Cooperative control method for front and rear wheel turning angles of drive-by-wire four-wheel steering vehicle

Abstract

The invention relates to a cooperative control method for front and rear wheel turning angles of a drive-by-wire four-wheel steering vehicle, which belongs to the technical field of vehicle dynamics control, and comprises the following steps of: S1, designing a variable angle transmission ratio of the drive-by-wire front wheel steering vehicle on the basis of invariable steady-state yaw velocity gain; s2, calculating a target side slip angle and a target yaw velocity of the drive-by-wire front wheel steering vehicle based on a given steering wheel angle input; and S3, generating a front wheel steering angle and a rear wheel steering angle of the drive-by-wire four-wheel steering vehicle by taking the dynamic output of the front wheel steering vehicle as a target based on a multi-objective optimization framework of model predictive control MPC. The control inconsistency of the steering system caused by the change of the vehicle speed is avoided, the steering characteristics of the front wheel steer-by-wire vehicle can be accurately tracked, and the driving burden is effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle dynamics control and relates to a method for coordinated control of front and rear wheel angles of a wire-controlled four-wheel steering vehicle. Background Art

[0002] With the rapid development of advanced driver assistance systems (ADAS) such as adaptive cruise control (ACC) and automated parking, front-wheel steering systems are gradually transitioning from traditional mechanical linkages to steer-by-wire (SBW) systems. The core advantage of SBW systems lies in the complete decoupling of the mechanical connection between the steering wheel and steering mechanism. Steering is performed by an electric motor controlled by electrical signals, achieving a highly electronic and intelligent steering system. This structural decoupling allows the SBW system to flexibly set the steering ratio, enabling real-time adjustments based on a variety of factors, including vehicle speed, dynamic conditions, and driver needs. This ensures a certain degree of steering sensitivity at low speeds and sluggishness at high speeds, effectively reducing the driver's workload.

[0003] The rear-wheel steer-by-wire system (RWS) is connected to the rear wheel toe rods, and a motor controls the left and right movement of the rods to achieve active rear-wheel steering. This system dynamically adjusts the rear wheel steering angle based on vehicle speed, thereby reducing the turning radius and improving maneuverability at low speeds. At high speeds, the system must maintain the same steering sensitivity as a traditional front-wheel steering vehicle while also maintaining a good vehicle trajectory and posture. Specifically, the yaw rate gain must be similar to that of a traditional front-wheel steering vehicle, and the sideslip angle must be as close to zero as possible.

[0004] However, currently, variable steering ratios for the front wheels and rear wheel angle control are mostly designed independently, lacking systematic research and design methods for coordinated front and rear wheel steering angle control. This decoupling of front and rear wheel steering control limits further improvements in vehicle handling performance, making it difficult to achieve optimal vehicle dynamic response, especially under complex operating conditions. Summary of the Invention

[0005] In view of this, an object of the present invention is to provide a method for coordinated control of front and rear wheel angles of a wire-controlled four-wheel steering vehicle.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for coordinated control of front and rear wheel angles of a wire-controlled four-wheel steering vehicle comprises the following steps:

[0008] S1: Design of variable angle transmission ratio for steer-by-wire front-wheel vehicle based on the constant steady-state yaw rate gain;

[0009] S2: Calculate the target sideslip angle and yaw rate of the steer-by-wire vehicle based on the given steering wheel angle input;

[0010] S3: A multi-objective optimization framework based on Model Predictive Control (MPC) generates the front and rear wheel steering angles of a 4WD vehicle with a front-wheel steering vehicle as the target.

[0011] Furthermore, the design of the variable angle transmission ratio of the front-wheel steer-by-wire vehicle based on the constant steady-state yaw rate gain in step S1 specifically includes the following steps:

[0012] S11: Based on Newton's second law, the differential equation of the lateral dynamics model of a two-wheeled vehicle with two degrees of freedom is established, which is expressed as:

[0013]

[0014] Where m is the vehicle mass, I z is the vehicle mass, l f is the distance from the front axle to the center of mass of the vehicle, l r is the distance from the rear axle to the center of mass of the vehicle, v x is the vehicle longitudinal velocity, is the vehicle's lateral acceleration, r is the vehicle's yaw rate, is the vehicle yaw angular acceleration, F yf is the lateral force of the front tire, F yr is the lateral force of the rear tire;

[0015] S12: In the differential equation, replace the tire lateral force with the cornering stiffness C α The product of the tire slip angle α is:

[0016]

[0017] Among them C αf is the front wheel cornering stiffness, C αr is the rear wheel cornering stiffness; α f is the front wheel slip angle, α r is the rear wheel slip angle, and the calculation formula for the front and rear wheel slip angles is:

[0018]

[0019] where v y is the vehicle lateral velocity, δ f is the vehicle's front wheel turning angle;

[0020] Rewrite the original differential equation as:

[0021]

[0022] S13: Let the vehicle lateral speed v y The derivative of the vehicle yaw rate r is 0, and the steady-state response of the two-degree-of-freedom model is obtained, which is expressed as:

[0023]

[0024] Combining the rewritten differential equation with the steady-state response of the two-degree-of-freedom model, we can obtain the yaw rate r and the front wheel angle δ f The display expression k γ :

[0025]

[0026] Where L is the wheelbase and K is the stability factor, which is calculated as follows:

[0027]

[0028] Convert the front wheel angle into the steering wheel angle and introduce the steering system transmission ratio into the calculation formula of the steady-state yaw rate gain;

[0029] S14: Calculate the vehicle's steady-state yaw rate gain k w , as shown below:

[0030]

[0031] where δ sw is the steering wheel angle, i is the variable angle transmission ratio of the ideal front wheel steer-by-wire vehicle;

[0032] S15: Calculate the variable angle transmission ratio of the ideal front wheel steer-by-wire vehicle as shown in the following formula:

[0033]

[0034] Among them, i min is the minimum value of the angular transmission ratio, i max is the maximum value of the angular transmission ratio, u1 is the lower critical speed, and u2 is the upper critical speed.

[0035] Furthermore, step S2 calculates the target sideslip angle and target yaw rate of the front-steer-by-wire vehicle based on the given steering wheel angle input, specifically including the following steps:

[0036] S21: Calculate the steady-state yaw rate gain k w Display expressions at different vehicle speeds:

[0037]

[0038] Where K1 is the desired yaw rate gain, that is, the yaw rate gain increases with vehicle speed in the low-speed zone, remains constant in the medium-speed zone, and increases with vehicle speed in the high-speed zone.

[0039] S22: Calculate the target yaw rate r of the front-wheel steering vehicle * :

[0040] r * =k w δ sw

[0041] S23: Considering the vehicle's response characteristics and the driver's burden, the target center of mass side slip angle β of the front-wheel steering vehicle is obtained. * :

[0042] β * =0.

[0043] Furthermore, the multi-objective optimization framework based on model predictive control in step S3 generates the front wheel steering angle and the rear wheel steering angle of the wire-controlled four-wheel steering vehicle with the dynamic output of the front-wheel steering vehicle as the target, specifically including the following steps:

[0044] S31: Considering the coupling characteristics of the vehicle's lateral motion and yaw motion, construct the state space expression of the controlled system;

[0045] S32: In the prediction time domain, based on the current system state observation value x(k) and the future control input sequence U=[u(k|k),u(k+1|k),…,u(k+N c -1|k)], and recursively predict the future N by discretizing the state space equation p The state sequence and output sequence of the step system:

[0046]

[0047] y(k+i|k)=Cx(k+i|k),i=1,2,…,N p

[0048] The prediction time domain N p and control time domain N c Satisfy N c ≤N p ; A i is the i-th power of the system matrix A, which represents the evolution of the state after i steps. i-j-1 To describe the influence of input u(k+j|k) on the future state, B is the control matrix and C is the output matrix;

[0049] S33: Construct the objective function of the optimization problem;

[0050] S34: Define constraints and explicitly embed them into the optimization problem;

[0051] S35: Solve the optimization problem using the quadratic programming method to obtain the optimal control input sequence;

[0052] S36: Apply the first control variable to the controlled system. When the system advances to the next sampling moment, update the state estimation and rolling prediction time domain, and re-execute steps S31-S35 to realize closed-loop model predictive control.

[0053] Furthermore, step S31 specifically includes the following steps:

[0054] S311: Considering the coupling characteristics of the vehicle's lateral motion and yaw motion, construct the two-degree-of-freedom dynamic differential equation of the four-wheel steering vehicle:

[0055]

[0056] in is the sideslip angular velocity of the center of mass, δ r is the rear wheel turning angle of the vehicle, β is the sideslip angle of the center of mass;

[0057] S312: Based on the lateral dynamics differential equation of a two-degree-of-freedom four-wheel vehicle, assuming that the sideslip angle β and the yaw angular velocity r are known, the state space of the controlled object is established:

[0058]

[0059] where the state vector x = [β, r] T , control input vector u=[δ f ,δ r ], output vector y = [β, r] T , A is the system matrix, B is the control matrix, and C is the output matrix; the expressions of each matrix are as follows:

[0060]

[0061] in:

[0062]

[0063] Furthermore, step S33 constructs the objective function of the optimization problem, specifically including the following steps:

[0064] S331: Construct a weighted quadratic cost function that minimizes tracking error and control input:

[0065]

[0066] Where Q is the weight matrix of tracking state error, and R is the weight matrix of control input;

[0067] S332: Expand the weighted quadratic cost function into a matrix form:

[0068] J=Y T QY+U T RU

[0069] where Y=[y(k+i|k),…,y(k+N p |k)] T To predict the output sequence, and is the weight matrix, r(k+i) is the reference from the vehicle two-degree-of-freedom lateral dynamics model (v y ,r)trajectory.

[0070] Furthermore, the constraints in step S34 include input, output and state constraints;

[0071] Embed constraints into the optimization problem, including:

[0072] The input constraints are determined by the actuator physical constraints:

[0073] |δ f |≤δ fmax

[0074] |δ r |≤δ rmax

[0075] where δ fmax is the maximum front wheel turning angle, δ rmax is the maximum rear wheel turning angle;

[0076] Output or state quantity constraints are determined by stability bounds:

[0077] |β|≤β max

[0078]

[0079] where β max is the maximum sideslip angle at the center of mass, μ is the road adhesion coefficient, g is the acceleration of gravity, and v is the vehicle speed.

[0080] Furthermore, the step S35 of solving the optimization problem includes:

[0081] Substitute the prediction model into the objective function and construct a quadratic programming problem with U as the optimization variable:

[0082]

[0083] Among them, the second-order sensitivity matrix G of the control input to the objective function and the linear driving vector F of the deviation between the reference vector and the current state prediction to the objective function are generated by the system model and the weight matrix. The constraint matrix G and the constraint vector h are constructed by the constraint conditions, as follows:

[0084] Hessian matrix H and linear term vector F:

[0085]

[0086] in, is a lower triangular matrix with elements Where i ≥ j;

[0087]

[0088] Constraint matrix G and constraint vector h:

[0089]

[0090] Among them, G u , G Δu and G y are the control quantity, control quantity change rate and output quantity constraint matrix respectively, h u 、h Δu 、h y They are the control quantity, the control quantity change rate and the output quantity constraint vector:

[0091]

[0092] in, mN c ×mN c The identity matrix of represents the Kronecker product, Is of length N c All 1 vectors; u max =[u 1,max ,..,u m,max ] T ,u min =[u 1,min ,..,u m,min ] T ;

[0093]

[0094] Where D is N c-1 ×N c The difference matrix of

[0095]

[0096] The beneficial effects of the present invention are:

[0097] 1) This paper proposes a front wheel variable angle transmission ratio design method based on a constant steady-state yaw rate gain. By maintaining the yaw response characteristics at different vehicle speeds, the control inconsistency caused by vehicle speed changes in traditional steering systems is minimized.

[0098] 2) The present invention designs a four-wheel steering multi-objective predictive control architecture, which accurately tracks the steering characteristics of front-wheel steer-by-wire vehicles by unifying the modeling of front and rear wheel angle amplitude constraints, yaw angular velocity, and center of mass sideslip angle tracking error penalties, effectively reducing the driving burden.

[0099] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0101] Figure 1 This is a logic structure diagram of the coordinated control of the front and rear wheel angles of a wire-controlled four-wheel steering vehicle;

[0102] Figure 2 Schematic diagram of the two-degree-of-freedom vehicle lateral dynamics model;

[0103] Figure 3 Schematic diagram of the steering ratio of a front-wheel steer-by-wire vehicle based on a constant steady-state yaw rate gain;

[0104] Figure 4 is the steady-state yaw rate gain k w Schematic diagram at different vehicle speeds. DETAILED DESCRIPTION

[0105] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0106] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0107] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the embodiments of the present invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring the embodiments of the present invention.

[0108] Example 1:

[0109] like Figures 1 to 4 As shown, the present invention provides a method for coordinated control of front and rear wheel angles of a wire-controlled four-wheel steering vehicle, which specifically includes the following steps:

[0110] Step S1: Designing the steering transmission ratio of the front-wheel steer-by-wire vehicle based on the constant steady-state yaw rate gain, specifically comprising the following steps:

[0111] S11: Establish its differential equation as follows:

[0112]

[0113] Where m is the vehicle mass, I z is the vehicle mass, l f is the distance from the front axle to the center of mass of the vehicle, l r is the distance from the rear axle to the center of mass of the vehicle, v x is the vehicle longitudinal velocity, is the vehicle's lateral acceleration, r is the vehicle's yaw rate, is the vehicle yaw angular acceleration, F yf is the lateral force of the front tire, F yr is the lateral force on the rear tire.

[0114] S12: Write the tire lateral force as the cornering stiffness C α The product of the sideslip angle α is:

[0115]

[0116] The calculation formula for the front and rear wheel slip angle α is:

[0117]

[0118] where v y is the vehicle lateral velocity, δ f is the vehicle's front wheel turning angle.

[0119] Rewrite the original differential equation as:

[0120]

[0121] S13: Steady-state response of the two-degree-of-freedom model:

[0122]

[0123] Combining the above two equations, we can get the yaw rate r and the front wheel angle δ f The display expression k γ

[0124]

[0125] Where L is the wheelbase and K is the stability factor, which can be calculated as follows:

[0126]

[0127] Convert the front wheel angle in the above equation into the steering wheel angle, and introduce the steering system transmission ratio into the calculation formula of the steady-state yaw rate gain;

[0128] S14: The vehicle steady-state yaw rate gain k w Such as:

[0129]

[0130] where δ sw is the steering wheel angle, i is the variable angle transmission ratio of the ideal front wheel steer-by-wire vehicle;

[0131] To prevent the vehicle from being too sensitive at low speeds and too slow at high speeds, the variable angle transmission ratio of an ideal steer-by-wire vehicle should be limited.

[0132] S15: The variable angle transmission of an ideal wire-controlled front-wheel steering vehicle is as follows:

[0133]

[0134] Among them, i min is the minimum value of the angular transmission ratio, i max is the maximum value of the angular transmission ratio, u1 is the lower critical speed, and u2 is the upper critical speed;

[0135] Step S2: Calculating a target sideslip angle and a target yaw rate of the front-steer-by-wire vehicle based on a given steering wheel angle input, specifically comprising the following steps:

[0136] S21: Steady-state yaw rate gain k w Display expressions at different vehicle speeds:

[0137]

[0138] Where K1 is the desired yaw rate gain, that is, the yaw rate gain increases with vehicle speed in the low-speed zone, remains constant in the medium-speed zone, and increases with vehicle speed in the high-speed zone.

[0139] S22: Target yaw rate of the front-wheel steer-by-wire vehicle:

[0140] r * =k w δ sw (10)

[0141] S23: Taking into account the vehicle's response characteristics and driver burden, the target center of mass slip angle of the steer-by-wire vehicle is:

[0142] β * =0 (11)

[0143] Step S3: Based on a multi-objective optimization framework of model predictive control (MPC), the front wheel steering angle and the rear wheel steering angle of the steer-by-wire vehicle are generated with the dynamic output of the steer-by-wire vehicle as the target, specifically including the following steps:

[0144] S31: Constructing the two-degree-of-freedom dynamic differential equations for a four-wheel steering vehicle

[0145]

[0146] in is the sideslip angular velocity of the center of mass, δ r is the rear wheel turning angle of the vehicle, β is the sideslip angle of the center of mass;

[0147] State Space:

[0148]

[0149] where the state vector x = [β, r]T , control input vector u=[δ f ,δ r ], output vector y = [β, r] T , A is the system matrix, B is the control matrix, and C is the output matrix. The matrices are expressed as follows:

[0150]

[0151] in

[0152]

[0153] S32: System status and output prediction:

[0154] Based on the current state of the system x(k) and the future control sequence U=[u(k|k),u(k+1|k),…,u(k+N c -1|k)], predicting the future N of the system p Step status and output:

[0155]

[0156] y(k+i|k)=Cx(k+i|k), (i=1,2,…,N p ) (twenty four)

[0157] where N p is the prediction time domain, N c To control the time domain (N c ≤N p );A i is the i-th power of the system matrix A, which represents the evolution of the state after i steps. i-j-1 To describe the impact of input u(k+j|k) on the future state.

[0158] S33: Construct optimization objective function:

[0159] The weighted quadratic cost function that minimizes the tracking error and control input is:

[0160]

[0161] in is the sideslip angular velocity of the center of mass, δ r is the rear wheel turning angle of the vehicle, β is the sideslip angle of the center of mass;

[0162] Expanded into matrix form:

[0163] J=Y T QY+U T RU (26)

[0164] where Y=[y(k+i|k),…,y(k+N p |k)] T To predict the output sequence, and is the weight matrix, r(k+i) is the reference from the vehicle two-degree-of-freedom lateral dynamics model (v y ,r)trajectory.

[0165] S34: Define constraints:

[0166] Explicitly embed input, output, or state constraints into the optimization problem:

[0167] The input constraints are determined by the actuator physical constraints:

[0168] |δ f |≤δ fmax (27)

[0169] |δ r |≤δ rmax (28)

[0170] where δ fmax is the maximum front wheel turning angle, δ rmax is the maximum rear wheel turning angle;

[0171] The output or state constraints are determined by the stability bounds:

[0172] |β|≤β max (29)

[0173]

[0174] where β max is the maximum sideslip angle at the center of mass, μ is the road adhesion coefficient, g is the acceleration of gravity, and v is the vehicle speed.

[0175] S35: Solve the optimization problem and obtain the control input:

[0176] Substitute the prediction model into the objective function and construct a quadratic programming problem with U as the optimization variable:

[0177]

[0178] Among them, the second-order sensitivity matrix H (Hessian matrix) of the control input to the objective function and the linear driving vector F (linear term vector) of the deviation between the reference vector and the current state prediction to the objective function are generated by the system model and the weight matrix. The constraint matrix G and the constraint vector h are constructed by the constraint conditions, as follows:

[0179] Hessian matrix H and linear term vector F:

[0180]

[0181] in, is a lower triangular matrix with elements (when i ≥ j);

[0182] Constraint matrix G and constraint vector h:

[0183]

[0184] Among them, G u , G Δu and G y are the control quantity, control quantity change rate and output quantity constraint matrix respectively, h u 、h Δu 、h y They are the control quantity, the control quantity change rate and the output quantity constraint vector:

[0185]

[0186] in, mN c ×mN c The identity matrix of represents the Kronecker product, Is of length N c All 1 vectors; u max =[u 1,max ,..,u m,max ] T , similarly u min .

[0187]

[0188] Where D is N c-1 ×N c The difference matrix of .

[0189]

[0190] S36: Apply control input and scroll the time field:

[0191] Take the first control vector of the optimized solution [δ f ,δ r ] acts on the system, the system advances to time k+1, takes x(k+1) as the new initial state and returns to step S31, and re-executes the above steps.

[0192] Example 2:

[0193] An electronic device comprising a memory and a processor;

[0194] The memory is used to store computer programs;

[0195] The processor is configured to implement the method described in Example 1 when executing the computer program.

[0196] Example 3:

[0197] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method described in Example 1 is implemented.

[0198] Example 4:

[0199] A computer program product includes a computer program, which implements the method described in embodiment 1 when executed by a processor.

[0200] In the above embodiments, references to "this embodiment" in the specification indicate that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily refer to the same embodiment.

[0201] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those skilled in the art based on the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the present invention are intended to encompass all such alternatives, modifications, and variations that fall within the broad scope of the appended claims.

[0202] Regarding the computer-readable storage medium in this embodiment, those skilled in the art will appreciate that all or part of the steps in the aforementioned method embodiments can be implemented using hardware associated with the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps in the aforementioned method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0203] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication with each other. The memory is used to store computer programs, the communication interface is used for communication, and the processor and the transceiver are used to run computer programs so that the electronic terminal executes the various steps of the above method.

[0204] In this embodiment, the memory may include a random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), such as at least one disk storage.

[0205] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, and discrete hardware components.

[0206] The present invention can be used in a wide variety of general-purpose or special-purpose computing system environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments that include any of the above.

[0207] The present invention may be described in the general context of computer-executable instructions, such as program modules, executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and the like that perform specific tasks or implement specific abstract data types. The present invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media, including storage devices.

[0208] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for coordinated control of front and rear wheel angles of a four-wheel steer-by-wire vehicle, characterized by: The following steps are involved: S1: Design of variable angle transmission ratio for steer-by-wire front-wheel vehicle based on the constant steady-state yaw rate gain; S2: Calculate the target sideslip angle and yaw rate of the steer-by-wire vehicle based on the given steering wheel angle input; S3: A multi-objective optimization framework based on model predictive control (MPC) generates the front and rear wheel steering angles of a four-wheel steering vehicle with the front-wheel steering vehicle's dynamic output as the target.

2. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 1, characterized in that: The step S1 of designing the variable angle transmission ratio of the front-wheel steer-by-wire vehicle based on the constant steady-state yaw rate gain specifically includes the following steps: S11: Based on Newton's second law, the differential equation of the lateral dynamics model of a two-wheeled vehicle with two degrees of freedom is established, which is expressed as: Where m is the vehicle mass, I z is the vehicle mass, l f is the distance from the front axle to the center of mass of the vehicle, l r is the distance from the rear axle to the center of mass of the vehicle, v x is the vehicle longitudinal velocity, is the vehicle's lateral acceleration, r is the vehicle's yaw rate, is the vehicle yaw angular acceleration, F yf is the lateral force of the front tire, F yr is the lateral force of the rear tire; S12: In the differential equation, replace the tire lateral force with the cornering stiffness C α The product of the tire slip angle α is: Among them C αf is the front wheel cornering stiffness, C αr is the rear wheel cornering stiffness; α f is the front wheel slip angle, α r is the rear wheel slip angle, and the calculation formula for the front and rear wheel slip angles is: where v y is the vehicle lateral velocity, δ f is the vehicle's front wheel turning angle; Rewrite the original differential equation as: S13: Let the vehicle lateral speed v y The derivative of the vehicle yaw rate r is 0, and the steady-state response of the two-degree-of-freedom model is obtained, which is expressed as: Combining the rewritten differential equation with the steady-state response of the two-degree-of-freedom model, we can obtain the yaw rate r and the front wheel angle δ f The display expression k γ : Where L is the wheelbase and K is the stability factor, which is calculated as follows: Convert the front wheel angle into the steering wheel angle and introduce the steering system transmission ratio into the calculation formula of the steady-state yaw rate gain; S14: Calculate the vehicle's steady-state yaw rate gain k w , as shown below: where δ sw is the steering wheel angle, i is the variable angle transmission ratio of the ideal front wheel steer-by-wire vehicle; S15: Calculate the variable angle transmission ratio of the ideal front wheel steer-by-wire vehicle as shown in the following formula: Among them, i min is the minimum value of the angular transmission ratio, i max is the maximum value of the angular transmission ratio, u1 is the lower critical speed, and u2 is the upper critical speed.

3. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 1, wherein: Step S2, based on a given steering wheel angle input, calculates a target center-of-mass sideslip angle and a target yaw rate of the front-steer-by-wire vehicle, specifically comprising the following steps: S21: Calculate the steady-state yaw rate gain k w Display expressions at different vehicle speeds: Where K1 is the desired yaw rate gain, that is, the yaw rate gain increases with vehicle speed in the low-speed zone, remains constant in the medium-speed zone, and increases with vehicle speed in the high-speed zone. S22: Calculate the target yaw rate r of the front-wheel steering vehicle * : r * =k w d sw S23: Considering the vehicle's response characteristics and the driver's burden, the target center of mass side slip angle β of the front-wheel steering vehicle is obtained. * : β * ＝0。 4. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 1, wherein: The multi-objective optimization framework based on model predictive control in step S3 generates the front wheel steering angle and the rear wheel steering angle of the wire-controlled four-wheel steering vehicle with the dynamic output of the front-wheel steering vehicle as the target, and specifically includes the following steps: S31: Considering the coupling characteristics of the vehicle's lateral motion and yaw motion, construct the state space expression of the controlled system; S32: In the prediction time domain, based on the current system state observation value x(k) and the future control input sequence U=[u(k|k),u(k+1|k),…,u(k+N c -1|k)], and recursively predict the future N by discretizing the state space equation p The state sequence and output sequence of the step system: y(k+i|k)=Cx(k+i|k),i=1,2,…,N p The prediction time domain N p and control time domain N c Satisfy N c ≤N p ; A i is the i-th power of the system matrix A, which represents the evolution of the state after i steps. i-j-1 To describe the influence of input u(k+j|k) on the future state, B is the control matrix and C is the output matrix; S33: Construct the objective function of the optimization problem; S34: Define constraints and explicitly embed them into the optimization problem; S35: Solve the optimization problem using the quadratic programming method to obtain the optimal control input sequence; S36: Apply the first control variable to the controlled system. When the system advances to the next sampling moment, update the state estimation and rolling prediction time domain, and re-execute steps S31-S35 to realize closed-loop model predictive control.

5. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 4, characterized in that: Step S31 specifically includes the following steps: S311: Considering the coupling characteristics of the vehicle's lateral motion and yaw motion, construct the two-degree-of-freedom dynamic differential equation of the four-wheel steering vehicle: in is the sideslip angular velocity of the center of mass, δ r is the rear wheel turning angle of the vehicle, β is the sideslip angle of the center of mass; S312: Based on the lateral dynamics differential equation of a two-degree-of-freedom four-wheel vehicle, assuming that the sideslip angle β and the yaw angular velocity r are known, the state space of the controlled object is established: where the state vector x = [β, r] T , control input vector u=[δ f ,δ r ], output vector y = [β, r] T , A is the system matrix, B is the control matrix, and C is the output matrix; the expressions of each matrix are as follows: in:

6. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 4, characterized in that: Step S33 constructs the objective function of the optimization problem, specifically including the following steps: S331: Construct a weighted quadratic cost function that minimizes tracking error and control input: Where Q is the weight matrix for penalizing state errors, and R is the weight matrix for controlling inputs; S332: Expand the weighted quadratic cost function into a matrix form: J=Y T QY+U T RU where Y=[y(k+i|k),…,y(k+N p |k)] T To predict the output sequence, and is the weight matrix, r(k+i) is the reference from the vehicle two-degree-of-freedom lateral dynamics model (v y ,r)trajectory.

7. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 4, characterized in that: The constraints in step S34 include input, output and state constraints; Embed constraints into the optimization problem, including: The input constraints are determined by the actuator physical constraints: |d f |≤δ fmax |d r |≤δ rmax where δ fmax is the maximum front wheel turning angle, δ rmax is the maximum rear wheel turning angle; Output or state quantity constraints are determined by stability bounds: |β|≤β max where β max is the maximum sideslip angle at the center of mass, μ is the road adhesion coefficient, g is the acceleration of gravity, and v is the vehicle speed.

8. The method for coordinated control of front and rear wheel angles of a 4WD vehicle according to claim 4, characterized in that: Solving the optimization problem in step S35 includes: Substitute the prediction model into the objective function and construct a quadratic programming problem with U as the optimization variable: Among them, the second-order sensitivity matrix H of the control input to the objective function and the linear driving vector F of the deviation between the reference vector and the current state prediction to the objective function are generated by the system model and the weight matrix. The constraint matrix G and the constraint vector h are constructed by the constraint conditions, as follows: Hessian matrix H and linear term vector F: in, is a lower triangular matrix with elements Where i ≥ j; Constraint matrix G and constraint vector h: Among them, G u , G Δu and G y are the control quantity, control quantity change rate and output quantity constraint matrix respectively, h u 、h Δu 、h y They are the control quantity, the control quantity change rate and the output quantity constraint vector: in, mN c ×mN c The identity matrix of represents the Kronecker product, Is of length N c All 1 vectors; u max =[u 1,max ,..,u m,max ] T ,u min =[u 1,min ,..,u m,min ] T ; Where D is N c-1 ×N c The difference matrix of 9. An electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is configured to implement the front and rear wheel angle coordinated control method of a wire-controlled four-wheel steering vehicle as described in any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the front and rear wheel angle coordinated control method of the wire-controlled four-wheel steering vehicle according to any one of claims 1 to 8 is implemented.

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