Vehicle lateral motion control method based on polar region two-degree-of-freedom dynamic model

Abstract

The application discloses a vehicle lateral motion control method based on a polar region two-degree-of-freedom dynamics model, which comprises the following steps: a two-degree-of-freedom dynamics model of a vehicle is established in a vehicle body Cartesian coordinate system; the two-degree-of-freedom model of the vehicle is converted to a vehicle body polar coordinate system, and a coordinate of a vehicle speed centroid in the polar coordinate system is taken as a control variable to complete vehicle centroid control; and the two-degree-of-freedom dynamics model of the vehicle in the vehicle body polar coordinate system and the coordinate of the vehicle speed centroid are converted to a polar region through polar transformation, and the coordinate of the vehicle speed centroid in the polar region is taken as a control variable to complete vehicle polar region centroid control. By converting the two-degree-of-freedom dynamics model to the vehicle body polar coordinate system, the state variables of the model are changed into a centroid side slip angle and a steering curvature, the state can be directly output to track the curvature and direction of a road, the two-degree-of-freedom dynamics model is converted to the polar region through polar transformation, and the complexity of the model is reduced under the condition that the precision of the model is unchanged, so that calculation is facilitated.

Description

Technical Field

[0001] This invention belongs to the field of vehicle stability control technology, specifically relating to a vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model. Background Technology

[0002] With the development of autonomous vehicles, it is necessary to digitally describe these vehicles so that the central computing unit can calculate their state and control them. Therefore, establishing a two-degree-of-freedom (DOF) model of the vehicle is crucial. Existing two-DOF models are all established in the vehicle's Cartesian coordinate system based on Newton's second law. Then, based on the established model, the vehicle's state is changed by altering the front wheel steering angle, thereby controlling the vehicle's lateral motion, and this method has extremely wide applications.

[0003] Among existing two-degree-of-freedom dynamic models for front-wheel steering vehicles, Chinese invention patent application number CN202010214423.9, entitled "A Multi-Point Pre-aiming LQR Lateral Control Method Based on the Fiala Brush Tire Model," discloses a method for establishing a two-degree-of-freedom dynamic model of the vehicle. It uses lateral velocity and yaw rate as state variables and front wheel angle as control variable. By controlling the magnitude of the front wheel angle, the state variables are continuously corrected to minimize the error with the desired value, thereby controlling the vehicle's lateral motion to track the reference trajectory. However, the above method only has one control variable in its two-degree-of-freedom dynamic model. Under low-speed conditions, the vehicle's turning radius is large, and under high-speed conditions, the vehicle's stability is low. It is only applicable to front-wheel steering vehicles and not to four-wheel independent steering vehicles or multi-wheel independent steering vehicles, thus having limitations.

[0004] Among the existing two-degree-of-freedom dynamic models of four-wheel independent steering vehicles, Chinese invention patent application number CN201710565455.1, entitled "A Dynamic Switching Method for Four-Wheel Independent Steering Electric Vehicles - Front / Rear Wheel Steering," discloses a two-degree-of-freedom dynamic model for four-wheel independent steering. It uses lateral velocity and yaw rate as state variables and four tire angles as control variables. By controlling the magnitude of the four tire angles, the state variables are continuously corrected to minimize the error with the desired value, thereby controlling the vehicle's lateral motion to track the reference trajectory. Based on the Ackermann steering principle, two control variables are eliminated to achieve decoupling. However, it uses proportional control, resulting in only one tire angle as the control variable, which greatly limits the trajectory tracking capability of four-wheel independent steering vehicles. Furthermore, current models of four-wheel independent steering vehicles ignore the difference in left and right wheel angles, simplifying them into a single-track model. This introduces significant errors and low stability under low-speed, large-angle conditions, failing to fully utilize the vehicle's lateral motion performance. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, the present invention aims to provide a vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model, in order to solve the problems of large turning radius at low speeds, low stability at high speeds, and low model accuracy at low speeds and large turning angles in the existing technologies.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The present invention provides a vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamics model, comprising the following steps:

[0008] 1) Establish a two-degree-of-freedom dynamic model of the vehicle in the Cartesian coordinate system;

[0009] 2) Transform the two-degree-of-freedom model of the vehicle into the polar coordinate system of the vehicle body, and use the coordinates of the instantaneous center of the vehicle velocity in the polar coordinate system as the control variable to complete the instantaneous center control of the vehicle.

[0010] 3) Through polar transformation, the vehicle's two-degree-of-freedom dynamic model and instantaneous center coordinates of vehicle velocity in the polar coordinate system are transformed to the polar domain, and the instantaneous center coordinates of vehicle velocity in the polar domain are used as control variables to complete the vehicle polar domain instantaneous center control.

[0011] Furthermore, the steps for establishing the two-degree-of-freedom dynamic model of the vehicle in the Cartesian coordinate system in step 1) are as follows:

[0012] 11) Using Newton's second law, force analysis is performed on a four-wheel steering vehicle, resulting in the following formula;

[0013]

[0014] In the formula, m, v y v x r represents the vehicle mass, lateral velocity at the center of mass, longitudinal velocity at the center of mass, and yaw rate around the center of mass, respectively; F yfl F yfr F yfl F yrr These represent the lateral forces of the left front, right front, left rear, and right rear tires, respectively. f , l r I represents the distance from the center of mass to the front and rear axles, respectively. z This represents the yaw moment of inertia of a vehicle.

[0015] The vehicle body Cartesian coordinate system is as follows: with the vehicle's longitudinal axis as the x-axis, the vehicle's forward direction as the positive direction, and the x-axis rotated 90° counterclockwise to obtain the y-axis, the coordinate system xoy with the vehicle's center of mass o as the origin is the vehicle body Cartesian coordinate system.

[0016] The formula for calculating tire lateral force adopts the simplified Magic Tire formula, as follows:

[0017] F yi =μF zi sin(DarctanBα i (2)

[0018] In the formula, μ represents the road surface adhesion coefficient, B and D are the coefficients to be fitted, and F zi Represents the vertical load on the tire, i = fl, fr, rl, rr, F zfl F zfr F zrl F zrr These represent the vertical loads on the left front, right front, left rear, and right rear tires, respectively, α. i The slip angle of the tire is represented by i = fl, fr, rl, rr α fl α fr α rl α rr The sideslip angles of the left front, right front, left rear, and right rear tires are respectively expressed in the Cartesian coordinate system of the vehicle body as follows:

[0019]

[0020] In the formula, δ i The tire's turning angle is represented by i = fl, fr, rl, rr, δ fl δ fr δ rl δ rr These represent the turning angles of the front left, front right, rear left, and rear right tires, respectively, and d represents half the track width.

[0021] Furthermore, step 2) specifically includes the following steps:

[0022] 21) The two-degree-of-freedom dynamic model of the vehicle in step 11) is expressed in the polar coordinate system of the vehicle body as follows:

[0023]

[0024] In the formula, The sideslip angle of the vehicle's center of gravity; ρ = rcosβ / v x , where is the vehicle's steering curvature;

[0025] The vehicle body polar coordinate system is as follows: the vehicle's center of mass o is the pole, the vehicle's negative half-axis of y-axis is the polar axis, the distance oP from the vehicle's center of mass o to the instantaneous center of velocity P is the polar radius R (also known as the turning radius), and its reciprocal ρ = 1 / R is called the turning curvature. The angle between the polar axis and the polar radius is the polar angle β (also known as the center of mass sideslip angle), and the vehicle body polar coordinate system is βoρ.

[0026] 22) The formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the Cartesian coordinate system of the vehicle body in step 11) are expressed in the polar coordinate system of the vehicle body as follows:

[0027]

[0028] Furthermore, the calculation formulas for the slip angles of the left front, right front, left rear, and right rear tires in the vehicle polar coordinate system in step 22) are decoupled using the following formula:

[0029]

[0030] In the formula, β s , ρ s Let β be the coordinate components of the instantaneous center of velocity P in the vehicle's polar coordinate system. s , ρ s As a control variable, it is used to complete the instantaneous center of gravity control of the vehicle; the instantaneous center of gravity control of the vehicle includes two modes of vehicle lateral motion, specifically: Mode 1, based on the two-degree-of-freedom dynamic model of the vehicle in the polar coordinate system, by controlling β s , ρ s By keeping the sideslip angle β constant and changing the polar radius R, a smaller turning radius results in a larger turning curvature ρ, allowing the vehicle to approach the reference trajectory more quickly. Alternatively, based on a two-degree-of-freedom vehicle dynamics model in polar coordinates, β is controlled... s , ρ s By keeping the extreme radius R and steering curvature ρ constant, and changing the magnitude of the center of gravity sideslip angle β, the vehicle can approach the reference trajectory more quickly.

[0031] Furthermore, step 3) of transforming the two-degree-of-freedom vehicle dynamics model in the polar coordinate system to the polar domain specifically includes the following steps:

[0032] 31) Perform a polar transformation on the vehicle's two-degree-of-freedom dynamic model in the polar coordinate system from step 21) to obtain the following description of the vehicle's two-degree-of-freedom dynamic model in the polar domain:

[0033]

[0034] 32) The formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the polar coordinate system of the vehicle body in step 22) are subjected to polar transformation to obtain the following expressions for the formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the polar domain:

[0035]

[0036] 33) The formulas for calculating the rotation angles of the left front, right front, left rear, and right rear tires in the polar coordinate system of the vehicle body in step 22) are subjected to polar transformation to obtain the following formulas for calculating the rotation angles of the left front, right front, left rear, and right rear tires in the polar domain:

[0037]

[0038] In the formula, Let β be the coordinate component of the instantaneous center of velocity P in the polar region. s , ρ s As a control variable, it is used to complete the instantaneous center control of the vehicle in the extreme domain.

[0039] Furthermore, the vehicle polar-domain instantaneous center control is derived from the vehicle instantaneous center control via polar transformation, and its control method is as follows: based on the two-degree-of-freedom dynamic model of the vehicle in the polar domain, the instantaneous center coordinates of the vehicle velocity in the polar domain are controlled. This allows control over the vehicle's state in extreme regions. Compared with reference state To minimize the error, so as to control the lateral motion of the vehicle and track the reference trajectory;

[0040] The aforementioned pole transformation can reduce the computational load while ensuring the accuracy of the vehicle dynamics model;

[0041] The reference state The reference trajectory is given; the reference trajectory is the target trajectory that the vehicle is to follow, which is obtained by the vehicle-mounted sensors identifying road information.

[0042] Furthermore, the polar transformation formulas for converting the vehicle dynamics model to the polar domain in step 31) and for converting the calculation formulas for the slip angles of the left front, right front, left rear, and right rear tires to the polar domain in step 32) are as follows:

[0043]

[0044] Furthermore, in step 33), the calculation formulas for the steering angles of the left front, right front, left rear, and right rear tires are transformed into polar transformation formulas in the polar domain as follows:

[0045]

[0046] The beneficial effects of this invention are:

[0047] This invention transforms the original four tire steering angle control quantities into two instantaneous center coordinate component control quantities through instantaneous center control, achieving decoupled control of the four tire steering angles. This decoupling method is also applicable to multi-wheel independent steering vehicles. By transforming the two-degree-of-freedom dynamic model in the vehicle's Cartesian coordinate system to the vehicle's polar coordinate system, the model's state becomes the centroid sideslip angle and steering curvature, which can directly output the state to track the curvature and direction of the road. Through polar transformation, the two-degree-of-freedom dynamic model in the vehicle's polar coordinate system is transformed to the polar domain, reducing the model's complexity and facilitating calculation while ensuring the model's accuracy remains unchanged. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the method of the present invention;

[0049] Figure 2 This is an analysis diagram of the vehicle model of the present invention;

[0050] Figure 3 This is a schematic diagram of the vehicle instantaneous center control method in this invention;

[0051] Figure 4 This is a schematic diagram of the second method of vehicle instantaneous center control in this invention. Detailed Implementation

[0052] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0053] Reference Figure 1 , Figure 2 As shown, the present invention provides a vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamics model, comprising the following steps:

[0054] 1) Establish a two-degree-of-freedom dynamic model of the vehicle in the Cartesian coordinate system;

[0055] The steps for establishing the two-degree-of-freedom dynamic model of the vehicle in the Cartesian coordinate system are as follows:

[0056] 11) Using Newton's second law, force analysis is performed on a four-wheel steering vehicle, resulting in the following formula;

[0057]

[0058] In the formula, m, v y v x r represents the vehicle mass, lateral velocity at the center of mass, longitudinal velocity at the center of mass, and yaw rate around the center of mass, respectively; F yfl F yfr F yrl F yrrThese represent the lateral forces of the left front, right front, left rear, and right rear tires, respectively. f , l r I represents the distance from the center of mass to the front and rear axles, respectively. z This represents the yaw moment of inertia of a vehicle.

[0059] The vehicle body Cartesian coordinate system is as follows: with the vehicle's longitudinal axis as the x-axis, the vehicle's forward direction as the positive direction, and the x-axis rotated 90° counterclockwise to obtain the y-axis, the coordinate system xoy with the vehicle's center of mass o as the origin is the vehicle body Cartesian coordinate system.

[0060] The formula for calculating tire lateral force adopts the simplified Magic Tire formula, as follows:

[0061] F yi =μF zi sin(DarctanBα i (2)

[0062] In the formula, μ represents the road surface adhesion coefficient, B and D are the coefficients to be fitted, and F zi Represents the vertical load on the tire, i = fl, fr, rl, rr, F zfl F zfr F zrl F zrr These represent the vertical loads on the left front, right front, left rear, and right rear tires, respectively, α. i The slip angle of the tire is represented by i = fl, fr, rl, rr α fl α fr α rl α rr The sideslip angles of the left front, right front, left rear, and right rear tires are respectively expressed in the Cartesian coordinate system of the vehicle body as follows:

[0063]

[0064] In the formula, δ i The tire's turning angle is represented by i = fl, fr, rl, rr, δ fl δ fr δ rl δ rr These represent the turning angles of the front left, front right, rear left, and rear right tires, respectively, and d represents half the track width.

[0065] 2) Transform the vehicle's two-degree-of-freedom model to the vehicle's polar coordinate system, and use the coordinates of the vehicle's instantaneous center of velocity in the polar coordinate system as the control variable to complete the vehicle's instantaneous center of velocity control; specifically, this includes the following steps:

[0066] 21) The two-degree-of-freedom dynamic model of the vehicle in step 11) is expressed in the polar coordinate system of the vehicle body as follows:

[0067]

[0068] In the formula, The sideslip angle of the vehicle's center of gravity; ρ = rcosβ / v x , where is the vehicle's steering curvature;

[0069] The vehicle body polar coordinate system is as follows: the vehicle's center of mass o is the pole, the vehicle's negative half-axis of y-axis is the polar axis, the distance oP from the vehicle's center of mass o to the instantaneous center of velocity P is the polar radius R (also known as the turning radius), and its reciprocal ρ = 1 / R is called the turning curvature. The angle between the polar axis and the polar radius is the polar angle β (also known as the center of mass sideslip angle), and the vehicle body polar coordinate system is βoρ.

[0070] 22) The formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the Cartesian coordinate system of the vehicle body in step 11) are expressed in the polar coordinate system of the vehicle body as follows:

[0071]

[0072] Specifically, the calculation formulas for the slip angles of the left front, right front, left rear, and right rear tires in the vehicle polar coordinate system in step 22) are decoupled using the following formula:

[0073]

[0074] In the formula, β s , ρ s Let β be the coordinate components of the instantaneous center of velocity P in the vehicle's polar coordinate system. s , ρ s As a control variable, it is used to complete the instantaneous centering control of the vehicle.

[0075] Reference Figure 3 , Figure 4 As shown, the instantaneous center of gravity control of the vehicle includes two modes of lateral vehicle motion: Mode 1, based on the two-degree-of-freedom dynamic model of the vehicle in the polar coordinate system, controls β... s , ρ s By keeping the sideslip angle β constant and changing the polar radius R, a smaller turning radius results in a larger turning curvature ρ, allowing the vehicle to approach the reference trajectory more quickly. Alternatively, based on a two-degree-of-freedom vehicle dynamics model in polar coordinates, β is controlled... s , ρ s By keeping the extreme radius R and steering curvature ρ constant, and changing the magnitude of the center of gravity sideslip angle β, the vehicle can approach the reference trajectory more quickly.

[0076] 3) Through polar transformation, the vehicle's two-degree-of-freedom dynamic model and instantaneous velocity center coordinates in the polar coordinate system are transformed to the polar domain, and the instantaneous velocity center coordinates in the polar domain are used as the control quantity to complete the vehicle's polar domain instantaneous center control.

[0077] The specific steps for transforming the two-degree-of-freedom vehicle dynamics model in the polar coordinate system to the polar domain include:

[0078] 31) Perform a polar transformation on the vehicle's two-degree-of-freedom dynamic model in the polar coordinate system from step 21) to obtain the following description of the vehicle's two-degree-of-freedom dynamic model in the polar domain:

[0079]

[0080] 32) The formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the polar coordinate system of the vehicle body in step 22) are subjected to polar transformation to obtain the following expressions for the formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the polar domain:

[0081]

[0082] 33) The formulas for calculating the rotation angles of the left front, right front, left rear, and right rear tires in the polar coordinate system of the vehicle body in step 22) are subjected to polar transformation to obtain the following formulas for calculating the rotation angles of the left front, right front, left rear, and right rear tires in the polar domain:

[0083]

[0084] In the formula, Let β be the coordinate component of the instantaneous center of velocity P in the polar region. s , ρ s As a control variable, it is used to complete the instantaneous center control of the vehicle in the extreme domain.

[0085] The vehicle polar-domain instantaneous center control is derived from the vehicle instantaneous center control via polar transformation, and its control method is as follows: Based on the two-degree-of-freedom dynamic model of the vehicle in the polar domain, the instantaneous center coordinates of the vehicle velocity in the polar domain are controlled. This allows control over the vehicle's state in extreme regions. Compared with reference state To minimize the error, so as to control the lateral motion of the vehicle and track the reference trajectory;

[0086] The aforementioned pole transformation can reduce the computational load while ensuring the accuracy of the vehicle dynamics model;

[0087] The reference state The reference trajectory is given; the reference trajectory is the target trajectory that the vehicle is to follow, which is obtained by the vehicle-mounted sensors identifying road information.

[0088] Specifically, the polar transformation formulas for converting the vehicle dynamics model to the polar domain in step 31) and for converting the calculation formulas for the slip angles of the left front, right front, left rear, and right rear tires to the polar domain in step 32) are as follows:

[0089]

[0090] Specifically, in step 33), the calculation formulas for the steering angles of the left front, right front, left rear, and right rear tires are converted to polar transformation formulas in the polar domain as follows:

[0091]

[0092] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamics model, characterized in that, The steps are as follows: 1) Establish a two-degree-of-freedom dynamic model of the vehicle in the Cartesian coordinate system of the vehicle body; 2) Transform the two-degree-of-freedom model of the vehicle into the polar coordinate system of the vehicle body, and use the coordinates of the instantaneous center of the vehicle velocity in the polar coordinate system as the control variable to complete the instantaneous center control of the vehicle. 3) Through polar transformation, the vehicle's two-degree-of-freedom dynamic model and instantaneous velocity center coordinates in the polar coordinate system are transformed to the polar domain, and the instantaneous velocity center coordinates in the polar domain are used as the control quantity to complete the vehicle's polar domain instantaneous center control. The steps for establishing the two-degree-of-freedom dynamic model of the vehicle in the Cartesian coordinate system in step 1) are as follows: 11) Using Newton's second law, force analysis is performed on a four-wheel steering vehicle, resulting in the following formula; （1）； In the formula, , , , These represent the vehicle's mass, lateral velocity at the center of mass, longitudinal velocity at the center of mass, and yaw rate around the center of mass, respectively. , , , These represent the lateral forces of the left front, right front, left rear, and right rear tires, respectively. These represent the distances from the center of mass to the front and rear axles, respectively. This represents the yaw moment of inertia of a vehicle. The vehicle body's Cartesian coordinate system is: with the vehicle's longitudinal axis as... The axle, with the vehicle's forward direction as the positive direction, will... Rotating the axis counterclockwise by 90° is... Axis, with the vehicle's center of gravity Coordinate system with origin The vehicle body uses a Cartesian coordinate system; The formula for calculating tire lateral force adopts the simplified Magic Tire formula, as follows: （2）； In the formula, Indicates the road surface adhesion coefficient. and The coefficients to be fitted are... This represents the vertical load on the tire, i = fl, fr, rl, rr. , , , These represent the vertical loads on the left front, right front, left rear, and right rear tires, respectively. This represents the tire slip angle, i = fl, fr, rl, rr , , , The sideslip angles of the left front, right front, left rear, and right rear tires are respectively expressed in the Cartesian coordinate system of the vehicle body as follows: （3）； In the formula, This represents the tire's steering angle, where i = fl, fr, rl, rr. , , , These represent the turning angles of the front left, front right, rear left, and rear right tires, respectively. It represents half the wheelbase; Step 2) specifically includes the following steps: 21) The two-degree-of-freedom dynamic model of the vehicle in step 11) is expressed in the polar coordinate system of the vehicle body as follows: （4）； In the formula, , is the sideslip angle of the vehicle's center of gravity; , where is the vehicle's steering curvature; The polar coordinate system of the vehicle body is: vehicle centroid At the extreme point, the vehicle The negative half-shaft is the polar axis, and the vehicle's center of gravity is... To speed instantaneous heart distance Polar radius , take the polar diameter The reciprocal of is the vehicle's steering curvature. The angle between the polar axis and the polar radius is the polar angle. The vehicle body polar coordinate system is ; 22) The formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the Cartesian coordinate system of the vehicle body in step 11) are expressed in the polar coordinate system of the vehicle body as follows: （5）。 2. The vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model according to claim 1, characterized in that, The calculation formulas for the slip angles of the left front, right front, left rear, and right rear tires in the vehicle polar coordinate system in step 22) are decoupled using the following formula: （6）； In the formula, For speed instantaneous heart The coordinate components in the polar coordinate system of the vehicle body, and the instantaneous center of velocity Coordinate components in the vehicle polar coordinate system As a control variable, it is used to complete the instantaneous center of gravity control of the vehicle; the instantaneous center of gravity control of the vehicle includes two modes of vehicle lateral motion, specifically: Mode 1, based on the two-degree-of-freedom dynamic model of the vehicle in the polar coordinate system, by controlling... This makes the centroid side slip angle Unchanged, change the polar diameter Size, small turning radius with large turning curvature Method 1: The vehicle approaches the reference trajectory; Method 2: Based on the vehicle's two-degree-of-freedom dynamics model in the polar coordinate system, control... Make the polar diameter Unchanged, turning curvature It remains unchanged, but the sideslip angle of the center of mass changes. The size is adjusted so that the vehicle approximates the reference trajectory.

3. The vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model according to claim 2, characterized in that, Step 3) involves transforming the two-degree-of-freedom vehicle dynamics model in the polar coordinate system to the polar domain, specifically including the following steps: 31) Perform a polar transformation on the two-degree-of-freedom vehicle dynamics model in the polar coordinate system of step 21) to obtain the following description of the two-degree-of-freedom vehicle dynamics model in the polar domain: （7）； 32) The formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the polar coordinate system of the vehicle body in step 22) are subjected to polar transformation to obtain the following expression of the formulas for calculating the slip angles of the left front, right front, left rear, and right rear tires in the polar domain: （8）； 33) The formulas for calculating the rotation angles of the left front, right front, left rear, and right rear tires in the polar coordinate system of the vehicle body in step 22) are subjected to polar transformation to obtain the following expressions for the formulas for calculating the rotation angles of the left front, right front, left rear, and right rear tires in the polar domain: （9）； In the formula, For speed instantaneous heart The coordinate components in the polar region will have the instantaneous center of velocity. Coordinate components in the polar region As a control variable, it is used to complete the instantaneous center control of the vehicle in the extreme domain.

4. The vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model according to claim 3, characterized in that, The vehicle polar-domain instantaneous center control is derived from the vehicle instantaneous center control via polar transformation, and its control method is as follows: Based on the two-degree-of-freedom dynamic model of the vehicle in the polar domain, the instantaneous center coordinates of the vehicle velocity in the polar domain are controlled. This allows control over the vehicle's state in extreme regions. Compared with reference state To minimize the error, so as to control the lateral motion of the vehicle and track the reference trajectory; The aforementioned pole transformation can reduce the computational load while ensuring the accuracy of the vehicle dynamics model; The reference state The reference trajectory is given; the reference trajectory is the target trajectory that the vehicle is to follow, which is obtained by the vehicle's onboard sensors identifying the road.

5. The vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model according to claim 3, characterized in that, The polar transformation formulas for converting the vehicle dynamics model to the polar domain in step 31) and for converting the calculation formulas for the slip angles of the left front, right front, left rear, and right rear tires to the polar domain in step 32) are as follows: （10）。 6. The vehicle lateral motion control method based on a polar domain two-degree-of-freedom dynamic model according to claim 3, characterized in that, In step 33), the calculation formulas for the steering angles of the left front, right front, left rear, and right rear tires are transformed into polar transformation formulas in the polar domain as follows: （11）。

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