All-wheel-drive unmanned vehicle tracking control and torque control method based on residual error model

Abstract

The invention relates to an all-drive unmanned vehicle tracking control and torque control method based on a residual error model. The method comprises the following steps: establishing a nonlinear vehicle dynamics model and a Gaussian process-based residual error model; combining the two models to obtain a vehicle dynamics model based on the residual error model; establishing a Gaussian-model predictive control GP-MPC controller for path tracking by taking transverse compensation and course angle minimization as optimization targets and taking a vehicle dynamics model based on a residual model as a prediction model; a multi-target torque control algorithm is designed, the optimal control quantity output by the GP-MPC controller is distributed, and the expected longitudinal force of each tire is obtained; and designing a tire longitudinal force observer and an anti-interference current control law. According to the invention, the defects of poor tracking precision and poor stability of an all-drive unmanned vehicle are effectively overcome.

Description

Technical Field

[0001] The present application relates to the technical field of dynamic control of unmanned ground vehicles, and in particular to a tracking control and torque control method for an all-wheel drive unmanned vehicle based on a residual model. Background Art

[0002] Dynamic control of all-wheel-drive unmanned ground vehicles (UGVs) in complex terrain is a key technology for achieving high maneuverability and stability. Its core lies in achieving coordinated wheel drive through torque control and dynamic model correction. Traditional approaches typically design control strategies based on simplified vehicle models, such as those assuming small-angle steering, and distribute torque using fixed weights to balance maneuverability and stability. However, in unstructured terrain, the dynamics of road adhesion and the complex coupling between tire forces and yaw moments lead to significant errors in traditional models due to their neglect of parameter time-varying and disturbance accumulation. Existing studies often employ fixed-parameter model predictive control (MPC) or static torque distribution strategies, which are difficult to adapt to dynamic scenarios such as tire slip and sudden load changes and fail to fully integrate real-time sensor data to correct model biases. Furthermore, traditional residual models rely on a five-dimensional state space, requiring extensive training data and limiting their generalization in dynamic environments. Therefore, a control method that can adaptively correct model errors, efficiently distribute torque, and address multi-objective optimization is urgently needed to improve the maneuverability and robustness of all-wheel-drive UGVs in complex terrain. Summary of the Invention

[0003] The purpose of the present invention is to provide a tracking control and torque control method for an all-wheel drive unmanned vehicle based on a residual model. The residual model is used to bridge the gap between theory and practice, predict the unmodeled error of the vehicle dynamics model, and thus improve the tracking accuracy. With tire utilization, energy consumption, and yaw stability as multiple objectives, the expected longitudinal force of each wheel is optimized online to avoid single-wheel slip and improve operational stability during tracking.

[0004] The technical solution adopted by the present invention is: a tracking control and torque control method for an all-wheel drive unmanned vehicle based on a residual model, comprising the following steps: S1: Establish a nonlinear vehicle dynamics model and perform error analysis to obtain a nonlinear vehicle dynamics error model; S2: Identify the error source through the expression of the nonlinear vehicle dynamics error model and establish a residual model based on Gaussian process to eliminate the error; S3: combining the nonlinear vehicle dynamics model with the Gaussian process-based residual model to obtain a residual model-based vehicle dynamics model, and learning and compensating for dynamic errors in the nonlinear vehicle dynamics error model in real time; S4: mathematically modeling the path tracking problem to obtain lateral compensation and heading angle errors, minimizing the lateral compensation and heading angle as optimization objectives, and using the residual model-based vehicle dynamics model as a prediction model to establish a Gaussian-model predictive control (GP-MPC) controller for path tracking; S5: With the goal of minimizing the torque distribution error, the minimum slip based on kinematics, and the minimum tire load rate, a multi-objective torque control algorithm is designed in combination with the tire force limit and the tire torque output characteristic limit. The optimal control quantity output by the GP-MPC controller, namely the total longitudinal force of the tire and the external yaw moment, is distributed to obtain the output matrix ,in, is the expected longitudinal force of the jth tire, j = 1, 2, 3, ..., 4; S6: Design the tire longitudinal force observer based on Lyapunov stability theory and convert the output matrix The input is sent to the tire longitudinal force observer to form a closed-loop control of the desired longitudinal force of each tire; S7: Using the expected longitudinal force of each tire as the expected value and the output of the tire longitudinal force observer as the feedback value, an anti-interference current control law is designed to enable the actual tire longitudinal force to quickly follow the expected longitudinal force.

[0005] Furthermore, the nonlinear vehicle dynamics model is expressed as: ; in, represents the vehicle longitudinal acceleration, represents the sideslip angular velocity of the center of mass, represents the yaw angular acceleration, represents the sideslip angle of the center of mass, represents the vehicle longitudinal velocity, represents the yaw rate, m represents the vehicle mass, represents the sum of the four tire longitudinal force vectors, Indicates the steering angle of the front and rear wheels, c indicates the lateral stiffness, L indicates the front and rear wheelbase of the car, represents the vehicle's yaw moment of inertia, represents the external yaw moment; The expression of the nonlinear vehicle dynamics error model is: ; in, Indicates the vehicle's longitudinal acceleration The error, Indicates the sideslip angular velocity of the center of mass The error, represents the yaw angular acceleration The error, Indicates longitudinal force The error, represents the external yaw moment error.

[0006] Furthermore, the expression of the residual model based on Gaussian process is: ; in, , Represents the Gaussian process for the vehicle longitudinal velocity The predicted mean of the residuals, represents the sideslip angle of the Gaussian process to the vehicle's center of mass The predicted mean of the residuals, Represents the Gaussian process for the vehicle's yaw rate The predicted mean of the residuals, , Represents the Gaussian process for the vehicle longitudinal velocity The prediction variance of represents the sideslip angle of the Gaussian process to the vehicle's center of mass The prediction variance of Represents the Gaussian process for the vehicle's yaw rate The prediction variance of Indicates the mean , the variance is Multivariate Gaussian distribution of ; The expression of the vehicle dynamics model based on the residual model is: ; in, represents the longitudinal velocity of the vehicle at discrete time step k+1 The predicted value of represents the sideslip angle of the center of mass of the vehicle at discrete time step k+1 The predicted value of represents the yaw rate of the vehicle at discrete time step k+1 The predicted value of represents the discrete form of the nonlinear function of the nonlinear vehicle dynamics model at discrete time step k, Represented by the residual model based on Gaussian process The compensation amount obtained at discrete time step k.

[0007] Furthermore, the longitudinal tire forces of the four wheels are taken as features of the residual model based on Gaussian process to reduce the dimension of the feature space: ; Among them, z represents the characteristics of the residual model based on Gaussian process, Fx1 Indicates the longitudinal force of the left front wheel, F x2 Indicates the longitudinal force of the right front wheel, F x3 Indicates the longitudinal force of the left rear wheel, F x4 Indicates the longitudinal force on the right rear wheel.

[0008] Furthermore, the expression of the Gaussian-model predictive control GP-MPC controller is: ; ; ; ; ; ; ; ; in, represents the predicted value of the vehicle dynamics model based on the residual model, represents the discrete form of the nonlinear function of the nonlinear vehicle dynamics model at discrete time step k, Represented by the residual model based on Gaussian process The compensation amount obtained at discrete time step k is, represents the longitudinal velocity of the vehicle at discrete time step k+1 The predicted value of represents the sideslip angle of the center of mass of the vehicle at discrete time step k+1 The predicted value of represents the yaw rate of the vehicle at discrete time step k+1 The predicted value of is the regularization term at discrete time step k+1, , which is used to impose a penalty on the control input and its rate of change to ensure smooth control action and prevent sudden changes in trajectory; Represents state quantity of -weighted 2-norm, Indicates control input of -weighted 2-norm, R x Represents state quantity The weight matrix, R u Indicates control input The weight matrix; Q is the lateral compensation term The weight matrix, R is the heading angle error term The weight matrix; N represents the pre-set prediction step value, represents the control input at discrete time step k+1 The predicted value of represents the increment of the control input at discrete time step k, represents the lateral compensation at discrete time step k, represents the transpose of the lateral compensation at discrete time step k, Indicates the lateral compensation at discrete time step k+1 The predicted value of Indicates the time step k used to update the lateral compensation A nonlinear function of the vehicle state and the desired heading angle related, represents the heading angle error at discrete time step k, Represents the heading angle error at discrete time step k+1 The predicted value of Indicates the heading error to be updated at discrete time step k A nonlinear function of the vehicle state and the expected curvature related, Indicates the minimum value of the system state, Indicates the maximum value of the system state, represents the regularization term The amount of change, Indicated by the state quantity and input The regularization term composed of The set of constraints, Represents the change in regularization term The set of constraints.

[0009] Furthermore, the specific expression of the objective function for minimizing the torque distribution error is: ; in, represents the objective function of torque distribution error, represents the control demand weight matrix, which is used to balance the ratio between the longitudinal force demand and the yaw moment demand. , represents the longitudinal force demand weight, represents the yaw moment demand weight, represents the input matrix, B represents the control efficiency matrix, represents the demand matrix; The objective function of minimum slip based on kinematics is: ; in, represents the sliding objective function based on the basis kinematics, represents the tire slip loss coefficient, , represents the expected speed of the jth wheel, represents the speed of the jth tire, n represents the reduction ratio of the transmission system, Indicates the radius of the tire; The objective function of minimum tire load rate is: ; in, represents the objective function of tire load rate, represents the sliding friction coefficient of the jth tire, represents the longitudinal force of the jth tire, represents the vertical load force of the jth tire; The specific expression of tire force limitation is: ; in, represents the lateral force of the jth tire; The specific expression of the tire torque output characteristic limitation is: ; in, Indicates the maximum torque output by the motor. Indicates the maximum safety factor of the motor output that can be set.

[0010] Furthermore, the expression of the tire longitudinal force observer is: ; ; in, is the estimated longitudinal tire force of the jth wheel, represents the wheel moment of inertia, is the observer gain, represents the bus current, represents the adjustable design parameters of the jth wheel, represents the speed of the jth wheel, represents the observer gain versus time The first derivative of .

[0011] Furthermore, the anti-interference control law is the control law of the input current, and the specific expression is: ; in, represents the saturation function, represents the desired longitudinal tire force on the jth wheel, is the coefficient of the controller, represents the expected longitudinal tire force of the jth wheel versus time The first derivative of represents the damping coefficient, Indicates the motor torque constant.

[0012] The beneficial effects of the present invention are: (1) By introducing the Gaussian process residual model, the present invention can learn and correct the model dynamic errors caused by the longitudinal tire force and yaw moment deviation in real time, significantly improving the accuracy of the model in complex terrain. At the same time, the use of a low-dimensional feature space reduces the computational complexity and improves the real-time control efficiency. (2) The multi-objective torque control strategy for single wheel load designed in this invention comprehensively considers the constraints of minimizing torque distribution error, minimum slip based on kinematics, and minimum tire load rate, and combines tire force limitation with tire torque output characteristic limitation to achieve coordinated optimization of maneuverability and stability; (3) The present invention further improves the longitudinal force tracking accuracy through a tire force estimation method based on a disturbance observer, and proves the exponential convergence of the observation error through the Lyapunov function; the residual model is integrated with the model predictive control (MPC) framework, which significantly improves the trajectory tracking performance and torque control effectiveness under complex terrain, and enhances the robustness and practicality of the control strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0014] Figure 1 is a control block diagram of an embodiment of the present invention; Figure 2 A comparison diagram of tracking curves between the embodiment of the present invention and the traditional control method; Figure 3 A comparison diagram of longitudinal speed curves between an embodiment of the present invention and a conventional control method; Figure 4 A comparison diagram of the lateral velocity curves of the embodiment of the present invention and the traditional control method; Figure 5 2 is a comparison diagram of the yaw rate curves of the embodiment of the present invention and the traditional control method. DETAILED DESCRIPTION

[0015] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0016] like Figure 1 As shown, an embodiment of the present invention provides a tracking control and torque control method for an all-wheel drive unmanned vehicle based on a residual model, comprising the following steps: S1: Establish a nonlinear vehicle dynamics model and perform error analysis to obtain a nonlinear vehicle dynamics error model. Unlike traditional vehicles, each wheel of a four-wheel independent drive vehicle is independently driven by a motor through a reducer and a transmission connecting rod. This allows for easy generation of large turning angles and external yaw torques to adjust the vehicle's yaw and lateral motions. Therefore, the small-angle theory no longer holds true. Ignoring pitch and roll motions, the vehicle's handling dynamics in the yaw plane are: ; ; ; in, represents the vehicle longitudinal velocity, represents the lateral velocity of the vehicle, represents the yaw angular velocity, Indicates the vehicle mass, represents the vehicle longitudinal acceleration, represents the lateral acceleration, represents the sum of the four tire longitudinal force vectors, represents the sum of the four tire lateral force vectors, Indicates the steering angle of the front and rear wheels of the vehicle. represents the yaw moment of inertia, represents the yaw angular velocity, is the front and rear wheelbase of the car, represents the yaw angular velocity, Represents the external yaw moment, which is generated by the longitudinal tire force difference between the left and right wheels.

[0017] External yaw moment The specific expression is: ; in, represents the longitudinal tire force of the jth wheel, represents the distance from the jth wheel to the center axis of the vehicle body, Represents a symbolic variable, when Take positive when on the right side of the axle and negative when on the left side of the axle.

[0018] Side slip angle of center of mass The specific expression is: ; Its differential form is as follows: ; remember is the sum of the longitudinal force vectors of the four tires, are the four tire lateral force vectors, where Is the inherent deformation property of the tire, and the cornering stiffness and the wheel slip angle Assuming the same cornering stiffness of the front and rear wheels, the lateral force vectors of the four tires are The specific expression is: ; Combining the above formulas, we can get the specific expression of the nonlinear vehicle dynamics model: ; ; ; in, represents the vehicle longitudinal acceleration, represents the sideslip angular velocity of the center of mass, represents the yaw angular velocity.

[0019] by is the state variable of the system, is the input variable of the system, and the matrix form of the nonlinear vehicle dynamics model can be expressed as: ;

[0020] In the vehicle dynamics model, the steering angles of the front and rear wheels of the vehicle are taken into account. The reference value has known and time-varying characteristics, and the vehicle mass , the front and rear wheelbase of the vehicle , yaw moment of inertia and cornering stiffness are considered fixed elements because they can be precisely measured through experimental calibration and exhibit negligible invariance during operation. In contrast, the four tire longitudinal force vectors and and external yaw moment Considered as variable elements, the longitudinal tire forces and external yaw forces may deviate from the model during operation due to factors such as road conditions, tire pressure, temperature, and tire wear. In addition, the four tire longitudinal force vectors and and external yaw moment The coupling between the tire force and the yaw force further affects the accuracy of the model. The deviation between the tire force and the yaw force constitutes the main source of inconsistency in the vehicle total moment model. Therefore, the specific expression of the nonlinear vehicle dynamics error model is: ;

[0021] in, Indicates the vehicle's longitudinal acceleration The error, Indicates the sideslip angular velocity of the center of mass The error, represents the yaw angular acceleration The error, Indicates longitudinal force The error, represents the external yaw moment error.

[0022] S2: The error sources are identified through the expression of the nonlinear vehicle dynamics error model, and a Gaussian process-based residual model is established to eliminate the error. This Gaussian process-based residual model can learn the model dynamic errors caused by longitudinal tire force and yaw moment deviations in real time, and it reduces computational complexity by utilizing a low-dimensional feature space.

[0023] In order to gradually improve the accuracy of the nonlinear vehicle dynamics model and adapt to changes in vehicle dynamics, a Gaussian process is used in the formulation of the nonlinear vehicle dynamics model, leveraging its flexibility and probabilistic properties to learn the deviations caused by variable elements. The residual model based on the Gaussian process is expressed as: ; in, , Represents the Gaussian process for the vehicle longitudinal velocity The predicted mean of the residuals, represents the sideslip angle of the Gaussian process to the vehicle's center of mass The predicted mean of the residuals, Represents the Gaussian process for the vehicle's yaw rate The predicted mean of the residuals; , Represents the Gaussian process for the vehicle longitudinal velocity The prediction variance of represents the sideslip angle of the Gaussian process to the vehicle's center of mass The prediction variance of Represents the Gaussian process for the vehicle's yaw rate The prediction variance of Indicates the mean , the variance is Multivariate Gaussian distribution of . Training data for the residual model It is obtained by calculating the deviation between the sensor measurement and the predicted value provided by the theoretical model: ; in, , is the variance Gaussian noise, The mean is 0 and the variance is Gaussian distribution, represents the Gaussian noise of the first dimension, represents the Gaussian noise of the second dimension, represents the Gaussian noise in the third dimension, represents Gaussian noise in the fourth dimension, is the residual model The coefficient matrix of The Moore–Penrose generalized inverse of Indicates that at the test point In addition, assuming that each dimension of the residual model output is uncorrelated with other dimensions, under this assumption, the Gaussian process can provide a test point The vehicle dynamics error model at dimensional The mean in and variance The posterior prediction of : ; ; in, Indicates test point The mean value at Indicates test point The variance at , Y represents the training set, represents the mth training data in the training set Y, express The transpose of Indicates the Gaussian noise in dimensions, I represents the unit matrix, Represents the training dataset No. All row data of the column, is the training set size required for the Gaussian process, the matrix represents the covariance evaluated on all pairs of points in the training set, Indicates test point The covariance with itself, that is, the test point The prior variance of , Indicates test point The covariance between Represents a vector The transpose of .

[0024] The squared exponential SE kernel function is used to define the Gaussian process kernel function : ; in, Represents training data points and training data points The covariance between them is used to construct the covariance matrix , reflecting the similarity within the training data; represents the diagonal length scale matrix, represents the data noise variance, represents the prior noise variance, Represents training data points and training data points The weighted Euclidean distance between Represents training data points and training data points The transpose of the weighted Euclidean distance between .

[0025] Residual Model The final multivariate GPs approximation is obtained by aggregating the outputs of each dimension, based on the expression of the residual model of the Gaussian process: .

[0026] In the prior art, the features of the residual model relative to the single track dynamic model are usually selected as the vehicle state The dynamic part of the vehicle is expanded to a five-dimensional feature space, where T represents the driving torque. This requires a large training set to cover the entire feature space, resulting in an unacceptable computational burden; in addition, it is not feasible to control the vehicle to traverse every region of this five-dimensional space. Therefore, the existing technology can only achieve satisfactory performance under specific, fixed operating conditions. Since the main sources of vehicle dynamics error model formation are the four tire longitudinal force vectors and and external yaw moment The difference between the tire model and the external yaw moment is the actual tire force Therefore, the residual of the vehicle dynamic model can be expressed as the longitudinal tire force of the jth wheel Therefore, the embodiment of the present invention selects the longitudinal tire forces of the four wheels as the features of the residual model to reduce the dimension of the feature space: ; Where z represents the characteristics of the low-dimensional residual model of the external yaw force, F x1 Indicates the longitudinal force of the left front wheel, F x2 Indicates the longitudinal force of the right front wheel, F x3 Indicates the longitudinal force of the left rear wheel, F x4 Indicates the longitudinal force on the right rear wheel.

[0027] S3: Combining the nonlinear vehicle dynamics model with the Gaussian process-based residual model to obtain a residual model-based vehicle dynamics model, and learning and compensating for dynamic errors in the nonlinear vehicle dynamics error model in real time.

[0028] The expression of the vehicle dynamics model based on the residual model is: ; in, represents the longitudinal velocity of the vehicle at discrete time step k+1 The predicted value of represents the sideslip angle of the center of mass of the vehicle at discrete time step k+1 The predicted value of represents the yaw rate of the vehicle at discrete time step k+1 The predicted value of represents the discrete form of the nonlinear function of the nonlinear vehicle dynamics model at discrete time step k, Represented by the residual model based on Gaussian process The compensation amount obtained at discrete time step k.

[0029] S4: The path tracking problem is mathematically modeled to obtain lateral compensation and heading angle errors, and the minimization of lateral compensation and heading angle is used as the optimization goal. The vehicle dynamics model based on the residual model is used as the prediction model to establish a Gaussian-model predictive control GP-MPC controller for path tracking.

[0030] The path tracking error is expressed as: ; ; ; in, Indicates the vehicle's center of gravity CoG in the global coordinate system The horizontal axis below, Indicates the vehicle's center of gravity CoG in the global coordinate system The vertical coordinate below, represents the heading angle error, represents the vehicle heading angle, represents the desired heading angle, Represents the longitudinal error in its own coordinate system, Represents the lateral error in its own coordinate system, represents the horizontal coordinate of the desired point in the global coordinate system, Indicates the vertical coordinate of the desired point in the global coordinate system. And minimizes the vertical error in the own coordinate system and the lateral error in its own coordinate system As the target, the GP-MPC controller will introduce a lag problem. In order to make the vehicle accurately track the target path, the path tracking problem is equivalent to minimizing the yaw angle error. and lateral compensation : ; in, is the look-ahead distance, which is a variable parameter.

[0031] Yaw angle error and lateral compensation The inverse of time t is as follows: ; ; in, Indicates the yaw angle error The inverse of time t, represents the reference curvature, Indicates lateral compensation The inverse of time t.

[0032] In the prediction domain of the Gaussian-model predictive control GP-MPC controller for path tracking, the error state can be obtained by recursion of the dynamic model: ; ; in, represents the lateral compensation at discrete time step k, represents the lateral compensation at discrete time step k+1 The predicted value of represents the lateral velocity at discrete time step k, represents the longitudinal velocity at discrete time step k, represents the vehicle heading angle at discrete time step k, represents the heading angle at discrete time step k, represents the expected heading angle at discrete time step k, represents the sampling time, represents the heading angle error at discrete time k, Represents the heading angle error at discrete time step k+1 The predicted value of represents the yaw rate at discrete time step k, represents the longitudinal velocity at discrete time step k, represents the reference path curvature at discrete time step k.

[0033] The expression of the Gaussian-model predictive control GP-MPC controller is: ; ; ; ; ; ; ; ; in, represents the predicted value of the vehicle dynamics model based on the residual model, represents the discrete form of the nonlinear function of the nonlinear vehicle dynamics model at discrete time step k, Represented by the residual model based on Gaussian process The compensation amount obtained at discrete time step k is, represents the longitudinal velocity of the vehicle at discrete time step k+1 The predicted value of represents the sideslip angle of the center of mass of the vehicle at discrete time step k+1 The predicted value of represents the yaw rate of the vehicle at discrete time step k+1 The predicted value of is the regularization term at discrete time step k+1, , which is used to impose a penalty on the control input and its rate of change to ensure smooth control actions and prevent sudden changes in trajectory; Represents state quantity of -weighted 2-norm, Indicates control input of -weighted 2-norm, R x Represents state quantity The weight matrix, R u Indicates control input The weight matrix; Q is the lateral compensation term The weight matrix, R is the heading angle error term The weight matrix; N represents the pre-set prediction step value, represents the control input at discrete time step k+1 The predicted value of represents the increment of the control input at discrete time step k, represents the lateral compensation at discrete time step k, represents the transpose of the lateral compensation at discrete time step k, Indicates the lateral compensation at discrete time step k+1 The predicted value of Indicates the time step k used to update the lateral compensation A nonlinear function of the vehicle state and the desired heading angle related, represents the heading angle error at discrete time step k, Represents the heading angle error at discrete time step k+1 The predicted value of Indicates the heading error to be updated at discrete time step k A nonlinear function of the vehicle state and the expected curvature related, Indicates the minimum value of the system state, Indicates the maximum value of the system state, represents the regularization term The amount of change, Indicated by the state quantity and input The regularization term composed of The set of constraints, Represents the change in regularization term The set of constraints.

[0034] ; in, represents an m-dimensional real vector space.

[0035] In order to ensure the feasibility of the optimization problem, all constraints are modeled as soft constraints. Therefore, the optimal solution of the GP-MPC controller optimization problem is: ; in, represents the optimal solution set from discrete time step k to discrete time step k+1 until the Nth moment k+N-1, represents the optimal solution at discrete time step k.

[0036] The control sequence at the next moment is: ; in, represents the control input value of the future i-th step in the optimization of discrete time step k; represents the control input value of the future i-1 step in the optimization of discrete time step k; It represents the incremental change of the control input of the future i-th step relative to the previous step in the prediction of discrete time step k.

[0037] By considering only the first element of the current input increment, which is of the form , the current optimal input can be determined as: ; in, represents the optimal control input at discrete time step k, represents the control input at discrete time k-1, represents the input increment at discrete time step k. The optimal control input obtained by GP-MPC controller optimization , the expected longitudinal force of each wheel will be obtained through a multi-objective optimization allocation algorithm.

[0038] S5: With the goal of minimizing the torque distribution error, the minimum slip based on kinematics, and the minimum tire load rate, a multi-objective torque control algorithm is designed in combination with the tire force limit and the tire torque output characteristic limit. The optimal control quantity output by the GP-MPC controller, namely the total longitudinal force of the tire and the external yaw moment, is distributed to obtain the output matrix ,in, is the expected longitudinal force of the jth tire, j = 1, 2, 3, …, 4.

[0039] (1) Objective function for minimizing torque distribution error The longitudinal force distribution must first meet the requirements of the additional yaw moment and the maximum total longitudinal force calculated by the upper-level MPC controller, that is: ; ; in, represents the desired longitudinal force, represents the expected additional yaw moment, Obtained from the GP-MPC controller output, is the wheel width, Indicates the steering angle of the left front wheel, represents the steering angle of the right front wheel, represents the steering angle of the left rear wheel, Indicates the steering angle of the right rear wheel, Indicates the wheelbase between the front and rear wheels.

[0040] Writing the above formula into matrix form, we can get: ; in, represents the demand matrix, ; represents the output matrix, The steering process is caused by the yaw moment and the longitudinal additional yaw moment Composition, of which represents the natural yaw moment coefficient matrix, represents the additional yaw moment coefficient matrix, and B represents the control efficiency matrix.

[0041] Since the embodiment of the present invention has removed the yaw moment when calculating the error model, the required external yaw moment The distribution is only done by the longitudinal additional yaw moment. Therefore, the control efficiency matrix B is expressed as: ; .

[0042] The specific expression of the objective function for minimizing the torque distribution error is: ; in, represents the objective function of torque distribution error, represents the control demand weight matrix, which is used to balance the ratio between the longitudinal force demand and the yaw moment demand. , represents the longitudinal force demand weight, represents the yaw moment demand weight, represents the output matrix, B represents the control efficiency matrix, Represents the demand matrix.

[0043] (2) Kinematics-based minimum slip objective function Tire loss mainly includes rolling resistance energy loss and longitudinal slip energy loss. Unreasonable tire longitudinal force distribution will accelerate tire wear and increase tire slip energy loss. When the vehicle is turning, the lateral acceleration increases. In addition, during the acceleration and deceleration process, the vertical load is transferred between the front and rear axles, which will cause the tire to slip more and aggravate the tire slip energy loss. Tire slip loss depends on whether the tire force in the slip zone is adapted to the actual speed. The embodiment of the present invention designs a slip energy loss objective function based on kinematics, where the slip speed It is defined as the deviation between the theoretical value of the vehicle center speed and the actual wheel speed, that is: ; in, represents the expected speed of the jth wheel, represents the speed of the jth tire, n represents the reduction ratio of the transmission system, Indicates the radius of the tire.

[0044] The objective function of the kinematics-based minimum slip is: ; in, represents the sliding objective function based on the basis kinematics, represents the tire slip loss coefficient, .

[0045] (3) Objective function of minimum tire load rate The ratio of tire force to the maximum adhesion provided by the road is the tire load rate, which represents the degree to which the tire utilizes the road's adhesion capacity. The smaller the tire load rate, the further the tire force is from saturation and the greater the vehicle stability margin. The specific expression of the tire load rate is: ; in, is the jth tire load rate, satisfying , is the sliding friction coefficient of the jth tire, represents the longitudinal force of the jth tire, represents the lateral force of the jth tire, represents the vertical load force of the jth tire.

[0046] Taking the minimization of the weighted sum of the squares of tire load rates as one of the objectives for optimizing torque distribution, in this embodiment of the present invention, it is assumed that the road conditions on which the wheels are located are the same and the road adhesion coefficient is known and unchanged. The objective function for the minimum tire load rate is: ; in, represents the objective function of tire load rate.

[0047] By optimizing the distribution of tire longitudinal force, the tire load rate generated by the tire longitudinal force is made as small as possible, thereby reducing the utilization of the tire longitudinal force on the road adhesion, improving the longitudinal force output margin and vehicle stability margin, and at the same time improving the tire's ability to generate lateral force, preventing the tire from slipping or sliding, and avoiding instability.

[0048] (4) Tire force limitation The relationship between the longitudinal and lateral forces of a tire is also known as the adhesion ellipse, meaning that the combined force of the two should be less than the maximum adhesion provided by the road surface. It can be expressed as: .

[0049] The vector sum of the longitudinal force and the lateral force is less than the maximum adhesion provided by the road surface , indicating that the vehicle can run normally; if the vector sum of the two exceeds At this time, there is no extra road adhesion for the tires to use, the tires are in a slipping state, and the vehicle is at risk of instability.

[0050] (5) Tire torque output characteristic limitations The maximum output torque of the motor is different at different speeds. Therefore, the longitudinal force allocated to each tire must also meet the limit of the maximum output torque of the motor, that is: ; in, Indicates the maximum torque output by the motor. Indicates the maximum safety factor of the motor output that can be set.

[0051] S6: Design the tire longitudinal force observer based on Lyapunov stability theory and convert the output matrix The input is sent to the tire longitudinal force observer to form a closed-loop control of the desired longitudinal force of each tire.

[0052] First, define a mathematical model for the drive wheel. A fully-drive UGV is powered directly by a wheel hub motor or engine. The electromechanically coupled drive wheel, consisting of a power source and tire, can be considered an independent information module and constructed as a drive wheel. For example, in vehicle state estimation, current sensors and speed encoders can be used to measure the current and speed within the drive wheel. Kalman filtering is then used to estimate the longitudinal force on the wheel. The state equation for the drive wheel is expressed as: ; in, represents the load torque of the wheel motor, is the longitudinal tire force, represents the moment of inertia of the electric wheel, represents the speed of the jth wheel, represents the derivative of the speed of the jth wheel with respect to time t.

[0053] The torque balance equation of the output shaft of the electric drive wheel is: ; in, is the damping coefficient, is the motor torque constant, which can be calibrated using experimental data; is the rotor inertia of the hub motor, is the bus current. , defined as the wheel moment of inertia.

[0054] Combining the above two equations, we can get the rotational dynamics equation of the wheel: .

[0055] Secondly, in the multi-objective torque control strategy based on the wheel load, the optimal control sequence is assigned to each wheel as the expected value. The wheel rotational dynamics in the torque estimation and control algorithm based on the disturbance observer can be expressed as: .

[0056] For the rotational dynamics equation of the wheel, if the desired acceleration of each wheel is known, , the desired control signal for each motor can be calculated according to the following formula: ; in, represents the expected current of the driving motor of the jth wheel.

[0057] Due to the presence of noise in wheel speed measurement, the Cannot directly Therefore, a tire force observer is used to update the motor control signal to provide a true tire force estimate, thereby designing the control law for the motor input current.

[0058] Assume there is a non-negative constant , making , a tire longitudinal force observer can be constructed to estimate the tire force and calculate the anti-interference control law. The expression of the tire longitudinal force observer is: ; ; in, is the estimated longitudinal tire force of the jth wheel, represents the wheel moment of inertia, is the observer gain, represents the bus current, represents the adjustable design parameters of the jth wheel, represents the speed of the jth wheel, represents the observer gain versus time The first derivative of .

[0059] S7: Using the expected longitudinal force of each tire as the expected value and the output of the tire longitudinal force observer as the feedback value, an anti-interference current control law is designed to ensure that the actual tire longitudinal force quickly follows the expected longitudinal force and that the current control has a certain degree of robustness. The anti-interference control law is the control law of the input current, and the specific expression is: ; in, represents the saturation function, represents the desired longitudinal tire force on the jth wheel, is the coefficient of the controller, represents the expected longitudinal tire force of the jth wheel versus time The first derivative of represents the damping coefficient, Indicates the motor torque constant.

[0060] Based on the above formula, the dynamics of tire force estimation can be written as: ; in, Represents the first derivative of the tire force estimate.

[0061] Design the following Lyapunov function: ; ; Where V represents the Lyapunov function, represents the first derivative of the Lyapunov function with respect to time t, represents the first derivative of the observer of the tire longitudinal force, represents the adjustment parameter in Young’s inequality, which is: .

[0062] remember: ; .

[0063] Pick , then P1 = 0. For P2, substitute the input equation to get: ;

[0064] in, satisfy , is a saturation function.

[0065] The above conditions ensure that the symbols in the two brackets of part P2 remain the same, so The Lyapunov convergence property can be guaranteed to converge asymptotically over a large range. The anti-interference control law designed in the embodiment of the present invention can effectively control the tire force to track the desired value.

[0066] The method described in the embodiment of the present invention is compared with the NMPC method, the PID method and the LQR method, and the following results are obtained: Figures 2 to 5 The experimental results are shown in the comparison chart.

[0067] like Figure 2 As shown in Figure 3, 4, and 5, in path tracking experiments, the vehicle tracking performance at locations with significant path curvature, using the method described in this embodiment of the present invention and the NMPC method, was superior to that achieved by the LQR and PID methods. As shown in Figures 3, 4, and 5, the fluctuation amplitudes of longitudinal velocity, lateral velocity, and yaw rate using the method described in this embodiment of the present invention and the PID method were lower than those achieved using the other methods. Furthermore, compared to the PID method, the control strategy of this embodiment of the present invention significantly improved the vehicle's terminal longitudinal velocity, demonstrating its ability to optimize dynamic performance while maintaining stability margins.

[0068] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A tracking control and torque control method for an all-wheel drive unmanned vehicle based on a residual model, characterized in that: The steps include: S1: Establish a nonlinear vehicle dynamics model and perform error analysis to obtain a nonlinear vehicle dynamics error model; S2: Identify the error source through the expression of the nonlinear vehicle dynamics error model and establish a residual model based on Gaussian process to eliminate the error; S3: combining the nonlinear vehicle dynamics model with the Gaussian process-based residual model to obtain a residual model-based vehicle dynamics model, and learning and compensating for dynamic errors in the nonlinear vehicle dynamics error model in real time; S4: mathematically modeling the path tracking problem to obtain lateral compensation and heading angle errors, minimizing the lateral compensation and heading angle as optimization objectives, and using the residual model-based vehicle dynamics model as a prediction model to establish a Gaussian-model predictive control (GP-MPC) controller for path tracking; S5: With the goal of minimizing the torque distribution error, the minimum slip based on kinematics, and the minimum tire load rate, a multi-objective torque control algorithm is designed in combination with the tire force limit and the tire torque output characteristic limit. The optimal control quantity output by the GP-MPC controller, namely the total longitudinal force of the tire and the external yaw moment, is distributed to obtain the output matrix ,in, is the expected longitudinal force of the jth tire, j = 1, 2, 3, ..., 4; S6: Design the tire longitudinal force observer based on Lyapunov stability theory and output the matrix The input is sent to the tire longitudinal force observer to form a closed-loop control of the desired longitudinal force of each tire; S7: Using the expected longitudinal force of each tire as the expected value and the output of the tire longitudinal force observer as the feedback value, an anti-interference current control law is designed to enable the actual tire longitudinal force to quickly follow the expected longitudinal force.

2. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 1, characterized in that: The expression of the nonlinear vehicle dynamics model is: ； in, represents the vehicle longitudinal acceleration, represents the sideslip angular velocity of the center of mass, represents the yaw angular acceleration, represents the sideslip angle of the center of mass, represents the vehicle longitudinal velocity, represents the yaw rate, m represents the vehicle mass, represents the sum of the four tire longitudinal force vectors, Indicates the steering angle of the front and rear wheels, c indicates the lateral stiffness, L indicates the front and rear wheelbase of the car, represents the vehicle's yaw moment of inertia, represents the external yaw moment; The expression of the nonlinear vehicle dynamics error model is: ； in, Indicates the vehicle's longitudinal acceleration The error, represents the sideslip angular velocity of the center of mass The error, represents the yaw angular acceleration The error, Indicates longitudinal force The error, represents the external yaw moment error.

3. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 2, characterized in that: The expression of the residual model based on Gaussian process is: ； in, , Represents the Gaussian process for the vehicle longitudinal velocity The predicted mean of the residuals, represents the sideslip angle of the Gaussian process to the vehicle's center of mass The predicted mean of the residuals, Represents the Gaussian process for the vehicle's yaw rate The predicted mean of the residuals, , Represents the Gaussian process for the vehicle longitudinal velocity The prediction variance of represents the sideslip angle of the Gaussian process to the vehicle's center of mass The prediction variance of Represents the Gaussian process for the vehicle's yaw rate The prediction variance of Indicates the mean , the variance is Multivariate Gaussian distribution of ; The expression of the vehicle dynamics model based on the residual model is: ； in, represents the longitudinal velocity of the vehicle at discrete time step k+1 The predicted value of represents the sideslip angle of the center of mass of the vehicle at discrete time step k+1 The predicted value of represents the yaw rate of the vehicle at discrete time step k+1 The predicted value of represents the discrete form of the nonlinear function of the nonlinear vehicle dynamics model at discrete time step k, Represented by the residual model based on Gaussian process The compensation amount obtained at discrete time step k.

4. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 3, characterized in that: The longitudinal tire forces of the four wheels are taken as features of the residual model based on Gaussian process to reduce the dimension of the feature space: ； Where z represents the characteristics of the residual model based on Gaussian process, F x1 Indicates the longitudinal force of the left front wheel, F x2 Indicates the longitudinal force of the right front wheel, F x3 Indicates the longitudinal force of the left rear wheel, F x4 Indicates the longitudinal force on the right rear wheel.

5. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 4, characterized in that: The expression of the Gaussian-model predictive control GP-MPC controller is: ； ； ； ； ； ； ； ； in, represents the predicted value of the vehicle dynamics model based on the residual model, represents the discrete form of the nonlinear function of the nonlinear vehicle dynamics model at discrete time step k, Represented by the residual model based on Gaussian process The compensation amount obtained at discrete time step k is, represents the longitudinal velocity of the vehicle at discrete time step k+1 The predicted value of represents the sideslip angle of the center of mass of the vehicle at discrete time step k+1 The predicted value of represents the yaw rate of the vehicle at discrete time step k+1 The predicted value of is the regularization term at discrete time step k+1, , which is used to impose a penalty on the control input and its rate of change to ensure smooth control action and prevent sudden changes in trajectory; Represents state quantity of -weighted 2-norm, Indicates control input of -weighted 2-norm, R x Represents state quantity The weight matrix, R u Indicates control input The weight matrix; Q is the lateral compensation term The weight matrix, R is the heading angle error term The weight matrix; N represents the pre-set prediction step value, represents the control input at discrete time step k+1 The predicted value of represents the increment of the control input at discrete time step k, represents the lateral compensation at discrete time step k, represents the transpose of the lateral compensation at discrete time step k, Indicates the lateral compensation at discrete time step k+1 The predicted value of Indicates the time step k used to update the lateral compensation A nonlinear function of the vehicle state and the desired heading angle related, represents the heading angle error at discrete time step k, Represents the heading angle error at discrete time step k+1 The predicted value of Indicates the heading error to be updated at discrete time step k A nonlinear function of the vehicle state and the expected curvature related, Indicates the minimum value of the system state, Indicates the maximum value of the system state, represents the regularization term The amount of change, Indicated by the state quantity and input The regularization term composed of The set of constraints, Represents the change in regularization term The set of constraints.

6. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 5, characterized in that: The specific expression of the objective function for minimizing the torque distribution error is: ； in, represents the objective function of torque distribution error, represents the control demand weight matrix, which is used to balance the ratio between the longitudinal force demand and the yaw moment demand. , represents the longitudinal force demand weight, represents the yaw moment demand weight, represents the input matrix, B represents the control efficiency matrix, represents the demand matrix; The objective function of minimum slip based on kinematics is: ； in, represents the sliding objective function based on the basis kinematics, represents the tire slip loss coefficient, , represents the expected speed of the jth wheel, represents the speed of the jth tire, n represents the reduction ratio of the transmission system, Indicates the radius of the tire; The objective function of minimum tire load rate is: ； in, represents the objective function of tire load rate, represents the sliding friction coefficient of the jth tire, represents the longitudinal force of the jth tire, represents the vertical load force of the jth tire; The specific expression of tire force limitation is: ； in, represents the lateral force of the jth tire; The specific expression of the tire torque output characteristic limitation is: ； in, Indicates the maximum torque output by the motor. Indicates the maximum safety factor of the motor output that can be set.

7. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 6, characterized in that: The expression of the tire longitudinal force observer is: ； ； in, is the estimated longitudinal tire force of the jth wheel, represents the wheel moment of inertia, is the observer gain, represents the bus current, represents the adjustable design parameters of the jth wheel, represents the speed of the jth wheel, represents the observer gain versus time The first derivative of .

8. The tracking control and torque control method of an all-wheel drive unmanned vehicle based on a residual model according to claim 7, characterized in that: The anti-interference control law is the control law of the input current, and the specific expression is: ； in, represents the saturation function, represents the desired longitudinal tire force on the jth wheel, is the coefficient of the controller, represents the expected longitudinal tire force of the jth wheel versus time The first derivative of represents the damping coefficient, Indicates the motor torque constant.

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