A method for high-speed cornering control of vehicles that integrates trajectory tracking and drift control

Abstract

This invention discloses a high-speed cornering control method for vehicles that integrates trajectory tracking and drift control, belonging to the field of vehicle racing. The method includes the following steps: solving the shortest-time cornering problem, observing the solution results, and dividing the high-speed cornering process into three stages; using cubic Bézier curves to plan a smooth path from the starting point to the drift initiation point, and solving the optimal control problem to make the vehicle track the corresponding trajectory; constructing a vehicle drift tracking model, linearizing it near the equilibrium point, using MPC model predictive control as the control algorithm, and optimizing the front wheel slip angle and rear wheel driving force; setting a new equilibrium point target value, stabilizing the vehicle's sideslip angle and yaw rate to near 0, causing the vehicle to exit the drift state and return to normal driving conditions. This invention can achieve high-speed cornering of vehicles under extreme and normal conditions, improving the safety and operability of autonomous vehicle racing.

Description

Technical Field

[0001] This invention belongs to the field of vehicle racing, and in particular relates to a method for high-speed cornering control of vehicles that integrates trajectory tracking and drift control. Background Technology

[0002] With the continuous development of the automotive industry and the increasing maturity of various intelligent driver assistance technologies, active safety has become one of the important principles of modern vehicle design. However, existing safety control technologies minimize or limit the lateral forces on the tires within a linear range to enable ordinary drivers to maintain control of the vehicle in emergency situations. However, under some extreme driving conditions, such as high-speed cornering on slippery surfaces, traditional vehicle control methods are ineffective in stabilizing the vehicle, causing the tires to slip and lose control, potentially leading to accidents and injuries.

[0003] In rally racing, professional drivers utilize the full capabilities of their vehicles to avoid accidents. When cornering at high speeds, they increase rear-wheel drive force and counter-steer, causing the vehicle to move at a large sideslip angle. The rear tires are at full saturation; this cornering technique is called drifting. Mastering drifting not only reduces cornering time, enhancing the spectacle and excitement of rally racing, but also expands the vehicle's safe handling range while maintaining stability.

[0004] For example, Chinese patent document CN115384529A discloses a two-stage drift control method and safety assistance system for three-axle commercial vehicles to cope with extreme operating conditions, including an environmental perception module, a path tracking module, a vehicle-road cooperative module, and a vehicle system module. A path tracking model for a dual-track three-axle vehicle with nonlinear tires is constructed. Steady-state drift state variables are calculated based on curve characteristics, stability analysis is performed on the root locus of the state variables, and a time-varying model prediction algorithm is used to track the desired steady-state drift equilibrium state to achieve assisted drift control. Preview road information is obtained, lateral and heading errors are calculated, and control modes are switched accordingly to meet the drift driving requirements of unmanned commercial vehicles under complex operating conditions.

[0005] In existing technologies, although it is possible to control a vehicle to enter a drift state, the trajectory during the drift is not planned and controlled, which may lead to premature exit from the drift state or deviation from the predetermined path. In addition, if the trajectory before drifting is not planned and controlled, it may lead to increased cornering time and reduced traffic efficiency. Summary of the Invention

[0006] The purpose of this invention is to overcome the defects in the prior art and provide a vehicle high-speed cornering control method that integrates trajectory tracking and drift control, which can track a specified trajectory while maintaining high-speed cornering, thereby improving the vehicle's handling and safety under extreme conditions.

[0007] The specific technical solution adopted in this invention is as follows:

[0008] This invention provides a vehicle high-speed cornering control method that integrates trajectory tracking and drift control, comprising the following steps:

[0009] (1) By solving the problem of the shortest time for the vehicle to corner, the aggressive high-speed cornering process is decomposed into three parts: the guided entry stage, the drift tracking stage, and the exit from the drift stage.

[0010] (2) For the curve entry guidance stage, a smooth path from the starting point to the drift point is planned using cubic Bézier curves, and a three-degree-of-freedom dynamic model of the vehicle and an error tracking model in the curve coordinate system are constructed. The optimal control rate is obtained by solving the optimization problem.

[0011] (3) For the drift tracking stage, the drift equilibrium point is calculated based on the vehicle model and the error model, and the constructed drift tracking model is linearized near the drift equilibrium point. The MPC control method is used to keep the vehicle drifting.

[0012] (4) For the exit drift stage, reset the vehicle's balance point, set the expected values ​​of yaw rate and vehicle sideslip angle to 0, so that the vehicle exits the drift state and returns to normal driving conditions.

[0013] Preferably, the construction process of the shortest time cornering problem in step (1) is as follows:

[0014] (2-1) Construction state quantities Its dimension is a 5*1 vector, and its expression is as follows:

[0015] ;

[0016] in For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. The error between the vehicle's center of gravity and the road reference point. This refers to the vehicle's heading angle error;

[0017] (2-2) Selecting the control variable Its dimension is a 2*1 vector, and its expression is as follows:

[0018] ;

[0019] in, This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive force of the vehicle;

[0020] (2-3) The expression for the shortest time cornering problem with constraints is:

[0021] ; ; ; ; ; ; ; in, Let be the objective function to be optimized. This represents the path the vehicle traveled in its initial state. This refers to the path the vehicle traveled when it was in a terminated state. For road curvature, For the vehicle traveling on a path of length of The state quantity at time, For the vehicle traveling on a path of length of State quantity at time, These are the vehicle constraints in the initial state. These are the constraints when the vehicle is in a terminated state. For road width, for The amount of control at any given moment and These are the minimum and maximum values ​​of the control quantity, respectively. for Constantly control the increase in quantity. and These are the maximum and minimum values ​​of the control quantity increment, respectively. Let this be the distance the vehicle travels along the given road. State variables Regarding path length The derivative of .

[0022] Preferably, in step (2), a collision-free smooth path from the starting point to the drift point is constructed using a cubic Bézier curve, ensuring that the velocity directions at the starting point and the drift point are parallel to the tangent direction of the path; then, by solving the optimal control problem, the vehicle can track the given path while cornering in the shortest time. The construction process of the optimization problem is as follows:

[0023] (3-1) The expression for a cubic Bézier curve is:

[0024] ;

[0025] in, Here are the parameters of the Bézier curve. , , , Four control points were selected; to minimize the change in vehicle acceleration during movement, the selection of control points needs to meet the following requirements. and Parallel and ;

[0026] (3-2) The vehicle dynamics equations for a single-track, three-degree-of-freedom vehicle are expressed as:

[0027] ; ; ;

[0028] in, Let be the derivative of the vehicle's speed. The derivative of the vehicle's sideslip angle. The derivative of the vehicle's yaw rate. For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive of the vehicle, For vehicle quality, Let Z be the moment of inertia of the vehicle about the Z-axis. and These are the distances from the vehicle's center of gravity to the front and rear wheels, respectively. and These are the lateral forces on the front and rear wheels of the vehicle, respectively.

[0029] The lateral forces of the front and rear wheels are obtained using the Magic Tire Formula:

[0030] ;

[0031] Among them, when for hour This represents the lateral force on the front wheel, when for hour Indicates the lateral force on the rear wheel. The road surface adhesion coefficient, This refers to the vertical load on the tire. and These are the parameters for the Magic Tire model;

[0032] (3-3) In step (3-2) of the formula and These are the slip angles of the front and rear tires, respectively, and the calculation formulas are as follows:

[0033] ; ;

[0034] (3-4) To describe the pose changes of the vehicle in the global coordinate system, the kinematic equations are constructed as follows:

[0035] ; ; ;

[0036] in, and These are the derivatives of the vehicle's x and y coordinates in the world coordinate system, respectively. The vehicle's heading angle;

[0037] (3-5) For the purpose of optimizing the calculation, a curvilinear coordinate system is used to describe the motion state of the vehicle relative to the road. The calculation formula is as follows:

[0038] ; ; ;

[0039] in Let be the derivative of the distance the vehicle travels along a given road. This is the derivative of the error between the vehicle's center of gravity and the road reference point. For road curvature, This refers to the vehicle's heading angle error. For vehicle sideslip angle, The derivative of the vehicle's yaw rate;

[0040] (3-6) Multiply the derivatives of all state variables with respect to time by Operator, obtain state quantity with respect to travel distance The derivative of The calculation formula is as follows:

[0041] ;

[0042] in For the speed of the two vehicles, The error between the vehicle's center of gravity and the road reference point. For road curvature, This refers to the vehicle's heading angle error. The vehicle's sideslip angle;

[0043] (3-7) Once a path connecting the starting point and the drift point is planned, the optimal control problem is solved to enable the vehicle to follow the corresponding path and reach the drift point in the shortest time. The optimization problem is as follows:

[0044] ;

[0045] ; ; ; ;

[0046] ;

[0047] ;

[0048] in, State variables Regarding path length The derivative of , These are the vehicle speed, sideslip angle, yaw rate, and heading angle deviation at the initial moment, respectively. , These are the vehicle speed, sideslip angle, yaw rate, and heading angle deviation at the drift equilibrium point, respectively. The radius of curvature of the path varies with the path length. Changing function values, , The driving routes are respectively The vehicle speed, sideslip angle, yaw rate, and heading angle deviation at that time , The driving routes are respectively The values ​​of vehicle speed, sideslip angle, yaw rate, and heading angle deviation at that time are given, where g is the acceleration due to gravity.

[0049] Preferably, in step (3), the MPC control method is used to control the vehicle to track a given trajectory while maintaining a drift state. This requires expanding the state-space equations at the equilibrium point and constructing a quadratic programming problem. The calculation process is as follows:

[0050] (4-1) The drift tracking model constructed is shown below:

[0051] ; ; ; ; ;

[0052] in, The tracking error between the vehicle and the road reference point. This is the deviation between the vehicle's heading angle and the road tangent.

[0053] (4-2) The drift tracking model is linearized near the equilibrium point as follows: ;

[0054] in, , , These are the five state variables of the vehicle. For input quantity, and These are the drift balance point settings, and A and B are the Jacobian matrices;

[0055] (3-3) The objective function constructed using the drift tracking model predictive control is shown below:

[0056] ;

[0057] in, and The weight matrix is ​​the cost function. for The predicted value of the state variable at time step [time]. for The value of the change in the control quantity is constantly monitored.

[0058] Preferably, in step (4), a new equilibrium point is set for the three-degree-of-freedom vehicle model, and the MPC control method is used to make the vehicle exit the drift state and enter the normal driving state. The new equilibrium point is set as follows:

[0059] ;

[0060] in, This is the speed of the vehicle at the end of the drift.

[0061] Compared with the prior art, the present invention has the following advantages:

[0062] This invention first solves the shortest-time cornering problem, dividing the high-speed cornering process into three stages, providing a theoretical basis for subsequent trajectory planning and tracking control. Second, it guides the entry path into the corner using Bézier curve planning, ensuring the smoothness and feasibility of the path. Then, it obtains the optimal control rate by solving an optimization problem, enabling the vehicle to reach the drift point at the fastest speed while tracking the path. Furthermore, it uses MPC model predictive control, linearizing the vehicle model near the drift equilibrium point and solving a quadratic programming problem to obtain the front wheel deflection angle and rear wheel driving force as control inputs. Finally, it modifies the equilibrium point to allow the vehicle to exit the drift state and return to normal driving conditions. Attached Figure Description

[0063] Figure 1 This is a flowchart of a vehicle high-speed cornering control method that integrates trajectory tracking and drift control according to the present invention.

[0064] Figure 2 This is a schematic diagram illustrating the solution to the shortest time cornering problem in this invention.

[0065] Figure 3 This is a schematic diagram of the vehicle dynamics model in this invention;

[0066] Figure 4 This is a schematic diagram of the curve coordinate system in this invention;

[0067] Figure 5 This is a schematic diagram of the car's position on the MATLAB simulation platform in an embodiment of the present invention;

[0068] Figure 6 This is a schematic diagram of the changes in the state variables of the car on the MATLAB simulation platform in an embodiment of the present invention. Detailed Implementation

[0069] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly, provided that there is no mutual conflict.

[0070] Example

[0071] like Figure 1 As shown, this invention provides a vehicle high-speed cornering control method that integrates trajectory tracking and drift control. The method mainly includes the following steps:

[0072] Step 1, Decision-making phase: By solving the problem of minimizing the vehicle's cornering time and observing the results, the optimization problem that needs to be solved is:

[0073] ; ; ; ; ; ; ;

[0074] in, Let be the objective function to be optimized. This represents the path the vehicle traveled in its initial state. This refers to the path the vehicle traveled when it was in a terminated state. For road curvature, For the vehicle traveling on a path of length of State quantity at time, For the vehicle traveling on a path of length of State quantity at time, These are the vehicle constraints in the initial state. These are the constraints when the vehicle is in a terminated state. For road width, for The amount of control at any given moment and These are the minimum and maximum values ​​of the control quantity, respectively. for Constantly control the increase in quantity. and These are the maximum and minimum values ​​of the control quantity increment, respectively. Let this be the distance the vehicle travels along the given road. State variables Regarding path length The derivative of .

[0075] State variables in optimization problems It is a vector containing 5 variables, represented as:

[0076] ;

[0077] in For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. The error between the vehicle's center of gravity and the road reference point. This represents the vehicle's heading angle error.

[0078] The control variable u is a vector containing two variables, represented as:

[0079] ;

[0080] in, This refers to the front wheel deflection angle of the vehicle. It provides rear-wheel drive.

[0081] In this embodiment, the solution to the optimization problem is as follows: Figure 2 As shown in the figure, the solution results show that during the high-speed cornering process, there is a relatively obvious counter-steering and a large body sideslip angle. Therefore, a complete cornering process is decomposed into three stages as described below (i.e., the cornering guidance stage, the drift tracking stage, and the drift exit stage).

[0082] Step 2, Cornering Guidance Stage: Based on the planned path and vehicle dynamics model, construct the optimal control problem, and obtain the front wheel deflection angle and rear wheel driving force by solving the optimization problem, so that the vehicle can reach the drift point while tracking the trajectory.

[0083] In this embodiment, the specific steps are as follows:

[0084] Step 2-1: Based on the initial velocity direction of the vehicle and the selected drift starting point, a smooth path from the starting point to the drift starting point is planned using cubic Bézier curves as the path planning method. The expression for a cubic Bézier curve is:

[0085] ;

[0086] in, Here are the parameters of the Bézier curve. , , , These are the four selected control points. To minimize the change in vehicle acceleration during movement, the selection of control points must satisfy certain conditions. and Parallel and .

[0087] Step 2-2: Use the following dynamic model (i.e., the vehicle's single-track three-degree-of-freedom vehicle dynamics equations) to describe the vehicle's motion state, as shown in the schematic diagram below. Figure 3 As shown:

[0088] ; ; ;

[0089] in, The derivative of the vehicle speed. The derivative of the vehicle's sideslip angle. The derivative of the vehicle's yaw rate. For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive of the vehicle, For vehicle quality, Let Z be the moment of inertia of the vehicle about the Z-axis. and These are the distances from the vehicle's center of gravity to the front and rear wheels, respectively. and These are the lateral forces on the front and rear wheels of the vehicle, respectively.

[0090] The lateral forces of the front and rear wheels can be obtained using the Magic Tire Formula:

[0091] ;

[0092] Among them, when for When represents the lateral force of the front wheel, for The time indicates the lateral force of the rear wheel. The road surface adhesion coefficient, The vertical load on the tire; and The parameters for the magic tire model can be obtained through post-fitting.

[0093] In the above formula and These are the slip angles of the front and rear tires, respectively, and the calculation formulas are as follows:

[0094] ; ;

[0095] Using a curvilinear coordinate system to describe the motion of a vehicle relative to the road, such as Figure 4 As shown, using this coordinate system makes it easier to formulate the initial and final conditions, reducing computational complexity. The calculation formula is as follows:

[0096] ; ; ; ;

[0097] in Let be the derivative of the distance the vehicle travels along a given road. This is the derivative of the error between the vehicle's center of gravity and the road reference point. For road curvature, This refers to the vehicle's heading angle error. The derivative of the vehicle's heading angle error. This refers to the vehicle's sideslip angle.

[0098] Steps 2-3 involve constructing and solving the optimal control problem, enabling the vehicle to reach the drift point in the shortest possible time and follow the planned path. The objective function of the optimization problem includes penalties for motion time and tracking error, as shown below:

[0099] ;

[0100] ; ; ;

[0101] ; ; ;

[0102] in, State variables Regarding path length The derivative of , These are the vehicle speed, sideslip angle, yaw rate, and heading angle deviation at the initial moment, respectively. , These are the vehicle speed, sideslip angle, yaw rate, and heading angle deviation at the drift equilibrium point, respectively. The radius of curvature of the path varies with the path length. The changing function value. and These are the minimum and maximum values ​​of the control quantity, respectively. for Constantly control the increase in quantity. and These are the maximum and minimum values ​​of the control quantity increment, respectively. , The driving routes are respectively The vehicle speed, sideslip angle, yaw rate, and heading angle deviation at that time , The driving routes are respectively The values ​​of vehicle speed, sideslip angle, yaw rate, and heading angle deviation at that time are given, where g is the acceleration due to gravity.

[0103] Step 3, Drift Tracking Stage: When the vehicle reaches the starting drift point, the drift tracking model is linearized near the equilibrium point, and the MPC control method is used as the control algorithm so that the vehicle can track the corresponding arc trajectory while maintaining the drift state.

[0104] In this embodiment, the specific steps are as follows:

[0105] Step 3-1: Construct the vehicle drift tracking model as shown below:

[0106] ; ; ; ; ;

[0107] in, The tracking error between the vehicle and the road reference point. This is the derivative of the tracking error between the vehicle and the road reference point. This is the deviation between the vehicle's heading angle and the road tangent. It is the derivative of the deviation between the vehicle's heading angle and the road tangent. The derivative of the vehicle speed. The derivative of the vehicle's sideslip angle. The derivative of the vehicle's yaw rate. For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive of the vehicle, For vehicle quality, Let Z be the moment of inertia of the vehicle about the Z-axis. and These are the distances from the vehicle's center of gravity to the front and rear wheels, respectively. and These are the lateral forces on the front and rear wheels of the vehicle, respectively.

[0108] Step 3-2: Calculate the drift equilibrium point. Set the first derivative of the state equation to 0 and calculate the equilibrium point of the system. The specific calculation equation is shown below:

[0109] ; ; ; ; ;

[0110] in, The tracking error between the vehicle and the road reference point. This is the deviation between the vehicle's heading angle and the road tangent. For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive of the vehicle, For vehicle quality, Let Z be the moment of inertia of the vehicle about the Z-axis. and These are the distances from the vehicle's center of gravity to the front and rear wheels, respectively. and These are the lateral forces on the front and rear wheels of the vehicle, respectively.

[0111] Step 3-3: Place the model at the calculated equilibrium point. The linearized expansion is as follows:

[0112] ;

[0113] in , , These are the five states of a vehicle. It is the controller input. and It is the drift balance point setting value.

[0114] In the above formula, A and B are Jacobian matrices, expressed as:

[0115] ;

[0116] ; ; ; ; ; ; ; ; ; ; ;

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] ;

[0124] ; ;

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] ; ;

[0130] ;

[0131] ;

[0132] The objective function constructed using the MPC control method is shown below:

[0133] ;

[0134] in, and The weight matrix is ​​the cost function. for The predicted value of the state variable at time step [time]. for The value of the change in the control quantity is constantly monitored.

[0135] Step 4, Exit the drift phase: Reset the vehicle's balance point, set the expected values ​​of yaw rate and vehicle sideslip angle to 0, so that the vehicle exits the drift state and returns to normal driving conditions.

[0136] In this embodiment, when the vehicle reaches the end of the curve, the new equilibrium point is set as follows:

[0137] ;

[0138] in, The speed at which the vehicle exits the drift state and returns to normal driving conditions.

[0139] In summary, as Figure 1 The diagram shown is the overall flowchart of this invention, divided into four parts. First, it presents the theoretical basis for dividing the high-speed cornering process into three stages by solving the shortest-time cornering problem. The solution results are as follows: Figure 2 As shown in the diagram, the phase with noticeable counter-steering and a large sideslip angle is called the drift phase. Figure 3 As shown, a schematic diagram of the vehicle dynamics model is given, such as... Figure 4 The diagram shows a vehicle kinematics model in a curvilinear coordinate system. Combining the two models allows for a more accurate description of the vehicle's motion.

[0140] like Figure 5 The figure shows a schematic diagram of the vehicle's position change under the MATLAB simulation platform. It can be seen from the figure that the deviation between the vehicle's actual position and the desired position is controlled within a certain range, indicating good trajectory tracking control performance. Figure 6 The figure shows the changes in the vehicle's speed, sideslip angle, and yaw rate over time during the movement of the vehicle. As can be seen from the figure, when cornering, the vehicle's yaw rate is opposite to the direction of the front wheel deflection angle and is basically stable around a certain value, indicating that the vehicle is in a stable drift state.

[0141] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A vehicle high-speed cornering control method integrating trajectory tracking and drift control, characterized in that, Includes the following steps: (1) By solving the problem of the shortest time for the vehicle to corner, the cornering process is decomposed into three parts: the guided entry stage, the drift tracking stage, and the exit drift stage. (2) For the guided curve stage, a smooth path from the starting point to the drift point is planned using cubic Bézier curves, and a three-degree-of-freedom dynamic model of the vehicle and an error tracking model in the curve coordinate system are constructed. The optimal control rate is obtained by solving the optimization problem. (3) For the drift tracking stage, the drift equilibrium point is calculated based on the vehicle model and the error model, and the constructed drift tracking model is linearized near the drift equilibrium point. The MPC control method is used to keep the vehicle drifting. (4) For the exit drift stage, reset the vehicle's balance point, set the expected values ​​of yaw rate and vehicle sideslip angle to 0, so that the vehicle exits the drift state and returns to normal driving conditions.

2. The vehicle high-speed cornering control method integrating trajectory tracking and drift control according to claim 1, characterized in that, In step (1), the construction process of the shortest time cornering problem is as follows: (2-1) Construction state quantities Its dimension is a 5*1 vector, and its expression is as follows: ； in For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. The error between the vehicle's center of gravity and the road reference point. This refers to the vehicle's heading angle error; (2-2) Selecting the control variable Its dimension is a 2*1 vector, and its expression is as follows: ； in, This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive force of the vehicle; (2-3) The expression for the shortest time cornering problem with constraints is: ； ； ； ； ； ； ； in, Let be the objective function to be optimized. This represents the path the vehicle traveled in its initial state. This refers to the path the vehicle traveled when it was in a terminated state. For road curvature, For the vehicle traveling on a path of length of The state quantity at time, For the vehicle traveling on a path of length of The state quantity at time, These are the vehicle constraints in the initial state. These are the constraints when the vehicle is in a terminated state. For road width, for The amount of control at any given moment and These are the minimum and maximum values ​​of the control quantity, respectively. for Constantly control the increase in quantity. and These are the maximum and minimum values ​​of the control quantity increment, respectively. Let this be the distance the vehicle travels along the given road. State variables Regarding path length The derivative of .

3. The vehicle high-speed cornering control method integrating trajectory tracking and drift control according to claim 1, characterized in that, In step (2), a collision-free smooth path from the starting point to the drift point is constructed using a cubic Bézier curve, ensuring that the velocity directions at the starting point and the drift point are parallel to the tangent direction of the path; then, by solving the optimal control problem, the vehicle can track the given path while cornering in the shortest time. The construction process of the optimization problem is as follows: (3-1) The expression for a cubic Bézier curve is: ； in, Here are the parameters of the Bézier curve. , , , Four control points were selected; to minimize the change in vehicle acceleration during movement, the selection of control points needs to meet the following requirements. and Parallel and ; (3-2) The vehicle dynamics equations for a single-track, three-degree-of-freedom vehicle are expressed as: ； ； ； in, Let be the derivative of the vehicle's speed. The derivative of the vehicle's sideslip angle. The derivative of the vehicle's yaw rate. For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive of the vehicle, For vehicle quality, Let Z be the moment of inertia of the vehicle about the Z-axis. and These are the distances from the vehicle's center of gravity to the front and rear wheels, respectively. and These are the lateral forces on the front and rear wheels of the vehicle, respectively. The lateral forces of the front and rear wheels are obtained using the Magic Tire Formula: ； Among them, when for hour This represents the lateral force on the front wheel, when for hour Indicates the lateral force on the rear wheel. The road surface adhesion coefficient, This refers to the vertical load on the tire. and These are the parameters for the Magic Tire model; (3-3) In step (3-2) of the formula and These are the slip angles of the front and rear tires, respectively, and the calculation formulas are as follows: ； ； (3-4) To describe the pose changes of the vehicle in the global coordinate system, the kinematic equations are constructed as follows: ； ； ； in, and These are the derivatives of the vehicle's x and y coordinates in the world coordinate system, respectively. The vehicle's heading angle; (3-5) For the purpose of optimizing the calculation, a curvilinear coordinate system is used to describe the motion state of the vehicle relative to the road. The calculation formula is as follows: ； ； ； in Let this be the distance the vehicle travels along the given road. Let be the derivative of the distance the vehicle travels along a given road. The error between the vehicle's center of gravity and the road reference point. This is the derivative of the error between the vehicle's center of gravity and the road reference point. For road curvature, This refers to the vehicle's heading angle error. For vehicle sideslip angle, This is the derivative of the vehicle's yaw rate; (3-6) Multiply the derivatives of all state variables with respect to time by Operator, obtain state quantity with respect to travel distance The derivative, The calculation formula is as follows: ； in For the speed of the two vehicles, The error between the vehicle's center of gravity and the road reference point. For road curvature, This refers to the vehicle's heading angle error. The vehicle's sideslip angle; (3-7) Once a path connecting the starting point and the drift point is planned, the optimal control problem is solved to enable the vehicle to follow the corresponding path and reach the drift point in the shortest time. The optimization problem is as follows: ； ； ； ； ； ； ； in, State variables Regarding path length The derivative, , These are the vehicle speed, sideslip angle, yaw rate, and heading angle deviation at the initial moment, respectively. , These are the vehicle speed, sideslip angle, yaw rate, and heading angle deviation at the drift equilibrium point, respectively. The radius of curvature of the path varies with the path length. Changing function values, , The driving routes are respectively The vehicle speed, sideslip angle, yaw rate, and heading angle deviation at that time , The driving routes are respectively The values ​​of vehicle speed, sideslip angle, yaw rate, and heading angle deviation at that time are given, where g is the acceleration due to gravity.

4. The vehicle high-speed cornering control method integrating trajectory tracking and drift control according to claim 1, characterized in that, In step (3), the MPC control method is used to control the vehicle to track a given trajectory while maintaining a drift state. This requires expanding the state-space equations at the equilibrium point and constructing a quadratic programming problem. The calculation process is as follows: (4-1) The drift tracking model constructed is shown below: ； ； ； ； ； in, The error between the vehicle's center of gravity and the road reference point. This refers to the vehicle's heading angle error; Let be the derivative of the vehicle's speed. The derivative of the vehicle's sideslip angle. The derivative of the vehicle's yaw rate. For vehicle speed, For vehicle sideslip angle, Let yaw rate be the vehicle's angular velocity. This refers to the front wheel deflection angle of the vehicle. For the rear-wheel drive of the vehicle, For vehicle quality, Let Z be the moment of inertia of the vehicle about the Z-axis. and These are the distances from the vehicle's center of gravity to the front and rear wheels, respectively. and These are the lateral forces on the front and rear wheels of the vehicle, respectively. (4-2) The drift tracking model is linearized near the equilibrium point as follows: ； in, , , These are the five state variables of the vehicle. For input quantity, and These are the drift balance point settings, and A and B are the Jacobian matrices; (4-3) The objective function constructed using the drift tracking model predictive control is shown below: ； in, and Let be the weight matrix of the cost function. for The predicted value of the state variable at time step [time]. for The value of the change in the control quantity at all times.

5. The vehicle high-speed cornering control method integrating trajectory tracking and drift control according to claim 1, characterized in that, In step (4), a new equilibrium point for the three-degree-of-freedom vehicle model is set, and the MPC control method is used to make the vehicle exit the drift state and enter the normal driving state. The new equilibrium point is set as follows: ； in, This is the speed of the vehicle at the end of the drift.

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