Variable prediction time vehicle path tracking control method, system, device and medium
By dynamically adjusting the prediction time and offset distance, the vehicle path tracking control method solves the problem of inaccurate path tracking under fixed prediction time, and achieves high-precision and stable path tracking under complex road conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHONGQING UNIV
- Filing Date
- 2024-01-04
- Publication Date
- 2026-05-29
AI Technical Summary
Existing model predictive control methods with fixed prediction times cannot ensure the accuracy and stability of path tracking in critical scenarios such as icy roads.
A vehicle path tracking control method with variable prediction time is adopted. By establishing a vehicle state prediction model, the prediction time and discrete time step are dynamically adjusted according to the current reference path curvature, vehicle longitudinal speed and road adhesion coefficient. Combined with adaptive soft constraints of front wheel steering angle, front wheel steering angle increment and front and rear wheel slip angles, the path tracking control is optimized.
It improves the accuracy and smoothness of path tracking, reduces the amount of computation, and enhances the stability and tracking accuracy of vehicles under complex road conditions.
Smart Images
Figure CN117842008B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of path tracking technology, and in particular to a vehicle path tracking control method, system, device and medium with variable prediction time. Background Technology
[0002] Autonomous vehicles have the potential to improve driving safety, alleviate traffic congestion, and increase transportation efficiency, and have received widespread attention from academia and industry in recent decades. As one of the core technologies for motion control in autonomous vehicles, path tracking has become a global research focus. The main goal of path tracking is to optimize its accuracy and smoothness while maintaining vehicle stability through automatic steering. Model predictive control (MPC) is one feasible method for achieving path tracking. Currently, the fixed prediction time in MPC cannot guarantee path tracking performance in certain critical scenarios (such as icy roads). Summary of the Invention
[0003] The purpose of this invention is to provide a vehicle path tracking control method, system, device, and medium with variable prediction time, which improves the accuracy of path tracking.
[0004] To achieve the above objectives, the present invention provides the following solution:
[0005] This invention provides a vehicle path tracking control method with variable prediction time, comprising:
[0006] A vehicle state prediction model is established based on the vehicle dynamics model, tire model, and path tracking model of the target vehicle.
[0007] Based on the current reference path curvature, vehicle longitudinal speed, and road surface adhesion coefficient, the optimal time prediction model is used to output the current optimal prediction time.
[0008] Determine the current discrete time step and the current prediction time domain based on the current optimal prediction time.
[0009] The vehicle state at the current moment is input into the vehicle state prediction model, and the vehicle state prediction time series is output; the vehicle state prediction time series includes the vehicle state at each current discrete time step within the current prediction time domain.
[0010] The objective function for path tracking is constructed based on the vehicle state prediction time series. The constraints of the objective function are determined based on the physical constraints of the front wheel steering angle, the front wheel steering angle increment constraints, and the adaptive soft constraints of the front and rear wheel slip angles in the control time domain. The objective function includes the path error between the tracking path and the reference path in the vehicle state prediction time series, the control increment, and the degree of relaxation of the soft constraints.
[0011] The objective function is optimized to obtain the optimized control time series;
[0012] The target vehicle is subjected to path tracking control based on the optimized control time sequence.
[0013] This invention provides a vehicle path tracking control system with variable prediction time, comprising:
[0014] The vehicle state prediction model building module is used to build a vehicle state prediction model based on the target vehicle's vehicle dynamics model, tire model, and path tracking model.
[0015] The optimal prediction time prediction module is used to output the current optimal prediction time based on the current reference path curvature, vehicle longitudinal speed and road adhesion coefficient using the optimal time prediction model.
[0016] The discrete time step and prediction time domain determination module is used to determine the current discrete time step and the current prediction time domain based on the current optimal prediction time.
[0017] The vehicle state prediction time series determination module is used to input the vehicle state at the current moment into the vehicle state prediction model and output the vehicle state prediction time series; the vehicle state prediction time series includes the vehicle state at each current discrete time step within the current prediction time domain.
[0018] The objective function construction module for path tracking is used to construct the objective function for path tracking based on the vehicle state prediction time series. The constraints of the objective function are determined based on the physical constraints of the front wheel steering angle, the front wheel steering angle increment constraints, and the adaptive soft constraints of the front and rear wheel slip angles in the control time domain. The objective function includes the path error between the tracking path and the reference path in the vehicle state prediction time series, the control increment, and the degree of relaxation of the soft constraints.
[0019] The objective function optimization module is used to optimize the objective function to obtain the optimized control time series;
[0020] The path tracking control module is used to perform path tracking control on the target vehicle based on the optimized control time sequence.
[0021] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the above-described variable prediction time vehicle path tracking control method.
[0022] The present invention also provides a computer-readable storage medium storing a computer program, which is executed by a processor of the above-described vehicle path tracking control method with variable prediction time.
[0023] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:
[0024] This invention determines the current discrete time step and the current prediction time domain based on the current road conditions and vehicle speed. The vehicle state prediction model outputs the vehicle state prediction time series as the vehicle state at each current discrete time step within the current prediction time domain, realizing vehicle path tracking control with variable prediction time and improving the accuracy and smoothness of path tracking. Attached Figure Description
[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0026] Figure 1 This is a schematic flowchart of a vehicle path tracking control method with variable prediction time provided in an embodiment of the present invention;
[0027] Figure 2 A schematic diagram of a vehicle path tracking control method with variable prediction time provided in an embodiment of the present invention;
[0028] Figure 3 This is a schematic diagram of a two-degree-of-freedom planar vehicle dynamics model provided in an embodiment of the present invention;
[0029] Figure 4 This is a schematic diagram of the path tracking model provided in an embodiment of the present invention;
[0030] Figure 5 This is a schematic diagram of the whale-optimized backpropagation neural network structure provided in an embodiment of the present invention;
[0031] Figure 6 A schematic diagram illustrating the principle of the optimal prediction time model based on a whale-optimized backpropagation neural network provided in an embodiment of the present invention;
[0032] Figure 7 A comparative diagram of path tracking results for three controllers provided in this embodiment of the invention. Figure 1 ;
[0033] Figure 8 A comparison of computation time results for AMPC and VPT-AMPC provided in this embodiment of the invention. Figure 1 ;
[0034] Figure 9This is a schematic diagram comparing the tire slip angle results of LMPC and VPT-AMPC under different constraints provided in the embodiments of the present invention. Figure 1 ;
[0035] Figure 10 A comparative diagram of path tracking results for three controllers provided in this embodiment of the invention. Figure 2 ;
[0036] Figure 11 A comparison of computation time results for AMPC and VPT-AMPC provided in this embodiment of the invention. Figure 2 ;
[0037] Figure 12 This is a schematic diagram comparing the tire slip angle results of LMPC and VPT-AMPC under different constraints provided in the embodiments of the present invention. Figure 2 . Detailed Implementation
[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0039] The purpose of this invention is to provide a vehicle path tracking control method, system, device, and medium with variable prediction time, which improves the accuracy of path tracking.
[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0041] Example 1
[0042] like Figure 1 As shown in the figure, this embodiment provides a vehicle path tracking control method with variable prediction time, which includes the following steps.
[0043] Step 101: Establish a vehicle state prediction model based on the target vehicle's vehicle dynamics model, tire model, and path tracking model.
[0044] Step 102: Based on the current reference path curvature, vehicle longitudinal speed, and road surface adhesion coefficient, the optimal time prediction model is used to output the current optimal prediction time.
[0045] Step 103: Determine the current discrete time step and the current prediction time domain based on the current optimal prediction time.
[0046] Step 104: Input the current vehicle state into the vehicle state prediction model and output the vehicle state prediction time series; the vehicle state prediction time series includes the vehicle state at each current discrete time step within the current prediction time domain.
[0047] Step 105: Construct an objective function for path tracking based on the vehicle state prediction time series; the constraints of the objective function are determined based on the physical constraints of the front wheel steering angle, the front wheel steering angle increment constraints, and the adaptive soft constraints of the front and rear wheel slip angles in the control time domain; the objective function includes the path error between the tracking path and the reference path in the vehicle state prediction time series, the control increment, and the degree of relaxation of the soft constraints.
[0048] Step 106: Optimize the objective function to obtain the optimized control time series.
[0049] Step 107: Perform path tracking control on the target vehicle based on the optimized control time sequence.
[0050] Figure 2 This embodiment presents the principle framework of a vehicle path tracking control method with variable prediction time. The road adhesion coefficient estimator uses existing methods to obtain an estimate of the road adhesion coefficient at the current time step. The variable prediction time module calculates the discrete time step T based on a neural network model. d And the prediction time domain (prediction time range) N p The neural network model utilizes the reference path curvature κ and the vehicle's longitudinal velocity v x The road surface adhesion coefficient μ is used as input. Subsequently, the vehicle state prediction model derives the vehicle tracking state throughout the entire prediction time domain. Based on the current vehicle state, road surface adhesion coefficient, and variable discrete time interval, constraints such as physical limitations, steering angle change rate, and tire slip angle soft constraints are adaptively adjusted. Finally, the path tracking control is formulated as a quadratic optimization problem, and the front wheel steering angle is obtained by solving it, thereby tracking the reference path.
[0051] In step 101, the vehicle dynamics model of the target vehicle is a two-degree-of-freedom planar vehicle dynamics model, such as... Figure 3 As shown, the assumptions for establishing the vehicle dynamics model are:
[0052] 1) The vehicle's roll, pitch, and vertical motion are all negligible;
[0053] 2) The vehicle's longitudinal speed is constant;
[0054] 3) The vehicle configuration is symmetrical on both sides;
[0055] 4) The front wheel steering angle is small enough.
[0056] The Newton-Euler equations for the target car are then expressed as:
[0057]
[0058] Where m is the mass of the target vehicle, v x and v y These are the vehicle's longitudinal and lateral speeds, respectively. For v y The derivative of γ; γ is the yaw rate of the vehicle. F is the derivative of γ; yf and F yr These represent the lateral forces of the front and rear tires, respectively; I z The yaw moment of inertia of the vehicle; f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively.
[0059] In step 101, the tire model is a linear equivalent brush tire model proposed based on the brush tire model. In this embodiment, the tire model is represented as follows:
[0060] F y =C eq α (2)
[0061] Among them, F y α is the lateral force of the tire; α is the tire slip angle; C eq The equivalent tire lateral stiffness can be calculated using the following formula:
[0062]
[0063] Where μ is the road surface adhesion coefficient; F z For the vertical load of the tire; C y For tire lateral stiffness; α sat The saturation sideslip angle is calculated using the following formula:
[0064]
[0065] Based on the assumptions made in the vehicle dynamics model, the front and rear wheel slip angles are:
[0066]
[0067] Where δ is the front wheel steering angle, α f The front wheel slip angle, α r This refers to the rear wheel slip angle.
[0068] In addition, the vertical loads on the front and rear wheels are:
[0069]
[0070] Among them, F zf For the vertical load on the front wheel, F zr ρ is the vertical load on the rear wheel, and g is the acceleration due to gravity.
[0071] Path tracking models such as Figure 4 As shown, the path tracing model is represented as follows:
[0072]
[0073] Among them, e d This represents the lateral distance error between the current position of the vehicle's center of gravity and the orthogonal projection point on the reference path. For e d The derivative of for The derivative; The actual yaw angle of the vehicle Tangent angle with reference path The heading angle error between them for The derivative of for The derivative of .
[0074] Assuming heading angle error If it is small enough, then equation (7) can be written as:
[0075]
[0076] Where κ is the reference path curvature.
[0077] A vehicle state prediction model is established based on the established vehicle dynamics model, tire model, and path tracking model. The vehicle state prediction model is defined as follows:
[0078]
[0079] Where x is the state variable, y is the output variable, w is the disturbance variable, and u is the control variable.
[0080] Therefore, the state space can be defined as:
[0081]
[0082] in, E c =[0 0 0 -v x ] T , C eqf and C eqr These are the equivalent lateral stiffness of the front and rear tires, respectively.
[0083] Discretization is performed using the forward Euler method:
[0084]
[0085] In the formula, A d =I+A c T d B d =B c T d E d =E c T d C d =C c I is the identity matrix, T d Let x(k+1) represent the state variable at time k+1, x(k) represent the state variable at time k, u(k) represent the control variable at time k, w(k) represent the additional variable at time k, and y(k) represent the output variable at time k.
[0086] Augmentation is achieved by incorporating control inputs into the system state:
[0087]
[0088] Where ξ(k) represents the augmented state variable, and u(k-1) represents the control variable at time k-1.
[0089] The augmented state space can then be represented as:
[0090]
[0091] In the formula, Δu=u(k)-u(k-1), C = [C d 0 2×1 ].
[0092] The predicted state at time step k can be represented as:
[0093]
[0094] In the formula, N p For prediction in the time domain; N c To control the time domain, ξ(k|k) is the state variable at time k, ξ(k+1|k) is the state variable at time k+1 predicted from the state variable at time k, ξ(k+2|k) is the vehicle state at time k+2 predicted from the state variable at time k, and ξ(k+N) is the vehicle state at time k+2 predicted from the state variable at time k. c |k) Predict k+N based on the state variables at time k. c The state variable at time ξ(k+N) p|k) Predict k+N based on the state variables at time k. p The state variable at any given time.
[0095] The control time domain is less than or equal to the prediction time domain. The control time domain is determined based on the prediction time domain, and the specific determination is based on experience or test results.
[0096] Therefore, the vehicle state prediction model is: Y(k)=CX(k) (15)
[0097] Among them, Y(k)=[y(k+1|k) y(k+2|k) … y(k+N p |k)] T , Z(k)=[ξ(k+1|k) ξ(k+2|k)… ξ(k+N p |k)] T .
[0098] X(k) represents the augmented state variable sequence in the prediction time domain.
[0099] Combining formula (14), the vehicle state prediction model is expressed as:
[0100] Y(k)=Ψξ(k)+ΘΔU(k)+ΓW(k) (16)
[0101] In the formula,
[0102]
[0103]
[0104]
[0105] Where Y(k) represents the vehicle state prediction time series output by the vehicle state prediction model based on the vehicle state at time k, ΔU(k) is the predicted control signal time series at time k, W(k) is the predicted additional variable time series at time k, and Ψ, Θ, Γ, A, B, C, E, A d B d C d E d A c B c C d E d These are all intermediate parameters. C = [C d 0 2×1 A d =I+A c T d B d =B c Td E d =E c T d C d =C c I is the identity matrix, T d N is the discrete time step. c To control the time domain, N p For prediction in the time domain;
[0106]
[0107]
[0108] E c =[0 0 0 -v x ] T , C eqf C represents the equivalent lateral stiffness of the front tire. eqr Let m be the equivalent lateral stiffness of the rear tire, m be the vehicle mass, and v be the lateral stiffness. x For the longitudinal speed of the vehicle, l f l is the distance from the vehicle's center of gravity to the front axle. r I is the distance from the vehicle's center of gravity to the rear axle. z Let T represent the vehicle's yaw moment of inertia, and T denote the transpose; Δu(k|k) represents the control increment at time k, and Δu(k+1|k) represents the control increment at time k+1 predicted based on the change in front wheel steering angle at time k; Δu(k+N) represents the control increment at time k+1 predicted based on the change in front wheel steering angle at time k. c -1|k) represents the prediction of k+N at time k. c The control increment at time -1, w(k|k) represents the additional variable at time k, w(k+1|k) represents the additional variable at time k+1 predicted from time k, and w(k+N) represents the control increment at time k+1. p -1|k) represents the prediction of k+N at time k. p Additional variables at time -1, N p and N c All are integers greater than 1.
[0109] The formula for calculating the predicted time is: t p =N p T d (17)
[0110] Establish as Figure 5The Whale Optimized Backpropagation (WOA-BP) neural network shown is illustrated. The input layer contains the reference path curvature, vehicle longitudinal speed, and road adhesion coefficient; the output layer contains the corresponding optimal prediction time; and the hidden layer has 10 nodes. Sufficient reference path curvature, vehicle longitudinal speed, road adhesion coefficient, and corresponding optimal prediction time are collected as a dataset, with 90% of the data used as the training set and 10% as the test set. The Whale Optimization (WOA) algorithm is used to optimize the weights and biases in the backpropagation (BP) neural network. The final result is shown below. Figure 6 The figure shows the optimal prediction time model based on the WOA-BP neural network.
[0111] The optimal time prediction model is obtained by training a whale-optimized backpropagation neural network using a training set. The sample data in the training set includes input data and label data. The input data includes reference path curvature, vehicle longitudinal speed, and road surface adhesion coefficient. The label data is the optimal prediction time.
[0112] Step 103 further determines the prediction time domain N at time k in MPC. p (k) and discrete time step T d (k), specifically including:
[0113] 1) If the curvature of the reference path at the current moment is less than the set curvature value, then the preset discrete time step (the default discrete time step T) will be adjusted. d0 Using the current discrete time step as the preset prediction time domain (the default prediction time domain N), the prediction time domain is used as the preset prediction time domain (the default prediction time domain N). p0 This is used as the current prediction time domain. The curvature value is set to 0.005.
[0114]
[0115] 2) If the curvature of the reference path at the current moment is greater than or equal to the set curvature value, the optimal prediction time model trained based on the WOA-BP neural network outputs the corresponding optimal prediction time, and divides it into two cases:
[0116] a) The current optimal prediction time is less than or equal to the preset prediction time domain (t) p,opt (k)≤t p,0 If the preset discrete time step is used as the current discrete time step, the current prediction time domain is calculated based on the current optimal prediction time and the preset discrete time step.
[0117] The current prediction time domain is calculated based on the current optimal prediction time and the preset discrete time step. Specifically, the prediction time domain N at time k is calculated according to formula (17). p (k), and then round up.
[0118]
[0119] b) If the current optimal prediction time is greater than the preset prediction time domain, then the preset prediction time domain is used as the current prediction time domain, and the current discrete time step is calculated based on the current optimal prediction time and the preset prediction time domain.
[0120] The current discrete time step is calculated based on the current optimal prediction time and the preset prediction time domain. Specifically, the discrete time step at time k is calculated according to formula (17).
[0121]
[0122] This method is used to update the predicted temporal domain N within each time step. p (k) and discrete time step T d (k) can improve the accuracy of MPC path tracing without increasing the amount of computation.
[0123] Three constraints are added to the path tracking controller: physical constraint on the front wheel steering angle, incremental constraint on the front wheel steering angle, and adaptive soft constraint on the front and rear wheel slip angles.
[0124] 1) Front wheel steering angle constraint: The control sequence in the control time domain can be predicted by the following formula:
[0125]
[0126] The above expression can be written in the following form:
[0127] U(k)=U k-1 (k)+A I ΔU(k) (22)
[0128] In the formula, U(k)=[u(k∣k)u(k+1∣k)…u(k+N c -1∣k)] T ,
[0129] The front wheel steering angle should be subject to physical constraints, namely:
[0130] U min ≤U(k)≤U max (twenty three)
[0131] In the formula, δ min and δ max These are the minimum and maximum front wheel steering angles, respectively.
[0132] Combining formula (22), the inequality constraint can be written as:
[0133]
[0134] 2) Variable Constraints on Front Wheel Steering Angle Increment: Within the prediction time domain, the constraints on the control increment should also change according to the varying discrete time steps in the prediction model. Therefore, the variable constraint is:
[0135] ΔU min (k)≤ΔU(k)≤ΔU max (k) (25)
[0136] In the formula, ΔU min (k)=-ΔU max (k), ω max This represents the maximum steering angular velocity of the front wheels.
[0137] 3) Adaptive Tire Slip Angle Soft Constraint: To reduce potential instability during vehicle operation, it is crucial to ensure that both front and rear tire slip angles remain within the linear region. Furthermore, the tire should be able to enter the non-linear region to maximize the utilization of the road adhesion coefficient, but not reach the saturation limit. Therefore, the adaptive soft constraint can be expressed as:
[0138]
[0139] In the formula, p is a constant in the range [0,1] as a scaling factor; α f,sat (k) and α r,sat (k) represents the saturated sideslip angle of the front and rear wheels; ε f (k) and ε r (k) are respectively [0, (1-p)α f,sat [k)] and [0, (1-p)α r,sat Slack variables within the range of [k], α f (k) is the front wheel slip angle at time k, α r (k) represents the rear wheel slip angle at time k.
[0140] According to formula (5), the front and rear wheel slip angles can be predicted by the following formula:
[0141]
[0142] In the formula, Y f (k)=[α f (k+1|k) α f (k+2|k)…α f (k+N p ∣k)] T Y r (k)=[α r (k+1|k) αr (k+2|k) … α r (k+N p ∣k)] T C f =[1 / v x l r / v x [0 0 -1], C r =[1 / v x -l r / v x 0 0 0].
[0143] Among them, Y f (k) represents the sequence of the front wheel slip angle in the prediction time domain, Y r (k) represents the sequence of the rear wheel slip angle in the prediction time domain, C f and C r It is a coefficient matrix.
[0144] Similar to formula (16), the above formula can be written as:
[0145]
[0146] Combining formula (26), the constraint output in the predicted time domain is:
[0147]
[0148] In the formula, Y f,min (k)=-Y f,max (k), Y r,min (k)=-Y r,max (k),
[0149] Based on formulas (24), (25), and (29), these three types of constraints can be summarized as follows:
[0150]
[0151]
[0152] in, N c For the control time domain, W(k) represents the time series of the additional variables predicted at time k, ΔU(k) is the time series of the control signal predicted at time k, and ε f (k) represents the first slack variable, ε r (k) represents the second slack variable, ε f The range of values for (k) is [0, (1-p)αf,sat (k)],ε r The range of values for (k) is [0, (1-p)α r,sat (k)],α f,sat (k) is the front wheel saturation sideslip angle at time k, α r,sat (k) is the rear wheel saturation sideslip angle at time k. δ min and δ max These are the minimum and maximum front wheel steering angles, Θ. f and Θ f Both are coefficient matrices, U k-1 (k) represents the sequence of control variables at time k-1, Y f,max (k) represents the sequence of maximum front wheel slip angles, Y f,min (k) represents the sequence of minimum front wheel slip angles, Y r,max (k) represents the sequence of maximum rear wheel slip angles, Y r,min (k represents the sequence of minimum rear wheel slip angles, Ψ) f and Ψ r Let Γ be the coefficient matrix. f and Γ r Let ΔU be the coefficient matrix. min (k) represents the sequence controlling the minimum increment, ΔU max (k) represents the sequence that controls the maximum value of the increment.
[0153] The purpose of a path-following controller is to facilitate vehicle travel along a reference path. This requires minimizing lateral distance and heading angle errors relative to the reference path. Furthermore, smooth control is desirable to avoid sudden changes.
[0154] The objective function for path tracing is expressed as:
[0155]
[0156] Where J represents the objective function value, Y(k) represents the vehicle state prediction time series output by the vehicle state prediction model based on the vehicle state at time k, and ΔU(k) is the predicted control signal time series at time k. and These are all intermediate parameters. Q is the weight matrix for the system output increment, R is the weight matrix for the system control input increment, and N... c To control the time domain, N p For the prediction time domain, ρ is the weighting coefficient of the relaxation factor, and ε f (k) represents the first slack variable, ε r (k) represents the second slack variable, ε fThe range of values for (k) is [0, (1-p)α f,sat (k)],ε r The range of values for (k) is [0, (1-p)α r,sat (k)], p is the scaling factor, and the value of p ranges from [0,1], α f,sat (k) is the front wheel saturation sideslip angle at time k, α r,sat (k) is the rear wheel saturation sideslip angle at time k.
[0157] The first term in the objective function represents the accuracy of the tracking performance, the second term represents the smoothness of the control input, and the third term represents the relaxation level of the solution.
[0158] The constraints of the objective function are given by formulas (30) and (31).
[0159] Therefore, the trajectory tracking problem can be transformed into a quadratic programming problem:
[0160]
[0161] Formulas (30) and (31) are given.
[0162] In the formula, H and f are both intermediate parameters.
[0163] The optimal control sequence Δu can be solved from formula (33). * Due to the adaptive discrete time step T d (k) and controller execution time step T s The inconsistency in the optimal control input u(k), i.e., the front wheel steering angle of the car, can be calculated by the following formula:
[0164]
[0165] In the formula, u(k-1) is the front wheel steering angle of the vehicle at the previous time step (time k-1).
[0166] In this embodiment, joint simulation tests were conducted using the vehicle dynamics software CarSim and the mathematical software MATLAB / Simulink. Two typical scenarios were designed, using the same double lane change reference path but with different vehicle speeds and road adhesion coefficients. To highlight the advantages of this method, three controllers were used for comparison:
[0167] 1. The first controller is LMPC: Utilizing the two-degree-of-freedom vehicle planar dynamics, linear equivalent brush tire model, and path tracking model in this invention, MPC calculations are performed under constant constraints and a fixed prediction time (i.e., a fixed prediction time domain and discrete time step). The constant constraint condition for tire sideslip with relaxation variables is set to [-5,5]deg.
[0168] 2. The second type of controller is AMPC: an MPC controller similar to LMPC, but which uses the adaptive constraints in the method of this invention.
[0169] 3. The third type of controller is VPT-AMPC: The controller generated using the method of this invention uses adaptive constraints and variable prediction time.
[0170] The default prediction time domain is 20s, and the default discrete time step is 0.02s (consistent with the controller sampling time step).
[0171] Example 1: In this scenario, the longitudinal vehicle speed is set to 54 km / h, and the road surface adhesion coefficient is set to 0.7. Figure 7 and Figure 8 The path tracking performance and computation time of the controller are described separately. Table 1 lists the quantitative results of Example 1, including the maximum lateral error e. max Horizontal root mean square error e RMSE And the total computation time T for all simulation steps c . Figure 9 The tire slip angles under different constraint conditions for LMPC and VPT-AMPC are shown. Figure 9 (a) is the front wheel slip angle. Figure 9 (b) represents the rear wheel slip angle.
[0172] Table 1. Quantitative results from Example 1
[0173]
[0174] Figure 7 In the simulation, using a linear equivalent brush tire model, all three controllers demonstrated satisfactory tracking performance. Specifically, LMPC and AMPC exhibited similar tracking performance, hence their curves largely overlapped, and VPT-AMPC's e max and e RMSE Smaller Figure 7 (a) shows a comparison of the lateral positions of the tracking paths of the three controllers. Figure 7 (b) shows a comparison of the lateral deviations of the tracking paths of the three controllers. Figure 7 (c) shows a comparison of the front wheel steering angles between the three controllers. Figure 7(d) shows a comparison of the centroid sideslip angles of the three controllers. As shown in Table 1, compared to LMPC and AMPC, e max and e RMSE The accuracy was reduced by 10.91% and 20.41% respectively, demonstrating that the method has higher tracking accuracy. Figure 8 In (a), the prediction time of VPT-AMPC decreases at the corresponding position, as shown below. Figure 8 The prediction time domain shown in (b) is also reduced accordingly, and the computation time of the final controller is also reduced. Figure 8 (c) demonstrates that this method can improve the computational efficiency of the controller. Figure 8 The front and rear wheel slip angles of both the LMPC and VPT-AMPC are within their respective constraints and the constraint conditions are not triggered.
[0175] Example 2: In this scenario, the longitudinal vehicle speed is set to 72 km / h, and the road surface adhesion coefficient is set to 0.3. Figure 10 and Figure 11 The path tracking performance and computation time of the controller are described respectively. Figure 10 (a) shows a comparison of the lateral positions of the tracking paths of the three controllers. Figure 10 (b) shows a comparison of the lateral deviations of the tracking paths of the three controllers. Figure 10 (c) shows a comparison of the front wheel steering angles between the three controllers. Figure 10 (d) shows a comparison of the centroid sideslip angles of the three controllers. Table 2 lists the quantitative results of Example 2, including the maximum lateral error e. max Horizontal root mean square error e RMSE And the total computation time T for all simulation steps c . Figure 12 The tire slip angles under different constraint conditions for LMPC and VPT-AMPC are shown.
[0176] Table 2. Quantitative results from Example 2
[0177]
[0178] Figure 10 This demonstrates that VPT-AMPC in this embodiment can better track the reference path, while LMPC and AMPC both exhibit significant lateral and yaw rate deviations. Table 2 illustrates the e-values of VPT-AMPC. max and e RMSE Compared to AMPC, the accuracy decreased by 47.16% and 47.76% respectively, demonstrating that this method can improve path tracking accuracy. In addition, VPT-AMPC also exhibits certain advantages in vehicle lateral stability. Figure 10In example (d), the maximum sideslip angle of the VPT-AMPC is 1.28 degrees, which is smaller than the maximum sideslip angle of the AMPC (2.76 degrees), demonstrating the effectiveness of this method in improving vehicle stability. In this embodiment, the prediction time of the VPT-AMPC is as follows... Figure 11 As shown in (a), the adaptive increase occurs, and in this case, the discrete time step of the controller is as follows: Figure 11 The corresponding increase is shown in (b). Since the discrete time step does not affect the controller's computation time, therefore... Figure 11 The calculation time of the controller in (c) remains unchanged. Figure 12 In LMPC, the use of fixed constraints forces the rear wheel slip angle to exceed the constraints to obtain a feasible solution, thus affecting vehicle stability. Figure 12 (a) is the front wheel slip angle. Figure 12 In Figure (b), the rear wheel slip angle is shown. The front wheel slip angle of the VPT-AMPC is constrained by adaptive constraints, while the rear wheels always meet the constraints, ensuring the lateral stability of the vehicle.
[0179] Example 2
[0180] This embodiment provides a vehicle path tracking control system with variable prediction time, including:
[0181] The vehicle state prediction model building module is used to build a vehicle state prediction model based on the target vehicle's vehicle dynamics model, tire model, and path tracking model.
[0182] The optimal prediction time prediction module is used to output the current optimal prediction time based on the current reference path curvature, vehicle longitudinal speed and road adhesion coefficient using the optimal time prediction model.
[0183] The discrete time step and prediction time domain determination module is used to determine the current discrete time step and the current prediction time domain based on the current optimal prediction time.
[0184] The vehicle state prediction time series determination module is used to input the vehicle state at the current moment into the vehicle state prediction model and output the vehicle state prediction time series; the vehicle state prediction time series includes the vehicle state at each current discrete time step within the current prediction time domain.
[0185] The objective function construction module for path tracking is used to construct the objective function for path tracking based on the vehicle state prediction time series. The constraints of the objective function are determined based on the physical constraints of the front wheel steering angle, the front wheel steering angle increment constraints, and the adaptive soft constraints of the front and rear wheel slip angles in the control time domain. The objective function includes the path error between the tracking path and the reference path in the vehicle state prediction time series, the control increment, and the degree of relaxation of the soft constraints.
[0186] The objective function optimization module is used to optimize the objective function to obtain the optimized control time series;
[0187] The path tracking control module is used to perform path tracking control on the target vehicle based on the optimized control time sequence.
[0188] Example 3
[0189] This embodiment provides an electronic device, including a memory and a processor. The memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the vehicle path tracking control method with variable prediction time as described in Embodiment 1.
[0190] This embodiment also provides a computer-readable storage medium storing a computer program, which is executed by a processor using the vehicle path tracking control method with variable prediction time described in Embodiment 1.
[0191] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.
[0192] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A vehicle path tracking control method with variable prediction time, characterized in that, include: A vehicle state prediction model is established based on the vehicle dynamics model, tire model, and path tracking model of the target vehicle. Based on the current reference path curvature, vehicle longitudinal speed, and road surface adhesion coefficient, an optimal time prediction model is used to output the current optimal prediction time. The optimal time prediction model is obtained by training a whale-optimized backpropagation neural network using a training set. The sample data in the training set includes input data and label data. The input data includes the reference path curvature, vehicle longitudinal speed, and road surface adhesion coefficient, and the label data is the optimal prediction time. Determine the current discrete time step and the current prediction time domain based on the current optimal prediction time. The vehicle state at the current moment is input into the vehicle state prediction model, and the vehicle state prediction time series is output; the vehicle state prediction time series includes the vehicle state at each current discrete time step within the current prediction time domain. The objective function for path tracking is constructed based on the vehicle state prediction time series. The constraints of the objective function are determined based on the physical constraints of the front wheel steering angle, the front wheel steering angle increment constraints, and the adaptive soft constraints of the front and rear wheel slip angles in the control time domain. The objective function includes the path error between the tracking path and the reference path in the vehicle state prediction time series, the control increment, and the degree of relaxation of the soft constraints. The objective function is optimized to obtain the optimized control time series; The target vehicle is subjected to path tracking control based on the optimized control time sequence.
2. The vehicle path tracking control method with variable prediction time according to claim 1, characterized in that, The vehicle state prediction model is expressed as follows: ； In the formula, ; ； ； ； ； in, This represents the vehicle state prediction time series output by the vehicle state prediction model based on the vehicle state at time k. The time series of the control signal predicted at time k. For the additional variable time series predicted at time k, , , , , , , , , , , , , , , These are all intermediate parameters. , , , , , , , , It is the identity matrix. For discrete time steps, To control the time domain, For prediction in the time domain; ； ； , ; This represents the equivalent lateral stiffness of the front tire. This represents the equivalent lateral stiffness of the rear tire. For vehicle quality, For the longitudinal speed of the vehicle, This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. Let the vehicle's yaw moment of inertia be... T Indicates transpose; This represents the control increment at time k. This represents the increment of the control quantity predicted at time k+1 from time k. Represents the prediction of k at time k. Increment of control quantity at any given time, This represents the additional variable at time k. This represents the additional variable predicted at time k+1 from time k. Represents the prediction at time k Additional variables at time, and All are integers greater than 1.
3. The vehicle path tracking control method with variable prediction time according to claim 1, characterized in that, The current discrete time step and the current prediction time domain are determined based on the current optimal prediction time, specifically including: If the curvature of the reference path at the current moment is less than the set curvature value, then the preset discrete time step is used as the current discrete time step, and the preset prediction time domain is used as the current prediction time domain. If the curvature of the reference path at the current moment is greater than or equal to the set curvature value, and the current optimal prediction time is less than or equal to the preset prediction time domain, then the preset discrete time step is used as the current discrete time step, and the current prediction time domain is calculated based on the current optimal prediction time and the preset discrete time step. If the curvature of the reference path at the current moment is greater than or equal to the set curvature value, and the current optimal prediction time is greater than the preset prediction time domain, then the preset prediction time domain is used as the current prediction time domain, and the current discrete time step is calculated based on the current optimal prediction time and the preset prediction time domain.
4. The vehicle path tracking control method with variable prediction time according to claim 1, characterized in that, The objective function for path tracing is expressed as: ； in, Represents the objective function value. This represents the vehicle state prediction time series output by the vehicle state prediction model based on the vehicle state at time k. The time series of the control signal predicted at time k. and These are all intermediate parameters. , , The system outputs an incremental weight matrix. The weight matrix for the system control input increment. To control the time domain, To predict the time domain, These are the weighting coefficients of the relaxation factor. Denotes the first slack variable. Represents the second slack variable. The range of values is , The range of values is , As a scaling factor, The range of values is , Let k be the front wheel saturation sideslip angle. Let be the rear wheel saturation sideslip angle at time k.
5. The vehicle path tracking control method with variable prediction time according to claim 1, characterized in that, The constraints of the objective function are expressed as follows: ； ； in, , To control the time domain, This represents the time series of additional variables predicted at time k. The time series of the control signal predicted at time k. Denotes the first slack variable. Represents the second slack variable. The range of values is , The range of values is , Let k be the front wheel saturation sideslip angle. Let k be the rear wheel saturation sideslip angle at time k. , , and These are the minimum and maximum front wheel steering angles, respectively. Both are coefficient matrices. This represents the sequence of control variables at time k-1. A sequence representing the maximum front wheel slip angle. This represents the sequence of minimum front wheel slip angles. A sequence representing the maximum rear wheel slip angle. This represents the sequence of minimum rear wheel slip angles. and The coefficient matrix, and Both are coefficient matrices. This represents a sequence that controls the minimum increment. This represents a sequence that controls the maximum value of the increment.
6. A vehicle path tracking control system with variable prediction time, characterized in that, The variable prediction time vehicle path tracking control system applies the variable prediction time vehicle path tracking control method of claim 1, wherein the variable prediction time vehicle path tracking control system comprises: The vehicle state prediction model building module is used to build a vehicle state prediction model based on the target vehicle's vehicle dynamics model, tire model, and path tracking model. The optimal prediction time prediction module is used to output the current optimal prediction time based on the current reference path curvature, vehicle longitudinal speed and road adhesion coefficient using the optimal time prediction model. The discrete time step and prediction time domain determination module is used to determine the current discrete time step and the current prediction time domain based on the current optimal prediction time. The vehicle state prediction time series determination module is used to input the vehicle state at the current moment into the vehicle state prediction model and output the vehicle state prediction time series; the vehicle state prediction time series includes the vehicle state at each current discrete time step within the current prediction time domain. The objective function construction module for path tracking is used to construct the objective function for path tracking based on the vehicle state prediction time series. The constraints of the objective function are determined based on the physical constraints of the front wheel steering angle, the front wheel steering angle increment constraints, and the adaptive soft constraints of the front and rear wheel slip angles in the control time domain. The objective function includes the path error between the tracking path and the reference path in the vehicle state prediction time series, the control increment, and the degree of relaxation of the soft constraints. The objective function optimization module is used to optimize the objective function to obtain the optimized control time series; The path tracking control module is used to perform path tracking control on the target vehicle based on the optimized control time sequence.
7. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to cause the electronic device to perform the vehicle path tracking control method with variable prediction time according to any one of claims 1 to 5.
8. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the vehicle path tracking control method with variable prediction time as described in any one of claims 1 to 5.