Trajectory tracking control method based on multi-point linearization model of gaussian process

Abstract

The application discloses a kind of based on Gaussian process's multi-point linearization model prediction trajectory tracking control method, including for the trajectory tracking problem of autonomous surface unmanned vehicle ASV, constructs ASV dynamics model;Gaussian process GP is used to approximate the unmodeled dynamics of ASV trajectory tracking system, GP prediction model is obtained;Based on dictionary size limit and maximum likelihood method, the updating criterion of dictionary data and hyperparameter is established, and GP prediction model is optimized;Combined with the optimized GP prediction model and ASV dynamics model, using learning-based model predictive control MPC method, GP-MPC framework is constructed, and terminal state set is designed;Based on multi-point linearization method, combined with local linear model predictive control LMPC method, the algorithm for solving GP-MPC framework optimization problem is designed, and the real-time control of ASV trajectory tracking is realized.The application can ensure the trajectory tracking precision of ASV, and significantly reduce the calculation time.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent control, and relates to a multi-point linearization model predictive trajectory tracking control method based on a Gaussian process. BACKGROUND

[0002] Autonomous surface vehicles (ASVs) have gained wide applications in marine environmental monitoring, resource exploration, rescue operations, and military fields in recent years. In these application scenarios, ASVs need to perform trajectory tracking tasks in complex, variable, and uncertain marine environments, thus putting forward extremely high requirements for the robustness, accuracy, and real-time performance of their control systems. However, existing ASV control methods, such as the classic proportional-integral-derivative (PID) control, linear quadratic regulator (LQR) control, and standard model predictive control (MPC) method, usually rely on accurate modeling of system dynamics. However, in actual environments, ASV motion involves complex nonlinear hydrodynamics and unknown environmental disturbances (see Teng F, Han S. Nonlinear dynamics of marine vehicles under environmental disturbances. Journal of Marine Science and Technology, 2020: 1340-1350.), which makes it difficult for control methods based on accurate models to achieve ideal results in dynamic and uncertain scenarios.

[0003] MPC is an advanced control method that has been widely applied in industrial and robot control fields (see Camacho EF, Bordons C. Model predictive control. Springer Science & Business Media, 2013.) due to its ability to generate multi-step prediction and control sequences through a rolling optimization strategy. One of the significant advantages of MPC is its ability to handle system constraints and improve control accuracy through online optimization. However, the performance of MPC is heavily dependent on the accuracy of the system model. In the face of the complex nonlinear dynamics and uncertainties of ASVs, traditional MPC methods are difficult to effectively cope with.

[0004] Although GP-MPC has shown significant potential in solving nonlinear control problems, it still faces challenges in reducing computational complexity as the size of the dataset increases (see Quinonero-Candela J, Rasmussen CE. Aunifying view of sparse approximate Gaussian process regression. Journal of Machine Learning Research, 2005: 1939-1959.). However, current theoretical analysis of the iterative feasibility and asymptotic stability of the GP-MPC method is still insufficient, which limits its widespread promotion in practical applications.

[0005] Furthermore, MPC can be divided into linear MPC (LMPC) and nonlinear MPC (NMPC) (see Mayne DQ, Rawlings JB. Model predictive control: Theory and design. Nob Hill Publishing, 2009.). Although NMPC is applicable to nonlinear dynamic models, its optimization problem is complex and difficult to achieve real-time control (see Diehl M, Bock HG. Efficient solution of nonlinear MPC problems. IEEE Transactions on Automatic Control, 2005: 255-269.). In contrast, LMPC uses linear models to reduce the computational burden, but when the state deviates from the linearization point, the model accuracy decreases rapidly, resulting in reduced control performance (see Wang L. Model predictive control system design and implementation using MATLAB. Springer, 2009.). Summary of the Invention

[0006] Objective of the invention: The objective of the present invention is to provide a Gaussian process-based multi-point linearized model predictive trajectory tracking control (GP-MP-LMPC) method that significantly reduces the computation time while ensuring the ASV trajectory tracking accuracy.

[0007] Technical solution: The multi-point linearized model prediction trajectory tracking control method based on Gaussian process of the present invention includes the following steps:

[0008] S1. Aiming at the trajectory tracking problem of autonomous surface vehicle (ASV), an ASV dynamics model is constructed.

[0009] S2, introduce the Gaussian process GP into the ASV trajectory tracking system to approximate the unmodeled dynamics of the system and obtain the GP prediction model;

[0010] S3. Based on dictionary size limitation and maximum likelihood method, establish the update criteria of dictionary data and hyperparameters to optimize the GP prediction model;

[0011] S4. Combining the optimized GP prediction model with the ASV dynamics model, using the learning-based model predictive control MPC method, constructing the GP-MPC framework, and designing the terminal state set;

[0012] S5. Based on the multi-point linearization method, the state prediction model in the prediction time domain is derived. Combined with the local linear model predictive control LMPC method, an algorithm is designed to solve the GP-MPC framework optimization problem to achieve real-time control of ASV trajectory tracking.

[0013] Furthermore, the ASV kinetic model constructed in step S1 is expressed as:

[0014]

[0015] in, is the time derivative of the state variable x, x = [η T v T ] T =[xy ψ uvr] T , is a generalized coordinate vector, where x, y, and ψ are the horizontal coordinate, vertical coordinate, and heading angle of ASV in the Earth coordinate system, respectively. is the velocity vector, u, v, and r are the forward velocity, roll velocity, and yaw velocity of the ASV in the hull coordinate system, respectively. T is the transpose of the matrix, u is the control input, u=τ, τ=[τ u τ v τ r ] T is the torque of the control force, τ u is the torque in the direction of forward speed, τ v is the moment in the direction of the rolling velocity, τ r is the torque in the direction of yaw angular velocity, R(η) is the rotation matrix, A(v)=-M -1 (C(v)+D(v)), B=M -1 , M -1 is the inverse matrix of M, M is the positive definite symmetric inertia matrix, C(v) is the Coriolis matrix, D(v) is the damping matrix, represents the unmodeled dynamics in the ASV trajectory tracking problem, e1(v) is the component of the unmodeled dynamics that affects the forward velocity, e2(v) is the component of the unmodeled dynamics that affects the roll velocity, and e3(v) is the component of the unmodeled dynamics that affects the yaw velocity.

[0016] Furthermore, when solving the ASV trajectory tracking problem in step S1, each state of the ASV trajectory tracking system has a corresponding reference state x r (t) = [x r (t), y r (t), ψ r (t),u r (t), v r (t), r r (t)] T , defined as follows:

[0017]

[0018] v r (t) = 0,

[0019]

[0020] Among them, x r (t) is the reference horizontal coordinate, y r (t) is the reference ordinate, ψ r (t) is the reference heading angle, u r (t) is the reference forward speed, v r (t) is the reference roll velocity, r r (t) is the reference yaw angular velocity, is x r The derivative of (t) with respect to time, y r The derivative of (t) with respect to time, for The derivative with respect to time, for With respect to the time derivative, atan2 represents the four-quadrant inverse tangent operator.

[0021] Furthermore, in step S2, the Gaussian process GP is introduced into the ASV trajectory tracking system to approximate the unmodeled dynamics of the system and obtain the GP prediction model, including:

[0022] (1) Apply GP to each dimension e of the unmodeled dynamics E(v) j (v) Modeling, j = 1, 2, 3, given a GP prior and a training set containing n groups of data z i For the training set The i-th group of input data, y i is the training set The i-th group of output data, the GP posterior distribution d of the j-th dimension of the unmodeled dynamics at the test point z GP (z) is:

[0023]

[0024] where e j (z) represents the value of the j-th dimension of the unmodeled dynamics at the test point z, d GP The mean and covariance of (z) are:

[0025]

[0026] where Z is the dictionary input data set, Y is the dictionary output data set, [K(z, Z)] 1i = k(z, z i ), [K(Z, Z)] ij = k(z i , z j ), K(z, Z) is the covariance matrix of z and Z, K(Z, Z) is the covariance matrix of Z and Z, is the covariance of the GP noise, I is the unit matrix, K(z, z) is the covariance of z and z, K(Z, z) is the transpose of K(z, Z); let the mean function m(z) = 0, and the covariance function be:

[0027]

[0028] where, is the output variance, z' is the derivative of z, is the length scale covariance matrix, which is represented as:

[0029]

[0030] where l i ≥ 0, i = 1,..., n z , n z is the dimension of the test point z, and the hyperparameters of the kernel function are:

[0031]

[0032] (2) Apply the explicit fourth-order Runge-Kutta method to discretize the ASV dynamics model with additional perturbations as:

[0033]

[0034] where, t k +1 moment status, By discrete state variables and discrete control inputs The components of is the transformation matrix for the state, is the transformation matrix for the control input, f true represents the actual ASV dynamics model, f nom represents the nominal ASV dynamics model, is a multidimensional GP constructed by independently trained GPs in each dimension to approximate the unmodeled dynamics E(v), The distribution of is:

[0035]

[0036] in, Indicates that unmodeled dynamics are at the test point The value vector at , represents the unmodeled dynamics of the jth dimension at the test point The value at The mean and variance Respectively expressed as:

[0037]

[0038] in, for Corresponding GP The mean value at for Corresponding GP The covariance at , d represents the Gaussian process;

[0039] The distribution of Gaussian process noise ω is is the covariance of the single-dimensional GP noise, the state input matrix B d Used to select states affected by model errors.

[0040] Furthermore, in step S3, based on the dictionary size limit and the maximum likelihood method, the update criteria for the dictionary data and hyperparameters are established, including:

[0041] (1) Dictionary Design a maximum capacity n max , n max When the number of data points exceeds this preset threshold, the point with the lowest covariance function value is removed to maintain this limit;

[0042] (2) Maximum likelihood method is used to find the hyperparameter θ that makes the observed data most likely * ,θ * Obtained by the following formula:

[0043] θ * =argmax θ logp(Y|Z,θ)

[0044] The log-likelihood function is:

[0045]

[0046] Among them, Z is the dictionary input data set, Y is the dictionary output data set, K(Z, Z) is the covariance matrix of Z and Z, is the covariance of GP noise, I is the identity matrix, K y The inverse matrix of , θ is the hyperparameter vector of the kernel function.

[0047] Furthermore, the GP-MPC framework constructed in step S4 includes:

[0048] The objective function is:

[0049]

[0050] in, is the mean sequence of all states in the control time domain at time t, u 0：N-1|t is the sequence of all control inputs in the control domain at time t, is the state mean of the kth step in the control domain at time t, x r (k|t) is the reference state of the kth step in the control time domain at time t, u k|t is the control input of the kth step in the control domain at time t, is the terminal state mean in the control time domain at time t, x r (N|t) is the terminal reference state in the control time domain at time t, l is the stage cost function, l f is the terminal cost function, N is the control time domain;

[0051] The initial conditions are:

[0052]

[0053] in, is the initial state mean in the control time domain at time t, and xt is the real system state at time t;

[0054] The prediction equation is:

[0055]

[0056] in, is the state mean of the k+1th step in the control domain at time t, is the Gaussian process mean of the kth step in the control time domain at time t, B d is the state input matrix;

[0057] The state and control input constraints are:

[0058]

[0059] in, is the set of feasible states, is the set of feasible control inputs;

[0060] The terminal state constraints are:

[0061]

[0062] in, is the terminal state set;

[0063] At each time step, the optimization problem of the GP-MPC framework is solved to obtain the control input sequence is the optimal initial control input, is the optimal terminal control input, and Applied to the system; using linearized approximation methods to propagate the desired state, specifically:

[0064]

[0065] in, is the state mean at time k+1, is the state mean at time k, is the Gaussian process mean at time k, u k is the discrete control input.

[0066] Furthermore, the method for designing the terminal state set is:

[0067] Consider a terminal control law:

[0068]

[0069] in, is the control input obtained by updating the terminal control law, μ x is the mean of the state, is the terminal feedback gain, u r is the ideal reference control input; the terminal state set Designed to:

[0070]

[0071] wherein, is obtained by substituting the calculation result of the terminal control law into the prediction equation.

[0072] Further, the method for designing the algorithm for solving the GP-MPC framework optimization problem in step S5 is:

[0073] (1) At each time t, solve the MPC framework to obtain the predicted state sequence X t = [x 1|t , x 2|t ,..., x N|t ] T and the executed control input sequence U t = [u 0|t , u 1|t ,..., u N-1|t ] T , wherein X 1|t is the predicted state at time t+1, x 2|t is the predicted state at time t+2, X N|t is the predicted state at time t+N, u 0|t is the control input executed at time t, u 1|t is the control input executed at time t+1, and u N-1|t is the control input executed at time t+N-1; the multi-point linearization model of the ASV is based on the predicted state sequence X t-1 and the control input sequence U t-1 , which is expressed as:

[0074]

[0075] wherein x k+1|t is the state at the k+1 step in the control time domain at time t, f est is the predicted ASV dynamics function, x k+1|t-1 is the state at the k+1 step in the control time domain at time t-1, u k+1|t-1 is the control input at the k+1 step in the control time domain at time t-1, is the gradient with respect to the state, is the gradient with respect to the control input, x k|t is the state at the k step in the control time domain at time t, u k|t is the control input at the k step in the control time domain at time t, x is a state variable, and u is a control input, and:

[0076]

[0077] (2) The mean and covariance matrix of the first-order derivative of GP are:

[0078]

[0079] Where d′ GP (z) is the first-order derivative of GP, μ d ′(z) is the mean of the first-order derivative of GP at z, ∑ d ′(z) is the covariance of the first-order derivative of GP at z, K(z, Z) is the covariance matrix of z and Z, K(Z, Z) is the covariance matrix of Z and Z, is the covariance of GP noise, I is the identity matrix, and K(z, z) is the covariance of z and z;

[0080] (3) Based on the multi-point linearization model of ASV in step (1), the state prediction model in the prediction time domain is:

[0081] X t =P x x(t)+P u U t +P e D e

[0082] in:

[0083]

[0084] in,

[0085] (4) The cost function of the GP-based multi-point linearized MPC is reformulated as:

[0086]

[0087] Among them, J is the cost function, is the reference state at time t+1, is the reference state at time t+2, is the reference state at time t+N, the matrix Q is the state weight matrix, Q f is the terminal state weight matrix, R is the weighted matrix. Substituting the state prediction model into the above formula, we get:

[0088]

[0089]

[0090] in, For U t The transposed matrix of

[0091] After omitting the top that is not relevant to the control input sequence, the cost function is summarized in quadratic form:

[0092]

[0093] in, is the simplified cost function;

[0094] Through the multi-point linearization method, the GP-based nonlinear MPC optimization problem is transformed into a quadratic cost function in step (4) and a multi-point prediction model in step (3).

[0095] The system corresponding to the method includes:

[0096] The dynamic model building unit is used to build the ASV dynamic model for the trajectory tracking problem of the autonomous surface vehicle (ASV);

[0097] Unmodeled dynamics approximation unit, used to introduce Gaussian process GP into the trajectory tracking system of ASV, approximate the unmodeled dynamics of the system, and obtain the GP prediction model;

[0098] An update criterion establishment unit is used to establish update criteria for dictionary data and hyperparameters based on dictionary size restrictions and maximum likelihood method to optimize the GP prediction model;

[0099] The GP-MPC framework and terminal state set construction unit is used to combine the optimized GP prediction model with the ASV dynamic model, use the learning-based model predictive control MPC method, build the GP-MPC framework, and design the terminal state set;

[0100] The optimization control unit is used to derive the state prediction model in the prediction time domain based on the multi-point linearization method, and design an algorithm to solve the GP-MPC framework optimization problem in combination with the local linear model predictive control LMPC method to achieve real-time control of ASV trajectory tracking.

[0101] A computer-readable storage medium for storing and executing the method, wherein the computer-readable storage medium stores computer instructions, and when the computer instructions are called, the computer instructions are used to execute the steps of the multi-point linearization model prediction trajectory tracking control method based on Gaussian process.

[0102] Beneficial effects: Compared with the existing technology, the significant technical effects of the present invention are: (1) Based on the multi-point linearization model of ASV, a corresponding local linear model predictive control (LMPC) method is proposed and combined with the GP-MPC framework; compared with other trajectory tracking control methods based on GP-MPC, the solution characteristics of MPC rolling time domain are combined, the utilization rate of historical data is fully improved, the calculation amount of MPC solution optimization problem is greatly reduced, and the requirements of real-time control can be met; (2) Compared with other trajectory tracking control methods based on GP-MPC, the present invention proposes a terminal control law and Based on this, a terminal state set is designed in the GP-MPC framework, which provides theoretical help to ensure the iterative feasibility and asymptotic stability of the GP-MPC framework; (3) Based on the dictionary size limit and the maximum likelihood method, the dictionary data and hyperparameter update criteria are established; by limiting the size of the dictionary data set, the computational complexity problem caused by the excessive size of the data set is effectively prevented, and supplemented by the hyperparameter update criteria, the prediction accuracy of the GP model is guaranteed while reducing the amount of calculation; (4) It can be easily expanded to drones or unmanned vehicle systems, as well as other motion control problems, and has broad application prospects and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 Schematic diagram of the steps of the multi-point linearized model prediction trajectory tracking control method based on Gaussian process of the present invention;

[0104] Figure 2 It is a diagram showing the change of position state and control input during the ASV trajectory tracking process of the simulation 1 of the present invention;

[0105] Figure 3 Schematic diagram of ASV trajectory tracking results based on different control methods in simulation 1 of the present invention;

[0106] Figure 4 It is a diagram showing the change of position state and control input during the ASV trajectory tracking process of simulation 2 of the present invention;

[0107] Figure 5 It is a diagram showing the changes in disturbance and prediction error during the ASV trajectory tracking process of simulation 2 of the present invention;

[0108] Figure 6 This is a schematic diagram of the ASV trajectory tracking results based on different control methods in simulation 2 of the present invention. DETAILED DESCRIPTION

[0109] In order to make the invention purpose, technical scheme and beneficial effects of the present application more clear and explicit, the invention purpose, technical scheme and beneficial effects of the present application will be further described in detail below in combination with the drawings and specific embodiments. It should be noted that the embodiments are only used to explain and understand the present application, and are not used to limit the present application.

[0110] As shown in Figure 1 , the GP-MP-LMPC method disclosed in the embodiments of the present application is used for trajectory tracking control based on a Gaussian process multi-point linearization model. Firstly, a dynamic model is constructed for the trajectory tracking problem of an autonomous surface vehicle (ASV). Then, the Gaussian process (GP) is applied to the trajectory tracking control system to approximate the unmodeled dynamics of the system. Then, based on the dictionary size constraint and the maximum likelihood method, the dictionary data and the hyperparameter updating criterion are established. Then, the GP-MPC framework is constructed by combining the learning-based model predictive control (MPC) method, and the terminal state set is designed. Then, based on the local linear MPC (LMPC) method of the multi-point linearization model, the solving algorithm for the trajectory tracking problem is designed, which can significantly reduce the calculation time while ensuring the trajectory tracking accuracy of the ASV.

[0111] Specifically, in the embodiments of the present application, the trajectory tracking control method based on the Gaussian process multi-point linearization model mainly comprises the following steps:

[0112] Step 1, for the trajectory tracking problem of an autonomous surface vehicle (ASV), a dynamic model of the ASV is constructed. The specific process of this step is as follows:

[0113] Step 1-1, the three-degree-of-freedom nonlinear dynamic model of the autonomous surface vehicle (ASV) describes the horizontal position of the ASV in the earth coordinate system, wherein the horizontal coordinate is the vertical coordinate is and the heading angle is In the body coordinate system, the forward speed is the roll speed is and the yaw angle speed is which collectively represent the motion state of the autonomous surface vehicle. The dynamic model of the ASV is as follows:

[0114]

[0115] wherein, is a generalized coordinate vector, is the derivative of η with respect to time, is a velocity vector, T is the transpose of a matrix, is the derivative of v with respect to time. The unmodeled dynamics caused by gravity, buoyancy and environmental forces and moments are represented by Indicates that e1(v) is the component that affects the forward velocity in the unmodeled dynamics, e2(v) is the component that affects the roll velocity in the unmodeled dynamics, and e3(v) is the component that affects the yaw angular velocity in the unmodeled dynamics; the torque of the control force is τ = [τ u τ v τ r ] T , τ u is the torque in the direction of forward speed, τ v is the moment in the direction of the rolling velocity, τ r is the torque in the direction of yaw angular velocity. R(η) is the rotation matrix, defined as:

[0116]

[0117] Where ψ is the heading angle.

[0118] M is a positive definite symmetric inertia matrix, expressed as:

[0119]

[0120] in, m is the mass of the ASV, is the hydrodynamic coefficient related to the first derivative of u, is the hydrodynamic coefficient related to the first derivative of v, I z is the identity matrix, is the hydrodynamic coefficient related to the first derivative of r, x g are the relevant ASV model parameters, is the hydrodynamic coefficient related to the first derivative of r.

[0121] C(v) is the Coriolis matrix, defined as:

[0122]

[0123] Among them, C 13 (v)=-M 22 v s -M 23 r s , C 23 (v)=M 11 u s .

[0124] D(v) is the damping matrix, expressed as:

[0125]

[0126] The damping coefficient is:

[0127] D 11 (v) = -Xu -X |u|u |u|-X uuu u 2 ,

[0128] D 22 (v)=-Y v -Y |v|v |v|-Y |r|v |r|,

[0129] D 23 (v)=-Y r -Y |v| r|v|-Y |r|r |r|,

[0130] D 32 (v)=-N v -N |v|v |v|-N |r|v |r|,

[0131] D 33 (v)=-N r -N |v|r |v|-N |r|r |r|.

[0132] Among them, X (·) , Y (·) and N (·) are the hydrodynamic coefficients, X u 、X |u|u 、X uuu are the hydrodynamic coefficients related to u, Y v 、Y |v|v 、N v 、N |v|v are the hydrodynamic coefficients related to v, Y |r|v 、Y |v|r 、N |r|v 、N |v|r are the hydrodynamic coefficients related to r and v, Y r 、Y |r|r 、N r 、N |r|r are all hydrodynamic coefficients related to r, u is the forward speed of ASV in the hull coordinate system, v is the rolling speed of ASV in the hull coordinate system, and r is the yaw angular velocity of ASV in the hull coordinate system.

[0133] Step 1-2: Set the state variable x = [η T v T ] T =[xy ψ uvr] T, control input u = τ, x is the horizontal coordinate of ASV in the earth coordinate system, y is the vertical coordinate of ASV in the earth coordinate system. The dynamic model of ASV can be rewritten from equation (1) as:

[0134]

[0135] in, is the derivative of x with respect to time, A(v)=-M -1 (C(v)+D(v)), B=M -1 , M -1 is the inverse matrix of M.

[0136] Steps 1-3: When solving the ASV trajectory tracking problem, each state of the ASV dynamics model (6) has a corresponding reference state x r (t) = [x r (t), y r (t), ψ r (t),u r (t), v r (t), r r (t)] T , defined as follows:

[0137]

[0138] Among them, x r (t) is the reference horizontal coordinate, y r (t) is the reference ordinate, ψ r (t) is the reference heading angle, u r (t) is the reference forward speed, v r (t) is the reference roll velocity, r r (t) is the reference yaw angular velocity, is x r The derivative of (t) with respect to time, y r The derivative of (t) with respect to time, for The derivative with respect to time, for With respect to the time derivative, atan2 represents the four-quadrant tangent inverse operator. The above formula ensures that x r (t) satisfies the first ASV kinetic equation in the ASV kinetic model (1). Under the condition that the unmodeled kinetics is zero (i.e., E(v) = 0), x r (t) Substituting into the second ASV dynamics equation in the ASV dynamics model (1) we can get the ideal reference control input u r =τ r ,u ris the ideal reference control input, τ r The trajectory tracking problem of ASV is actually to design the control input u so that the actual state x closely follows the reference state x. r (t).

[0139] Step 2: Introduce the Gaussian process (GP) into the ASV trajectory tracking control system to approximate the unmodeled dynamics of the system, obtain the GP prediction model, and supplement the ASV dynamics model. The specific process of this step is:

[0140] Step 2-1: Apply GP to each dimension e of the unmodeled dynamics E(v) j (v) Modeling, j = 1, 2, 3, given a GP prior and a training set containing n groups of data z i For the training set The i-th group of input data, y i For the training set The GP posterior distribution d of the unmodeled dynamics of the jth dimension at the test point z for the i-th group of output data GP (z) is:

[0141]

[0142] Among them, e j (z) represents the value of the unmodeled dynamics of the jth dimension at the test point z, d GP The mean and covariance of (z) are:

[0143]

[0144] Among them, Z is the dictionary input data set, Y is the dictionary output dataset, [K(z,Z)] 1i =k(z, z i ), [K(Z, Z)] ij =k(z i , z j ), K(z, Z) is the covariance matrix of z and Z, K(Z, Z) is the covariance matrix of Z and Z, is the covariance of GP noise, I is the identity matrix, K(z, z) is the covariance of z and z, and K(Z, z) is the transpose of K(z, Z). Assume that the mean function m(z) = 0 and the covariance function k(z, z′) is:

[0145]

[0146] in, is the output variance, z′ is the derivative of z, is the length scale covariance matrix, denoted as

[0147]

[0148] where l i ≥ 0, i = 1,..., n z , n z is the dimension of the test point z, and the hyperparameters of the kernel function are:

[0149]

[0150] where, is the covariance of the GP noise ω.

[0151] Step 2-2, apply the explicit fourth-order Runge-Kutta method to discretize the ASV dynamics model with additional perturbations as:

[0152]

[0153] where, is the state at time t k +1, is composed of the partial components of the discrete state and the discrete control input of the ASV dynamics model, is the transformation matrix for the state, is the transformation matrix for the control input, which are assumed to be the factors affecting the model error. true denotes the actual ASV dynamics model, nom denotes the nominal ASV dynamics model. is a multi-dimensional GP approximation constructed by GPs trained independently for each dimension, and the prediction mean and variance for each dimension are calculated independently since there is no correlation between different dimensions. The distribution of z

[0154]

[0155] where, denotes the value vector of the unmodeled dynamics at the test point z denotes the value of the unmodeled dynamics in the jth dimension at the test point z The mean and variance of z are denoted as:

[0156]

[0157] where, is Corresponding GP The mean value at for Corresponding GP The covariance at , d represents the Gaussian process.

[0158] In addition, the distribution of the noise ω of the multidimensional Gaussian process is is the covariance of the single-dimensional GP noise, the state input matrix B d Used to select states affected by model errors.

[0159] Step 3: Based on the dictionary size limit and the maximum likelihood method, establish the update criteria for dictionary data and hyperparameters to optimize the GP prediction model; to ensure the prediction accuracy of GP and reduce the computational complexity of GP. The specific process of this step is:

[0160] Step 3-1, dictionary Design a maximum capacity n max , when the number of data points exceeds this preset threshold (maximum capacity n max ), this constraint is maintained by removing the points with the lowest covariance function values, which reduces the computational complexity of GP regression by limiting the number of data points in the dictionary.

[0161] Step 3-2: Maximum likelihood method is used to find the hyperparameter θ that makes the observed data most likely * ,θ * It can be obtained by the following formula:

[0162] θ * =argmax θ logp(Y|Z,θ) (16)

[0163] The log-likelihood function is:

[0164]

[0165] in, K y is the inverse matrix of , and θ is the hyperparameter vector defined above.

[0166] Step 4: Combine the optimized GP prediction model with the ASV dynamic model, use the learning-based model predictive control MPC method, build the GP-MPC framework, and design the terminal state set. The specific process of this step is:

[0167] Step 4-1, the objective function of the GP-MPC framework is:

[0168]

[0169] in, is the mean sequence of all states in the control time domain at time t, u 0：N-1|t is the sequence of all control inputs in the control domain at time t, is the state mean of the kth step in the control domain at time t, x r (k|t) is the reference state of the kth step in the control time domain at time t, u k|t is the control input of the kth step in the control domain at time t, is the terminal state mean in the control time domain at time t, x r (N|t) is the terminal reference state in the control time domain at time t, l is the stage cost function, l f is the terminal cost function, N is the control time domain;

[0170] The initial conditions are:

[0171]

[0172] in, is the initial state mean in the control time domain at time t, and xt is the real system state at time t;

[0173] The prediction equation is:

[0174]

[0175] in, is the state mean of the k+1th step in the control domain at time t, is the mean of the Gaussian process of step k in the control time domain at time t;

[0176] The state and control input constraints are:

[0177]

[0178] in, is the set of feasible states, is the set of feasible control inputs;

[0179] The terminal state constraints are:

[0180]

[0181] Where N represents the control time domain, is the terminal state set, and the objective function is composed of the stage cost function l and the terminal cost function l f Composition, defined as follows:

[0182]

[0183] in, Representative state x and reference state x r The deviation, for The transposed matrix, u T is the transposed matrix of u. The weight matrices Q, R and Q f are all positive definite matrices.

[0184] At each time step, the optimization problem of the GP-MPC framework is solved to obtain the control input sequence is the optimal initial control input, is the optimal terminal control input, and Applied to the system. To improve the computational efficiency of the prediction equation and maintain computational feasibility, a linearized approximation method is used to propagate the desired state, specifically:

[0185]

[0186] in, is the state mean at time k+1, is the state mean at time k, is the Gaussian process mean at time k;

[0187] Step 4-2, consider a terminal control law:

[0188]

[0189] in, is the control input obtained by updating the terminal control law, μ x is the mean of the state, is the terminal feedback gain. The terminal state set Designed to:

[0190]

[0191] Among them, the terminal prediction state It is obtained by substituting the calculation results of the terminal control law into the prediction equation.

[0192] Step 5: Based on the multi-point linearization method, derive the state prediction model in the prediction time domain, combine it with the local linear model predictive control LMPC method, design an algorithm to solve the GP-MPC framework optimization problem, and realize the real-time control of ASV trajectory tracking. The specific process of this step is:

[0193] Step 5-1: At each time t, solve the MPC framework to obtain the predicted state sequence X t =[x 1|t , x 2|t ,...,x N|t] T and the executed control input sequence U t = [u 0|t , u 1|t ,..., u N-1|t ] T where x 1|t is the predicted state at time t+1, x 2|t is the predicted state at time t+2, X N|t is the predicted state at time t+N, u 0|t is the control input executed at time t, u 1|t is the control input executed at time t+1, and u N-1|t is the control input executed at time t+N-1. The multi-point linearization model of the ASV is based on the predicted state sequence X t-1 and the control input sequence U t-1 , which is expressed as:

[0194]

[0195] where x k+1|t is the state at the k+1th step in the control horizon at time t, f est is the predicted ASV dynamics function, x k+1|t-1 is the state at the k+1th step in the control horizon at time t-1, u k+1|t-1 is the control input at the k+1th step in the control horizon at time t-1, is the gradient with respect to the state, is the gradient with respect to the control input, X k|t is the state at the kth step in the control horizon at time t, u k|t is the control input at the kth step in the control horizon at time t, f est (x, u) = f nom (x, u) + B d d GP (z), and:

[0196]

[0197] In addition, in the multi-point linearization process, it is assumed that the planning input at the Nth step is the same as that at the N-1th step, i.e., u N|t-1 = u N-1|t-1 .

[0198] Step 5-2, when calculating and , the derivative of the Gaussian process (GP) needs to be used. According to previous research, the derivative of the GP is still a GP. Considering the GP model in the foregoing, the output vector d GP is known, and the output vector d ′ is unknown. GPThe joint probability density function of also obeys Gaussian distribution. The mean and covariance matrix of the first-order derivative of GP are:

[0199]

[0200]

[0201] Where d′ GP (z) is the first-order derivative of GP, μ d ′(z) is the mean of the first-order derivative of GP at z, ∑ d ′(z) is the covariance of the first-order derivative of GP at z.

[0202] Step 5-3: Based on the multi-point linearization model of ASV in step 5-1, the state prediction model in the prediction time domain can be summarized as follows:

[0203] X t =P x x(t)+P u U t +P e D e (32)

[0204] in:

[0205]

[0206] in,

[0207]

[0208] Step 5-4: Re-express the cost function of the GP-based multi-point linearized MPC as:

[0209]

[0210] Among them, J is the cost function, is the reference state at time t+1, is the reference state at time t+2, is the reference state at time t+N, the matrix Q is the state weight matrix, Q f is the terminal state weight matrix, Substituting the state prediction model into the above formula, we can get:

[0211]

[0212] in, For U t The transposed matrix of

[0213] After omitting the top that is not related to the control input sequence, the quadratic cost function is summarized as:

[0214]

[0215] in, is the simplified cost function.

[0216] Through the multi-point linearization method, the GP-based nonlinear MPC optimization problem is transformed into a quadratic cost function in step 5-4 and a state prediction model in the time domain in step 5-3.

[0217] The following is a simulation verification of the ASV trajectory tracking control of the multi-point linearized model prediction trajectory tracking control framework based on Gaussian processes under environmental disturbances designed by the present invention.

[0218] For ASV dynamics, the multivariate GP approximation d GP The dimension is 3, that is, n d =3.d GP Each dimension corresponds to the unmodeled dynamics E(v) = [e1(v) e2(v) e3(v)] T A dimension of . Then the matrix B d It is given by:

[0219]

[0220] The unmodeled dynamic components e1(v), e2(v), and e3(v) represent gravity, buoyancy, and environmental forces and their torques, respectively. These components depend on the ASV's shape, displacement, and motion state, affecting its trajectory tracking performance, such as its ability to maintain heading and speed. In the simulation, the unmodeled dynamics are given by:

[0221] e1(v)=0.279uv 2 +0.342v 2 r

[0222] e2(v)=0.912u 2 v

[0223] e3(v)=0.156ur 2 +0.278urv 3

[0224] Based on the above equation, it can be expressed that in is a zero matrix, and:

[0225]

[0226] The remaining ASV model parameters are summarized in Table 1.

[0227] Table 1

[0228]

[0229] All subsequent calculations were performed using MATLAB R2020a on a computer equipped with a 2.60 GHz i9 processor and 16 GB of memory. The fmincon function in MATLAB was used with an interior point method, a maximum of 6 iterations, and 10 -3 The optimization tolerance setting is used to balance control performance and computational efficiency.

[0230] The ASV trajectory tracking experiment is conducted in two scenarios: straight trajectory and curved trajectory.

[0231] Simulation experiment 1:

[0232] The reference straight line trajectory used in simulation experiment 1 is generated by the following formula:

[0233] y r =x r -1

[0234] According to steps 1-3, the reference state x r The corresponding components are as follows:

[0235] x r (t) = t + 3, y r (t) = t + 2,

[0236] ψ r (t) = tan -1 (1),

[0237] v r (t) = 0, r r (t)=0.

[0238] The weighting matrix is ​​set to R = diag([0.1, 0.1, 0.1]), Q = diag([10 6 , 10 6 , 10 3 , 10 2 , 10 2 , 10 2 ]) and Q f =2Q, and the prediction range of MPC is N=8. According to the actual needs of ASV, the upper limit of the control input is set to 200. The initial hyperparameter is set to σ f =[0.01,0.01,0.01]T, and σ n =diag(σ f / 3). Subsequently, these hyperparameters are optimized from the initial values. The maximum number of points in the dictionary is set to n max = 300. The simulation time is 12 seconds with a time step of 0.02 seconds. The initial pose of the ASV is η0= [6.0, 0.0, 0.0] T , and the initial velocity is V0= [0.0, 0.0, 0.0] T .

[0239] Under the GP-MP-LMPC framework, the changes of position states (x and y) and control inputs u during the ASV trajectory tracking process are shown in Fig. 3 Figure 2 . From the initial position, the GP model is used for prediction immediately, and its dictionary is updated constantly by new data points. After 1.5 seconds, the GP model continues to make predictions, but the dictionary is no longer updated. As can be seen from Fig. 3 Figure 2 , the ASV successfully tracks the reference trajectory after about 3 seconds, and there is no deviation in the subsequent simulation process. After the change period of the first 3 seconds, the control inputs gradually stabilize to zero.

[0240] Figure 3 The trajectory tracking performance of the GP-MP-LMPC framework is compared with that of MP-LMPC and GP-NMPC. It can be seen that all three methods successfully achieve trajectory tracking of the ASV, among which GP-NMPC and GP-MP-LMPC perform best, with little difference in performance. MP-LMPC takes longer to achieve satisfactory tracking effect, and there is a large uncertainty in the initial stage of the trajectory. Some control performance indicators of the three control frameworks are shown in Table 2.

[0241] Table 2

[0242] index GP-MP-LMPC MP-LMPC GP-NMPC Prediction error 0.00126 66.2696 0.00125 Calculation time (seconds) 10 7 5624

[0243] where the prediction error is defined as the absolute value of the difference between the actual system dynamic model f true and the prediction model f nom + B d d GP , and only the first 3 seconds (150 time steps) are calculated. As can be seen from Table 2, the prediction errors of GP-MP-LMPC and GP-NMPC are significantly smaller than that of MP-LMPC. In addition, GP-MP-LMPC has shorter calculation time, which indicates that the GP-MP-LMPC framework proposed by us has higher calculation efficiency while achieving effective trajectory tracking. Further analysis shows that both GP-MP-LMPC and MP-LMPC frameworks support real-time control.

[0244] It's worth noting that in Simulation Experiment 1, since the reference trajectory is a straight line, the ASV tracks the reference trajectory after 3 seconds. Therefore, no significant directional adjustments are required. The velocity components v and r in the state become very small, resulting in a small perturbation E value. Consequently, the prediction error after 3 seconds is very small, and the GP's learning effect is not very obvious. Therefore, we choose the total prediction error in the first 3 seconds for comparison.

[0245] Simulation experiment 2:

[0246] To better demonstrate the control performance of the proposed framework, in simulation experiment 2, we replaced the ASV's tracking trajectory with the following figure-8 trajectory:

[0247] x r (t)=6.8sin(0.3t)-0.5

[0248] y r (t)=9.6cos(0.15t)-6

[0249] The initial posture of ASV is η0 = [-0.4, 0.0, 0.0] T , the initial speed is the same as that set in simulation experiment 1. In order to fully demonstrate the “8”-shaped trajectory, the simulation time is set to 42 seconds, and the other parameter settings are consistent with simulation experiment 1.

[0250] Figure 4 The figure shows the time evolution of the position state (x and y) and control input during the ASV trajectory tracking process using the GP-MP-LMPC framework. It can be seen that the ASV begins to track the reference trajectory after about 3 seconds, and the control input tends to stabilize with small regular fluctuations. Figure 5 The figure shows the effect of the disturbance E and the GP model on the prediction error. In the first three seconds, the ASV had not yet reached the reference trajectory and needed to accelerate, which increased the disturbance E. However, the GP model effectively mitigated the impact of the disturbance. With GP, the prediction error decreased to a very small level after three seconds, and the total prediction error was about ten times smaller than the disturbance.

[0251] Figure 6 The tracking performance of the three control methods, GP-MP-LMPC, MP-LMPC, and GP-NMPC, on a figure-8 curve trajectory is demonstrated. The numerical values ​​of the control performance indicators (prediction error and computation time) are shown in Table 3.

[0252] Table 3

[0253] index GP-MP-LMPC MP-LMPC GP-NMPC Prediction error 0.78149 79.2069 0.72263 Calculation time (seconds) 40 34 14622

[0254] from Figure 6As can be seen from Table 3, GP-MP-LMPC and GP-NMPC are able to quickly guide the ASV to the reference trajectory, while MP-LMPC exhibits poor control performance and large fluctuations in the early stages. Furthermore, the GP-MP-LMPC framework ensures comparable prediction error to GP-NMPC while reducing computation time, which is crucial for practical applications. Similarly, similar to Simulation Experiment 1, only the GP-MP-LMPC and MP-LMPC frameworks support real-time control.

[0255] Based on the above two simulation experiments, the Gaussian process-based multi-point linearized model predictive trajectory tracking control (GP-MP-LMPC) framework design method designed in the present invention realizes the trajectory tracking control of the autonomous surface vehicle (ASV) under the condition of environmental disturbance with high uncertainty, and can meet the accuracy and real-time requirements.

[0256] It is worth noting that the above is only a more preferred embodiment of the present invention, which is only used to verify and explain the present invention, and does not constitute a limitation to the present invention. Various changes, equivalent substitutions and modifications made by relevant technical personnel without departing from the technical ideas of the present invention are all included in the scope of protection of the present invention.

Claims

1. A multi-point linearized model prediction trajectory tracking control method based on Gaussian process, characterized by: The following steps are involved: S1. Aiming at the trajectory tracking problem of autonomous surface vehicle (ASV), an ASV dynamics model is constructed. S2. Introducing Gaussian Process (GP) into the ASV trajectory tracking system to approximate the unmodeled dynamics of the system and obtain the GP prediction model; including: (1) Apply GP to each dimension e of the unmodeled dynamics E(v) j (v) Modeling, j = 1, 2, 3, given a GP prior and a training set containing n groups of data z i For the training set The i-th group of input data, y i For the training set The GP posterior distribution d of the unmodeled dynamics of the jth dimension at the test point z for the i-th group of output data GP (z) is: Among them, e j (z) represents the value of the unmodeled dynamics of the jth dimension at the test point z, d GP The mean and covariance of (z) are: Among them, Z is the dictionary input data set, Y is the dictionary output dataset, [K(z,Z)] 1i =k(z,z i ), [K(Z,Z)] ij =k(z i ,z j ), K(z,Z) is the covariance matrix of z and Z, K(Z,Z) is the covariance matrix of Z and Z, is the covariance of GP noise, I is the identity matrix, K(z,z) is the covariance of z and z, and K(Z,z) is the transpose of K(z,Z). Assume that the mean function m(z) = 0, and the covariance function is: in, is the output variance, z ′ is the derivative of z, is the length scale covariance matrix, expressed as: Among them, l i ≥0, i=1,…,n z , n z is the dimension of the test point z, and the hyperparameters of the kernel function are: (2) Applying the explicit fourth-order Runge-Kutta method, the ASV dynamics model with additional disturbance is discretized as: in, t k +1 moment status, By discrete state variables and discrete control inputs The components of is the transformation matrix for the state, is the transformation matrix for the control input, f true represents the actual ASV dynamics model, f nom represents the nominal ASV dynamics model, is a multidimensional GP constructed by independently trained GPs in each dimension to approximate the unmodeled dynamics E(v), The distribution of is: in, Indicates that unmodeled dynamics are at the test point The value vector at , represents the unmodeled dynamics of the jth dimension at the test point The value at The mean and variance Respectively expressed as: in, for Corresponding GP The mean value at for Corresponding GP The covariance at , d represents the Gaussian process; The distribution of Gaussian process noise ω is is the covariance of the single-dimensional GP noise, the state input matrix B d Used to select states affected by model errors; S3. Based on dictionary size limitation and maximum likelihood method, establish the update criteria of dictionary data and hyperparameters to optimize the GP prediction model; S4. Combining the optimized GP prediction model with the ASV dynamics model, using the learning-based model predictive control MPC method, constructing the GP-MPC framework, and designing the terminal state set; S5. Based on the multi-point linearization method, the state prediction model in the prediction time domain is derived. Combined with the local linear model predictive control LMPC method, an algorithm is designed to solve the GP-MPC framework optimization problem to achieve real-time control of ASV trajectory tracking.

2. The multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to claim 1 is characterized in that: The ASV kinetic model constructed in step S1 is expressed as: in, is the time derivative of the state variable x, x = [η T v T ] T =[xy ψ uvr] T , is a generalized coordinate vector, where x, y, and ψ are the horizontal coordinate, vertical coordinate, and heading angle of ASV in the Earth coordinate system, respectively. is the velocity vector, u, v, and r are the forward velocity, roll velocity, and yaw velocity of the ASV in the hull coordinate system, respectively. T is the transpose of the matrix, u is the control input, u=τ, τ=[τ u τ v τ r ] T is the torque of the control force, τ u is the torque in the direction of forward speed, τ v is the moment in the direction of the rolling velocity, τ r is the torque in the direction of yaw angular velocity, R(η) is the rotation matrix, A(v)=-M -1 (C(v)+D(v)), B=M -1 , M -1 is the inverse matrix of M, M is the positive definite symmetric inertia matrix, C(v) is the Coriolis matrix, D(v) is the damping matrix, represents the unmodeled dynamics in the ASV trajectory tracking problem, e1(v) is the component of the unmodeled dynamics that affects the forward velocity, e2(v) is the component of the unmodeled dynamics that affects the roll velocity, and e3(v) is the component of the unmodeled dynamics that affects the yaw velocity.

3. The multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to claim 2 is characterized in that: When solving the ASV trajectory tracking problem in step S1, each state of the ASV trajectory tracking system has a corresponding reference state x r (t) = [x r (t),y r (t),ψ r (t),u r (t),v r (t),r r (t)] T , defined as follows: v r (t)=0, Among them, x r (t) is the reference horizontal coordinate, y r (t) is the reference ordinate, ψ r (t) is the reference heading angle, u r (t) is the reference forward speed, v r (t) is the reference roll velocity, r r (t) is the reference yaw angular velocity, is x r The derivative of (t) with respect to time, y r The derivative of (t) with respect to time, for The derivative with respect to time, for With respect to the time derivative, atan2 represents the four-quadrant inverse tangent operator.

4. The multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to claim 1 is characterized in that: In step S3, based on the dictionary size limit and the maximum likelihood method, the update criteria for dictionary data and hyperparameters are established, including: (1) Dictionary Design a maximum capacity n max , n max When the number of data points exceeds this preset threshold, the point with the lowest covariance function value is removed to maintain this limit; (2) Maximum likelihood method is used to find the hyperparameter θ that makes the observed data most likely * ,θ * Obtained by the following formula: θ * =argmax θ logp(Y|Z,θ) The log-likelihood function is: Among them, Z is the dictionary input data set, Y is the dictionary output data set, K(Z,Z) is the covariance matrix of Z and Z, is the covariance of GP noise, I is the identity matrix, K y The inverse matrix of , θ is the hyperparameter vector of the kernel function.

5. The multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to claim 1 is characterized in that: The GP-MPC framework constructed in step S4 includes: The objective function is: in, is the mean sequence of all states in the control time domain at time t, u 0:N-1|t is the sequence of all control inputs in the control domain at time t, is the state mean of the kth step in the control domain at time t, x r (k|t) is the reference state of the kth step in the control time domain at time t, u k|t is the control input of the kth step in the control domain at time t, is the terminal state mean in the control time domain at time t, x r (N|t) is the terminal reference state in the control domain at time t, l is the stage cost function, l f is the terminal cost function, N is the control time domain; The initial conditions are: in, is the initial state mean in the control time domain at time t, x t is the real system state at time t; The prediction equation is: in, is the state mean of the k+1th step in the control time domain at time t, is the Gaussian process mean of the kth step in the control time domain at time t, B d is the state input matrix; The state and control input constraints are: in, is the set of feasible states, is the set of feasible control inputs; The terminal state constraints are: in, is the terminal state set; At each time step, the optimization problem of the GP-MPC framework is solved to obtain the control input sequence is the optimal initial control input, is the optimal terminal control input, and Applied to the system; using linearized approximation methods to propagate the desired state, specifically: in, is the state mean at time k+1, is the state mean at time k, is the Gaussian process mean at time k, u k is the discrete control input.

6. The multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to claim 5, characterized in that: The method for designing the terminal state set is: Consider a terminal control law: in, is the control input obtained by updating the terminal control law, μ x is the mean of the state, is the terminal feedback gain, u r is the ideal reference control input; the terminal state set Designed to: in, It is obtained by substituting the calculation results of the terminal control law into the prediction equation.

7. The multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to claim 1 is characterized in that: The method for designing an algorithm for solving the GP-MPC framework optimization problem in step S5 is: (1) At each time t, solve the MPC framework to obtain the predicted state sequence X t =[x 1|t ,x 2|t ,…,x N|t ] T and the control input sequence U executed t =[u 0|t ,u 1|t ,…,u N-1|t ] T , where x 1|t is the predicted state at time t+1, x 2|t is the predicted state at time t+2, x N|t is the predicted state at time t+N, u 0|t is the control input executed at time t, u 1|t is the control input executed at time t+1, u N-1|t is the control input executed at time t+N-1; the multi-point linearization model of ASV is based on the state sequence X predicted in the previous step t-1 and control input sequence U t-1 , which is expressed as: Among them, x k+1|t is the state of the k+1th step in the control time domain at time t, f est To predict the ASV dynamics function, x k+1|t-1 is the state of the k+1th step in the control time domain at time t-1, u k+1|t-1 is the control input of the k+1th step in the control domain at time t-1, is the gradient of the state, is the gradient of the control input, x k|t is the state of the kth step in the control time domain at time t, u k|t is the control input of the kth step in the control domain at time t, x is the state variable, u is the control input, and: (2) The mean and covariance matrix of the first-order derivative of GP are: Where d′ GP (z) is the first-order derivative of GP, μ d′ (z) is the mean of the first-order derivative of GP at z, ∑ d′ (z) is the covariance of the first-order derivative of GP at z, K(z,Z) is the covariance matrix of z and Z, K(Z,z) is the covariance matrix of Z and Z, is the covariance of GP noise, I is the identity matrix, and K(z,z) is the covariance of z and z; (3) Based on the multi-point linearization model of ASV in step (1), the state prediction model in the prediction time domain is: X t =P x x(t)+P u U t +P e D e in: in, (4) The cost function of the GP-based multi-point linearized MPC is reformulated as: Among them, J is the cost function, is the reference state at time t+1, is the reference state at time t+2, is the reference state at time t+N, the matrix Q is the state weight matrix, Q f is the terminal state weight matrix, R is the weighted matrix. Substituting the state prediction model into the above formula, we get: in, For U t The transposed matrix of After omitting terms that are not relevant to the control input sequence, the cost function is summarized in quadratic form: in, is the simplified cost function; Through the multi-point linearization method, the GP-based nonlinear MPC optimization problem is transformed into a quadratic cost function in step (4) and a multi-point prediction model in step (3).

8. A system for the multi-point linearized model prediction trajectory tracking control method based on Gaussian process according to any one of claims 1 to 7, characterized in that: include: The dynamic model building unit is used to build the ASV dynamic model for the trajectory tracking problem of the autonomous surface vehicle (ASV); Unmodeled dynamics approximation unit, used to introduce Gaussian process GP into the trajectory tracking system of ASV, approximate the unmodeled dynamics of the system, and obtain the GP prediction model; An update criterion establishment unit is used to establish update criteria for dictionary data and hyperparameters based on dictionary size restrictions and maximum likelihood method to optimize the GP prediction model; The GP-MPC framework and terminal state set construction unit is used to combine the optimized GP prediction model with the ASV dynamic model, use the learning-based model predictive control MPC method, build the GP-MPC framework, and design the terminal state set; The optimization control unit is used to derive the state prediction model in the prediction time domain based on the multi-point linearization method, and design an algorithm to solve the GP-MPC framework optimization problem in combination with the local linear model predictive control LMPC method to achieve real-time control of ASV trajectory tracking.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, which, when called, are used to execute the steps of the multi-point linearization model prediction trajectory tracking control method based on Gaussian process according to any one of claims 1 to 7.

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