Four-wheel steering vehicle path tracking method based on extension control theory

Abstract

The invention discloses a four-wheel steering vehicle path tracking method based on an extension control theory, and relates to the technical field of path tracking. The method comprises the following steps: establishing a vehicle-road coupling state through an extension controller in a decision control module, constructing a control plane by taking a road curvature and a vehicle speed as parameters, and calculating the correlation degree of a prediction point in the control plane through the extension controller, judging the area of the vehicle in the control plane according to the correlation degree so as to determine a control coefficient equation between the steering angles of the front wheel and the rear wheel; a model prediction controller in the control execution module dynamically optimizes the steering angles of the front wheel and the rear wheel through a segmented affine model of tire lateral force and vehicle stability constraint based on a vehicle path model. According to the invention, different vehicle road environments can be well coped with, and the path tracking precision is improved while the vehicle driving stability is ensured.

Description

Technical Field

[0001] This invention belongs to the field of path tracking technology, and in particular relates to a path tracking method for four-wheel steering vehicles based on extension control theory. Background Technology

[0002] The rapid development of intelligent driving technology has placed extremely high demands on the accuracy and stability of vehicle path tracking control. As a core component of intelligent driving, path tracking performance directly determines the vehicle's autonomous navigation capabilities and driving safety. Early research mainly focused on traditional two-wheel steering vehicles, achieving path tracking by controlling the front wheel steering angle. However, this method is prone to problems such as path deviation and stability deterioration under high-speed sharp curves or complex conditions.

[0003] With advancements in chassis control technology, four-wheel steering offers a novel solution for improving path tracking performance through coordinated steering of the front and rear wheels. Research shows that four-wheel steering vehicles can eliminate steady-state errors under ideal conditions, a goal that traditional front-wheel steering vehicles struggle to achieve. The core advantage of four-wheel steering systems lies in significantly enhancing vehicle handling and stability under complex conditions by coordinating the steering angles of the front and rear wheels. Especially in highly automated driving scenarios, four-wheel steering systems effectively reduce the turning radius at low speeds, improving vehicle agility; simultaneously, they improve directional stability at high speeds, suppressing oversteer or understeer.

[0004] However, the introduction of four-wheel steering systems has significantly increased control complexity. Path tracking control is no longer simply about controlling the front wheel steering angle; it requires coordinated management of steering commands from both the front and rear wheels while ensuring the vehicle's lateral stability. This multi-objective, multi-constraint control problem poses a serious challenge to traditional control theory. In the research on path tracking control of four-wheel steering vehicles, improving path tracking accuracy and ensuring vehicle stability have become two indispensable key aspects, and the coordination and balance between the two constitute the core difficulty of current research.

[0005] For example, model predictive control (MRC) plays an important role in current research. These methods establish a vehicle dynamics model and solve the optimal control problem in the finite time domain online within each sampling period to achieve coordinated control of the front and rear wheel steering angles. However, MRC methods are highly dependent on model accuracy, and their adaptability decreases significantly under high-speed, high-curvature conditions, while also incurring a heavy real-time computational burden.

[0006] For example, the sliding mode variable structure control method introduces a sideslip angle and uses a sliding mode controller to bring lateral offset and heading error close to zero, maintaining vehicle stability under extreme conditions. The advantage of sliding mode control is its strong robustness to model uncertainties and external disturbances, but its inherent control input chattering problem may exacerbate actuator wear and affect ride comfort.

[0007] Due to the lack of a systematic coordination mechanism, existing control methods struggle to fully realize the potential of four-wheel steering systems. Most control methods focus only on a specific steering mode, failing to dynamically adjust the relative steering relationship between the front and rear wheels according to driving conditions, thus limiting the vehicle's overall performance under different conditions. Furthermore, when road surface adhesion conditions suddenly change or vehicle dynamic characteristics shift due to load transfer, fixed-parameter control systems struggle to adjust their control strategies in a timely manner, leading to performance degradation. For example, on low-adhesion surfaces, when a traditional differential power steering system operates alone, lateral and longitudinal deviations increase by 50% and 30%, respectively, and the root mean square values ​​of yaw rate, sideslip angle, and lateral acceleration also increase significantly. This demonstrates that existing control strategies are insufficient to provide robust solutions for complex driving environments.

[0008] Therefore, this application provides a path tracking method for four-wheel steering vehicles based on extension control theory. Summary of the Invention

[0009] The purpose of this invention is to provide a four-wheel steering vehicle path tracking method based on extension control theory. The method utilizes an extension controller in the decision control module to determine the control laws for the front and rear wheels. This extension controller establishes the vehicle-road coupling state through extension control methods, linking different control strategies with the front / rear wheel steering coefficients. The control execution module calculates the front and rear wheel angles using model predictive control. This control architecture strategically uses the front and rear wheel sideslip angles as real-time constraints, simultaneously considering path tracking accuracy and vehicle stability, thus solving the problems of existing technologies lacking adaptability to different operating conditions, poor compatibility, and limited applicability.

[0010] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: This invention relates to a path tracking method for four-wheel steering vehicles based on extension control theory, comprising the following steps: Step S1: Establish the vehicle-road coupling state through the extension controller in the decision control module, construct the control plane with road curvature and vehicle speed as parameters, and divide the control plane into classical domain, extension domain and non-domain, where the extension domain includes extension domain I, extension domain II and extension domain III; the extension controller establishes the vehicle-road coupling state through extension control method, associates different control strategies and front / rear wheel steering coefficients with the system, and constructs the control plane; Step S2: Calculate the correlation degree of the predicted point in the control plane using the extension controller, and determine the area where the vehicle is located in the control plane based on the correlation degree to determine the control coefficient equation between the front and rear wheel steering angles; Step S3: The model prediction controller in the control execution module dynamically optimizes the steering angles of the front and rear wheels based on the vehicle path model, through a piecewise affine model of tire lateral force and vehicle stability constraints.

[0011] Furthermore, the overall architecture of the path tracking method consists of a decision control module and a control execution module. The decision control module determines the control laws for the front and rear wheels through an extension controller. The control execution module calculates the angles of the front and rear wheels through model predictive control.

[0012] Furthermore, in step S2, the method for calculating the correlation degree of the predicted points in the control plane using the extension controller is as follows: ; Among them, X C X1, X2, X3 and X N Let E1, E2, E3, and E4 be the classical domain, extensional domain I, extensional domain II, extensional domain III, and non-domain in the control plane, respectively, and let E3, E4, and E5 be points in the control plane, where the coordinates of the points (V) are given by the coordinates of the points (V). S4 (0) is point E4, E p To control any prediction point in the plane, For non-domain correlation parameters, |EiEj| represents the distance between points Ei and Ej; Eo, E1, E2, and E3 are the line connections between the predicted point and E4, and V=0, V=V, respectively. S1 V=V S2 and V=V S3 The intersection point.

[0013] Furthermore, in step S2, the method for determining the area where the vehicle is located in the control plane based on the correlation degree includes the following steps: like satisfy Then the vehicle state corresponds to the classical domain, and the rear wheels are set to perform maximum angle reverse steering; like satisfy Then the vehicle state corresponds to the extension domain I, and the rear wheel steering angle is determined by proportional control combined with a two-degree-of-freedom vehicle model. like satisfy The vehicle state corresponds to the extension domain II, and the rear wheel steering angle is determined by the yaw rate; like satisfy The vehicle state corresponds to the extension domain III, and the rear wheel steering angle is determined by the yaw rate; like satisfy The vehicle state corresponds to the non-domain, and the rear wheel steering angle is determined by the rear wheel yaw angle threshold.

[0014] Furthermore, it also includes: calculating vehicle state parameters through the vehicle road module and providing inputs for the extension controller and model predictive controller; the vehicle road module is established in the Frenet-Serret vehicle-road coordinate system and includes a vehicle path model and a piecewise affine model of tire lateral forces.

[0015] Furthermore, the segmented affine model divides the tire lateral force characteristics into a linear region, a near-saturated region, and a saturated region, with each region corresponding to a different tire slip angle range.

[0016] Furthermore, the piecewise affine model, based on the piecewise affine method of the Brush tire model, characterizes the tire lateral force, which is: ; in, This refers to the tire slip angle. , Corresponding to the front tire, Corresponding rear tire; , and These are model parameters, and , and This is the dividing point; when At that time, the tire is considered to be operating within the linear region; when At that time, the tires were considered to be operating near the saturation range; when At that time, the tire is considered to be operating in the saturation region.

[0017] Furthermore, the vehicle state parameters include lateral offset e y and heading error , The motion error dynamic equation representing the spatial relationship between the vehicle and the path in the vehicle path model is as follows: ; Among them, v x and v y These represent the longitudinal velocity and the lateral velocity in the coordinate system of a fixed object, respectively. The curvature of the parameterized target path is evaluated at the projection point. This indicates the yaw rate of the vehicle. s represents the longitudinal position of the vehicle along the target path relative to its curvature; Let yaw angle be the vehicle's yaw angle in the vehicle's fixed coordinate system. The angle between the tangent direction of the target path and the horizontal direction.

[0018] Furthermore, the vehicle road module employs a two-degree-of-freedom vehicle model to establish a two-degree-of-freedom vehicle lateral dynamics model, which is as follows: ; in, Indicates the vehicle's sideslip angle. Corresponding to the total mass of the vehicle, This represents the yaw moment of inertia about the vehicle's vertical axis. and These represent the longitudinal distances from the center of gravity to the front and rear axles, respectively. and These represent the lateral forces generated by the front and rear wheels, respectively.

[0019] Furthermore, in step S3, the model predictive controller also obtains a continuous-time model through vehicle path dynamics discretization. The continuous-time model is as follows: ; Where Ts is the sampling time, The state vector includes the lateral offset e. y and heading error , To control the input vector, including the front wheel steering angle and the rear wheel steering angle, Let A be the perturbation vector. d B d C d and D d Let τ be the system matrix, and let τ represent the local time interval from 0 to Ts.

[0020] Furthermore, the model predictive controller determines the optimal control input by solving a constrained optimization problem, the cost function of which is: ; in: , It is the reference state matrix. It is the scope of control. This is the prediction range, where R and Q are weight matrices. Let R = Set to Q= , The control input for time k+i is predicted at time k. This represents the change in angle.

[0021] The present invention has the following beneficial effects: This invention establishes the vehicle-road coupling state through an extension controller in the decision control module, constructs a control plane using road curvature and vehicle speed as parameters, and divides the control plane into classical, extension, and non-domain regions. The extension controller calculates the correlation degree of the predicted points in the control plane, and determines the region where the vehicle is located in the control plane based on the correlation degree to determine the control coefficient equation between the front and rear wheel steering angles. The model predictive controller in the control execution module is based on the vehicle path model and dynamically optimizes the steering angles of the front and rear wheels through a piecewise affine model of tire lateral force and vehicle stability constraints. The correlation degree dynamically establishes the steering coordination relationship between the front and rear wheels under different vehicle-road conditions. The model predictive controller, considering the stability constraints of tire slip angle, is designed to simultaneously determine the steering angles of the front and rear wheels during path tracking. By considering the front and rear wheel steering angles as a whole, it can improve the vehicle's path tracking accuracy while ensuring vehicle stability. It also takes into account changes in vehicle speed and road parameters, which can improve the path tracking accuracy and driving stability of four-wheel steering vehicles.

[0022] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the path tracking method for four-wheel steering intelligent vehicles based on extension control and model predictive control according to the present invention. Figure 2 This is a schematic diagram of a vehicle-road model based on the Frenet-Serret coordinate system. Figure 3 This is a schematic diagram showing the relationship between tire slip angle and tire lateral force. Figure 4 This is a schematic diagram of the control plane. Detailed Implementation

[0025] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0026] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0027] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0028] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0029] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0030] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0031] Example 1: Please see Figure 1As shown, this invention is a path tracking method for four-wheel steering vehicles based on extension control theory, comprising the following steps: Step S1: Establish the vehicle-road coupling state through the extension controller in the decision control module, based on road curvature. and vehicle speed Construct a control plane for the parameters and divide the control plane into classical domain, extension domain, and non-domain. Among them, the extension domains include extension domain I, extension domain II and extension domain III; Step S2: Calculate the correlation degree of the predicted point in the control plane using the extension controller, and determine the area where the vehicle is located in the control plane based on the correlation degree to determine the control coefficient equation between the front and rear wheel steering angles; Step S3: The model prediction controller in the control execution module dynamically optimizes the steering angles of the front and rear wheels based on the vehicle path model, through a piecewise affine model of tire lateral force and vehicle stability constraints.

[0032] The decision control module determines the control laws for the front and rear wheels through an extension controller. The extension controller establishes the vehicle-road coupling state using extension control methods, linking different control strategies with the front / rear wheel steering coefficients. The control execution module calculates the front and rear wheel angles using model predictive control. This control architecture strategically uses the front and rear wheel slip angles as real-time constraints, balancing path tracking accuracy and vehicle stability. This method effectively addresses various vehicle-road environments, improving path tracking accuracy while ensuring vehicle stability.

[0033] Example 2: This invention relates to a four-wheel steering vehicle path tracking method based on extension control theory. Based on Embodiment 1, this method is implemented using a vehicle path tracking system. The overall architecture of the path tracking method consists of a decision control module and a control execution module. The decision control module determines the control laws for the front and rear wheels through an extension controller. The control execution module calculates the angles of the front and rear wheels using model predictive control. The system includes: a decision control module, a control execution module, and a vehicle path module.

[0034] As attached Figure 4 As shown, in a preferred embodiment of the present invention, the decision control module determines the control laws of the front and rear wheels through an extension controller. The control execution module predicts the front and rear wheel angles through a model prediction controller; the extension controller establishes the vehicle-road coupling state through extension control methods, correlates different control strategies with the front / rear wheel steering coefficients, and constructs a control plane. — , Indicates the curvature of the road. The vehicle speed is represented by the control plane, which is divided into three parts: the classical domain, the extension domain, and the non-domain. The extension domain is further subdivided into three different regions. Based on this, the critical value of road curvature and the classical domain of vehicle speed are respectively set as... and The critical value of road curvature and the vehicle speed I of the extended region are respectively set as and The critical value of road curvature and the vehicle speed II of the extrinsic domain are respectively set as follows: and The critical value of road curvature and the vehicle speed Ⅲ of the scalable domain are respectively set as follows: and As attached Figure 4 As shown. Based on this, the critical value of road curvature and the classical domain of vehicle speed are respectively set as... and The critical value of road curvature and the vehicle speed I of the extended region are respectively set as and The critical value of road curvature and the vehicle in the extrinsic region are respectively set as and The critical value of road curvature and the vehicle speed of the extrinsic domain are respectively set as follows: and .

[0035] As an embodiment of the present invention, preferably, the control execution module includes a model prediction controller, which, based on a vehicle path model, determines the steering angles of the front and rear wheels, so that... Switch between different areas of the PWA.

[0036] As an embodiment of the present invention, preferably, the vehicle-road module, based on the commonly used two-degree-of-freedom front-wheel steering model, introduces active rear-wheel drive to establish an enhanced steering dynamics architecture. The developed two-degree-of-freedom four-wheel steering model is mathematically embedded into the Frenet-Serret vehicle-road coordinate system, as shown in the appendix. Figure 2 As shown.

[0037] Example 3: Please see Figure 1 As shown, this invention is a path tracking method for four-wheel steering vehicles based on extension control theory, comprising the following steps: Step S1: The overall architecture of the path tracking method consists of a decision control module and a control execution module. The decision control module determines the control laws of the front and rear wheels through an extension controller, and the control execution module calculates the angles of the front and rear wheels through model predictive control. The vehicle-road coupling state is established through the extension controller in the decision control module, taking into account the road curvature. and vehicle speed Construct a control plane for the parameters and divide the control plane into a classical domain, an extension domain, and a non-domain. The extension domain includes extension domain I, extension domain II, and extension domain III. Step S2: Calculate the correlation degree of the predicted point in the control plane through the extension controller. Determine the area where the vehicle is located in the control plane based on the correlation degree to determine the control coefficient equation between the front and rear wheel steering angles. Step S3: The model prediction controller in the control execution module dynamically optimizes the steering angles of the front and rear wheels based on the vehicle path model, through a piecewise affine model of tire lateral force and vehicle stability constraints.

[0038] As attached Figure 4 As shown, in a preferred embodiment of the present invention, the method for calculating the correlation degree of the predicted point in the control plane using the extension controller in step S2 is as follows: ; Among them, X C X1, X2, X3 and X N They are respectively represented as appendices Figure 4 Classical domain, extensional domain I, extensional domain II, extensional domain III and non-domain, E1, E2, E3 and E4 are the control planes. - The point in the middle, where the coordinates of the point (V) S4 (0) is point E4, E p To control any prediction point in the plane, For non-domain correlation parameters, |EiEj| represents the distance between points Ei and Ej; Eo, E1, E2, and E3 are the line connections between the predicted point and E4, and V=0, V=V, respectively. S1 V=V S2 and V=V S3 The intersection point.

[0039] As an embodiment of the present invention, preferably, the extension controller determines the predicted feature state in the control plane. Location to determine The coefficient equation for the rear wheel steering angle, The output of the extension controller is defined as follows: The control equations represent the relationship between the steering angles of the front and rear wheels of a vehicle. The control domain division and the corresponding control method selection are as follows: like satisfy The vehicle state corresponds to the classical domain. In this state, the vehicle speed is low, the road curvature of the target path is large, the rear wheels are set to perform maximum angle reverse steering, and the control coefficient equation is: ; like satisfy The vehicle state corresponds to the extension domain I. In this state, the vehicle speed is in the low to medium speed range, the road surface curvature is moderate, and the main objective during path following is to ensure tracking accuracy. Proportional control combined with a two-degree-of-freedom vehicle model is used to determine the rear wheel steering angle. The equation for the control coefficient is: ; like satisfy The vehicle state corresponds to Expansion Domain II. In this state, the vehicle speed is in the medium-to-high speed range, the road curvature is relatively small, and maintaining vehicle stability during path tracking becomes the primary consideration. The rear wheel steering angle increases proportionally with vehicle speed. The rear wheel steering angle is determined using yaw rate, combined with... Combining the two-degree-of-freedom vehicle model, the control coefficient equations are: ; like satisfy The vehicle state corresponds to Expansion Domain III. In this state, the vehicle speed is in the high-speed range. While prioritizing vehicle stability, path tracking accuracy is also considered. The rear wheel steering angle decreases as the vehicle speed increases. The yaw rate is used to determine the rear wheel steering angle, and the control coefficient equation is: ; like satisfy The vehicle state corresponds to the non-domain. The rear wheel steering angle is determined using the rear wheel yaw angle threshold in the same direction. To balance handling performance and stability, the rear wheels are configured to yaw by a limited angle in the same direction. The control coefficient equation is: ; in, The threshold for the maximum reverse steering angle of the rear wheels , The threshold for the rear wheel yaw angle in the same direction. , These are the longitudinal distances from the vehicle's center of gravity to the front and rear axles, respectively; m is the vehicle's total mass; and k is the weight of the vehicle. ji k ri These are the front tire stiffness and rear tire stiffness, respectively, v x For longitudinal velocity, This refers to the front wheel steering angle. The lateral angle; Therefore, the control coefficient equations output by the extension controller are: In the above formula, Follow It changes with the changes.

[0040] As an embodiment of the present invention, preferably, it further includes: calculating vehicle state parameters through a vehicle road module and providing inputs to the extension controller and the model predictive controller; the vehicle road module is established in the Frenet-Serret vehicle-road coordinate system and includes a vehicle path model and a piecewise affine model of tire lateral forces.

[0041] As an embodiment of the present invention, preferably, the segmented affine model divides the tire lateral force characteristics into a linear region, a near-saturated region, and a saturated region, with the linear region, near-saturated region, and saturated region corresponding to different tire slip angle ranges.

[0042] As an embodiment provided by the present invention, preferably, such as Figure 2 As shown, and These represent the front wheel angle and the rear wheel angle, respectively. and These represent the front wheel slip angle and the rear wheel slip angle, respectively. This indicates the lateral shift of the vehicle's center of gravity relative to the target path, while... The directional error of the vehicle relative to the target path. By analyzing the distance and direction relationship between the vehicle and the target path, motion error dynamics characterizing the spatial relationship between the vehicle and the path are derived. The vehicle state parameters include lateral offset e. y and heading error The motion error dynamic equation representing the spatial relationship between the vehicle and the path in the vehicle path model is as follows: ; Among them, v x and v y These represent the longitudinal velocity and the lateral velocity in the coordinate system of a fixed object, respectively. Curvature of the parameterized target path evaluated at the projection point , This indicates the vehicle's yaw rate. s represents the longitudinal position of the vehicle along the target path relative to its curvature; Let yaw angle be the vehicle's yaw angle in the vehicle's fixed coordinate system. The angle between the tangent direction of the target path and the horizontal direction.

[0043] As an embodiment of the present invention, preferably, the vehicle road module uses a two-degree-of-freedom vehicle model to establish a two-degree-of-freedom vehicle lateral dynamics model, assuming... As a constant, the lateral dynamics model of the vehicle is: ; in, Indicates the vehicle's sideslip angle. Corresponding to the total mass of the vehicle, This represents the yaw moment of inertia about the vehicle's vertical axis. and These represent the longitudinal distances from the center of gravity to the front and rear axles, respectively. and These represent the lateral forces generated by the front and rear wheels, respectively.

[0044] As attached Figure 3 As shown, in one embodiment of the present invention, preferably, after a comprehensive evaluation of the computational complexity of various tire models, the piecewise affine model characterizes the tire lateral force based on the piecewise affine method of the Brush tire model. The tire lateral force is: ; in, This refers to the tire slip angle. , Corresponding to the front tire, Corresponding rear tire; , and These are model parameters, and The piecewise affine approximation method divides the tire lateral force characteristics into three distinct operating regions: the linear region, the near-saturation region, and the saturation region. and This is the dividing point; when At that time, the tire is considered to be operating within the linear region; when At this point, the tire is considered to be operating in a near-saturation region, and the lateral force of the tire is close to saturation; when At that time, the tire is considered to be operating in the saturation region. and The relationship diagram is attached. Figure 3 As shown.

[0045] This invention comprehensively considers the different characteristics of various control methods and the unique steering characteristics of the front and rear wheels through an extension controller. This controller dynamically establishes the steering coordination relationship between the front and rear wheels under different vehicle-road conditions using a correlation function.

[0046] This invention is based on the PWA tire force model and designs a model predictive controller that considers tire slip angle stability constraints, which can simultaneously determine the steering angles of the front and rear wheels during path tracking.

[0047] The model prediction controller of this invention considers the front and rear wheel steering angles as a whole, which can improve the vehicle's path tracking accuracy while ensuring vehicle stability.

[0048] Example 4: Based on Embodiments 1 to 3, as an embodiment provided by the present invention, preferably, in step S3, the model prediction controller further obtains a continuous-time model through vehicle path dynamics discretization, and the continuous-time model is as follows: ; Where Ts is the sampling time, The state vector includes the lateral offset e. y and heading error , To control the input vector, including the front wheel steering angle and the rear wheel steering angle, Let A be the perturbation vector. d B d C d and D d Let τ be the system matrix, representing the local time interval from 0 to Ts. To ensure path tracking convergence, the lateral offset e is... y and heading error It must exhibit asymptotic stability, with an equilibrium point of zero. Furthermore, the controlled variables must change smoothly at each step. Mathematically, the above control objective can be expressed as a constrained optimization problem, where the performance index achieved is equivalent to minimizing the following quadratic cost function, and the optimization objective is to minimize the quadratic cost function: ; in: , It is the reference state matrix. It is the scope of control. This is the prediction range, where R and Q are weight matrices. Let R = Set to Q= , The control input for time k+i is predicted at time k. This represents the change in steering angle; the core of the extension control architecture lies in accurately determining the correlation coefficients between the angular displacements of the front and rear wheels, which are determined by the output of the extended controller. Therefore, The expression is as follows: .

[0049] As an embodiment of the present invention, preferably, in order to ensure the stability of the vehicle when tracking a trajectory, the slip angles of the front and rear tires must meet the following constraints: Furthermore, to account for the mechanical and physical design constraints of the steering mechanism, the steering angles of the front and rear wheels must comply with the following operating boundaries defined by the performance limits of the steering system: The optimal control input is obtained by solving the subsequent finite-time optimal control problem, denoted as: and : ; ; Constrained by the vehicle road model, PWA tire model, and extension controller: ; Instead of imposing rigid boundaries on vehicle stability constraints, non-negative relaxation variables are introduced. and Penalties are imposed for violations of constraints, thereby ensuring the feasibility of the optimization problem at all times. Weights And are assigned relatively large values ​​to ensure that even if the slack variable itself is relatively small, it is related to the slack variable. and Related items It can also dominate the cost function.

[0050] Example 5: Based on Embodiments 1 to 4, as an embodiment provided by the present invention, preferably, the tire slip angles of the wheel and the rear wheel are as follows: ; Combining the above formulas, we can obtain the following formula: ; ; ; The vehicle-road model can be represented as: ; ; ; ; ; in, and As the vehicle's condition changes, the tire slip angle is determined by the PWA's sub-model for that region when the tire force is within a specific area. The tire force and tire slip angle need to be switched between different regions of the PWA.

[0051] A path tracking method for four-wheel steering vehicles based on extension control theory is proposed. The extension controller divides the working area according to vehicle-road state parameters and determines the relationship between the front and rear wheel steering angles. A model predictive controller capable of simultaneously determining the steering angles of both the front and rear wheels is employed. This model predictive controller is based on the PWA tire force model and stability constraints of tire slip angle. The proposed method effectively improves path tracking accuracy and ensures vehicle driving stability. Furthermore, this invention considers both vehicle speed and road parameter variations, thereby enhancing both path tracking accuracy and vehicle driving stability in four-wheel steering vehicles.

[0052] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0053] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A path tracking method for four-wheel steering vehicles based on extension control theory, characterized in that, Includes the following steps: Step S1: Establish the vehicle-road coupling state through the extension controller in the decision control module, construct the control plane with road curvature and vehicle speed as parameters, and divide the control plane into classical domain, extension domain and non-domain, where the extension domain includes extension domain I, extension domain II and extension domain III. Step S2: Calculate the correlation degree of the predicted point in the control plane using the extension controller, and determine the area where the vehicle is located in the control plane based on the correlation degree to determine the control coefficient equation between the front and rear wheel steering angles; Step S3: The model prediction controller in the control execution module dynamically optimizes the steering angles of the front and rear wheels based on the vehicle path model, through a piecewise affine model of tire lateral force and vehicle stability constraints.

2. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 1, characterized in that, In step S2, the method for calculating the correlation degree of the predicted points in the control plane using the extension controller is as follows: ； Among them, X C X1, X2, X3 and X N Let E1, E2, E3, and E4 be the classical domain, extensional domain I, extensional domain II, extensional domain III, and non-domain in the control plane, respectively, and let E3, E4, and E5 be points in the control plane, where the coordinates of the points (V) are given by the coordinates of the points (V). S4 (0) is point E4, E p To control any prediction point in the plane, For non-domain correlation parameters, |EiEj| represents the distance between points Ei and Ej; Eo, E1, E2, and E3 are the line connections between the predicted point and E4, and V=0, V=V, respectively. S1 V=V S2 and V=V S3 The intersection point.

3. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 1, characterized in that, In step S2, the method for determining the area where the vehicle is located in the control plane based on the correlation degree includes the following steps: like satisfy Then the vehicle state corresponds to the classical domain, and the rear wheels are set to perform maximum angle reverse steering; like satisfy Then the vehicle state corresponds to the extension domain I, and the rear wheel steering angle is determined by proportional control combined with a two-degree-of-freedom vehicle model. like satisfy The vehicle state corresponds to the extension domain II, and the rear wheel steering angle is determined by the yaw rate; like satisfy The vehicle state corresponds to the extension domain III, and the rear wheel steering angle is determined by the yaw rate; like satisfy The vehicle state corresponds to the non-domain, and the rear wheel steering angle is determined by the rear wheel yaw angle threshold.

4. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 1, characterized in that, Also includes: The vehicle state parameters are calculated through the vehicle road module and provided as inputs to the extension controller and model predictive controller. The vehicle-road module is built in the Frenet-Serret vehicle-road coordinate system and includes a vehicle path model and a piecewise affine model of tire lateral forces.

5. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 4, characterized in that, The segmented affine model divides the tire lateral force characteristics into a linear region, a near-saturated region, and a saturated region, with each region corresponding to a different tire slip angle range.

6. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 4, characterized in that, The piecewise affine model, based on the piecewise affine method of the Brush tire model, characterizes the tire lateral force, which is: ； in, This refers to the tire slip angle. , Corresponding to the front tire, Corresponding rear tire; , and These are model parameters, and , and This is the dividing point; when At that time, the tire is considered to be operating within the linear region; when At that time, the tires were considered to be operating near the saturation range; when At that time, the tire is considered to be operating in the saturation region.

7. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 6, characterized in that, The vehicle state parameters include lateral offset e y and heading error , The motion error dynamic equation representing the spatial relationship between the vehicle and the path in the vehicle path model is as follows: ； Among them, v x and v y These represent the longitudinal velocity and the lateral velocity in the coordinate system of a fixed object, respectively. The curvature of the parameterized target path is evaluated at the projection point. This indicates the yaw rate of the vehicle. s represents the longitudinal position of the vehicle along the target path relative to its curvature; Let yaw angle be the vehicle's yaw angle in the vehicle's fixed coordinate system. The angle between the tangent direction of the target path and the horizontal direction.

8. The four-wheel steering vehicle path tracking method based on extension control theory according to claim 7, characterized in that, The vehicle road module uses a two-degree-of-freedom vehicle model to establish a two-degree-of-freedom vehicle lateral dynamics model. The vehicle lateral dynamics model is as follows: ； in, Indicates the vehicle's sideslip angle. Corresponding to the total mass of the vehicle, This represents the yaw moment of inertia about the vehicle's vertical axis. and These represent the longitudinal distances from the center of gravity to the front and rear axles, respectively. and These represent the lateral forces generated by the front and rear wheels, respectively.

9. A four-wheel steering vehicle path tracking method based on extension control theory according to claim 1, characterized in that, In step S3, the model predictive controller further obtains a continuous-time model through vehicle path dynamics discretization. The continuous-time model is as follows: ； Where Ts is the sampling time, The state vector includes the lateral offset e. y and heading error , To control the input vector, including the front wheel steering angle and the rear wheel steering angle, Let A be the perturbation vector. d B d C d and D d For the system matrix, Let Ts be the local time interval from 0 to Ts.

10. A four-wheel steering vehicle path tracking method based on extension control theory according to claim 9, characterized in that, The model predictive controller determines the optimal control input by solving a constrained optimization problem, the cost function of which is: ； in: , It is the reference state matrix. It is the scope of control. This is the prediction range, where R and Q are weight matrices. Let R = Set to Q= , The control input for time k+i is predicted at time k. This represents the change in angle.

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