitudinal velocity increment and the turning velocity increment of the unmanned vessel at the next sampling time, respectively. , The unmanned boat at the sampling time The longitudinal thrust increment and the yaw control moment increment;

[0075] Observation error of the longitudinal channel for: ;

[0076] Observation error of the steering channel for: ;

[0077] in, , The unmanned boat at the sampling time The estimated longitudinal velocity and the estimated steering velocity;

[0078] Design saturation operator ,for :

[0079] ;

[0080] in, As a preset saturation boundary, For input parameter variables in the definition of saturation operator functions;

[0081] The estimated value of the extended state perturbation is:

[0082] ;

[0083] ;

[0084] in, In a vertically expanding state The estimate, To transition to an expansion state The estimate, The pseudo-partial derivative of the longitudinal velocity The estimate, For the pseudo-partial derivative of the steering speed The estimate, , For longitudinal observer gain, , For the steering observer gain, The saturation limit for estimating the longitudinal expansion state. The saturation bound for estimating the transition to the expansion state.

[0085] The method for generating the compensated control input is as follows:

[0086] Unmanned boat sampling time longitudinal thrust increment and yaw control torque increment for:

[0087] ;

[0088] in, , All are for controlling step size. , The unmanned boat at the sampling time Longitudinal speed error and steering speed error;

[0089] Compensated control input:

[0090] ;

[0091] in, , These represent the longitudinal thrust and yaw control torque of the unmanned vessel after compensation at sampling time k, respectively.

[0092] The beneficial effects of this invention are:

[0093] 1. A signal holding mechanism based on a zero-order hold is introduced into the dual-loop control framework. This mechanism can effectively buffer and maintain the latest valid feedback measurement value during intermittent packet loss, preventing the controller from failing due to missing or undefined data. This ensures that the closed-loop system can maintain a continuous data stream and stable trajectory tracking even under periodic or random communication interruptions.

[0094] 2. A derivative suppression strategy and a first-order low-pass filter mechanism were incorporated into the outer-loop controller. By monitoring the communication status, the original discrete derivative of the tracking error is forced to zero at the precise moment of signal recovery, effectively blocking the propagation of spurious differential spikes to the controller. This significantly smooths the output desired speed and yaw rate commands, prevents instability in the downstream predictive control module, and improves the transient stability of the system.

[0095] 3. A model-free adaptive predictive controller with extended state observer compensation was designed in the inner loop. This significantly reduces the closed-loop system's dependence on an accurate model, improves trajectory tracking accuracy, ensures bounded convergence of velocity tracking errors, and enhances anti-interference capability and engineering feasibility. Attached Figure Description

[0096] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0097] Figure 1 This is a flowchart of the present invention.

[0098] Figure 2 This is a design diagram of the mapping from the body coordinate system to the inertial coordinate system of the present invention.

[0099] Figure 3This is a schematic diagram of the dual closed-loop control framework of the present invention.

[0100] Figure 4 This is a comparison diagram of the actual trajectory of the experimental hull and the reference trajectory of the present invention.

[0101] Figure 5 This is a comparison diagram of the longitudinal speed error and steering speed error of the experimental hull of the present invention.

[0102] Figure 6 This is a schematic diagram of the experimental hull speed estimation and disturbance estimation of the present invention. Detailed Implementation

[0103] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0104] This invention proposes a model-free adaptive trajectory tracking control method for unmanned surface vessels in packet loss environments, such as... Figure 1 As shown, the invention includes: establishing a kinematic model of the unmanned surface vessel (USV); designing a data loss prediction sequence compensation mechanism; using the output state vector as the input of a proportional-derivative (PD) controller and the output velocity vector as the input of an extended state observer; generating a reference signal; constructing a dual-closed-loop control framework with an outer loop of a PDR controller and an inner loop of a model-free adaptive controller; using the output of a zero-order hold as the reference input of the dual-closed-loop control framework; employing a first-order filter to prevent differential jumps during data loss recovery; designing a PDR controller, with the output desired velocity as the reference input of the model-free adaptive controller; establishing a discrete control system and deriving the system's dynamic linearization; designing a model-free adaptive controller, with its output as the control input before compensation; establishing a discrete extended state system and introducing observation errors; designing a nonlinear discrete extended state observer, with the output disturbance estimate as the disturbance compensation signal; and deriving the control input after compensation. This invention designs a robust control and compensation mechanism for signal loss conditions to ensure the safe and reliable operation of the USV under signal loss conditions.

[0105] The specific steps of this invention are as follows:

[0106] S1: Establish an underactuated unmanned surface vessel kinematic model, design a data packet loss prediction sequence compensation mechanism, and output the actual pose and actual velocity.

[0107] S1.1 Establish the inertial coordinate system and the body coordinate system, and define the position and attitude state of the unmanned vessel in the inertial coordinate system and the velocity state in the body coordinate system; select the longitudinal channel and the yaw channel as the control objects, and the control inputs are the longitudinal thrust and the yaw control torque.

[0108] like Figure 2 As shown, the body coordinate system and the inertial coordinate system are represented as follows: and Longitudinal velocity Along the longitudinal axis lateral speed Along the horizontal axis Steering speed This represents rotational motion along the vertical axis of an inertial coordinate system. This indicates the position and heading angle of the unmanned surface vessel in the inertial coordinate system. The yaw angle represents the counterclockwise rotation of the body's coordinate axes; the pose state of the unmanned surface vessel in the inertial coordinate system. Unmanned surface vessel velocity state in body coordinate system .

[0109] The present invention is applied to an underactuated unmanned surface vessel (USV). The longitudinal channel and yaw channel are selected as the control objects, and the control inputs are the longitudinal thrust and yaw control torque, denoted as... , For longitudinal propulsion, This is the yaw control torque; similarly, the underactuated unmanned surface vessel no longer directly controls the lateral velocity, but rather controls it through a combination of longitudinal and steering velocities, denoted as [velocity vector]. .

[0110] S1.2 Design a data packet loss prediction sequence compensation switching mechanism. In the event of data packet loss, the prediction sequence is used to control and mitigate the immediate impact of data loss.

[0111] Let binary indicator variables be defined. Indicates the first The network communication status at each sampling time. Specifically, This indicates that the current measurement data packet is lost, and This indicates that the data transmission was successful and timely.

[0112] To prevent inaccurate or erroneous control by the controller in the event of data loss, a predictive sequence of future states is constructed online to compensate for data loss. Let the number of steps in the predictive sequence be... At each normal sampling time Using the current valid measurement state as initial conditions, a prediction sequence is generated synchronously. The sequence covers the future in total. Information for each step. Among them, The length of each step is determined by the ability to adequately cover the maximum duration of continuous data packet loss in the network. The first step in this sequence... Prediction nodes for each step It encapsulates the predicted pose state, velocity state, and predicted inner-loop control input, and is defined as follows:

[0113] ;

[0114] in, The predicted sequence represents the first predicted sequence. The pose state at any given moment. The predicted sequence is the first... The velocity state at any given moment, The predicted sequence represents the first predicted sequence. Timing control input; when data packet loss occurs, assume the last successful communication time is... Then calculate the current time. and Time difference between and directly from the predicted sequence Extract the corresponding first Each prediction node serves as an information transmission point.

[0115] Therefore, the actual pose used by the controller Actual speed and actual inner loop control input All are determined by the following switching logic:

[0116] ;

[0117] in, In pose state, In terms of speed state, The input is used for inner-loop control. When data is successfully transmitted, the unmanned vessel uses the normal signal received at the current moment and performs model-free adaptive control. When data packet loss occurs, the predicted sequence based on the last valid moment is used as the information transmission and control input.

[0118] S2: Generate reference pose based on preset reference trajectory, and build a dual closed-loop control framework that combines an outer loop of proportional-derivative controller and an inner loop of model-free adaptive controller with discrete extended state observer.

[0119] Generate reference pose based on preset reference trajectory A dual-loop control framework was constructed, consisting of an outer loop proportional-derivative controller, an inner loop model-free adaptive controller, and a discrete extended state observer. The actual pose and actual velocity were used as reference inputs for the dual-loop control framework, and the control input was obtained through the inner loop model-free adaptive algorithm.

[0120] S2.1 Design a circular trajectory as a reference trajectory and send the reference trajectory to the unmanned vessel.

[0121] The longitudinal channel and yaw channel are selected as the control objects, and the control inputs are the longitudinal thrust and yaw control torque; the river center coordinates are used as the trajectory center, and... As a reference trajectory radius, design the reference trajectory. Current sampling time Reference trajectory Denote as the reference trajectory vector The reference pose corresponding to each sampling time is obtained. ;in, This is the longitudinal reference position of the unmanned surface vessel in the inertial coordinate system. This is the lateral reference position of the unmanned surface vessel in the inertial coordinate system. The reference heading angle of the unmanned surface vessel in the inertial coordinate system is given; the reference velocity is obtained through inverse transformation of the rotation matrix. The specific formula is as follows:

[0122] ;

[0123] The reference trajectory, reference pose, and reference velocity are sent to the unmanned surface vessel.

[0124] S2.2 Establish a dual closed-loop control framework for unmanned vessels.

[0125] like Figure 3 As shown, the dual-closed-loop control framework includes a prediction sequence, a proportional-derivative (PD) controller, a model-free adaptive controller (MFAC), and a discrete extended state observer (ESO), wherein:

[0126] The input to the prediction sequence module is the pose state of the unmanned vessel. and speed state Output the actual pose and actual speed State error vector (pose error) The input is fed to the outer loop proportional-derivative controller, which outputs the desired speed required by the inner loop through the proportional-derivative algorithm. The state error vector is derived from the reference pose. Compared with the actual pose after the prediction sequence module We obtain the result by subtraction. For longitudinal error, For lateral error, For heading angle error, For the desired longitudinal velocity of the unmanned vessel, The desired turning speed of the unmanned vessel.

[0127] Speed ​​tracking error vector (speed error) As the input to the inner-loop model-free adaptive controller, the output is compensated by the algorithm and the discrete extended state observer. , For longitudinal propulsion, This is the yaw control torque; where, Desired speed of underactuated unmanned ships Compared to the actual speed after passing through the prediction sequence module We obtain the result by taking the difference, where For longitudinal velocity error, This refers to the steering speed error.

[0128] The discrete extended state observer is used to estimate external disturbances, and the resulting disturbance estimation vector is... A model-free adaptive controller is used for disturbance compensation. To estimate longitudinal disturbances, To estimate yaw disturbance.

[0129] S3: Design an outer loop proportional-differential controller that takes the pose error between the reference pose and the actual pose as input and outputs the desired velocity.

[0130] A first-order low-pass filter is used to prevent differential jumps in the outer loop pose state tracking error during data packet loss recovery. A proportional-derivative controller is designed, and the desired velocity is output as the reference input of the model-free adaptive controller through the controller's proportional-derivative algorithm.

[0131] S3.1 Design a first-order low-pass filter to prevent differential jumps during data packet loss recovery.

[0132] To address the design challenges of outer-loop proportional-differential controllers (PDCs) and the adverse effects of data packet loss, a first-order low-pass filter is designed. During packet loss recovery, traditional numerical differential methods may generate massive spurious differential spikes on abrupt signal changes. The first-order low-pass filter can smoothly handle these transient tracking errors, preventing the propagation of spurious spikes and thus preventing instability in downstream controllers.

[0133] For unmanned vessels, state errors are applied in the inertial coordinate system. The actual tracking error is transformed into the fixed coordinate system of the aircraft by performing a coordinate rotation transformation. The outer loop controller can then generate the desired inner loop velocity based on the transformed error, expressed as:

[0134] ;

[0135] ;

[0136] in, Indicates longitudinal tracking error. Indicates the actual yaw angle. This indicates the longitudinal reference position of the unmanned surface vessel in the inertial coordinate system. This indicates the actual longitudinal position of the unmanned surface vessel in the inertial coordinate system. This indicates the lateral reference position of the unmanned surface vessel in the inertial coordinate system. This indicates the actual lateral position of the unmanned vessel in the inertial coordinate system. Indicates the yaw angle tracking error. This represents the reference heading angle of the unmanned surface vessel in the inertial coordinate system. This indicates the actual yaw angle of the unmanned vessel.

[0137] Based on the actual tracking error, design the original difference term. To accurately reflect the rate of change in position and heading errors, and to prevent the propagation of false spikes during packet loss recovery, its expression is as follows:

[0138] ;

[0139] ;

[0140] in, This indicates that data packet loss occurred at the previous sampling time. This indicates that data transmission was successful and timely at the current sampling moment. Indicates longitudinal tracking error Original discrete difference term, Indicates yaw angle tracking error Original discrete difference term.

[0141] A filtering update law is used to obtain a smoothing derivative term, which smooths the final output longitudinal and yaw angle commands. The expression is as follows:

[0142] ;

[0143] ;

[0144] in, These are the filter coefficients. For system sampling time, The filter time constant is This represents the derivative of the smoothed longitudinal error. This represents the derivative of the smoothed yaw angle error.

[0145] S3.2 Error dynamic characteristics and feedforward reference velocity after first-order low-pass filtering smoothing Design a proportional-derivative controller, with the output desired velocity serving as the reference input for a model-free adaptive controller.

[0146] The proportional-derivative controller is designed as follows:

[0147] ;

[0148] ;

[0149] in, Indicates the longitudinal expected velocity. Indicates the desired turning speed; The feedforward longitudinal velocity of the reference trajectory, The feedforward yaw rate of the reference trajectory; , , This is the proportional positive gain parameter. , The differential positive gain parameter; Indicates longitudinal tracking error. Indicates lateral error, determined by the lateral reference state. Lateral state after passing through the prediction sequence module Obtained by subtraction. This represents the yaw angle tracking error; when the unmanned vessel is extremely close to the target point, a distance constraint term is introduced. , recorded as Smaller positive distance threshold This is to prevent the rudder singularity problem caused by an excessively small denominator.

[0150] Consider a kinematic error system under the action of a proportional-derivative controller. If there exists , , , and If the outer loop error satisfies discrete-time input-state stability, and if both the inner loop velocity tracking error and the external disturbance are bounded, then the outer loop tracking error converges to the bounded region.

[0151] Proof: Define the outer loop pose state tracking error of the proportional-derivative controller as... The inner loop speed tracking error is In practice, considering disturbances, the actual outer-loop error system can be written as follows:

[0152] ;

[0153] in, Indicates the stable portion of the outer ring. This represents the matrix showing the influence of the inner loop velocity error on the outer loop error. This represents the matrix representing the influence of the outer loop disturbance on the outer loop error. Let be the outer-loop perturbation, representing the mathematical disturbance terms acting on the outer-loop kinematic error system. It is a set of bounded perturbations caused by the algorithm mechanism. Choose the following Lyapunov functions. The definition is as follows:

[0154] ;

[0155] ;

[0156] in, Furthermore, we can obtain:

[0157] ;

[0158] in, This represents a constant coefficient generated during the derivation of the outer-loop Lyapunov function inequality, used to define the inner-loop velocity error. The dynamic impact of outer ring pose error. Similarly, it represents a constant coefficient used to define the outer loop disturbance. The dynamic impact of the outer ring pose error.

[0159] Therefore, the corollary of Young's inequality is satisfied. It will not diverge and will eventually converge to a bounded neighborhood near the origin. The outer ring pose state error inner loop speed error and disturbance It conforms to input-state stability.

[0160] S4: Design an inner-loop model-free adaptive controller that takes the speed error between the desired speed and the actual speed as input and outputs the control input before compensation.

[0161] Establish a discrete control system and derive the system's dynamic linearization; design a model-free adaptive controller whose output is the control input before compensation.

[0162] S4.1 Establish a discrete control system and derive the system's dynamic linearization.

[0163] For a discrete-time nonlinear unmanned surface vessel velocity system, the following form holds:

[0164] ;

[0165] in, Let V be the velocity vector of the unmanned surface vessel in the body coordinate system. Let be the longitudinal velocity of the unmanned surface vessel in the body coordinate system. The turning speed of the unmanned vessel in the body coordinate system; To control the input, For longitudinal propulsion, For yaw control torque; , These are two unknown positive integers, representing the system's output order and input order, respectively.

[0166] According to discrete nonlinear systems, for ,in Indicates the sampling time The control increment is the difference between the control input at the current time and the control input at the previous time, resulting in a partial derivative matrix that varies over time. The dynamically linearized input-output increment relationship is expressed as follows:

[0167] ;

[0168] in, This represents the residual set term resulting from external disturbances, unmodeled dynamics, coupling effects, and approximation errors of dynamic nonlinearization.

[0169] The prediction model for obtaining the velocity vector is represented as follows:

[0170] .

[0171] The derived The loss function will be used to construct the inner-loop model-free adaptive control algorithm.

[0172] S4.2. Based on the dynamically linearized system, design a model-free adaptive controller and use the output as the control input before compensation.

[0173] Based on the dynamically linearized system, the loss function of the model-free adaptive controller control law is written in the following form:

[0174] ;

[0175] in, express The desired velocity at the sampling time is calculated by the outer loop proportional-differential controller;

[0176] Obtain the incremental control law of the model-free adaptive controller The expression is as follows:

[0177] ;

[0178] in, For the interval in Within the control step size, A positive weighting coefficient is used to prevent the denominator from suddenly becoming zero. The control input before compensation by the model-free adaptive controller can be obtained from the incremental form of the control law as follows:

[0179] ;

[0180] in, express The longitudinal propulsion force at the sampling moment, express Yaw control torque at the sampling time; , These represent the control step sizes for the longitudinal and steering channels, respectively. , These represent the positive weighting coefficients for the longitudinal and steering channels, respectively. , These represent the pseudo-partial derivatives of the longitudinal and steering channels, respectively;

[0181] Due to the pseudo-partial derivative matrix It is an unknown time-varying parameter, introducing the... The estimated value The corresponding loss function is designed, and its expression is as follows:

[0182] ;

[0183] Obtain the pseudo-partial derivative estimate The expression is as follows:

[0184] ;

[0185] in, For the interval in Within the control step size, It is a positive weighting coefficient to prevent the denominator from suddenly becoming zero.

[0186] Considering the inner-loop velocity error system based on dynamic linearization and model-free adaptive controller control law, if the reference signal... False partial derivative estimation error All are bounded and have a constant. Make The inner loop speed tracking error Regarding the lumped input after substituting the control law into the dynamic linearization model and combining them... Satisfy discrete-time input-state stability; when When it is bounded, The convergence to a bounded region means that the inner loop velocity tracking error is consistently bounded. Among these, Represents the identity matrix. This represents the nominal shrinkage control gain matrix.

[0187] Proof: According to the pseudo-partial derivative update law and the dynamic linearization expression, the pseudo-partial derivative estimation error satisfies:

[0188] ;

[0189] because It is non-extended, meaning The pseudo-partial derivative estimate at the sampling time, and , and The estimated values ​​are all bounded, therefore there exists Make That is, the error in the pseudo-partial derivative estimation is bounded.

[0190] Define the speed tracking error as:

[0191] ;

[0192] in, express The desired velocity state at the sampling time. This is the velocity vector of the unmanned surface vessel in the body coordinate system.

[0193] Substitute into the dynamic linearization expression The error recursion formula can be obtained as follows:

[0194] ;

[0195] in, Let be the nominal shrinkage matrix of the inner-loop error system. , It includes the reference signal. The set of all residual terms, including changes, pseudo-partial derivative estimation errors, etc. For the interval in Within the control step size, It is a pseudo-partial derivative matrix. This is an estimate of the pseudopartial derivative matrix.

[0196] To ensure input-to-state stability, the control parameters for the inner loop speed tracking error must meet the following requirements:

[0197] ;

[0198] in, It is a constant.

[0199] Choose the Lyapunov function as follows:

[0200] ;

[0201] ;

[0202] in, , ,and .at this time, It satisfies the discrete-time input-to-state stability condition. This represents the error attenuation coefficient in the Lyapunov difference inequality for the inner-loop error system. This represents the gain coefficient of the perturbation term in the inequality. This is a constant parameter used to derive the scaling of the cross terms.

[0203] because If it is bounded, then the following inequality holds:

[0204] ;

[0205] Therefore, the inner loop velocity tracking error satisfies input-to-state stability and is uniformly eventually bounded.

[0206] S5: Design an inner-loop discrete extended state observer, outputting a disturbance estimate as a disturbance compensation signal, and subtracting it from the control input before compensation to generate the control input after compensation.

[0207] A discrete extended state system is established, and observation errors are introduced. A nonlinear discrete extended state observer is designed, and the output disturbance estimate is used as the disturbance compensation signal. The control input after compensation is derived.

[0208] S5.1 Introduce extended states and construct a discrete extended state observer.

[0209] Design a discrete extended state observer, introducing the extended state as shown below:

[0210] ;

[0211] ;

[0212] in, and for The pseudo-partial derivatives of the longitudinal and steering velocities at the sampling time. and It is in a longitudinal and directional expansion state. express The longitudinal velocity increment at the sampling time, express The increment of steering speed at the sampling time, express The longitudinal thrust increment at the sampling time, express The increment of yaw control torque at the sampling time.

[0213] For the longitudinal and steering-controlled channels, a discrete extended state observer is constructed; the observation error of the longitudinal channel... Observation error of the steering channel , The estimated longitudinal velocity of the unmanned surface vessel in the body coordinate system is given. The estimated turning speed of the unmanned surface vessel in the body coordinate system is given. Let be the longitudinal velocity of the unmanned surface vessel in the body coordinate system. Let be the turning speed of the unmanned vessel in the body coordinate system.

[0214] S5.2 Introducing a discrete extended state observer with saturation operators to estimate disturbances in the longitudinal and steering channels online, preventing transient overcompensation caused by signal fluctuations during packet loss recovery.

[0215] Design saturation operator ,for saturation operator The definition is as follows:

[0216] ;

[0217] in, This indicates the preset saturation boundary. This represents the input parameter variable in the definition of the saturation operator function; the saturation operator is used to preset the maximum boundary of the extended state estimate to prevent the observer from generating a huge spurious disturbance compensation signal at the moment of data packet loss recovery, thereby avoiding transient overcompensation.

[0218] The expansion state estimation of the longitudinal channel and the steering channel is introduced, and the expressions are as follows:

[0219] ;

[0220] ;

[0221] in, The estimated longitudinal velocity of the unmanned surface vessel in the body coordinate system is given. The estimated turning speed of the unmanned surface vessel in the body coordinate system is given. In a vertically expanding state The estimate, To transition to an expansion state The estimate, express The longitudinal thrust increment at the sampling time, express The increment of yaw control torque at the sampling time. express estimation of the pseudo-partial derivative of the longitudinal channel at the sampling time. express Estimate of pseudo-partial derivatives of the steering channel at the sampling time. , For longitudinal observer gain, , For steering observer gain; The saturation limit for estimating the longitudinal channel expansion state. The saturation limit for estimating the expansion state of the steering channel.

[0222] Based on the control law, the expressions for the control increments of the longitudinal and steering channels after compensation by the extended state observer are as follows:

[0223] ;

[0224] in, , All are within the range Within the control step size, , These represent the longitudinal speed error and the steering speed error, respectively, obtained by subtracting the expected speed from the actual speed in the corresponding channel. The compensated control input expression is as follows:

[0225] ;

[0226] Consider the error system of a discrete extended state observer and its bounded perturbation input. If there exists an extended state observer error matrix... ,but The equation is the Shure stability matrix, and under bounded perturbation, the estimation error of the extended state observer converges to the bounded region.

[0227] Proof: Define the discrete error system of the extended state observer. The recurrence relation is as follows:

[0228] ;

[0229] in, , This represents a bounded set of perturbation terms that includes dynamically linearized residuals, saturated residuals, etc. Because Let be the Shure stability matrix, for any ,exist This makes the following equation true:

[0230] ;

[0231] Choose the Lyapunov function as follows:

[0232] ;

[0233] Using Young's inequality, we can obtain:

[0234] ;

[0235] in, , All are positive numbers. Because... It is bounded, therefore the discrete error of the extended state observer is... Consistency is ultimately bounded.

[0236] To verify the effectiveness of the trajectory tracking control method of the present invention, simulation experiments were conducted.

[0237] Set the following parameters for the unmanned surface vessel:

[0238] Waterline length of unmanned vessels Maximum draft The longitudinal pseudo-partial derivative weighting coefficient and the turning pseudo-partial derivative weighting coefficient are respectively , The weighting coefficients for the longitudinal control law and the steering control law are respectively... , The step size factors for the longitudinal pseudo-partial derivatives and the step size factors for the turning pseudo-partial derivatives are respectively... , The longitudinal control law step size factor and the steering control law step size factor are respectively , The sampling period is The preset longitudinal saturation threshold and turning saturation threshold are respectively , The longitudinal observer gain and the steering observer gain are respectively , , , .

[0239] The trajectory tracking curve of the unmanned vessel is as follows: Figure 4 As shown.

[0240] Longitudinal velocity error of unmanned surface vessel and steering speed error like Figure 5 As shown, the longitudinal velocity error of the unmanned vessel Stay Within the range, steering speed error Stay at about Within the acceptable range, the dual-closed-loop control framework exhibits a small error range under disturbances, demonstrating feasibility and reliability.

[0241] The estimation velocity and estimation disturbance of the discrete extended state observer are as follows: Figure 6 As shown, the discrete extended state observer continuously estimates the velocity and slowly changing perturbation components during the experiment. The estimated velocity has a very small error compared to the actual velocity, demonstrating the reliability of the extended state observer.

[0242] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A model-free adaptive trajectory tracking control method for unmanned surface vessels under packet loss conditions, characterized by the following steps: include: S1: Establish an underactuated unmanned surface vessel kinematic model, design a data packet loss prediction sequence compensation mechanism, and output the actual pose and actual velocity. S2: Generate reference pose based on preset reference trajectory, and build a dual closed-loop control framework that combines an outer loop of proportional-derivative controller and an inner loop of model-free adaptive controller with discrete extended state observer; S3: Design an outer loop proportional-derivative controller, taking the pose error between the reference pose and the actual pose as input, and outputting the desired velocity; S4: Design an inner-loop model-free adaptive controller, taking the speed error between the desired speed and the actual speed as input, and outputting the control input before compensation; S5: Design an inner-loop discrete extended state observer, output the extended state disturbance estimate as a disturbance compensation signal, and subtract it from the control input before compensation to generate the control input after compensation.

2. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 1, characterized in that, The method for outputting the actual pose and actual velocity in the designed data packet loss prediction sequence compensation mechanism is as follows: At each normal sampling time Using the current effective measurement state as the initial condition, construct the prediction sequence. , of which Predicting nodes for: ； in, , To predict sequence length, , , These represent the pose state, velocity state, and control input of the unmanned vessel at sampling time k, respectively. When data packet loss occurs, let the time of the last successful communication be... Calculate the current sampling time With the last successful communication time Time difference between directly from the predicted sequence Extract the first Each prediction node serves as an information transmission node; Actual pose Actual speed and actual control input The switching logic is determined by the following: ； in, For data to be successfully transmitted, For data packet loss, , , These represent the pose, velocity, and control input of the unmanned surface vessel at sampling time k. , , The unmanned ship was at the moment of its last successful communication. Predicted pose, velocity, and control inputs.

3. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 2, characterized in that, The outer-loop proportional-differential controller is designed to output the desired velocity using the pose error between the reference pose and the actual pose as input. The pose error in the inertial coordinate system is transformed by coordinate rotation to obtain the actual pose tracking error in the body coordinate system. A first-order low-pass filter is designed to smooth the difference term of the actual pose tracking error. The smoothed actual pose tracking error is used to generate the desired velocity by the outer loop proportional-differential controller, which serves as the reference input for the inner loop model-free adaptive controller.

4. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 3, characterized in that, The coordinate rotation transformation and the design method of the first-order low-pass filter are as follows: The coordinate rotation transformation is as follows: ； ； in, , , These represent the longitudinal reference position, lateral reference position, and reference yaw angle of the unmanned surface vessel at sampling time k, respectively. , These represent the actual longitudinal tracking error and the actual yaw angle tracking error of the unmanned surface vessel at sampling time k, respectively. , , These represent the actual longitudinal position, actual lateral position, and actual yaw angle of the unmanned vessel at sampling time k; Based on the actual longitudinal tracking error and the actual yaw angle tracking error, the original discrete difference term is designed. Set the differential term to zero the instant packet loss is recovered: ； ； in, Data packet loss occurred at the previous sampling time. For sampling time k, data was successfully transmitted. Actual longitudinal tracking error Original discrete difference term, Actual yaw angle tracking error Original discrete difference term, , These represent the actual longitudinal tracking error and the actual yaw angle tracking error of the unmanned vessel at the previous sampling time, respectively. The smoothing derivative term is obtained using a filter update law: ； ； in, These are the filter coefficients. Sampling time, The filter time constant is This is the derivative of the smoothed actual longitudinal error. This is the derivative of the smoothed actual yaw angle error.

5. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 4, characterized in that, The desired speed is: ； ； in, , Let be the longitudinal expected velocity and the turning expected velocity of the unmanned vessel at sampling time k, respectively. , These represent the feedforward longitudinal velocity and feedforward yaw rate of the unmanned surface vessel at sampling time k, corresponding to the reference trajectory. The actual lateral tracking error of the unmanned surface vessel at sampling time k. , , This is the proportional positive gain parameter. , All are differential positive gain parameters; For distance constraint terms, , This is the distance threshold.

6. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 2 or 5, characterized in that, The method for designing the inner-loop model-free adaptive controller, using the speed error between the desired speed and the actual speed as input, and outputting the control input before compensation, is as follows: Establish a discrete control system and derive the system dynamic linearization; design an inner-loop model-free adaptive controller based on the system dynamic linearization, and output the control input before compensation.

7. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 6, characterized in that, The method for establishing a discrete control system and deriving the dynamic linearization of the system is as follows: Discrete control systems are: ； in, Let V be the velocity vector of the unmanned vessel at the next sampling time. For unmanned ships at the sampling time The velocity vector, , These represent the longitudinal velocity and turning velocity of the unmanned vessel at sampling time k, respectively. This is the control input for the unmanned surface vessel at sampling time k. , These represent the longitudinal thrust and yaw control torque of the unmanned surface vessel at sampling time k, respectively. , They are two unknown positive integers; for There exists a time-varying pseudopartial derivative matrix. The dynamic linearized input-output increment relationship of the system is obtained as follows: ； in, This represents the velocity increment of the unmanned vessel at the next sampling time. For unmanned ships at the sampling time The control input increment, For residual set items; The prediction model for obtaining the velocity vector is: 。 8. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 7, characterized in that, The method for designing an inner-loop model-free adaptive controller based on system dynamic linearization, and outputting the control input before compensation, is as follows: Design the loss function for the inner-loop model-free adaptive controller control law: ； in, Let the unmanned vessel's expected velocity be at the next sampling time. It is a positive weighting coefficient; Differentiating the loss function and setting it to zero yields the control input increment. for: ； in, To control the step size; Control inputs before compensation: ； in, , These represent the longitudinal thrust and yaw control torque of the unmanned surface vessel before compensation at sampling time k, respectively. , These are the control step sizes for the longitudinal channel and the steering channel, respectively. , These are the positive weighting coefficients for the longitudinal channel and the turning channel, respectively. , The unmanned boat at the sampling time The pseudo-partial derivatives of longitudinal velocity and steering velocity; Design pseudopartial derivative estimate Loss function: ； pseudo-partial derivative estimate The update law is: ； in, To control the step size, It is a positive weighting coefficient. This is the incremental control input for the unmanned vessel at the previous sampling time.

9. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 8, characterized in that, The method for designing the inner-loop discrete extended state observer is as follows: Introducing an expansion state: ； ； in, , The unmanned boat at the sampling time The longitudinal expansion state and the directional expansion state, , These represent the longitudinal velocity increment and the turning velocity increment of the unmanned vessel at the next sampling time, respectively. , The unmanned boat at the sampling time The longitudinal thrust increment and the yaw control moment increment; Observation error of the longitudinal channel for: ; Observation error of the steering channel for: ; in, , The unmanned boat at the sampling time The estimated longitudinal velocity and the estimated steering velocity; Design saturation operator ,for : ； in, As a preset saturation boundary, For input parameter variables in the definition of saturation operator functions; The estimated value of the extended state perturbation is: ； ； in, In a vertically expanding state The estimate, To transition to an expansion state The estimate, The pseudo-partial derivative of the longitudinal velocity The estimate, For the pseudo-partial derivative of the steering speed The estimate, , For longitudinal observer gain, , For the steering observer gain, The saturation limit for estimating the longitudinal expansion state. The saturation bound for estimating the transition to the expansion state.

10. The unmanned surface vessel model-free adaptive trajectory tracking control method under packet loss environment according to claim 9, characterized in that, The method for generating the compensated control input is as follows: Unmanned boat sampling time longitudinal thrust increment and yaw control torque increment for: ； in, , All are for controlling step size. , The unmanned boat at the sampling time Longitudinal speed error and steering speed error; Compensated control input: ； in, , These represent the longitudinal thrust and yaw control torque of the unmanned vessel after compensation at sampling time k, respectively.

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