Vehicle bending control method based on lateral acceleration prediction

Abstract

The invention discloses a vehicle bending control method based on lateral acceleration prediction, and solves the problem of bending stability failure of an automatic driving vehicle under a limit working condition. The invention relates to the field of automatic driving. The system comprises a reference path module, a lateral acceleration prediction module, an expected braking torque design module, a model prediction control module and a vehicle module. Wherein the reference path module inputs an expected path into the model prediction control module; the lateral acceleration prediction module predicts lateral acceleration based on the vehicle state information; the expected braking torque design module generates an expected braking torque based on the lateral acceleration; and the model prediction control module combines the expected path, the vehicle state information and the expected braking torque, optimizes and solves the control information, sends the control information to the vehicle module, realizes path tracking control, feeds the vehicle state information back to the model prediction control module and the lateral acceleration prediction module, and improves the path tracking performance of the vehicle under the limiting working condition.

Description

Technical Field:

[0001] The present invention belongs to the field of autonomous driving, and particularly relates to a vehicle cornering control method based on lateral acceleration prediction. Background Art:

[0002] With the rapid development of autonomous driving technology, the safety problem of vehicles under extreme working conditions has become increasingly prominent. Taking high-speed cornering as an example, the rapid change of road curvature leads to a rapid increase in lateral acceleration, which in turn affects the friction force distribution between the tire and the road surface. When the lateral force of the tire exceeds the adhesion force provided by the road surface, it is easy to cause tire side slip and even vehicle instability. Therefore, how to adjust the braking torque and steering angle of the vehicle during cornering to ensure driving stability has become one of the core problems in the current autonomous driving control system. Regarding the vehicle cornering control problem, researchers have proposed a variety of control strategies to optimize the stability and handling performance of the vehicle, and each method has its advantages in specific application scenarios. However, under extreme working conditions, the existing methods generally have problems such as response lag and insufficient robustness, and it is difficult to achieve comprehensive and effective control.

[0003] Among various control methods, the Acceleration Vector Control (G-Vectoring Control, GVC) is regarded as a representative cornering control strategy. This method identifies the lateral acceleration changes during the vehicle operation in real time, determines whether it is in the corner entry stage, and realizes the "braking" effect based on the active adjustment of the engine torque, causing the vehicle's center of mass position to shift moderately to increase the front wheel load, enhancing the vehicle's steering response ability and cornering stability. On this basis, researchers have attempted to introduce advanced control strategies to expand and optimize GVC. For example, Patent CN116788242A combines the Model Predictive Control (MPC) with GVC, and adopts the four-wheel equal lateral tire lateral force margin distribution strategy for torque control, thereby enhancing the stability of MPC in the coordinated control of path tracking and braking torque. However, Patent CN116788242A does not fully utilize the data of historical moments of lateral acceleration and the change trend of lateral acceleration. In addition, the four-wheel equal tire lateral force margin distribution strategy distributes the braking torque by the wheelbase from the center of mass to the front and rear wheels, which will result in a larger lateral force margin for the front wheels than that for the rear wheels, leading to insufficient lateral force margin for the rear wheels under turning conditions and further causing vehicle instability. To further improve the vehicle's lateral stability, Patent CN115257704A derives the lateral acceleration expression by constructing a two-degree-of-freedom vehicle model, introduces a linear tire model to construct the state space equation, and applies it to the MPC framework to achieve the prediction of lateral acceleration. Patent CN115257704A can predict the lateral dynamic response of the vehicle during driving to a certain extent and provide feedforward information for the control system. However, when the tire enters the non-linear region, the linear tire model will be difficult to accurately describe the non-linear characteristics of the tire force, resulting in a large deviation between the predicted lateral acceleration and the actual value, thus affecting the control effect of the vehicle's lateral stability.

[0004] In summary, if the historical data of lateral acceleration can be fully integrated, and on this basis, the long-time domain prediction of lateral acceleration can be realized to improve the prediction ability of the vehicle when it is about to enter the unstable state. At the same time, combining the prediction results for the coordinated control of steering and braking will effectively improve the stability and safety of autonomous vehicles under cornering conditions. Summary of the Invention:

[0005] Aiming at the deficiencies of the existing technology, the present invention proposes a vehicle cornering control method based on lateral acceleration prediction. This method integrates path tracking, lateral acceleration prediction, and optimized distribution of braking torque, combines the MPC algorithm to perform multi-objective coordinated optimization on the front wheel steering angle and braking torque, realizes the coordinated control of lateral stability and longitudinal braking force adjustment, and enhances the cornering control performance of the vehicle.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention is a vehicle cornering control method based on lateral acceleration prediction, and this method includes a reference path module, a lateral acceleration prediction module, a desired braking torque design module, a model predictive control module, and a vehicle module.

[0008] This method includes the following steps:

[0009] Step 1, reference path module:

[0010] The reference path module provides an ideal driving trajectory of the vehicle within a future period of time. This path provides the desired path P t ={x ref , y ref} for the model predictive control algorithm, guiding the vehicle to reasonably adjust its driving state in a dynamic environment to ensure that the vehicle travels safely and smoothly along the expected trajectory, where x ref and y ref are the abscissa and ordinate of the desired path respectively.

[0011] Step 2, vehicle module:

[0012] The vehicle module executes the control information Q t output by the model predictive control module to achieve path tracking control and feedback the vehicle state information C t to the model predictive control module and the lateral acceleration prediction module. Among them, the vehicle state information C t includes: C t ={v x , v y , F x.ij , F y.ij , F z.ij , a x , γ, ψ, y, x, κ}, where y is the lateral position of the vehicle, x is the longitudinal position of the vehicle, κ is the road curvature, v x , v y are the longitudinal vehicle speed and lateral vehicle speed respectively, F x.ij , F y.ij , F z.ij are the longitudinal tire force, lateral tire force, and vertical load of the wheels respectively, where i = f, r represent the front wheels and rear wheels respectively, and j = ρ, σ represent the left wheels and right wheels respectively, a x is the longitudinal acceleration of the vehicle, γ is the yaw angular velocity of the vehicle, and ψ is the heading angle of the vehicle.

[0013] Step 3, lateral acceleration prediction module:

[0014] The lateral acceleration prediction module is used to predict the future lateral acceleration based on vehicle state information during the vehicle's turning-in process, enhancing the forward-looking nature of the control system. This module includes: a data preprocessing module, a model training module, and a prediction module. The specific steps are as follows:

[0015] Step 3.1, Data preprocessing module:

[0016] According to the vehicle state information, samples are screened out through the similarity measurement method to construct a data set; and the data set is normalized; on this basis, the sliding window technique is applied to extract time-series input-output pairs to capture time-dependent features; the extracted features and labels are organized into tensor data for model training use.

[0017] Step 3.2, Model training module:

[0018] The LSTM network receives the tensor data, generates the predicted value of the lateral acceleration, calculates the loss function in combination with the true value, and updates the network parameters; generates the LSTM network model and passes it to the prediction module to perform the prediction task of the lateral acceleration.

[0019] Step 3.3, Prediction module:

[0020] Receives the LSTM network model generated by the model training module, screens and retains the network model with the smallest loss value as the optimal model, and combines the tensor data generated by the data preprocessing module to perform the lateral acceleration prediction task, and outputs the final turning-in lateral acceleration a y .

[0021] Step 4, Desired braking torque design module:

[0022] This module receives the real-time prediction results provided by the lateral acceleration prediction module, combines the vehicle state information, generates the desired braking torque that meets the requirements of path tracking and stability, and provides it to the subsequent model predictive controller to achieve the distribution of the wheel braking torque.

[0023] Step 5, Model predictive control module:

[0024] The model predictive control module is used to perform tracking control on the reference path and distribute the desired braking torque among the wheels to ensure the stability of the wheels. This module includes: vehicle model construction, local linearization of the tire lateral force, construction of the tire lateral force margin distribution module, construction of the prediction model, and construction of the inverse tire model. The specific steps are as follows:

[0025] Step 5.1, Vehicle model construction:

[0026] To describe the yaw angular velocity and lateral motion response of the vehicle under the action of braking force, the following vehicle dynamics model is established, specifically as follows:

[0027]

[0028] Among them, is the derivative of the yaw rate, is the derivative of the lateral velocity, γ is the yaw rate, v y is the lateral velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, w is the wheelbase of the vehicle, m is the total mass of the vehicle, I z is the moment of inertia of the vehicle, F y.ij is the lateral tire force, T b,ij is the tire braking force, where i = f, r represent the front and rear wheels respectively, and j = ρ, σ represent the left and right wheels respectively.

[0029] Establish a tracking error model as follows:

[0030]

[0031] Among them, is the derivative of the heading deviation, is the derivative of the lateral deviation, γ is the yaw rate, Δψ is the heading angle rate error, e is the lateral error, v x is the longitudinal velocity of the vehicle, κ is the road curvature.

[0032] Step 5.2, Local linearization of the lateral tire force:

[0033] Perform local linearization on the function of the lateral force of the rear wheels with respect to the sideslip angle of the rear wheels within the prediction time domain through the look-up table method as follows:

[0034]

[0035] Among them, is the sideslip angle of the tire at time k, is the sideslip angle of the local state stiffness, F y,ij is the lateral tire force, α ij is the sideslip angle of the tire, is the sideslip angle of the local state lateral force, and j = ρ, σ represent the left and right wheels respectively.

[0036] Step 5.3, Construction of the lateral tire force margin distribution module:

[0037] Constrain the vehicle tire forces as follows:

[0038]

[0039] Among them, Fy,ij is the lateral force of the tire, F x,ij is the longitudinal force of the tire, F z,ij is the vertical load, and μ is the road adhesion coefficient.

[0040] On this basis, in order to ensure sufficient tire force margin for all four wheels, the following tire force margin distribution strategy is adopted, which is specifically as follows:

[0041]

[0042] Among them, is the lateral force margin of the tire, F z,ij is the vertical load, and μ is the road adhesion coefficient.

[0043] Step 5.4, Prediction model construction:

[0044] Substitute formula (3) in step 5.2 into formulas (1) and (2) in step 5.1 to obtain the specific integrated MPC controller model as follows:

[0045]

[0046] Among them, is the derivative of the yaw rate, is the derivative of the lateral velocity, γ is the yaw rate, v y is the lateral velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, w is the wheelbase of the vehicle, m is the total mass of the vehicle, I z is the moment of inertia of the vehicle, F y.ij is the lateral force of the tire, T b,ij is the braking force of the tire, κ is the road curvature, i = f, r respectively represent the front wheel and the rear wheel, j = ρ, σ respectively represent the left wheel and the right wheel.

[0047] Sort formula (6) into the standard state - space equation, specifically as follows:

[0048]

[0049] Among them, ξ = [γ v y Δψe d T is the state variable, Z = [F y,fρ F y,fσ T b,fρ T b,fσ T b,rρ T b,rσ T is the control variable, ζ is the control output, d is the disturbance input, A ξ 、B​​z , B d and C ξ are coefficient matrices.

[0050] In the formula,

[0051] Discretize formula (7) to obtain an incremental discrete system model as follows:

[0052]

[0053] where Δξ is the vehicle state increment, ΔZ is the control input increment, and Δd is the disturbance input increment.

[0054] To introduce the strategy of maximizing the utilization rate of tire lateral force margin into the control system for optimization, it needs to be written into the discrete system model formula (8) and the Jacobian matrix linearization formula (5) as follows:

[0055]

[0056] where represents taking the partial derivative of each term of in formula (5) with respect to the state variables ξ = [γv y Δψe d ; T represents taking the partial derivative of each term of in formula (5) with respect to the control variables Z = [F F y,fρ F y,fσ T b,fρ T b,fσ T b,rρ T b,rσ ; T Take the partial derivative of each term.

[0057] By combining formula (8) and formula (9), construct a controller system model based on tire lateral force margin as follows:

[0058]

[0059] In the formula O 3×6 represents a matrix with a value of 0 and a dimension of 3 rows and 6 columns.

[0060] The predicted output can be expressed as follows:

[0061] Γ(h + 1|h) = S ξ ·Δξ(h) + S Z ·ΔZ(h) + S dΔd(h)+E·Γ(h) (11)

[0062] where S Z = S BZ + S DZ , and S BZ , S DZ represents the control input increment matrix, which is a matrix with P rows and M columns.

[0063]

[0064] where P is the prediction horizon and M is the control horizon.

[0065] The predicted output sequence, control input sequence, and reference output sequence are defined as follows at h:

[0066]

[0067]

[0068]

[0069] Based on the discretized prediction model, the cost function of the controller is designed as follows:

[0070]

[0071] In the formula, Q is the optimization objective function, Θ Γ is the weight of the predicted output, Θ z is the weight of the predicted input, Γ(h + 1) is the predicted value, R(h + 1) is the actual value, ΔZ(h) is the control increment, Aeq = [001111], beq is the torque generated by the desired braking torque design module, z min , z max are the constraints on the control input, and Δz min , Δz max are the constraints on the change rate of the control input.

[0072] Finally, a constrained optimization problem is constructed to solve the optimal control quantity at the current moment, as follows:

[0073]

[0074] The optimization problem is transformed into a quadratic programming problem for solution:

[0075]

[0076] where H, q, C, are defined as follows:

[0077] E P (h + 1)= R(h + 1)-S ξ Δx(h)-Eζ(h), L z = diag([E nz ,…E nz ) M×M ),

[0078] where Z(h - 1) is the matrix of the measured values of the control input at time h - 1.

[0079] Step 5.5, Inverse tire model construction:

[0080] Use the inverse tire model to convert the lateral force of the front wheel optimized by MPC into the front wheel steering angle δ, specifically as follows:

[0081]

[0082] where δ fj is the steering angle of the front wheel, β is the sideslip angle of the center of mass, l f is the distance from the front axle to the center of mass, γ is the yaw rate, v x is the longitudinal speed of the vehicle, F y,fj is the lateral force of the front wheel, is used to convert the lateral force F y,fj of the front wheel into the tire sideslip angle α fj , where j = ρ, σ respectively represent the left wheel and the right wheel.

[0083] Finally, the front wheel steering angle δ fj and the braking torque T b,ij are used as the control information Q t and sent to the vehicle module to achieve the control of the vehicle entering the curve.

[0084] The beneficial effects of the present invention are as follows: The present invention designs a vehicle curve - entering control method based on lateral acceleration prediction. This method combines a lateral acceleration prediction mechanism with a model - predictive control strategy, can utilize the historical data of lateral acceleration, and on this basis, realizes the long - time - domain prediction of future lateral acceleration, enabling the control system to identify in advance that the vehicle is about to enter an unstable state, and combining the prediction results to adjust the steering and braking control system in advance. This method not only enhances the forward - looking nature of the control system, but also improves the stability and robustness of the vehicle under extreme conditions, and has good application prospects in the field of autonomous driving. Brief description of the drawings:

[0085] Figure 1It is a schematic diagram of a vehicle cornering control method based on lateral acceleration prediction.

[0086] Figure 2 It is a schematic diagram of the lateral acceleration prediction module. Specific implementation manner:

[0087] The present invention will be described in detail below with reference to the accompanying drawings.

[0088] As Figure 1 shown, the present invention is a vehicle cornering control method based on lateral acceleration prediction, with lateral acceleration prediction as the core, combined with path tracking and braking torque distribution to improve the stability of the vehicle during cornering. It includes five modules: a reference path module, a lateral acceleration prediction module, an expected braking torque design module, a model predictive control module, and a vehicle module. The reference path module provides an expected path as the path tracking target; the lateral acceleration prediction module predicts the lateral acceleration during cornering based on vehicle state information to perceive the instability risk in advance; the expected braking torque design module generates a braking torque according to the predicted lateral acceleration during cornering; the model predictive control module combines the expected path, vehicle state information, and expected braking torque, outputs optimized control information and sends it to the vehicle module to achieve path tracking control, and transmits the vehicle state information to the model predictive control and lateral acceleration prediction modules to achieve closed-loop control.

[0089] Step 1, reference path module:

[0090] The reference path module adopts a quintic polynomial fitting method to generate a smooth and controllable expected path P t ={x ref , y ref} based on the position information of the starting point and the ending point and their speed and acceleration boundary conditions, ensuring that the trajectory is physically feasible and continuous. The quintic polynomial expression is as follows:

[0091] y(x)=a0 + a1x + a2x 2 + a3x 3 + a4x 4 + a5x 5 (1)

[0092] Wherein, x represents the longitudinal coordinate, and y represents the corresponding lateral coordinate. By giving the boundary conditions of the starting point and the ending point, specifically including position, speed, and acceleration, six unknown coefficients a0~a5 can be solved, thereby generating an expected trajectory that meets the constraint conditions.

[0093] The coefficient system of a0~a5 in the formula can be expressed as:

[0094]

[0095] Wherein, a0 is the acceleration at the starting point, a1 is the acceleration at the end point, v0 is the velocity at the starting point, v1 is the acceleration at the end point, h = q1 - q0 is the lateral position change between the starting point and the end point, and T = t1 - t0 is the time change between the starting point and the end point.

[0096] Step 2, Vehicle module:

[0097] To verify the effectiveness and engineering feasibility of the proposed control strategy, the present invention introduces a vehicle dynamics model for system modeling and control verification. In the specific implementation method, the CarSim 2020 vehicle model is used as the simulation platform, and the vehicle dynamics system is constructed in combination with typical working conditions. Through the co-simulation of CarSim and Simulink, the effect evaluation of the path tracking and tire lateral force margin distribution strategy is realized, which serves as the verification basis before the real vehicle experiment. Taking a certain model of the CarSim automotive simulation software as the platform, the method of the present invention is specifically described below, and its main parameters are shown in Table 1:

[0098] Parameter Unit Parameter Value Automobile mass m kg 1414 <![CDATA[Distance l from the vehicle's center of mass to the front axle f > m 1.015 <![CDATA[Distance l from the vehicle's center of mass to the rear axle r > m 1.895 <![CDATA[Yaw moment of inertia I about the vertical axis passing through the center of mass of the vehicle z > <![CDATA[kgm 2 > 1536.7 Automobile track width w m 1.675 Effective wheel radius r m 0.31

[0099] The vehicle module executes the control information Q output by the model predictive control module t , to achieve path tracking control, and feedback the vehicle state information C t to the model predictive control module and the lateral acceleration prediction module. Among them, the vehicle state information C t includes: C t = {v x , v y , F x.ij , F y.ij , F z.ij , a x , γ, ψ, y, x, κ}, where y is the lateral position of the vehicle, x is the longitudinal position of the vehicle, κ is the curvature of the path passed by the vehicle, v x , v y are the longitudinal vehicle speed and lateral vehicle speed respectively, F x.ij , F y.ij , F z.ij are the longitudinal tire force, lateral tire force, and vertical load of the wheels respectively, where i = f, r represent the front wheels and rear wheels respectively, j = ρ, σ represent the left wheels and right wheels respectively, a x is the longitudinal acceleration of the vehicle, γ is the yaw rate of the vehicle, and ψ is the heading angle of the vehicle.

[0100] Step 3, Lateral acceleration prediction module:

[0101] As Figure 2 shown, the lateral acceleration prediction module is based on a deep neural network (such as an LSTM network), combined with the vehicle state information C t, perform lateral acceleration prediction, specifically including: a data preprocessing module, a model training module, and a prediction module.

[0102] Step 3.1, Data preprocessing module:

[0103] Step 3.1.1, First, the system receives the vehicle state information C t , and filters samples through a similarity measurement method to construct a data set. Among them, the Euclidean distance is selected as the matching degree measurement method for the vehicle state information and the matching information in the information library. Specifically as follows:

[0104]

[0105] Among them, the non - negative real number d(x,y) represents the Euclidean distance between two vectors, x i represents the n - dimensional vehicle state information, and y i represents the matching information in the information library.

[0106] Step 3.1.2, Use the Min - Max Normalization method to normalize the data set. Its purpose is to scale the data proportionally to the range of [0,1] to avoid the relatively large differences in the model training caused by the differences in the value ranges of different features. Specifically as follows:

[0107]

[0108] Step 3.1.3, After completing the normalization of the data set, use the sliding window technique to extract continuous input - output pairs to capture the time - series features, specifically as follows:

[0109] Take a time - series data X = [x1, x2, …, x N , set a fixed window size w, and define a sliding step size s.

[0110] For each window, the input data is composed of the historical values within the window, and the output data is the data at the end of the window. In the time series, the input data within the t - th window can be expressed as:

[0111] X input (t) = [x t , x t+1 , … x t+w-1 (5)

[0112] And the output data corresponding to this window is:

[0113] X output (t) = x t+w (6)

[0114] Step 3.1.4: Adjust the dimensions of the extracted input-output pairs according to the requirements of the LSTM network structure, and convert them into three-dimensional tensor data with dimensions (N, C, T), where N represents the batch size, C = 8 represents the feature dimensions (corresponding to the lateral displacement y, lateral velocity v y , yaw rate γ, front wheel steering angle δ, road curvature κ, heading angle ψ, longitudinal acceleration a x and its lateral acceleration a y ), and T = 4 represents the input sequence length (i.e., the model predicts the deceleration at the next moment based on the data of 4 consecutive historical moments).

[0115] Step 3.1.5: Divide the dataset into a training set, a validation set, and a test set. According to the set ratio (80% training set, 10% validation set, 10% test set), divide the dataset to prepare for subsequent training and evaluation.

[0116] Step 3.2: Model training module

[0117] Step 3.2.1: Initialize the LSTM network model to recognize the input tensor data. The LSTM network contains 2 layers of LSTM structures, and each layer has 128 hidden units.

[0118] Step 3.2.2: The LSTM network model calculates the prediction result through forward propagation, updates the state at each time step through the gating mechanism, and uses past historical information to predict the lateral acceleration.

[0119] Among them, the key gating mechanism of LSTM takes the input at time step t to include the hidden state h at the previous time step t and the input x at the current time step t , and these inputs are processed through different gating mechanisms. The specific key gating mechanism of LSTM is as follows

[0120] Forget gate f t : Controls the retention ratio of historical information. The specific formula is as follows

[0121] f t = σ(W f ·[h t-1 , x t + b f ) (7)

[0122] Among them, f t is the output of the forget gate, W f is the weight matrix of the forget gate, x t is the input at the current time step, h t-1 is the hidden state at the previous moment, b f is the bias term; σ is the Sigmoid activation function.

[0123] Input gate i t : Controls how the current input affects the memory unit, and the specific formula is as follows:

[0124] i t = σ(W i ·[h t-1 , x t +b i ) (8)

[0125] where i t is the output of the input gate, W t is the weight matrix of the input gate, and b t is the bias term.

[0126] Candidate memory unit Generates candidate new memory content, and the specific formula is as follows:

[0127]

[0128] where W c is the weight matrix of the candidate memory unit, b c is the bias term, and tanh is the hyperbolic tangent activation function.

[0129] Memory unit update C t : Integrates the outputs of the forget gate and the input gate to update the memory unit, and the formula is as follows:

[0130]

[0131] where f t controls the historical information to be retained, and i t controls the addition of new information.

[0132] Output gate o t : Controls the output of the hidden state, and the specific formula is as follows:

[0133] o t = σ(W o ·[h t-1 , x t +b o ) (11)

[0134] o t is the output of the output gate, W o is the weight matrix of the output gate, and b o is the bias term.

[0135] Step 3.2.3. Calculate the loss function using the mean squared error (MSE) based on the difference between the predicted value generated by the model and the true value (label). The specific formula is as follows:

[0136]

[0137] where n is the total number of samples, y i is the true value of the i-th sample, is the predicted value of the i-th sample.

[0138] Step 3.2.4: Through the backpropagation algorithm, the loss value propagates backward from the output layer to the input layer, and gradients are calculated for each parameter (i.e., the weights and biases in the LSTM unit) based on the loss value.

[0139] Step 3.2.5: Using the calculated gradients, the AdamW optimizer (with an initial learning rate of 0.01 and a weight decay coefficient of 0.001) is used to adjust the weights and biases in the LSTM network. The goal is to reduce the value of the loss function by adjusting the weights, thereby improving the accuracy of the model prediction.

[0140] Step 3.2.6: During the training process, the weights are continuously iteratively adjusted until the model converges, i.e., the loss reaches the minimum value. After the training is completed, all the trained weights and biases are integrated to form the final LSTM network model, and the network model is sent to the prediction module for subsequent prediction tasks.

[0141] Step 3.3: Prediction module:

[0142] Step 3.3.1: Receive the trained LSTM network model from the model training module. The model contains the weights, biases, and the corresponding loss function values learned during the training process.

[0143] Step 3.3.2: By comparing the loss function values of the validation set in each round of training, select the model with the minimum loss. This means that the model can optimally predict on the validation set, thus avoiding overfitting; usually, the "Early Stopping" strategy is adopted, that is, if the loss of the validation set does not decrease significantly in consecutive multiple training rounds, the training is stopped, and the model with the current minimum loss is retained.

[0144] Step 3.3.3: After the training and validation of the model are completed, the LSTM network model makes predictions based on the tensor data extracted by the data preprocessing module, and finally outputs the lateral acceleration a y .

[0145] Step 4: Desired braking torque design module:

[0146] For the design of braking torque, this paper adopts the G-Vectoring Control (GVC) method, which intervenes in the lateral dynamic response of the vehicle by adjusting the longitudinal braking torque, optimizes the attitude control of the vehicle in a bend, and GVC can effectively suppress the drastic change of lateral acceleration, thus improving the stability and responsiveness of the vehicle in a bend.

[0147] Step 4.1, GVC control module:

[0148] In the design of the GVC control module, first, taking the lateral acceleration change rate as the core adjustment basis, after first-order filtering and smoothing processing, it is mapped into the longitudinal braking acceleration input, and then the active adjustment of the vehicle attitude is realized, specifically as follows:

[0149]

[0150] Among them, G xc is the longitudinal braking acceleration, G y is the lateral acceleration, is the lateral acceleration change rate, C xy is the control gain, T s is the first-order filtering time constant.

[0151] Step 4.2, Braking torque mapping:

[0152] To reasonably convert the longitudinal braking acceleration generated by the GVC module into the wheel braking torque, this paper further designs a tire dynamics mapping model, comprehensively considering factors such as wheel moment of inertia, angular velocity change rate, and longitudinal acceleration, to ensure the executability and dynamic response characteristics of the braking torque output, specifically as follows:

[0153]

[0154] Among them, J is the wheel moment of inertia, is the derivative of the wheel angular velocity, R is the wheel radius, m t is the single-wheel mass, is the wheel longitudinal acceleration, T b is the output braking torque.

[0155] Through the combination of the above GVC control law and the braking torque mapping model, the longitudinal braking control intervention for the lateral dynamic trend is realized, providing the desired braking torque for model predictive control.

[0156] Step 5, Model predictive control module:

[0157] The model predictive control module is used to track and control the reference path and distribute the desired braking torque among the wheels to ensure the stability of the wheels. This module includes: vehicle model construction, local linearization of the tire lateral force, construction of the tire lateral force margin distribution module, construction of the prediction model, and construction of the inverse tire model. The specific steps are as follows:

[0158] Step 5.1, Vehicle model construction:

[0159] To describe the yaw rate and lateral motion response of the vehicle under the action of braking force, the following vehicle dynamics model is established, specifically as follows:

[0160]

[0161] Among them, is the derivative of the yaw rate, is the derivative of the lateral velocity, γ is the yaw rate, v y is the lateral velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, w is the wheelbase of the vehicle, m is the total mass of the vehicle, I z is the moment of inertia of the vehicle, F y.ij is the tire lateral force, T b,ij is the tire braking force, where i = f, r represent the front and rear wheels respectively, and j = ρ, σ represent the left and right wheels respectively.

[0162] Establish a tracking error model, specifically as follows:

[0163]

[0164] Among them, is the derivative of the heading deviation, is the derivative of the lateral deviation, γ is the yaw rate, Δψ is the heading angle rate error, e is the lateral error, v x is the longitudinal velocity of the vehicle, κ is the road curvature.

[0165] Step 5.2, Local linearization of the tire lateral force:

[0166] The local linearization of the rear wheel lateral force with respect to the rear wheel side slip angle within the prediction time domain is performed by means of a look-up table method, specifically as follows:

[0167]

[0168] Among them, is the tire side slip angle at time k, is the side slip angle of the local state stiffness, F y,ij is the tire lateral force, α ijTire sideslip angle is the sideslip angle of the local state lateral force

[0169] Step 5.3, Construction of the tire lateral force margin distribution module:

[0170] Constrain the vehicle tire forces as follows:

[0171]

[0172] Among them, F y,ij is the tire lateral force, F x,ij is the tire longitudinal force, F z,ij is the vertical load

[0173] On this basis, in order to ensure sufficient tire lateral force margin for all four wheels, adopt the following tire lateral force margin distribution strategy, specifically as follows:

[0174]

[0175] Among them, is the tire lateral force margin, F z,ij is the vertical load, and μ is the road adhesion coefficient

[0176] Step 5.4, Construction of the prediction model:

[0177] Substitute formula (17) in step 5.2 into formulas (15) and (16) in step 5.1 to obtain the integrated MPC controller model as follows:

[0178]

[0179] Among them, is the derivative of the yaw rate is the derivative of the lateral velocity, γ is the yaw rate, v y is the lateral velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, w is the wheelbase of the vehicle, m is the total mass of the vehicle, I z is the moment of inertia of the vehicle, F y.ij is the tire lateral force, T b,ij is the tire braking force, κ is the road curvature, i = f, r respectively represent the front and rear wheels, and j = ρ, σ respectively represent the left and right wheels

[0180] Rearrange formula (20) into the standard state - space equation as follows:

[0181]

[0182] where ξ = [γv y Δψe d T is the state variable, Z = [F y,fρ F y,fσ T b,fρ T b,fσ T b,rρ T b,rσ T is the control variable, ζ is the control output, d is the disturbance input, A ξ 、B z 、B d and C ξ are coefficient matrices.

[0183] In the formula,

[0184] For formula (21), discretize it through T s seconds (set according to the vehicle dynamic response requirements) to obtain an incremental discrete system model, specifically as follows:

[0185]

[0186] where Δξ is the vehicle state increment, ΔZ is the control input increment, and Δd is the disturbance input increment.

[0187] In order to introduce the strategy of maximizing the utilization rate of the tire side force margin into the control system for optimization, it is necessary to write it into the system model (22) and linearize equation (19) using the Jacobian matrix, specifically as follows:

[0188]

[0189] where, includes denotes the partial derivative of with respect to the yaw rate γ, denotes the partial derivative of y with respect to the lateral velocity v of denotes the partial derivative of with respect to the heading deviation Δψ, denotes the partial derivative of with respect to the lateral deviation e, includes denotes the partial derivative of y,fρ with respect to the left front wheel side force F of denotes the partial derivative of y,fσ with respect to the right front wheel side force F of denotes the partial derivative of x,fρ with respect to the left front wheel longitudinal force F​​ Find the partial derivative, denote based on the longitudinal force F of the right front wheel x,fr for find the partial derivative, denote based on the longitudinal force F of the left rear wheel x,rρ for find the partial derivative, denote based on the longitudinal force F of the right rear wheel x,rσ for find the partial derivative.

[0190] Construct a controller system model based on the tire side force margin by combining formula (23) and formula (22), as follows:

[0191]

[0192] where O 3×6 denotes a matrix with a value of 0 and a dimension of 3 rows and 6 columns.

[0193] The predicted output can be expressed as follows:

[0194] Γ(h + 1|h) = S ξ ·Δξ(h) + S Z ·ΔZ(h) + S d Δd(h) + E·Γ(h) (25)

[0195] where, S Z = S BZ + S DZ S BZ S DZ denote the control input increment matrix, which is a matrix with a dimension of P rows and M columns.

[0196]

[0197] where, P is the prediction horizon and M is the control horizon.

[0198] The predicted output sequence, control input sequence, and reference output sequence are defined at h as follows:

[0199]

[0200]

[0201]

[0202] Based on the discretized prediction model, construct a constrained optimization problem to solve the optimal control quantity at the current moment, as follows:

[0203]

[0204] In the formula, Q is the optimization objective function, Θ Γ is the weight of the predicted output, Θ z is the weight of the predicted input, Γ(h + 1) is the predicted value, R(h + 1) is the actual value, ΔZ(h) is the control increment, Aeq = [0 0 1 1 1 1], beq is the torque generated by the desired braking torque design module, z min , z max is the constraint on the control input, Δz min , Δz max is the constraint on the change rate of the control input.

[0205] The MPC optimization problem can be formulated as follows:

[0206]

[0207] Convert the optimization problem of formula (30) into a quadratic programming problem for solution:

[0208]

[0209] where H, q, C, are defined as follows:

[0210] E P (h + 1) = R(h + 1) - S ξ Δx(h) - Eζ(h), L z = diag([E nz , … E nz ) M×M ,

[0211] where Z(h - 1) is the matrix of the measured values of the control input at time h - 1.

[0212] Step 5.5, Inverse tire model construction:

[0213] Use the inverse tire model to convert the lateral force of the front wheel optimized by MPC into the front wheel steering angle δ, specifically as follows:

[0214]

[0215] where, δ fj is the steering angle of the front wheel, β is the sideslip angle of the center of mass, l f is the distance from the front axle to the center of mass, γ is the vehicle yaw angular velocity, v x is the longitudinal speed of the vehicle, F y,fjis the lateral force of the front wheel, which is used for numerical calculation by using the look-up table method. When a specific F y,fj is given, the corresponding sideslip angle α fj can be quickly calculated, where j = ρ, σ respectively represent the left wheel and the right wheel.

[0216] Finally, the front wheel steering angle δ fj and the braking torque T b,ij are used as the control information Q t and sent to the vehicle module to achieve the control of the vehicle entering the bend.

[0217] To sum up: The present invention proposes a vehicle entering bend control method based on lateral acceleration prediction. By collecting the real-time state of the vehicle, the future lateral acceleration is predicted, and the advance adjustment of the braking torque is realized. Compared with the traditional GVC model, this method uses the historical data of the lateral acceleration and realizes the long-time domain prediction of the future lateral acceleration on this basis. It can sense the potential lateral instability trend under the bend condition to improve the path tracking accuracy and stability. At the same time, combined with the improved tire lateral force margin distribution strategy and model predictive control, the optimal distribution of the braking torque is realized, and the stability and robustness of the vehicle under extreme conditions are enhanced, which has good application prospects in the field of autonomous driving.

Claims

1. A vehicle cornering control method based on lateral acceleration prediction, characterized in that: The method includes the following modules: a reference path module, a lateral acceleration prediction module, a desired braking torque design module, a model predictive control module, and a vehicle module; among them, the reference path module is used to provide a desired path to the model predictive control module; the lateral acceleration prediction module predicts the lateral acceleration of the vehicle during the cornering process according to the vehicle state information; the desired braking torque design module generates a desired braking torque according to the predicted lateral acceleration; the model predictive control module combines the desired path, the vehicle state information, and the desired braking torque, optimizes and solves the control information and sends it to the vehicle module to achieve path tracking control, and feeds back the vehicle state information to the model predictive control module and the lateral acceleration prediction module; The method includes the following steps: Step 1.

1. The reference path module provides the desired path P of the vehicle for the model predictive control module t ={x ref , y ref}, where x ref and y ref are the abscissa and ordinate of the desired path respectively; Step 1.2: The vehicle module executes the control information Q output by the model predictive control module t , to achieve path tracking control, and feed back the vehicle state information C t to the model predictive control module and the lateral acceleration prediction module; the vehicle state information C t includes: C t ={v x , v y , F x.ij , F y.ij , F z.ij , a x , γ, ψ, y, x, κ}, where y is the lateral position of the vehicle, x is the longitudinal position of the vehicle, κ is the road curvature, v x , v y are the longitudinal vehicle speed and the lateral vehicle speed respectively, F x.ij , F y.ij , F z.ij are the longitudinal tire force, the lateral tire force and the vertical load of the wheels respectively, where i = f, r represent the front wheels and the rear wheels respectively, j = ρ, σ represent the left wheels and the right wheels respectively, a x is the longitudinal acceleration of the vehicle, γ is the yaw angular velocity of the vehicle, ψ is the heading angle of the vehicle; Step 1.3, Lateral Acceleration Prediction Module, predicts the lateral acceleration a of the vehicle during the cornering process based on the vehicle state information C fed back by the vehicle module t , predicts the lateral acceleration a of the vehicle during the cornering process y ; Step 1.4, Desired braking torque design module, based on the predicted lateral acceleration a y , calculate the desired braking torque T z ; Step 1.5: The model predictive control module receives the desired path P t , the desired braking torque T z and the vehicle state information C t , optimally solves the control information Q t and sends it to the vehicle module to achieve path tracking control, where the control information Q t includes the braking torques of the four wheels and the front wheel steering angle.

2. The vehicle cornering control method based on lateral acceleration prediction according to claim 1, wherein: The lateral acceleration prediction module is used to predict the lateral acceleration a during the vehicle's cornering process in real time y , and specifically includes: a data preprocessing module, a model training module, and a prediction module. The specific steps are as follows: Step 2.1, Data preprocessing module: Construct a data set according to the vehicle state information output by the vehicle module, and perform normalization processing on the data set; on this basis, use the sliding window technique to extract input-output pairs to capture the time series characteristics in the data set, and convert the extracted time series characteristics and labels into tensor data; Step 2.2, Model training module: The long short-term memory network LSTM receives the tensor data output by the data preprocessing module to generate a predicted value of the lateral acceleration, and combines the true value of the lateral acceleration, calculates the loss function, updates the network parameters, and generates an LSTM network model; Step 2.3, Prediction module: Receive the LSTM network model generated by the training module of the receiving model, screen and retain the network model with the smallest loss value as the optimal model, combine it with the tensor data generated by the data preprocessing module to predict the lateral acceleration, and output the lateral acceleration a during the process of entering the curve y .

3. The vehicle cornering control method based on lateral acceleration prediction according to claim 1, wherein: The model predictive control module distributes the desired braking torque and performs path tracking control, including vehicle model construction, local linearization of the tire lateral force, construction of a tire lateral force margin distribution module, construction of a prediction model, and construction of an inverse tire model. The specific steps are as follows: Step 3.1, Vehicle model construction: To describe the yaw angular velocity and lateral motion response of the vehicle under the action of braking force, the following vehicle dynamics model is established, specifically as follows: Among them, is the derivative of the yaw rate, is the derivative of the lateral velocity, γ is the yaw rate, v y is the lateral velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, w is the track width of the vehicle, m is the total mass of the vehicle, I z is the moment of inertia of the vehicle, F y.ij is the lateral tire force, T b,ij is the tire braking force, where i = f, r respectively represent the front and rear wheels, and j = ρ, σ respectively represent the left and right wheels; Establish a tracking error model, specifically as follows: Among them, is the derivative of the heading deviation, is the derivative of the lateral deviation, γ is the yaw rate, Δψ is the heading angle rate error, e is the lateral error, v x is the longitudinal vehicle speed, and κ is the road curvature; Step 3.2, Local linearization of the tire lateral force: Perform local linearization on the rear wheel side slip angle within the prediction time domain of the model predictive control through the look-up table method, specifically as follows: Among them, is the tire sideslip angle at time k, is the sideslip angle of the local state stiffness, F y,ij is the tire lateral force, α ij is the tire sideslip angle, is the sideslip angle of the local state lateral force, j = ρ, σ which respectively represent the left wheel and the right wheel; Step 3.3, Construction of the tire lateral force margin distribution module: Constrain the vehicle tire force, specifically as follows: Among them, F y,ij is the lateral force of the tire, F x,ij is the longitudinal force of the tire, F z,ij is the vertical load, where i = f, r respectively represent the front wheel and the rear wheel, and j = ρ, σ respectively represent the left wheel and the right wheel; On this basis, in order to ensure that there is sufficient tire lateral force margin for the wheels, the following tire lateral force margin distribution strategy is adopted, specifically as follows: Among them, is the lateral force margin of the left front tire, and F z,ij is the vertical load, and μ is the road surface adhesion coefficient; Step 3.4, Prediction model construction: Substitute formula (3) in step 3.2 into formulas (1) and (2) in step 5.1 to obtain the MPC controller model, specifically as follows: Among them, is the derivative of yaw rate, is the derivative of lateral velocity, γ is the yaw rate, v y is the lateral velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, w is the track width of the vehicle, m is the total mass of the vehicle, I z is the moment of inertia of the vehicle, F y.ij is the lateral force of the tire, T b,ij is the braking force of the tire, κ is the road curvature, i = f, r respectively represent the front and rear wheels, j = ρ, σ respectively represent the left and right wheels; Arrange formula (6) into a standard state space equation, specifically as follows: where ξ = [γv y Δψe d T is the state variable, Z = [F y,fρ F y,fσ T b,fρ T b,fσ T b,rρ T b,rσ T is the control variable, ζ is the control output, d is the disturbance input, A ξ , B z , B d and C ξ are coefficient matrices;​​ In the formula, Discretize formula (7) to obtain an incremental discrete system model, specifically as follows: Among them, Δξ is the vehicle state increment, ΔZ is the control input increment, and Δd is the disturbance input increment; In order to introduce the strategy of maximizing the utilization rate of the tire lateral force margin into the control system for optimization, linearize formula (5) using the Jacobian matrix, specifically as follows: Among them, means to take the partial derivative of each term in formula (5) with respect to the state variables ξ = [γ v y Δψ e d T respectively; means to take the partial derivative of each term in formula (5) with respect to the control variables Z = [F y,fρ F y,fσ T b,fρ T b,fσ T b,rρ T b,rσ T respectively.​​ By combining formula (8) and formula (9), construct a controller system model based on the tire lateral force margin, specifically as follows: In the formula, O 3×6 represents a matrix with a value of 0 and a dimension of 3 rows and 6 columns; The predicted output can be expressed as follows: Γ(h + 1|h) = S ξ ·Δξ(h) + S Z ·ΔZ(h) + S d Δd(h) + E·Γ(h) (11) Among them, S Z = S BZ + S DZ , where S BZ and S DZ represent the control input increment matrix, which is a matrix with P rows and M columns; In the formula, where \(P\) is the prediction horizon and \(M\) is the control horizon; The predicted output sequence, the control input sequence, and the reference output sequence are defined at \(h\) as follows: Based on the discretized prediction model, the cost function of the controller is designed as follows: where Q is the optimization objective function, Θ Γ is the weight of the predicted output, Θ z is the weight of the predicted input, Γ(h + 1) is the predicted value, R(h + 1) is the actual value, ΔZ(h) is the control increment, Aeq = [0 0 1 1 1 1], beq is the torque generated by the desired braking torque design module, z min 、z max is the constraint on the control input, Δz min 、Δz max is the constraint on the rate of change of the control input; Finally, a constrained optimization problem is constructed to solve the optimal control quantity at the current moment, as follows: Furthermore, the optimization problem in Equation (16) is transformed into a quadratic programming problem for solution, in the form as follows: where H, q, C, are defined as follows: E P (h + 1)=R(h + 1)-S ξ Δx(h)-Eζ(h), where \(Z(h - 1)\) is the matrix of the measured values of the control input at time \(h - 1\); Step 3.5, Construction of the inverse tire model: The inverse tire model is used to convert the lateral force of the front wheel optimized by MPC into the front wheel steering angle \(\delta\), as follows: Among them, δ fj is the steering angle of the front wheels, β is the sideslip angle of the center of mass, l f is the distance from the front axle to the center of mass, γ is the yaw angular velocity of the vehicle, v x is the longitudinal velocity of the vehicle, F y,fj is the lateral force of the front wheels, is used to convert the front wheel lateral force F y,fj into the tire sideslip angle α fj , where j = ρ, σ respectively represent the left wheel and the right wheel; Finally, the front wheel steering angle δ fj and the braking torque T b,ij are used as the control information Q t and sent to the vehicle module to achieve the control of the vehicle entering the curve.

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