Vehicle path tracking and longitudinal speed control method based on gaussian process compensation

Abstract

The application discloses a vehicle path tracking and longitudinal speed control method based on a Gaussian process compensation, and belongs to the technical field of dynamics control, and comprises the following steps: S1, collecting data of a vehicle on a calibration road, constructing a Gaussian process residual model, and performing offline training; S2, performing online updating on the Gaussian process residual model after offline training; S3, calculating a three-channel compensation amount; S4, constructing a residual correction prediction model, and determining output prediction; S5, constructing a quadratic programming problem, and performing solving, so that a control increment, a steering input and a longitudinal acceleration input at a current time are obtained, and are applied to vehicle actuators. The sparse residual Gaussian process structure and the induced point maintenance strategy proposed in the application consider the online learning ability and the operation complexity, and are suitable for deployment on an existing automatic driving controller hardware platform.

Description

Technical Field

[0001] This invention belongs to the field of dynamic control technology, specifically relating to a vehicle path tracking and longitudinal speed control method based on Gaussian process compensation. Background Technology

[0002] With the accelerated application of autonomous driving and intelligent connected vehicle technologies in scenarios such as highways, urban roads, mining transportation, and closed test tracks, achieving high-precision path tracking and joint longitudinal speed control for unmanned ground vehicles under medium- and high-speed conditions has become a crucial foundation for ensuring driving safety and passenger comfort. Especially under complex conditions such as large variations in curve radius, significant fluctuations in road surface adhesion coefficient, and frequent changes in vehicle load, vehicle dynamics exhibit strong nonlinearity and strong coupling characteristics, placing higher demands on the modeling accuracy, adaptability, and real-time performance of controllers.

[0003] Currently, engineering widely employs model predictive control methods such as LQR and MPC, which are based on simplified monorail models and linear tire models. These methods typically identify fixed parameters offline during calibration tests or under single road conditions and maintain these parameters unchanged over long periods in actual operation. However, these methods struggle to accurately characterize the effects of tire nonlinear lateral slip characteristics, longitudinal and lateral coupling effects, and factors such as road adhesion coefficient and load transfer on vehicle dynamics. When a vehicle switches from calibration conditions to different roads, speeds, or load conditions, the residual between the nominal model and the actual dynamics increases significantly, leading to increased path tracking error, softer or more aggressive steering response, and a decreased safety margin. Traditional adaptive control or parameter estimation methods often rely on low-dimensional parameterized models, making it difficult to capture complex, time-varying high-dimensional residual dynamics while ensuring stability. Furthermore, they often struggle to balance control accuracy with implementation complexity.

[0004] In recent years, residual modeling methods based on Gaussian Processes (GPs) have been introduced into vehicle dynamics and trajectory tracking control to learn the mapping relationship between "model error - state / control" on the nominal model and perform feedforward compensation in MPC, thereby improving tracking accuracy. However, existing GP-MPC methods mostly rely on offline centralized training: a large number of samples need to be collected on the target road or similar working conditions to estimate hyperparameters and train the regression model; once the road geometry, adhesion conditions, or desired speed profile change, the model's generalization ability is limited, often requiring re-collection of data and offline training. In addition, the computational complexity of standard Gaussian process inference and updates increases cubically with the number of samples, making it difficult to achieve online updates and real-time control coupling under high sampling frequency and limited onboard computing power. Although existing sparse GP or online GP works have reduced the computational load through mechanisms such as induced points, they generally suffer from problems such as unconstrained growth in the number of induced points, lack of correlation between the addition / replacement strategy and closed-loop control performance, insufficient consideration of real-time and safety constraints, and even the introduction of new unstable factors such as overcompensation and oscillations when residual learning is inappropriate.

[0005] Therefore, there is an urgent need for a sparse online Gaussian process residual modeling method for joint control of path tracking and longitudinal velocity of unmanned vehicles. This method can achieve online learning and updating of model residuals under limited induction point size and limited computing resources. By tightly coupling with the model predictive control framework, it can improve the trajectory tracking accuracy and speed control performance of unmanned vehicles under different road conditions and operating conditions while ensuring closed-loop stability and constraint safety. Summary of the Invention

[0006] To address the above problems, this invention proposes a vehicle path tracking and longitudinal speed control method based on Gaussian process compensation.

[0007] The technical solution of this invention is: a vehicle path tracking and longitudinal speed control method based on Gaussian process compensation, comprising the following steps:

[0008] S1. Collect vehicle data on the calibrated road and construct a Gaussian process residual model for offline training;

[0009] S2. Collect vehicle data on the target road, determine the uncertainty index and normalized distance threshold, and update the Gaussian process residual model after offline training online;

[0010] S3. Calculate the three-channel compensation amount using the online-updated Gaussian process residual model;

[0011] S4. Based on the three-channel compensation amount, construct a residual correction prediction model and determine the output prediction;

[0012] S5. Based on the output prediction, construct a quadratic programming problem and solve it to obtain the control increment, steering input and longitudinal acceleration input at the current moment, and apply them to the vehicle actuators.

[0013] Furthermore, S1 includes the following sub-steps:

[0014] S11. Collect vehicle state vectors and control input vectors on the calibrated road;

[0015] S12. Based on the vehicle state vector and control input vector, construct the vehicle nominal dynamics model and discretize it to obtain the discrete-time nominal model.

[0016] S13. Collect time-series data on typical roads and use the discrete-time nominal model to calculate the nominal predicted state corresponding to the time-series data.

[0017] S14. Based on the nominal prediction state, construct the residual output and the input features of the Gaussian process;

[0018] S15. Stack the residual output and the input features of the Gaussian process to obtain the training dataset, which serves as discrete training samples.

[0019] S16. Calculate the sample mean and sample variance of the input features in the discrete training samples, as well as the sample mean and sample variance of the residual output.

[0020] S17. Calculate the input standard deviation vector based on the sample mean and sample variance of the input features; calculate the output standard deviation vector based on the sample mean and sample variance of the residual output.

[0021] S18. Calculate the first standardized variable and the second standardized variable based on the input standard deviation vector and the output standard deviation vector;

[0022] S19. Determine the standardized samples corresponding to the first and second standardized variables.

[0023] S110. Construct a Gaussian process residual model;

[0024] S111. Parameter identification is performed on the standardized samples to obtain hyperparameters. The hyperparameters and the set of induced points are used as the initial state of the Gaussian process residual model for offline training.

[0025] Furthermore, in S11, the vehicle state vector The expression is:

[0026] ;

[0027] in, Let X be the absolute position of the vehicle's center of mass along the X-axis in the world coordinate system. Let be the absolute position of the vehicle's center of mass along the axis in the world coordinate system. For heading angle, Let be the lateral velocity in the vehicle coordinate system. The longitudinal velocity in the vehicle coordinate system, The yaw rate is angular velocity. For transpose;

[0028] In S11, the control input vector The expression is:

[0029] ;

[0030] in, For the front wheel steering angle, This refers to either longitudinal acceleration or braking force commands.

[0031] In S12, the vehicle's nominal dynamics model The expression is:

[0032] ;

[0033] in, To map the current state and input to the state derivatives in the vehicle dynamics equations given vehicle parameters, A state vector consisting of vehicle state variables. This is the vehicle control input vector. A set of vehicle parameters;

[0034] In S12, the discrete-time nominal model The expression is:

[0035] ;

[0036] in, For discrete dynamic functions;

[0037] In S14, the residual output The expression is:

[0038] ;

[0039] in, For the first The residual of the longitudinal velocity at each sampling time, For the first Lateral velocity residual at each sampling time For the first Yaw velocity residual at each sampling time For the first The longitudinal velocity of the vehicle measured at each sampling time. For the first The lateral velocity of the vehicle measured at each sampling time. For the nominal model in the first The predicted longitudinal speed of the vehicle at each sampling time. For the nominal model The predicted lateral velocity of the vehicle at each sampling time point. For the first The vehicle yaw rate measured at each sampling time. For the nominal model in the first The vehicle yaw rate predicted at each sampling time;

[0040] Input characteristics of the Gaussian process in S14 The expression is:

[0041] ;

[0042] in, Choose a matrix for the state. Select the matrix for input. For the first The vehicle measurement state vector at each sampling time. In the first The vehicle control input vector at each sampling time point For the first The front wheel steering angle at each sampling time For the first The longitudinal acceleration at each sampling time, It is a 5-dimensional real vector space;

[0043] In S15, the training dataset The expression is:

[0044] ;

[0045] in, This represents the total number of samples in the offline training dataset.

[0046] In S18, the first standardized variable The expression is:

[0047] ;

[0048] in, The vector of sample means representing the input features. This represents the input standard deviation vector;

[0049] In S18, the second standardized variable The expression is:

[0050] ;

[0051] in, This represents the sample mean vector of the residual output. This indicates the output standard deviation vector.

[0052] Furthermore, S2 includes the following sub-steps:

[0053] S21. Collect the vehicle's state vector and control input vector at each sampling time on the target road;

[0054] S22. Using the discrete-time nominal model, predict the state vector and control input vector of the vehicle on the target road at each sampling time to obtain the nominal state at the next time step;

[0055] S23. Construct an online residual measurement vector based on the nominal next-time state and the measured state;

[0056] S24. Determine the standardized input based on the online residual measurement vector;

[0057] S25. Use the standardized input as the input to the Gaussian process residual model after offline training to obtain the prior distribution of residual prediction, and proceed to S26.

[0058] S26. Calculate the uncertainty index based on the predicted covariance;

[0059] S27. Calculate the normalized distance based on the current set of induced points;

[0060] S28. The uncertainty index satisfies the gate condition constructed by the normalized distance. At that time, the Gaussian process residual model is updated online; among which, As an uncertainty index, For uncertainty threshold, For normalized distance, This is the normalized distance threshold.

[0061] Furthermore, in S26, the uncertainty index The expression is:

[0062] ;

[0063] in, For the first The residual covariance matrix at each sampling time point For matrix trace operations;

[0064] In S27, the normalized distance threshold The expression is:

[0065] ;

[0066] in, The first in the current set of induced points The index of the induced points As the first standardized variable, For the current set of induction points, is the length scale vector for each input dimension.

[0067] Furthermore, S3 includes the following sub-steps:

[0068] S31. Construct a Gaussian process input based on the current measured state and the current or previous control quantity of the control quantity to be optimized.

[0069] S32. Standardize the Gaussian process input;

[0070] S33. Use the standardized Gaussian process input as the input of the updated Gaussian process residual model to obtain the predicted distribution of the three-channel residuals.

[0071] S34. Map the predicted distribution of the three-channel residuals from the normalized domain back to the physical quantity domain, and calculate the three-channel compensation amount.

[0072] Furthermore, in S31, the Gaussian process input... The expression is:

[0073] ;

[0074] in, Let be the lateral velocity in the vehicle coordinate system. The longitudinal velocity in the vehicle coordinate system, The yaw rate is angular velocity. For the front wheel steering angle, This is a longitudinal acceleration command or a braking force command. For transpose;

[0075] In S33, the expression for the predicted distribution of the three-channel residuals is:

[0076] ;

[0077] in, To standardize the mean of the residuals, To standardize the residual covariance matrix, It is a multivariate Gaussian distribution. The standardized residual prediction vector that follows this distribution;

[0078] In S34, the three-channel compensation amount The expression is:

[0079] ;

[0080] in, This is the compensation amount for lateral velocity. This is the compensation amount for the longitudinal velocity. This is the compensation amount for the yaw rate.

[0081] Furthermore, S4 includes the following sub-steps:

[0082] S41. Construct the residual injection matrix;

[0083] S42. Calculate the residual correction prediction model based on the residual injection matrix and the three-channel compensation amount;

[0084] S43. Perform first-order linearization on the residual correction prediction model to obtain a linear time-varying state-space model.

[0085] S44. Based on the prediction time domain length and the control time domain length, construct superimposed state prediction equations on the linear time-varying state space model;

[0086] S45. Based on the superposition state prediction equation, construct the output superposition equation in the prediction time domain;

[0087] S46. Determine the output prediction by superimposing the outputs in the prediction time domain.

[0088] Furthermore, in S41, the residual injection matrix The expression is:

[0089] ;

[0090] in, It is a 3×3 zero matrix. It is a 3×3 identity matrix. It is a 6×3 dimensional real matrix space;

[0091] In S42, the residual correction prediction model The expression is:

[0092] ;

[0093] in, Let be the vehicle's nominal discrete dynamics function. Let this be the current state vector. This is the current control input vector. For vehicle parameter set, Inject weights into the residuals. This is the compensation amount for three channels;

[0094] In S43, the expression for the linear time-varying state-space model is:

[0095] ;

[0096] in, This is the linearized state vector for the next time step. The state matrix, For the input matrix, For constant terms;

[0097] In S44, the expression for the superimposed state prediction equation is:

[0098] ;

[0099] in, To predict the superposition vector of states at each step in the time domain, To control the incremental superposition vector, To predict the time-domain state transition coefficient matrix, To predict the time-domain control increment coefficient matrix, This is the vector for predicting time-domain constant terms;

[0100] In S45, the expression for the output superposition equation in the prediction time domain is:

[0101] ;

[0102] in, To predict the superimposed output vector, To output the state mapping matrix of the superimposed vector, To output the coefficient matrix for the control increment, This is the vector of constant terms in the output equation.

[0103] Furthermore, S5 includes the following sub-steps:

[0104] S51. Based on the reference path of the target road, determine the reference output for each step in the prediction time domain;

[0105] S52. Determine the output error based on the reference output and output prediction at each step in the prediction time domain;

[0106] S53. Construct the first diagonal weighted matrix and the second diagonal weighted matrix;

[0107] S54. Calculate the weighted performance index in the prediction time domain based on the output error, the first diagonal weighting matrix, and the second diagonal weighting matrix.

[0108] S55. Construct state constraints;

[0109] S56. Based on the superposition state prediction equation and the superposition output equation in the prediction time domain, integrate the weighted performance index and state constraints in the prediction time domain into a quadratic programming problem.

[0110] S57. Use a quadratic programming solver to solve the quadratic optimization problem online to obtain the optimal control increment sequence. Take the first term of the optimal control increment sequence as the control increment at the current moment, and apply the steering input and longitudinal acceleration input to the vehicle actuator.

[0111] In S51, the reference output for each step in the time domain is predicted. The expression is:

[0112] ;

[0113] in, For the desired longitudinal velocity, To predict the length of the time domain, For transpose;

[0114] In S52, the output error The expression is:

[0115] ;

[0116] in, For output prediction;

[0117] In S53, the first diagonal weighted matrix The expression is:

[0118] ;

[0119] in, For longitudinal velocity error, For lateral error, As the heading angle error weight, It is a diagonal matrix operator;

[0120] In S53, the second diagonal weighted matrix The expression is:

[0121] ;

[0122] in, As the weight of the steering acceleration increment, For longitudinal acceleration increment weights;

[0123] In S54, the weighted performance index in the time domain is predicted. The expression is:

[0124] ;

[0125] in, To control the length of the time domain, To control the increment;

[0126] In S55, the expression for the state constraint condition is:

[0127] ;

[0128] ;

[0129] ;

[0130] in, This is the lower limit of the front wheel steering angle. For the first Front wheel angle, The upper limit of the front wheel steering angle. This is the lower bound of longitudinal acceleration. For the first longitudinal acceleration, This is the upper limit of longitudinal acceleration. This is the lower bound of the angle increment. For the first Step rotation increment, This is the upper bound of the angle increment. This is the lower bound of the acceleration increment. For the first Step acceleration increment, For the upper bound of acceleration, This is the lower bound of the lateral deviation. For at any time The predicted first Lateral deviation, This represents the upper limit of the lateral deviation. This is the lower bound of the longitudinal velocity. For at any time s predicted the first Step longitudinal velocity, This is the upper limit of the longitudinal velocity;

[0131] In S56, the expression for the quadratic programming problem is:

[0132] ;

[0133] in, To control the incremental superposition direction, The Hessian matrix of the quadratic cost. The vector of coefficients for linear terms. It is an inequality matrix. The inequality constraint vector;

[0134] In S57, the control increment at the current moment The expression is:

[0135] ;

[0136] in, This is the increment of the front wheel steering angle. This represents the longitudinal acceleration increment.

[0137] The beneficial effects of this invention are:

[0138] (1) This invention identifies residual Gaussian process hyperparameters offline on simple roads and passes them as priors to the online sparse model. This avoids the numerical instability and slow convergence caused by randomly initializing Gaussian process parameters from zero on the target road, allowing the online phase to enter an effective learning state in a short time. It also facilitates fair comparison with the traditional "offline GP only" baseline method.

[0139] (2) This invention introduces a dual-gated online update strategy based on normalized distance and prediction uncertainty, and combines a multi-factor scoring mechanism such as the age of the induced points, redundancy and posterior variance, to achieve adaptive coverage of the target road condition space with a limited number of induced points. Under typical multi-curved road conditions, it can significantly reduce the systematic error of the nominal model while maintaining real-time performance.

[0140] (3) This invention adopts a residual correction prediction model to embed a constraint model prediction control framework, and integrates lateral error, heading angle error and longitudinal velocity error into the same cost function for optimization. This invention can not only significantly improve path tracking accuracy and attitude stability, but also effectively improve longitudinal velocity tracking performance, avoiding the single performance optimization problem of "good lateral, poor velocity" or "good velocity, deteriorating lateral". It achieves overall improvement in multi-objective comprehensive indicators.

[0141] (4) The sparse residual Gaussian process structure and induced point maintenance strategy proposed in this invention take into account both online learning capability and computational complexity, and are suitable for deployment on existing autonomous driving controller hardware platforms. This provides an engineering-feasible technical solution for high-precision, adaptive path tracking and speed control of unmanned vehicles in complex road environments. Attached Figure Description

[0142] Figure 1 This is a flowchart of a vehicle path tracking and longitudinal speed control method based on Gaussian process compensation. Detailed Implementation

[0143] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0144] like Figure 1 As shown, this invention provides a vehicle path tracking and longitudinal speed control method based on Gaussian process compensation, comprising the following steps:

[0145] S1. Collect vehicle data on the calibrated road and construct a Gaussian process residual model for offline training;

[0146] S2. Collect vehicle data on the target road, determine the uncertainty index and normalized distance threshold, and update the Gaussian process residual model after offline training online;

[0147] S3. Calculate the three-channel compensation amount using the online-updated Gaussian process residual model;

[0148] S4. Based on the three-channel compensation amount, construct a residual correction prediction model and determine the output prediction;

[0149] S5. Based on the output prediction, construct a quadratic programming problem and solve it to obtain the control increment, steering input and longitudinal acceleration input at the current moment, and apply them to the vehicle actuators.

[0150] In this embodiment of the invention, S1 includes the following sub-steps:

[0151] S11. Collect vehicle state vectors and control input vectors on the calibrated road;

[0152] S12. Based on the vehicle state vector and control input vector, construct the vehicle nominal dynamics model and discretize it to obtain the discrete-time nominal model.

[0153] S13. Collect time-series data on typical roads and use the discrete-time nominal model to calculate the nominal predicted state corresponding to the time-series data.

[0154] S14. Based on the nominal prediction state, construct the residual output and the input features of the Gaussian process;

[0155] S15. Stack the residual output and the input features of the Gaussian process to obtain the training dataset, which serves as discrete training samples.

[0156] S16. Calculate the sample mean and sample variance of the input features in the discrete training samples, as well as the sample mean and sample variance of the residual output.

[0157] S17. Calculate the input standard deviation vector based on the sample mean and sample variance of the input features; calculate the output standard deviation vector based on the sample mean and sample variance of the residual output.

[0158] S18. Calculate the first standardized variable and the second standardized variable based on the input standard deviation vector and the output standard deviation vector;

[0159] S19. Determine the standardized samples corresponding to the first and second standardized variables.

[0160] S110. Construct a Gaussian process residual model;

[0161] S111. Parameter identification is performed on the standardized samples to obtain hyperparameters. The hyperparameters and the set of induced points are used as the initial state of the Gaussian process residual model for offline training.

[0162] In S13, a nominal path tracking controller is run on another typical road or test scenario to collect offline data: the vehicle is driven along a preset reference trajectory by an autonomous driving controller or manual driving, and time-series data is recorded.

[0163] In this embodiment of the invention, in S11, the vehicle state vector The expression is:

[0164] ;

[0165] in, Let X be the absolute position of the vehicle's center of mass along the X-axis in the world coordinate system. Let be the absolute position of the vehicle's center of mass along the axis in the world coordinate system. For heading angle, Let be the lateral velocity in the vehicle coordinate system. The longitudinal velocity in the vehicle coordinate system, The yaw rate is angular velocity. For transpose;

[0166] In S11, the control input vector The expression is:

[0167] ;

[0168] in, For the front wheel steering angle, This refers to either longitudinal acceleration or braking force commands.

[0169] In S12, the vehicle's nominal dynamics model The expression is:

[0170] ;

[0171] in, To map the current state and input to the state derivatives in the vehicle dynamics equations given vehicle parameters, A state vector consisting of vehicle state variables. This is the vehicle control input vector. A set of vehicle parameters;

[0172] In S12, a discrete-time nominal model is obtained through discretization methods (such as the zero-order preservation method or the forward Euler method). This model serves as a "baseline model" for subsequent residual learning, used to calculate the theoretical vehicle state evolution. Discrete-time nominal model The expression is:

[0173] ;

[0174] in, For discrete dynamic functions;

[0175] In S14, for the path tracking task, the 3D dynamic quantity that needs to be compensated is selected as the residual output. Residual Output The expression is:

[0176] ;

[0177] in, For the first The residual of the longitudinal velocity at each sampling time, For the first Lateral velocity residual at each sampling time For the first Yaw velocity residual at each sampling time For the first The longitudinal velocity of the vehicle measured at each sampling time. For the first The lateral velocity of the vehicle measured at each sampling time. For the nominal model in the first The predicted longitudinal speed of the vehicle at each sampling time. For the nominal model The predicted lateral velocity of the vehicle at each sampling time point. For the first The vehicle yaw rate measured at each sampling time. For the nominal model in the first The vehicle yaw rate predicted at each sampling time;

[0178] Define the state selection matrix and input selection matrix , so that:

[0179] ;

[0180] .

[0181] Input characteristics of the Gaussian process in S14 The expression is:

[0182] ;

[0183] in, Choose a matrix for the state. Select the matrix for input. For the first The vehicle measurement state vector at each sampling time. In the first The vehicle control input vector at each sampling time point For the first The front wheel steering angle at each sampling time For the first The longitudinal acceleration at each sampling time, It is a 5-dimensional real vector space;

[0184] In S15, the training dataset The expression is:

[0185] ;

[0186] in, This represents the total number of samples in the offline training dataset.

[0187] In S18, the first standardized variable The expression is:

[0188] ;

[0189] in, The vector of sample means representing the input features. This represents the input standard deviation vector;

[0190] In S18, the second standardized variable The expression is:

[0191] ;

[0192] in, This represents the sample mean vector of the residual output. This indicates the output standard deviation vector.

[0193] In this embodiment of the invention, statistical analysis is performed on the offline residual data to obtain normalized parameters for subsequent online learning:

[0194] Calculate the sample mean of the input features With variance Its expression is:

[0195] ;

[0196] ;

[0197] in, This indicates that the element-wise square operation is performed. This represents the number of offline samples.

[0198] Calculate the sample mean of the residual output. With variance :

[0199] ;

[0200] .

[0201] Obtain the input standard deviation vector and output standard deviation vector , used to construct standardized variables.

[0202] Construct a Gaussian process residual model and initialize hyperparameters and induced points. Based on standardized samples, establish a sparse online Gaussian process (SONIG) residual model with input noise, and determine the initial hyperparameters and induced point set offline.

[0203] Choosing the squared exponential kernel function as the covariance function, its expression is:

[0204] ;

[0205] in, To output scale parameters, For the input length scale matrix, The standardized input feature vector for the current operating condition. For another operating condition, the standardized input feature vector, The length scale parameter for the first input dimension. This is the length scale parameter for the 5th input dimension.

[0206] Using maximum likelihood or marginal likelihood optimization methods, a batch of standardized samples... Perform parameter identification to obtain kernel function hyperparameters. Input noise covariance With output noise covariance The initial value.

[0207] Based on the distribution of the training samples, several representative points are selected in the input space as the set of induced input points. Its expression is:

[0208] ;

[0209] in, This is the first induction point. For the nth u One induction point.

[0210] The selected strategy may be a greedy selection based on kernel correlation or a normalized distance threshold selection, so that the normalized distance between any training sample and the nearest induced point does not exceed a preset threshold.

[0211] Using the aforementioned hyperparameters and the set of induced points as the initial state of the Gaussian process residual model, we obtain the prior of the residual model after offline training, which is then used for online updates and control compensation on the target road.

[0212] In this embodiment of the invention, S2 includes the following sub-steps:

[0213] S21. Collect the vehicle's state vector and control input vector at each sampling time on the target road;

[0214] S22. Using the discrete-time nominal model, predict the state vector and control input vector of the vehicle on the target road at each sampling time to obtain the nominal state at the next time step;

[0215] S23. Construct an online residual measurement vector based on the nominal next-time state and the measured state;

[0216] S24. Determine the standardized input based on the online residual measurement vector;

[0217] S25. Use the standardized input as the input to the Gaussian process residual model after offline training to obtain the prior distribution of residual prediction, and proceed to S26.

[0218] S26. Calculate the uncertainty index based on the predicted covariance;

[0219] S27. Calculate the normalized distance based on the current set of induced points;

[0220] S28. The uncertainty index satisfies the gate condition constructed by the normalized distance. At that time, the Gaussian process residual model is updated online; among which, As an uncertainty index, For uncertainty threshold, For normalized distance, This is the normalized distance threshold.

[0221] In this embodiment of the invention, in S26, the uncertainty index The expression is:

[0222] ;

[0223] in, For the first The residual covariance matrix at each sampling time point For matrix trace operations;

[0224] In S27, the normalized distance threshold The expression is:

[0225] ;

[0226] in, The first in the current set of induced points The index of the induced points As the first standardized variable, For the current set of induction points, is the length scale vector for each input dimension.

[0227] In this embodiment of the invention, S3 includes the following sub-steps:

[0228] S31. Construct a Gaussian process input based on the current measured state and the current or previous control quantity of the control quantity to be optimized.

[0229] S32. Standardize the Gaussian process input;

[0230] S33. Use the standardized Gaussian process input as the input of the updated Gaussian process residual model to obtain the predicted distribution of the three-channel residuals.

[0231] S34. Map the predicted distribution of the three-channel residuals from the normalized domain back to the physical quantity domain, and calculate the three-channel compensation amount.

[0232] In this embodiment of the invention, in S31, the Gaussian process input... The expression is:

[0233] ;

[0234] in, Let be the lateral velocity in the vehicle coordinate system. The longitudinal velocity in the vehicle coordinate system, The yaw rate is angular velocity. For the front wheel steering angle, This is a longitudinal acceleration command or a braking force command. For transpose;

[0235] In S33, the expression for the predicted distribution of the three-channel residuals is:

[0236] ;

[0237] in, To standardize the mean of the residuals, To standardize the residual covariance matrix, It is a multivariate Gaussian distribution. The standardized residual prediction vector that follows this distribution;

[0238] In S34, the three-channel compensation amount The expression is:

[0239] ;

[0240] in, This is the compensation amount for lateral velocity. This is the compensation amount for the longitudinal velocity. This is the compensation amount for the yaw rate.

[0241] In this embodiment of the invention, S4 includes the following sub-steps:

[0242] S41. Construct the residual injection matrix;

[0243] S42. Calculate the residual correction prediction model based on the residual injection matrix and the three-channel compensation amount;

[0244] S43. Perform first-order linearization on the residual correction prediction model to obtain a linear time-varying state-space model.

[0245] S44. Based on the prediction time domain length and the control time domain length, construct superimposed state prediction equations on the linear time-varying state space model;

[0246] S45. Based on the superposition state prediction equation, construct the output superposition equation in the prediction time domain;

[0247] S46. Determine the output prediction by superimposing the outputs in the prediction time domain.

[0248] In this embodiment of the invention, in S41, the residual injection matrix The expression is:

[0249] ;

[0250] in, It is a 3×3 zero matrix. It is a 3×3 identity matrix. It is a 6×3 dimensional real matrix space;

[0251] In S42, the residual correction prediction model The expression is:

[0252] ;

[0253] in, Let be the vehicle's nominal discrete dynamics function. Let this be the current state vector. This is the current control input vector. For vehicle parameter set, Inject weights into the residuals. This is the compensation amount for three channels;

[0254] In S43, the expression for the linear time-varying state-space model is:

[0255] ;

[0256] in, This is the linearized state vector for the next time step. The state matrix, For the input matrix, For constant terms;

[0257] In S44, the expression for the superimposed state prediction equation is:

[0258] ;

[0259] in, To predict the superposition vector of states at each step in the time domain, To control the incremental superposition vector, To predict the time-domain state transition coefficient matrix, To predict the time-domain control increment coefficient matrix, This is the vector for predicting time-domain constant terms;

[0260] In S45, the expression for the output superposition equation in the prediction time domain is:

[0261] ;

[0262] in, To predict the superimposed output vector, To output the state mapping matrix of the superimposed vector, To output the coefficient matrix for the control increment, This is the vector of constant terms in the output equation.

[0263] In this embodiment of the invention, S5 includes the following sub-steps:

[0264] S51. Based on the reference path of the target road, determine the reference output for each step in the prediction time domain;

[0265] S52. Determine the output error based on the reference output and output prediction at each step in the prediction time domain;

[0266] S53. Construct the first diagonal weighted matrix and the second diagonal weighted matrix;

[0267] S54. Calculate the weighted performance index in the prediction time domain based on the output error, the first diagonal weighting matrix, and the second diagonal weighting matrix.

[0268] S55. Construct state constraints;

[0269] S56. Based on the superposition state prediction equation and the superposition output equation in the prediction time domain, integrate the weighted performance index and state constraints in the prediction time domain into a quadratic programming problem.

[0270] S57. Use a quadratic programming solver to solve the quadratic optimization problem online to obtain the optimal control increment sequence. Take the first term of the optimal control increment sequence as the control increment at the current moment, and apply the steering input and longitudinal acceleration input to the vehicle actuator.

[0271] In the next sampling period, using the new measured state New residual prediction With the updated Gaussian process residual model, repeat steps S2 to S4 to form a closed-loop rolling optimization process of "residual online learning + residual correction model predictive control" to achieve adaptive path tracking and speed control of the vehicle on the target road.

[0272] In S51, the reference output for each step in the time domain is predicted. The expression is:

[0273] ;

[0274] in, For the desired longitudinal velocity, To predict the length of the time domain, For transpose;

[0275] In S52, the output error The expression is:

[0276] ;

[0277] in, For output prediction;

[0278] In S53, the first diagonal weighted matrix The expression is:

[0279] ;

[0280] in, For longitudinal velocity error, For lateral error, As the heading angle error weight, It is a diagonal matrix operator;

[0281] In S53, the second diagonal weighted matrix The expression is:

[0282] ;

[0283] in, As the weight of the steering acceleration increment, For longitudinal acceleration increment weights;

[0284] In S54, the weighted performance index in the time domain is predicted. The expression is:

[0285] ;

[0286] in, To control the length of the time domain, To control the increment;

[0287] In S55, the expression for the state constraint condition is:

[0288] ;

[0289] ;

[0290] ;

[0291] in, This is the lower limit of the front wheel steering angle. For the first Front wheel angle, The upper limit of the front wheel steering angle. This is the lower bound of longitudinal acceleration. For the first longitudinal acceleration, This is the upper limit of longitudinal acceleration. This is the lower bound of the angle increment. For the first Step rotation increment, This is the upper bound of the angle increment. This is the lower bound of the acceleration increment. For the first Step acceleration increment, For the upper bound of acceleration, This is the lower bound of the lateral deviation. For at any time The predicted first Lateral deviation, This represents the upper limit of the lateral deviation. This is the lower bound of the longitudinal velocity. For at any time s predicted the first Step longitudinal velocity, This is the upper limit of the longitudinal velocity;

[0292] In S56, the expression for the quadratic programming problem is:

[0293] ;

[0294] in, To control the incremental superposition direction, The Hessian matrix of the quadratic cost. The vector of coefficients for linear terms. It is an inequality matrix. The inequality constraint vector;

[0295] In S57, the control increment at the current moment The expression is:

[0296] ;

[0297] in, This is the increment of the front wheel steering angle. This represents the longitudinal acceleration increment.

[0298] In this invention, a comprehensive solution is proposed to address two core problems in existing unmanned vehicle path tracking control: First, nominal dynamics models calibrated based on a single road condition suffer from systematic modeling errors on complex, winding roads, making it difficult to simultaneously address lateral, heading, and longitudinal speed errors. Second, traditional offline Gaussian process residual models have high computational complexity and are difficult to update online, failing to meet the real-time requirements of control cycles in the millisecond to tens of millisecond range. To address these issues, this invention proposes an unmanned vehicle path tracking and speed control method based on sparse residual Gaussian processes. Through an integrated design of "nominal dynamics model + sparse online Gaussian process residual model + constrained model predictive control," it achieves coordinated control and online adaptive compensation of the unmanned vehicle's longitudinal speed, lateral position, and heading angle.

[0299] The method of this invention generally includes the following technical ideas: First, vehicle operation data is collected on simple or regular roads (such as semi-circular arcs or multi-segment S-shaped roads). A residual relationship between the nominal model and the true response is established using standard Gaussian process regression, and hyperparameters such as kernel function length scale, signal variance, and noise variance are identified accordingly. Simultaneously, a normalized scale for the input and output is constructed. Then, the offline identification result is used as a priori to initialize the hyperparameters and numerical stability parameters of the sparse online Gaussian process model, and the input space for online residual learning is constructed by combining vehicle state and control variables. During closed-loop operation on the target road, residual samples are constructed using the error between the nominal model's single-step prediction and sensor measurements. The system triggers online updates through a dual-gating mechanism of uncertainty and normalized distance, and employs a dynamic maintenance strategy for the induced point dictionary to achieve a balance between real-time performance and coverage. Then, in each control cycle, the residuals of longitudinal velocity, lateral velocity, and yaw rate are predicted using the updated sparse Gaussian process, forming a three-channel compensation quantity. Finally, the compensation quantity is injected into the nominal dynamics model to construct a residual correction prediction model, which is then embedded into the constrained model predictive control framework. With the optimization objective of minimizing path lateral error, heading angle error, and longitudinal velocity error, the control inputs for steering angle and longitudinal acceleration are obtained online, thereby achieving accurate path tracking and speed control for unmanned vehicles in complex road environments.

[0300] Specifically, this invention employs a parallel structure of "nominal model + residual Gaussian process" at the modeling level. The nominal model uses a common three-degree-of-freedom vehicle dynamics model or its linearized discrete form. The state variables include the vehicle's center of mass coordinates, heading angle, longitudinal velocity, lateral velocity, and yaw rate. The inputs include the front wheel steering angle and longitudinal acceleration. By analyzing experimental data of the vehicle running along the test road under fixed or variable speed conditions, the difference between the nominal model's predicted values ​​and the sensor measurements is extracted as residual samples. A multi-output Gaussian process is then used to jointly model the longitudinal velocity residual, lateral velocity residual, and yaw rate residual. In the offline stage, a full-data Gaussian process regression is used to estimate the length scaling matrix of the kernel function, the output signal variance, and the observation noise variance. The mean and standard deviation of the input and output are obtained by statistically analyzing the training data to form a normalized configuration, providing a reasonable prior and scale for the subsequent online sparse model.

[0301] In constructing sparse residual Gaussian processes, this invention employs an online Gaussian process structure based on induced points. A finite number of representative points in the input space are used as induced inputs, and their corresponding Gaussian distributions induce outputs, approximating the covariance calculation of the entire data. To adapt to online control scenarios, this invention introduces two design aspects when constructing the sparse model: First, the length scale in the input dimension is obtained by back-calculating the diagonal elements of the covariance matrix of the offline Gaussian process, and the length scales of each dimension are uniformly adjusted to the specified target scale range under normalized coordinates. This ensures that the "distance" in different operating conditions during the online stage has a consistent physical meaning, which is beneficial for stabilizing the numerical performance of the kernel function and for ensuring the uniformity of the induced point distribution. Second, by performing statistical analysis on the offline data and setting appropriate input uncertainty and output noise levels, the covariance matrix remains symmetric and positive definite during online updates, improving the stability of the numerical solution.

[0302] In terms of online learning and induced point maintenance, this invention proposes a dynamic dictionary management mechanism that balances novelty, uncertainty, and real-time performance. First, in each sampling period, an input vector for a Gaussian process is constructed based on the state and control input of the previous time step. This vector is then normalized using the mean and standard deviation, and extreme values ​​are pruned to prevent outliers from damaging the model. Next, the normalized distance between the current input and the existing set of induced points, weighted by a length scale, and the corresponding kernel correlation are calculated to characterize the novelty of the current condition in the input space. Simultaneously, the residual between the nominal model prediction and the actual measurement at the current time step is slowly normalized and statistically analyzed on the output side. This updates the output mean and variance estimates, and sets reasonable upper and lower bounds on the output standard deviation to ensure it reflects long-term trends without being amplified by instantaneous large errors. The residual is then transformed into the standardized domain as the target for online learning.

[0303] Based on this, the present invention uses a dual-gating system of uncertainty and normalized distance to determine whether a structural update is worthwhile: if the kernel correlation between the current working condition and the nearest induced point is lower than a preset threshold, or if the prediction uncertainty obtained based on the Gaussian process posterior is significantly higher than the historical quantile level, then the current working condition is considered to belong to an input region that is "not yet fully covered," thus possessing the value of adding or replacing induced points. If the number of induced points has not yet reached the target scale, then the current working condition is directly added to the dictionary as a new induced point, provided that the minimum distance constraint is met; if the number of induced points is close to or has reached the target scale, then a comprehensive scoring function is constructed, using the "similarity to the new working condition, age of use, and posterior variance" of the induced point as redundancy indicators for weighting, prioritizing those induced points that are both old and redundant, and whose region has a low prediction variance, as replacement candidates. A warm start and delayed deletion strategy is adopted to retain both old and new induced points for inference in a short period of time, and then smoothly remove the old induced points after the new induced points have completed several updates, thereby avoiding model mutations. To limit computational complexity, this invention sets a time period for maintaining induced points and a maximum number of replacements within a single period. The above structural adjustments are only performed at periodic moments, and pruning operations are performed when the dictionary size exceeds the upper limit, deleting the batch of induced points with the highest redundancy, so that the number of induced points falls back to the target range.

[0304] In terms of residual prediction and compensation injection, this invention employs output space projection and channel decomposition, using the Gaussian process only to estimate the single-step residuals of three channels closely related to path tracking performance: longitudinal velocity, lateral velocity, and yaw rate, without directly modeling position information. This reduces the output dimension of the Gaussian process and gives the residuals a clearer physical meaning. In each control cycle, the Gaussian process input is constructed using the current state and the control input from the previous time step. After normalization and online Gaussian process inference, the residual prediction in the standardized domain is obtained, and then the compensation amount in the physical domain is restored using the standard deviation and mean of the output side. To prevent unnecessary aggressive behavior caused by residual compensation in model mismatch or extrapolation regions, this invention also introduces a compensation scaling factor and an uncertainty-based soft constraint mechanism. When the prediction uncertainty is large or in a sparse region of induced points, the compensation intensity is automatically weakened, allowing the Gaussian process residuals to play a major role in the "high model confidence region" and preferentially rely on the nominal dynamics model in the "low model confidence region," thus improving the robustness of control at the system level.

[0305] In terms of controller design, this invention embeds the residual-corrected vehicle dynamics model into a linear time-varying model predictive control framework. By linearizing and discretizing the nominal model under the current operating condition, the state transition matrix and input matrix are obtained. The residual compensation generated by the Gaussian process is injected into the prediction model in the form of an equivalent bias term, thereby continuously correcting the predictions of future lateral position, heading angle, and longitudinal speed during the rolling prediction process. The prediction layer constructs a finite prediction time domain with a fixed step size, interpolates the reference trajectory (including reference position, reference heading, and reference speed) for each prediction step, and defines a cost function in the output space to minimize the weighted sum of squares of the path lateral error, heading angle error, and longitudinal speed error over the entire prediction time domain. The control layer constructs a control change penalty matrix with the steering angle increment and longitudinal acceleration increment as optimization variables to suppress excessive steering jitter and acceleration / deceleration shocks. The constraint layer applies inequality constraints to the steering angle amplitude and rate of change, the upper and lower limits of longitudinal acceleration, the vehicle speed range, and lateral displacement to ensure that physical constraints and safety requirements are met in terms of tire sideslip, vehicle stability, and ride comfort. The above optimization problem can be transformed into a standard quadratic programming problem with a quadratic objective function and linear constraints after being sorted out. It is solved in each sampling period. The optimal control increment of the first step is superimposed on the control quantity of the previous moment as the actual steering and driving input of the current moment, so as to achieve closed-loop rolling optimization.

[0306] The following description is based on specific embodiments.

[0307] This invention provides a vehicle path tracking and longitudinal speed joint control method based on sparse online Gaussian process compensation, comprising the following steps S1-S5:

[0308] S1. Construct a residual dataset based on offline road data and initialize a sparse Gaussian process model.

[0309] Step S1 specifically includes the following processes S101-S109:

[0310] S101. Vehicle Platform and State Definition.

[0311] This embodiment uses a drive-by-wire vehicle as the controlled object. Vehicle state and control variables are acquired by combining an inertial measurement unit (IMU), wheel speed sensors, and steering angle sensors. The following six-dimensional state vector and two-dimensional control vector are defined in the vehicle coordinate system:

[0312] ;

[0313] in, Let X be the absolute position of the vehicle's center of mass along the X-axis in the world coordinate system. Let be the absolute position of the vehicle's center of mass along the axis in the world coordinate system. For heading angle, Let be the lateral velocity in the vehicle coordinate system. The longitudinal velocity in the vehicle coordinate system, The yaw rate is angular velocity. For transpose;

[0314] Control input is defined as:

[0315] ;

[0316] in, For the steering angle of the front wheels, This refers to the longitudinal acceleration command generated by the drive / brake actuator. The sampling period is denoted as... .

[0317] S102. Establishment and discretization of the nominal vehicle dynamics model.

[0318] Based on vehicle mass Moment of inertia Front and rear wheelbase Front and rear wheel lateral stiffness Using parameters such as linear two-degree-of-freedom or extended three-degree-of-freedom lateral dynamics models, combined with longitudinal uniform acceleration models, the nominal continuous-time vehicle dynamics equations are established:

[0319] ;

[0320] in, For vehicle parameter set, A state vector consisting of vehicle state variables. This is the vehicle control input vector. This is a nonlinear vehicle dynamics function.

[0321] During the sampling period The above model is then discretized using either first-order Euler discretization or the zero-order preservation method to obtain the nominal discrete-time model.

[0322] In subsequent steps, the nominal vehicle dynamics model is only responsible for providing "theoretical predictions," and the difference between it and the real vehicle is compensated by the residual model.

[0323] S103. Offline path selection and data collection.

[0324] To avoid "fitting from scratch on the target road", this embodiment prefers to collect offline training data on a road that is representative but not exactly the same as the target road, such as a test track road with a combination of semi-circular arc and straight line, or a curve with a single radius of curvature plus a uniform straight line segment.

[0325] On this offline road, a nominal path tracking controller is operated with a fixed longitudinal speed reference (e.g., 12 m / s) to enable the vehicle to cover different curvature ranges and typical operating conditions.

[0326] The offline training dataset was recorded throughout the experiment:

[0327] ;

[0328] in, Let this be the current state vector. This is the current control input vector. For the first The measured state vector at each sampling time. This represents the total number of samples in the offline training dataset.

[0329] S104. Residual Output Construction and Input Feature Selection.

[0330] To ensure that the Gaussian process learns only the parts that are "difficult to accurately characterize by the nominal model", this embodiment focuses residual modeling on three channels: longitudinal velocity, lateral velocity, and yaw rate, and defines offline residual output.

[0331] To balance model expressiveness with real-time online computation, this embodiment defines a Gaussian process input feature vector. Only the current longitudinal velocity, lateral velocity, yaw rate, current steering input, and longitudinal acceleration input are selected to avoid introducing redundant higher-order states or historical sequences, thus reducing the burden on subsequent online learning and prediction.

[0332] This yields the offline residual dataset. Its expression is:

[0333] .

[0334] S105. Input and output normalized statistics estimation.

[0335] Considering the significant differences in the dimensions of the state and residuals under different vehicle operating conditions, this embodiment normalizes both the input and output to improve the numerical stability and hyperparameter interpretability of the Gaussian process. Specifically:

[0336] Calculate the mean and standard deviation of the input feature samples, and calculate the mean and standard deviation of the residual output samples. Then, map all samples to the standardized space, and... It will be stored as a fixed normalized parameter in the subsequent online learning and prediction process.

[0337] S106. Offline complete Gaussian process hyperparameter identification.

[0338] Within the standardized space, this embodiment employs a quadratic exponential kernel Gaussian process regression model where each output channel is independent but shares the same input. For the first... Each output channel has a kernel function. Defined as:

[0339] ;

[0340] in, For the first The output at the ... Length scale on each input dimension For signal variance, The input feature dimension, The standardized input feature vector for the current operating condition. This is the standardized input feature vector for the current operating condition.

[0341] Based on offline residual dataset The hyperparameter set for each channel is obtained by maximizing the log-marginal likelihood of the training data. Its expression is:

[0342] ;

[0343] in, For the first The length scaling parameter vector of each output channel in 5 input dimensions. To observe the noise variance.

[0344] The obtained length scale and variance parameters not only reflect the sensitivity of different input dimensions and output channels to the residual, but also provide physically reasonable initial hyperparameters for the subsequent Sparse Gaussian process (SONIG), avoiding the risk of divergence caused by training from random values.

[0345] S107. Hyperparameter mapping to sparse online Gaussian process structure.

[0346] Considering the real-time requirements of online operation, this embodiment uses a sparse online Gaussian process (e.g., a SONIG structure based on a set of induced points) as the residual model. The length scale and variance identified in S106 are mapped to the hyperparameter form of SONIG, including:

[0347] Standardize spatial length scale As the kernel width parameter of SONIG; the signal variance As an output channel The kernel amplitude; the noise variance As the initial value of the measurement noise, it is used to construct the output covariance matrix.

[0348] Meanwhile, to match subsequent input perturbation modeling, this embodiment sets the input noise standard deviation as a certain proportion of the length scale, for example:

[0349] ;

[0350] in, For the first The noise standard deviation of each input dimension. This is the scaling factor between the input noise and the length scale. For the first Channel length scale In dimensions The median taken from the top, The value is set to 0.05-0.1. This setting balances input estimation uncertainty with numerical stability.

[0351] S108. Initial Pathfinder Set Setup and Clipping.

[0352] In sparse Gaussian processes, the set of induced points determines the "support position" of the model in the input space. This embodiment utilizes offline standardized input samples. The initial set of induction points is selected using a greedy approach. :

[0353] First, a portion of the samples are randomly selected as a candidate set, serving as the first batch of induction points;

[0354] Then, the remaining samples are traversed, and the kernel correlation between each sample and the current set of induced points is calculated. Its expression is:

[0355] ;

[0356] in, For the first The standardized input vector of each candidate induction point For the current sample at the th The standardized components of the dimension, For the first The induced point is at the th The standardized components of the dimension, For the first The length scale of each input dimension This is the standardized input vector for the current sample;

[0357] When the maximum correlation with all existing induction points is lower than a preset threshold When the number of induced points reaches the target upper limit, the sample is added to the set of induced points. Or stop when the traversal is complete.

[0358] The above layout ensures that the guidance points are evenly distributed in the typical working conditions of the offline road, avoiding the situation where "all are piled up near a few working conditions".

[0359] Finally, the obtained induced point locations, corresponding posterior mean and covariance of function values ​​are initialized into the SONIG structure, and auxiliary information such as the "age" of the induced points is recorded to facilitate subsequent online maintenance and replacement on the target road.

[0360] S109. Persistent storage of residual models and normalized parameters.

[0361] After steps S105-S108 are completed, the initialized residual sparse Gaussian process model and normalized parameters are obtained.

[0362] In this embodiment, the following information is persistently stored in the form of a configuration file:

[0363] Normalization parameter: ;

[0364] SONIG hyperparameters: length scale of each channel, signal variance, and noise variance;

[0365] Initial induction point location, posterior mean and covariance of the function;

[0366] Auxiliary strategy parameters: upper and lower limits of the number of induction points, distance threshold, kernel correlation threshold, etc.

[0367] In subsequent steps S2-S5, the controller directly loads the above configuration without needing to undergo offline training again, thus ensuring that the online learning process on the target road is repeatable and portable.

[0368] S2. During the operation of the target road, residual samples are constructed based on the single-step predicted values ​​and measured states of the nominal linear time-varying vehicle dynamics model. The SONIG online update rule, which combines uncertainty and normalized distance gating, is used to adaptively update the sparse Gaussian process residual model and its set of induced points.

[0369] In one embodiment, step S2 includes the following steps S201-S203:

[0370] S201. Initialization of target road and MPC control loop.

[0371] In this embodiment, the target road can be a combination of multiple "S"-shaped curves that are different from the offline road. A reference path is obtained through pre-discretization. And store it in the path table. For reference path in arc length global Location, For reference path in arc length global Location, For reference path in arc length The heading angle at that point, For reference path in arc length Reference longitudinal velocity at that location This represents the path arc length.

[0372] At each sampling time Based on the vehicle's current location and path arc length Determine the nearest reference point and the current reference arc length. Thus, the reference longitudinal velocity at that moment is obtained. Reference heading angle And the reference trajectory within the subsequent prediction domain. The MPC controller runs once in each sampling period, and internally requires joint prediction of the nominal model and the residual model. Therefore, the online residual update step of this embodiment is performed before the MPC call.

[0373] S202. Single-step nominal prediction and construction of true residuals.

[0374] At sampling time The current measured state is known. Control input applied in the previous control cycle .

[0375] First, a one-step prediction is performed using the nominal discrete model from step S102, extracting the nominal velocity and yaw rate components. Then, in the next sampling... Upon arrival, the actual measured status was obtained. Extract the true velocity and yaw rate components. Construct the true residual for this period. Its expression is:

[0376] ;

[0377] in, For the first The longitudinal velocity was measured at one sampling time. This represents the longitudinal velocity prediction of the nominal model at that moment. To measure the lateral velocity, This represents the nominal model's predicted lateral velocity. To measure the yaw rate, This represents the yaw rate prediction value of the nominal model.

[0378] S203. Online input feature construction and normalization.

[0379] To maintain consistency with the offline model, this embodiment uses the input feature definition from step S104 on the target road, that is, constructing the input vector using the state and control variables from the previous sampling time:

[0380] ;

[0381] The input and output are standardized online using the normalization statistics in step S105.

[0382] To avoid extreme outliers from disrupting the Gaussian process, this embodiment can perform standardization on... Perform shearing, for example, restricting each dimension to Within the interval, its expression is:

[0383] ;

[0384] in, For the first The sample at the th A dimensional standardized input vector, For symbolic functions, To take the smaller value.

[0385] S204. Generate prior predictions and uncertainties using the current sparse Gaussian process.

[0386] Before performing the online update, this embodiment first utilizes the current SONIG model in The residual prior prediction is generated and used to determine whether it is necessary to include the sample for learning.

[0387] Specifically, standardized input Input the SONIG structure to obtain the predicted standardized residual mean and covariance.

[0388] In this embodiment, the trace or the maximum value of the diagonal of the covariance matrix is ​​used as the global uncertainty index. The greater the uncertainty, the lower the confidence of the residual model near the current operating point, and the greater its learning value.

[0389] S205. Normalized distance calculation based on length scale.

[0390] To avoid excessive influence of samples "far from the known region" in the input space on the model, this embodiment introduces a normalized distance metric based on length scale.

[0391] Let the set of induction points of the current SONIG model be... Length scale vector for ,in, This represents the number of induction points in the current SONIG model. The length scale parameter for the first input dimension. This is the length scale parameter for the 5th input dimension.

[0392] Define the normalized Euclidean distance from the input sample to the induction point. First, normalize each input dimension according to the corresponding length scale. Then, measure the Euclidean distance in this space and take the minimum value. When the normalized distance threshold is... When the value is large, it indicates that the input point is far from any existing induced points. In this embodiment, it is more preferable to "first expand the coverage of induced points and then carefully update the model" rather than directly forcibly fitting the distant region with a small amount of data.

[0393] S206. Joint gating strategy of uncertainty and normalized distance.

[0394] In order to achieve "learning only when necessary and controlling the stability of learning" during online updates, this embodiment adopts a joint gating strategy of uncertainty and normalized distance.

[0395] The following two thresholds are preset:

[0396] Uncertainty threshold For example, selecting a historical uncertainty series. The 80th percentile;

[0397] Normalized distance threshold For the distribution of offline data, select the maximum distance or empirical value that can cover the main operating conditions.

[0398] The current sample is only considered if the following conditions are met simultaneously. Only then is it considered worthwhile to use it to update the SONIG model:

[0399] The model lacks confidence at this point:

[0400] ;

[0401] in, As an uncertainty index;

[0402] The input is located near an existing coverage area:

[0403] ;

[0404] This can avoid two types of undesirable situations:

[0405] If the uncertainty is very small ( The value is very small, indicating that the model has been sufficiently trained in this area and does not require frequent relearning.

[0406] If the distance is too large ( (The value is very large), indicating that the current point is far from the training distribution. Directly using a single sample to force learning can easily lead to instability of the model in the "extrapolation region". In this embodiment, we prioritize using induced points to manage and expand the coverage, and then gradually add stable samples.

[0407] S207. Construct a measurement distribution with input and output noise.

[0408] When the gating condition is met, this embodiment will This is used as a new measurement to update the SONIG model.

[0409] Considering that both the actual state estimation and the actuator contain noise, this embodiment does not include... Instead of treating them as fixed points, we construct Gaussian distributions for the input and output:

[0410] ;

[0411] in, To input the variance matrix, the settings from step S107 are used as before. Form a diagonal matrix; To output the measurement noise variance matrix, the noise variance is identified offline. Normalization yields the result.

[0412] This process is equivalent to explicitly considering measurement uncertainties during updates, which can avoid excessive perturbation of the posterior a priori value by a single outlier.

[0413] S208. Online measurement updates based on SONIG.

[0414] The above input and output measurement distributions are treated as a "residual observation with input noise" and fed into the SONIG update routine.

[0415] In its implementation, SONIG approximates the input distribution by performing a first- or second-order Taylor expansion in the kernel function space of the current set of induced points, thereby obtaining the incremental update formula for the output of the induced points and realizing the recursive correction of the posterior mean and covariance.

[0416] Unlike traditional batch sparse Gaussian processes, SONIG does not require storing all historical samples. It can digest a measurement using only the current set of induced points and hyperparameters. The update complexity is polynomial to the number of induced points, which meets the requirements of online real-time vehicle control.

[0417] S209. Online maintenance and constraints of the dictionary of inducing points.

[0418] Specifically, step S209 includes the following sub-steps S2091 to S2095:

[0419] S2091. Calculation of distance metric between induction points and kernel correlation.

[0420] Let the input characteristics of the current working condition to be evaluated be: The existing set of induced points is denoted as ,in, , For the longitudinal speed of the vehicle, For the vehicle's lateral speed, The yaw rate is angular velocity. For the front wheel steering angle, For longitudinal acceleration, This represents the number of induced points.

[0421] Normalized distance: The length scale obtained through offline identification. Normalize each dimension and define the first dimension. The normalized squared distance between each induced point and the current operating condition.

[0422] Kernel correlation: Based on a Gaussian kernel, it defines the correlation between the current operating condition and the first... The kernel correlation of each induction point is used, and the kernel correlation closest to the induction point is taken. Its expression is:

[0423] ;

[0424] in, Input the current operating condition With the Kernel correlation between induced points.

[0425] Prediction uncertainty: Standardizing the input The data is fed into the SONIG model to obtain the predicted standard deviation vector of the three-channel residuals. Its norm or components can be used as uncertainty indicators. ,For example:

[0426] ;

[0427] in, The predicted standard deviation of the longitudinal channel residuals This represents the predicted standard deviation of the lateral channel residuals. This represents the predicted standard deviation of the yaw channel residuals. It is a vector composed of the standard deviations of the three channels.

[0428] S2092. Criteria for adding induction points and initial point placement.

[0429] Initial point placement phase: When the number of induced points Smaller than the preset seed size At this time, the system is in the "dictionary initialization phase". A relatively lenient addition strategy is adopted at this stage:

[0430] If there is no current guidance point, then directly apply the current working condition. Add it to the dictionary as the first leading point;

[0431] If an induced point already exists, add a new induced point when the following equation is satisfied:

[0432] ;

[0433] in, Based on the basic distance threshold, This is a relaxation factor for the initialization phase. Input the current operating condition With the Normalized distance between induced points. Novelty + Uncertainty Criterion during Normal Operation: When When entering the normal operation phase, the value of the new induction point is first assessed based on kernel correlation and uncertainty:

[0434] Nuclear relevance criterion: The condition for considering the current operating conditions to be sufficiently "new" is:

[0435] ;

[0436] in, Novelty threshold Input the current operating condition The maximum value of the correlation with all induced point kernels.

[0437] Uncertainty criterion: When the prediction uncertainty exceeds a threshold:

[0438] ;

[0439] in, Input the current operating condition Uncertainty index, This is the uncertainty threshold.

[0440] This indicates that the model for this area is not yet reliable, and it is worthwhile to add directional points.

[0441] This embodiment uses the "OR condition" as the comprehensive criterion:

[0442] ;

[0443] in, This is a Boolean criterion function for determining whether adding a new induced point is worthwhile under the current operating conditions.

[0444] Distance constraint: To avoid the induced points being too densely packed, while satisfying... Under the premise of ensuring that the minimum distance from the existing guidance point is satisfied:

[0445] ;

[0446] in, This is the distance relaxation factor. If the above conditions are met and... Then the input corresponding to this working condition Add it to the dictionary as a new lead point.

[0447] S2093. Age- and redundancy-based induced point soft replacement.

[0448] When the dictionary size approaches the target size Or it has reached its limit. In order to continue to achieve better coverage in the new operating condition area, this embodiment introduces a soft replacement strategy:

[0449] Rating factor construction: For each existing induction point Construct the following three dimensionless indices:

[0450] Similarity to the new working condition :

[0451] ;

[0452] in, This is the standardized input vector for the new operating condition intended for replacement evaluation.

[0453] The greater the similarity, the higher the overlap between the induction point and the new operating condition, and the more suitable it is to be replaced.

[0454] Age index Record the number of update steps since the induction point was added or last "activated", and normalize it linearly to... The older they get, the more likely they are to be replaced.

[0455] Low variance index Based on the construction of the diagonal elements of the posterior covariance, let Then normalize to get The smaller the variance, the more well-learned the region where the induction point is located has been, and the more suitable it is as a replacement candidate. For the first Variance operator for each output channel For the first The standardized input feature vector corresponding to each induced point.

[0456] After linear normalization, the above indicators are used to construct a comprehensive score. :

[0457] ;

[0458] in, And the sum is 1, used to adjust the importance of the three items. The weights of the similarity index, As the weight of the age indicator, The weights for low variance indicators.

[0459] Candidate replacement point selection: For all induced points, according to Sort by size from largest to smallest, and select the index with the highest score. :

[0460] ;

[0461] Simultaneously calculate the median score. ,like ;in, For the first The overall score of each guidance point If the margin threshold is to be replaced, it is considered that there is a “sufficiently bad” inducing point, and a soft replacement can be performed.

[0462] Soft Replacement and Warm Startup: When the soft replacement conditions are met and the current replacement budget (the number of induced points that can be replaced per maintenance cycle) is not exhausted, perform the following steps:

[0463] New working condition position Add a new guide point The posterior mean and covariance of the new GP model are predicted using the existing model, and the prediction results are used as the initial parameters of the new induction point to achieve a "warm start".

[0464] Index of the point to be replaced Mark it as "to be deleted" and set a preset number of warm-up steps. In the next In each sample, both the old and new inductive points are temporarily retained to participate in the reasoning;

[0465] After the warm-up step count ends, then... The corresponding inducing points are physically removed from the dictionary, and the kernel matrix and posterior statistics are updated simultaneously to achieve a smooth transition of the dictionary without causing abrupt changes.

[0466] S2094. Pruning of induced points exceeding limits and dictionary size control.

[0467] To ensure both real-time performance and controlled computational complexity, this embodiment imposes a hard upper limit on the size of the induction point dictionary. When the number of induced points exceeds the target size or upper limit after maintenance operations, a pruning step is performed:

[0468] Redundancy index: for each induction point Calculate its maximum kernel correlation with other induced points. :

[0469] ;

[0470] in, As the induction point and Normalized squared distance. Redundancy. The larger the value, the greater the degree to which the point is "covered" by other induced points.

[0471] Pruning Scoring and Ranking: A pruning score is constructed by combining three indicators: redundancy, age, and low variance. :

[0472] ;

[0473] in, The weights of the similarity index during pruning. The weight of the age indicator at the time of pruning. This represents the weight of the low-variance index during pruning.

[0474] and according to Sort from largest to smallest, and prioritize deleting high-scoring leading points, i.e., those points that are "old, redundant, and have low variance".

[0475] Pruning execution: If the current number of induced points is The target size is Then it needs to be deleted. One leading indicator. Select the top-ranked... The induced point index is deleted, and the kernel matrix, posterior mean, and covariance matrix are updated synchronously to restore the dictionary to the target size.

[0476] S2095. Maintenance cycle and budget control.

[0477] To avoid frequent dictionary adjustments at every step and impacting real-time performance, this embodiment employs a mechanism of maintenance cycle plus replacement budget:

[0478] Maintenance Cycle: Set the maintenance cycle Only when the number of measurement steps meets the requirement A full maintenance is triggered at certain times, including adding, soft replacing, and pruning steps; at other times, only GP a posteriori updates are performed without modifying the set of induced points.

[0479] Replacement Budget: To prevent model oscillation caused by replacing too many induced points in a single cycle, this embodiment sets a maximum number of replacements for each maintenance cycle. Once the cumulative number of soft replacements reaches the upper limit within a cycle, replacements will no longer be performed even if subsequent operating conditions meet the replacement criteria, and the budget will be reallocated in the next maintenance cycle.

[0480] S3. Using the updated sparse Gaussian process residual model, the model residuals of the three channels of longitudinal velocity, lateral velocity and yaw rate are predicted, and the prediction uncertainty and working condition information are combined for weighted processing to obtain the safe and usable three-channel compensation amount.

[0481] Step S3 specifically includes the following processes S301-S305:

[0482] S301. Construction and normalization of input features at the current time.

[0483] At sampling time Given the current measured state vector and the actual control input applied in the previous control cycle.

[0484] This embodiment maintains consistency with the offline stage, defining the input features of the sparse Gaussian process.

[0485] Using the input normalization parameters obtained in step S105 We construct a standardized input and perform amplitude clipping on each dimension.

[0486] S302. Sparse Gaussian process residual prior prediction.

[0487] Standardize input The predicted mean and covariance of the standardized residuals are obtained by feeding them into the sparse Gaussian process (SONIG) model after initialization in step S1 and online update in step S2.

[0488] For ease of subsequent security filtering, the diagonal elements of the covariance matrix are denoted as follows in this embodiment:

[0489] ;

[0490] in, To standardize the diagonal elements of the residual covariance matrix in the vertical channel, To standardize the diagonal elements of the residual covariance matrix in the horizontal channel, To standardize the diagonal elements of the residual covariance matrix in the yaw channel, The predicted variance of the longitudinal channel residuals. This represents the predicted variance of the lateral channel residuals. This represents the predicted variance of the yaw channel residuals.

[0491] S303. Inverse normalization of residual prediction results.

[0492] Since both the controller and the nominal vehicle model operate in the physical dimension, it is necessary to map the standardized residual prediction results back to the physical dimension.

[0493] Using the output normalization parameter in step S105 The predicted mean is inversely normalized.

[0494] Similarly, the prediction standard deviation can be mapped back from the standardized domain to the physical domain as needed.

[0495] S304. Construction of three-channel residual compensation.

[0496] In this embodiment, the predicted three-channel residuals are regarded as the "output correction" of the nominal vehicle dynamics model to compensate for the systematic errors of the nominal model in longitudinal velocity, lateral velocity and yaw rate.

[0497] A three-channel compensation vector is defined. To facilitate integration with the six-dimensional state vector, this embodiment introduces a fixed injection matrix. :

[0498] ;

[0499] Map the three-channel residuals to a six-dimensional state compensation vector. :

[0500] ;

[0501] in, This is a six-dimensional state compensation vector. This is the longitudinal velocity compensation amount. This is the lateral velocity compensation amount. This is the yaw rate compensation amount.

[0502] S305. Uncertainty-based compensated safe scaling.

[0503] To avoid introducing excessive residual compensation in areas with high model uncertainty or extrapolation regions, this embodiment performs safe scaling of the three-channel compensation based on the prediction uncertainty.

[0504] In a preferred implementation, taking the longitudinal velocity residual uncertainty as an example, a scaling factor is constructed. :

[0505] ;

[0506] in, For the longitudinal channel at time The physical compensation ratio, This represents the maximum compensation ratio for the longitudinal channel. This is the sensitivity coefficient. The greater the uncertainty, the lower the sensitivity coefficient. The closer it is to 0.

[0507] Set compensation ratios for each of the three channels. Obtain the diagonal scaling matrix :

[0508] ;

[0509] in, This represents the compensation ratio for the longitudinal channel. This represents the compensation ratio for the horizontal channel. This is the compensation ratio for the sway channel.

[0510] Final safety compensation vector Defined as:

[0511] ;

[0512] And inject it into the state compensation:

[0513] ;

[0514] in, This is the state compensation vector.

[0515] In a simpler implementation, a fixed compensation ratio can also be used. Uniform scaling of all three channels, i.e.:

[0516] ;

[0517] in, This is the compensation ratio.

[0518] S4, Residual Corrected Vehicle Dynamics Model and its Rolling Prediction in Model Predictive Control.

[0519] In one embodiment, step S4 includes the following steps S401-S404:

[0520] S401. Residual Corrected Discrete-Time Vehicle Model.

[0521] Based on the nominal discrete model in step S102, the state compensation vector Treating this as an additional correction term for the next state, we construct a residual correction model:

[0522] ;

[0523] in, The data is updated in real time by step S3 in each sampling period, reflecting the deviation between the actual vehicle dynamics and the nominal model under the current operating conditions.

[0524] S402. Local linearization and augmented state representation.

[0525] To facilitate the construction of linear quadratic optimization problems in model predictive control, this embodiment performs first-order linearization on the residual correction model at the current operating point.

[0526] At any moment work site At this point, calculate the Jacobian matrix of the nominal model. :

[0527] ;

[0528] in, Let be the discrete-time nominal dynamic function. The state vector of the linearized operating point. This is the control input vector for the linearized operating point.

[0529] To facilitate constraint control increments in MPC, this embodiment uses augmented state representation, which represents the control quantity from the previous time step. Incorporate states and construct augmented state vectors :

[0530] ;

[0531] in, For the control increment at the current moment, For the control input at the current moment, This is the control input for the previous control cycle.

[0532] Discrete augmented system It can be written as:

[0533] ;

[0534] ;

[0535] in, To augment the state matrix of the system, For the input matrix of the augmented system, This is the input matrix of the augmented system.

[0536] S403. Definition of output variables and tracking error.

[0537] In this embodiment, longitudinal velocity, lateral position, and heading angle are used as the main output variables of MPC, and the output vector is defined as follows:

[0538] ;

[0539] ;

[0540] in, This is the output matrix.

[0541] The longitudinal velocity is extracted from the augmented state. Horizontal position With heading angle The reference trajectory in the arc length domain The above is given in advance as:

[0542] ;

[0543] in, To predict the reference output vector in the time domain, For reference longitudinal velocity, For reference horizontal position, For reference heading angle.

[0544] The output error within the prediction domain is defined as:

[0545] .

[0546] S404. Rolling forecast expansion under residual correction model.

[0547] With a prediction time domain length of Control time domain is In this case, augmented systems can be recursively derived Predicting the state step by step:

[0548] ;

[0549] in, For at any time The predicted first Step augmentation state, For at any time The predicted first Step-increase state.

[0550] Will The predicted states are superimposed and output through the matrix. Mapping to output prediction yields batch form:

[0551] ;

[0552] in, To control the incremental sequence, For the reason and The block matrix constructed recursively, For the reason and The block matrix constructed recursively, For the reason and The block matrix constructed recursively, For the reason Copy the stacked constant vector.

[0553] because The SONIG residual correction term is explicitly included in the prediction, so the systematic bias of the nominal model has been corrected online during the prediction process, achieving a more accurate forecast of the real vehicle dynamics.

[0554] S5. With the goal of minimizing the lateral error, heading angle error, and longitudinal speed error, the constraint MPC is solved online to obtain the steering and drive control inputs.

[0555] In one embodiment, step S5 includes the following steps S501-S505:

[0556] S501. Definition of performance metrics for multi-target tracking.

[0557] To simultaneously consider speed tracking, path tracking, and smoothness, this embodiment constructs a quadratic performance index.

[0558] The output error after expanding the prediction domain is written in stacked form:

[0559] ;

[0560] in , To predict the stacked vector of output errors in the time domain, This is the actual stacked vector of the output. This is a reference output column. Combined with batch prediction relationships. Cost function It can be written as:

[0561] ;

[0562] S502. Standardization of the quadratic form of the cost function.

[0563] The above cost function can be rearranged into a standard quadratic programming form:

[0564] ;

[0565] ;

[0566] ;

[0567] in, To control the transpose of the stacked control increment vectors at each step in the time domain, It is the coefficient matrix of the quadratic terms. It is a linear term.

[0568] because and It is a positive semi-definite matrix, and with appropriate additions of diagonal regularization terms, the matrix... It is symmetric positive definite, which guarantees that the quadratic programming problem has a unique optimal solution.

[0569] S503. Modeling of actuators and output constraints.

[0570] To meet the steering and driving limitations of real-world vehicles, this embodiment introduces constraints. All constraints are stacked within the prediction domain and can be uniformly written as:

[0571] ;

[0572] in, These are matrices and vectors obtained by combining control constraints and output constraints.

[0573] S504. Quadratic Programming Solution and Control Law Update.

[0574] At each sampling time The current augmented state Residual correction term Reference output sequence Substitute the values ​​and construct a quadratic programming problem:

[0575] ;

[0576] Using existing quadratic programming solvers (such as optimization modules based on interior point methods or active set methods), the optimal control increment sequence for the current sampling period can be obtained online. :

[0577] ;

[0578] in, For the control increment at the current moment, For the first Control increment at sampling time, To control the control increment at the last moment in the time domain.

[0579] Based on the rolling optimization principle, only the first control increment is applied to the vehicle:

[0580] ;

[0581] in, For the first Control variables at sampling time, This represents the control quantity at the current moment.

[0582] S505. Closed-loop update and repeated execution.

[0583] Execute control commands Subsequently, the vehicle evolves according to its actual dynamics within the sampling period, and the state at the next moment is obtained through sensor measurements. .

[0584] When the system enters the next sampling period, the following steps are repeated:

[0585] According to actual measurements With nominal model prediction Constructing new true residuals ;

[0586] The SONIG model is updated online using the gating strategy in step S2;

[0587] Step S3 is used to predict the residuals at the new operating point and generate the compensation amount. ;

[0588] In step S4, a new residual correction prediction model and rolling prediction are constructed;

[0589] Construct and solve a new quadratic programming problem according to step S5 to obtain the next control increment sequence.

[0590] Through the above-described iterative process, this embodiment can continuously correct the system deviation of the nominal vehicle model on the target road, achieving comprehensive optimization between longitudinal speed tracking, lateral path tracking, and heading stability. In comparison experiments with the pure offline Gaussian process compensation strategy, it demonstrates better steady-state accuracy and adaptability to changes in road conditions.

[0591] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A vehicle path tracking and longitudinal speed control method based on Gaussian process compensation, characterized in that, Includes the following steps: S1. Collect vehicle data on the calibrated road and construct a Gaussian process residual model for offline training; S2. Collect vehicle data on the target road, determine the uncertainty index and normalized distance threshold, and update the Gaussian process residual model after offline training online; S3. Calculate the three-channel compensation amount using the online-updated Gaussian process residual model; S4. Based on the three-channel compensation amount, construct a residual correction prediction model and determine the output prediction; S5. Based on the output prediction, construct a quadratic programming problem and solve it to obtain the control increment, steering input and longitudinal acceleration input at the current moment, and apply them to the vehicle actuators. S1 includes the following sub-steps: S11. Collect vehicle state vectors and control input vectors on the calibrated road; S12. Based on the vehicle state vector and control input vector, construct the vehicle nominal dynamics model and discretize it to obtain the discrete-time nominal model. S13. Collect time-series data on typical roads and use the discrete-time nominal model to calculate the nominal predicted state corresponding to the time-series data. S14. Based on the nominal prediction state, construct the residual output and the input features of the Gaussian process; S15. Stack the residual output and the input features of the Gaussian process to obtain the training dataset, which serves as discrete training samples. S16. Calculate the sample mean and sample variance of the input features in the discrete training samples, as well as the sample mean and sample variance of the residual output. S17. Calculate the input standard deviation vector based on the sample mean and sample variance of the input features; calculate the output standard deviation vector based on the sample mean and sample variance of the residual output. S18. Calculate the first standardized variable and the second standardized variable based on the input standard deviation vector and the output standard deviation vector; S19. Determine the standardized samples corresponding to the first and second standardized variables. S110. Construct a Gaussian process residual model; S111. Parameter identification is performed on the standardized samples to obtain hyperparameters. The hyperparameters and the set of induced points are used as the initial state of the Gaussian process residual model for offline training.

2. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 1, characterized in that, In S11, the vehicle state vector The expression is: ； in, Let X be the absolute position of the vehicle's center of mass along the X-axis in the world coordinate system. Let Y be the absolute position of the vehicle's center of mass along the Y-axis in the world coordinate system. For heading angle, The longitudinal velocity in the vehicle coordinate system, Let be the lateral velocity in the vehicle coordinate system. The yaw rate is angular velocity. For transpose; In S11, the control input vector The expression is: ； in, For the front wheel steering angle, For the first Longitudinal acceleration at each sampling time; In S12, the vehicle nominal dynamics model The expression is: ； in, To map the current state and input to the state derivatives in the vehicle dynamics equations given vehicle parameters, A state vector consisting of vehicle state variables. This is the vehicle control input vector. A set of vehicle parameters; In S12, the discrete-time nominal model The expression is: ； in, For discrete dynamic functions; In S14, the residual output The expression is: ； in, For the first The residual of the longitudinal velocity at each sampling time, For the first Lateral velocity residual at each sampling time For the first Yaw velocity residual at each sampling time For the first The longitudinal velocity of the vehicle measured at each sampling time point For the first The lateral velocity of the vehicle measured at each sampling time. For the nominal model in the first The predicted longitudinal speed of the vehicle at each sampling time. For the nominal model The predicted lateral velocity of the vehicle at each sampling time point. For the first The vehicle yaw rate measured at each sampling time. For the nominal model in the first The vehicle yaw rate predicted at each sampling time; In S14, the input characteristics of the Gaussian process The expression is: ； in, Choose a matrix for the state. Select the matrix for input. For the first The vehicle measurement state vector at each sampling time. In the first The vehicle control input vector at each sampling time point For the first The front wheel steering angle at each sampling time For the first The longitudinal acceleration at each sampling time, It is a 5-dimensional real vector space; In S15, the training dataset The expression is: ； in, This represents the total number of samples in the offline training dataset. In S18, the first standardized variable The expression is: ； in, The vector of sample means representing the input features. This represents the input standard deviation vector; In S18, the second standardized variable The expression is: ； in, This represents the sample mean vector of the residual output. This indicates the output standard deviation vector.

3. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 1, characterized in that, S2 includes the following sub-steps: S21. Collect the vehicle's state vector and control input vector at each sampling time on the target road; S22. Using the discrete-time nominal model, predict the state vector and control input vector of the vehicle on the target road at each sampling time to obtain the nominal state at the next time step; S23. Construct an online residual measurement vector based on the nominal next-time state and the measured state; S24. Determine the standardized input based on the online residual measurement vector; S25. Use the standardized input as the input to the Gaussian process residual model after offline training to obtain the prior distribution of residual prediction, and proceed to S26. S26. Calculate the uncertainty index based on the predicted covariance; S27. Calculate the normalized distance based on the current set of induced points; S28. The uncertainty index satisfies the gate condition constructed by the normalized distance. At that time, the Gaussian process residual model is updated online; among which, As an uncertainty index, For uncertainty threshold, For normalized distance, This is the normalized distance threshold.

4. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 3, characterized in that, In S26, the uncertainty index The expression is: ； in, For the first The residual covariance matrix at each sampling time point For matrix trace operations; In S27, the normalized distance The expression is: ； in, The first in the current set of induced points The index of the induced points As the first standardized variable, For the current set of induction points, is the length scale vector for each input dimension.

5. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 1, characterized in that, S3 includes the following sub-steps: S31. Construct a Gaussian process input based on the current measured state and the current or previous control quantity of the control quantity to be optimized. S32. Standardize the Gaussian process input; S33. Use the standardized Gaussian process input as the input of the updated Gaussian process residual model to obtain the predicted distribution of the three-channel residuals. S34. Map the predicted distribution of the three-channel residuals from the normalized domain back to the physical quantity domain, and calculate the three-channel compensation amount.

6. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 5, characterized in that, In S31, the Gaussian process input The expression is: ； in, Let be the lateral velocity in the vehicle coordinate system. The longitudinal velocity in the vehicle coordinate system, The yaw rate is angular velocity. For the front wheel steering angle, This is a longitudinal acceleration command or a braking force command. For transpose; In S33, the expression for the predicted distribution of the three-channel residuals is: ； in, To standardize the mean of the residuals, To standardize the residual covariance matrix, It is a multivariate Gaussian distribution. The standardized residual prediction vector that follows this distribution; In S34, the three-channel compensation amount The expression is: ； in, This is the compensation amount for lateral velocity. This is the compensation amount for the longitudinal velocity. This is the compensation amount for the yaw rate.

7. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 1, characterized in that, S4 includes the following sub-steps: S41. Construct the residual injection matrix; S42. Calculate the residual correction prediction model based on the residual injection matrix and the three-channel compensation amount; S43. Perform first-order linearization on the residual correction prediction model to obtain a linear time-varying state-space model. S44. Based on the prediction time domain length and the control time domain length, construct superimposed state prediction equations on the linear time-varying state space model; S45. Based on the superposition state prediction equation, construct the output superposition equation in the prediction time domain; S46. Determine the output prediction by superimposing the outputs in the prediction time domain.

8. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 7, characterized in that, In S41, the residual injection matrix The expression is: ； in, It is a 3×3 zero matrix. It is a 3×3 identity matrix. It is a 6×3 dimensional real matrix space; In S42, the residual correction prediction model The expression is: ； in, Let be the vehicle's nominal discrete dynamics function. Let this be the current state vector. This is the current control input vector. For vehicle parameter set, Inject weights into the residuals. This is the compensation amount for three channels; In S43, the expression for the linear time-varying state-space model is: ； in, This is the linearized state vector for the next time step. The state matrix, For the input matrix, For constant terms; In S44, the expression for the superimposed state prediction equation is: ； in, To predict the superposition vector of states at each step in the time domain, To control the incremental superposition vector, To predict the time-domain state transition coefficient matrix, To predict the time-domain control increment coefficient matrix, This is the vector for predicting time-domain constant terms; In S45, the expression for the output superposition equation in the prediction time domain is: ； in, To predict the superimposed output vector, To output the state mapping matrix of the superimposed vector, To output the coefficient matrix for the control increment, This is the vector of constant terms in the output equation.

9. The vehicle path tracking and longitudinal speed control method based on Gaussian process compensation according to claim 1, characterized in that, S5 includes the following sub-steps: S51. Based on the reference path of the target road, determine the reference output for each step in the prediction time domain; S52. Determine the output error based on the reference output and output prediction at each step in the prediction time domain; S53. Construct the first diagonal weighted matrix and the second diagonal weighted matrix; S54. Calculate the weighted performance index in the prediction time domain based on the output error, the first diagonal weighting matrix, and the second diagonal weighting matrix. S55. Construct state constraints; S56. Based on the superposition state prediction equation and the superposition output equation in the prediction time domain, integrate the weighted performance index and state constraints in the prediction time domain into a quadratic programming problem. S57. Use a quadratic programming solver to solve the quadratic optimization problem online to obtain the optimal control increment sequence. Take the first term of the optimal control increment sequence as the control increment at the current moment, and apply the steering input and longitudinal acceleration input to the vehicle actuator. In step S51, the reference output of each step in the prediction time domain is... The expression is: ； in, For the desired longitudinal velocity, To predict the length of the time domain, For transpose; In S52, the output error The expression is: ； in, For output prediction; In S53, the first diagonal weighting matrix The expression is: ； in, For longitudinal velocity error, For lateral error, As the heading angle error weight, It is a diagonal matrix operator; In S53, the second diagonal weighting matrix The expression is: ； in, As the weight of the steering acceleration increment, The weighting is the longitudinal acceleration increment. In S54, the weighted performance index in the time domain is predicted. The expression is: ； in, To control the length of the time domain, To control the increment; In S55, the expression for the state constraint condition is: ； ； ； in, This is the lower limit of the front wheel steering angle. For the first Front wheel angle, The upper limit of the front wheel steering angle. This is the lower bound of longitudinal acceleration. For the first longitudinal acceleration, This is the upper limit of longitudinal acceleration. This is the lower bound of the angle increment. For the first Step rotation increment, This is the upper bound of the angle increment. This is the lower bound of the acceleration increment. For the first Step acceleration increment, For the upper bound of acceleration, This is the lower bound of the lateral deviation. For at any time The predicted first Lateral deviation, This represents the upper limit of the lateral deviation. This is the lower bound of the longitudinal velocity. For at any time s predicted the first Step longitudinal velocity, This is the upper limit of the longitudinal velocity; In S56, the expression for the quadratic programming problem is: ； in, To control the incremental superposition direction, The Hessian matrix of the quadratic cost. The vector of coefficients for linear terms. It is an inequality matrix. The inequality constraint vector; In S57, the control increment at the current moment The expression is: ； in, This is the increment of the front wheel steering angle. This represents the longitudinal acceleration increment.

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