Double-track vehicle dynamics modeling method based on simplified tire model

Abstract

The invention discloses a double-track vehicle dynamics modeling method based on a simplified tire model, and relates to the technical field of vehicle dynamics modeling. The method comprises the following steps: constructing a double-track vehicle dynamics model according to a simplified tire model and a vehicle body dynamics model; the simplified tire model can describe the loss of tire lateral force caused by tire force saturation within a large longitudinal force output range, and when no longitudinal force is output, the simplified tire model is degraded into a corresponding tire model under a pure lateral deviation working condition; according to the condition that the course angle and the speed angle of the vehicle are inconsistent under the condition of a large side slip angle, a Frenet coordinate system kinematic model is constructed; building a tire load transfer model according to the dynamic response of the first-order response approximate tire load; and according to the double-track vehicle dynamic model, the Frenet coordinate system kinematic model and the tire load transfer model, a double-track vehicle state space equation is determined. According to the method, the model complexity is reduced, and meanwhile, high prediction precision is still achieved.

Description

Technical Field

[0001] This invention relates to the field of vehicle dynamics modeling technology, and in particular to a dual-track vehicle dynamics modeling method based on a simplified tire model. Background Technology

[0002] Accurate modeling of vehicle dynamics has long been a crucial research area in vehicle dynamics control. A precise dynamic model can provide better performance for current mainstream planning and control methods, while also improving safety and energy efficiency. Especially with the rapid development of autonomous driving and electric vehicle technologies, which are gradually becoming mainstream research directions, an accurate yet relatively simple vehicle dynamics model can be widely applied to electronic stability control systems and autonomous driving control systems. The most important part of the vehicle dynamics model is the interaction medium between the vehicle and the ground: the tires.

[0003] In existing technologies, model-based vehicle dynamics control methods mainly use linear tire models for vehicle dynamics and nonlinear tire models for pure sideslip conditions. Linear models perform well under low- and medium-speed constant-speed conditions, but are prone to model mismatch issues under high-speed constant-speed conditions. Nonlinear tire models using pure sideslip conditions perform well under constant-speed conditions at any speed, but also exhibit model mismatch problems when the vehicle undergoes significant acceleration or deceleration. This model mismatch is mainly caused by the saturation of total tire force, thus requiring more complex tire models to characterize the lateral and longitudinal force coupling of the tire. However, overly complex formulas and a large number of parameters make it difficult for tire models to update parameters online to adapt to different road surfaces. Summary of the Invention

[0004] Therefore, it is necessary to provide a dual-track vehicle dynamics modeling method based on a simplified tire model to address the above-mentioned technical problems. This method can reduce the complexity of the model while still maintaining high prediction accuracy.

[0005] The present invention adopts the following technical solution: This invention provides a method for dynamic modeling of dual-track vehicles based on a simplified tire model, comprising: Based on the simplified tire model and vehicle dynamics model, a dual-track vehicle dynamics model is constructed. The simplified tire model can describe the loss of tire lateral force due to tire force saturation within a large longitudinal force output range. When there is no longitudinal force output, the simplified tire model degenerates into the corresponding tire model for pure lateral slip conditions. Based on the situation where the heading angle and velocity angle of a vehicle are inconsistent under large sideslip angles, a kinematic model in the Frenet coordinate system is constructed. A tire load transfer model is constructed based on the first-order response approximating the dynamic response of the tire load. Based on the dynamics model of the dual-rail vehicle, the kinematic model of the Frenet coordinate system, and the tire load transfer model, the state-space equations of the dual-rail vehicle are determined.

[0006] Alternatively, the tire model can be simplified as follows: ; in, To account for tire lateral forces at tire force saturation; The tire lateral force calculated for a given pure sideslip condition is the tire lateral force obtained by ignoring the longitudinal slip ratio of the tire under the current tire sideslip angle. This refers to the longitudinal force of the tire; This refers to the vertical load on the tire; This is the adhesion coefficient of the road surface.

[0007] Optionally, the tire lateral force model under pure lateral slip conditions is as follows: ; in, These are the parameters for the Magic Tire formula; It represents the lateral slip ratio; subscript and These represent the front and rear wheels, respectively, with subscripts 1 and 2 indicating the left and right wheels, respectively; the lateral slip ratios of the four wheels are expressed as: ; in, The speed at the vehicle's center of gravity; It is the sideslip angle of the vehicle's center of gravity, that is, the angle between the velocity direction and the heading of the vehicle; The yaw rate of the vehicle; These are the distances from the vehicle's center of gravity to the front axle, the rear axle, and the center of the left and right tires, respectively. Indicates the front wheel steering angle.

[0008] Optionally, the vehicle body dynamics model is: ; ; ; in, The speed at the vehicle's center of gravity; It is the sideslip angle of the vehicle's center of gravity, that is, the angle between the velocity direction and the heading of the vehicle; The yaw rate of the vehicle; For the quality of the vehicle; For the execution office to bypass Moment of inertia of the shaft; These are the distances from the vehicle's center of gravity to the front axle, the rear axle, and the center of the left and right tires, respectively. Indicates the front wheel steering angle; Indicates tire force, subscript Indicates the longitudinal and lateral directions respectively, subscripts These represent the front and rear wheels, respectively, with subscripts. Represent the left and right wheels respectively; for any variable , This variable The derivative with respect to time.

[0009] Optionally, the kinematic model of the Frenet coordinate system is: ; in, This represents the vertical movement distance; for The derivative with respect to time; The speed at the vehicle's center of gravity; This refers to lateral error; for The derivative with respect to time; This represents the error between the vehicle speed direction and the Frenet coordinate system direction. for The derivative with respect to time; For the present The corresponding path curvature; The sideslip angle is the vehicle's center of gravity. for The derivative with respect to time.

[0010] Optionally, the tire load transfer model is as follows: ; ; ; ; in, For the vertical load of the tire, subscript and These represent the front wheel and the rear wheel, respectively, with subscripts 1 and 2 representing the left wheel and the right wheel, respectively. For the quality of the vehicle; These are the distances from the vehicle's center of gravity to the rear axle and the distances to the centers of the left and right tires, respectively. This is the distance between the front and rear axles of the vehicle. The height of the vehicle's center of gravity; It is the acceleration due to gravity; and These are the vehicle's steady-state accelerations along the x-axis and y-axis, respectively. and The calculation formula is: ; ; ; ; in, and These are the vehicle's pseudo-accelerations along the x and y axes, respectively. The speed at the vehicle's center of gravity; for The derivative with respect to time; The sideslip angle is the vehicle's center of gravity. for The derivative with respect to time; The yaw rate of the vehicle; It is the approximate characteristic time of the approximate first-order response from pseudo-acceleration to stable acceleration.

[0011] Optionally, the state-space equation for the dual-track vehicle is: ; in, State variables , The speed at the vehicle's center of gravity; The sideslip angle is the vehicle's center of gravity. The yaw rate of the vehicle; It represents the lateral slip ratio; This refers to lateral error; This represents the error between the vehicle speed direction and the Frenet coordinate system direction. and These are the vehicle's steady-state accelerations along the x-axis and y-axis, respectively. for The derivative with respect to time; This represents the equations formed by the dual-track vehicle dynamics model, the Frenet coordinate system kinematic model, and the tire load transfer model. To control the amount , Indicates the front wheel steering angle. These represent the longitudinal tire forces of the vehicle's left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0012] Optionally, the method further includes: The vehicle trajectory is tracked using a dual-track vehicle state-space equation.

[0013] This invention provides a dual-track vehicle dynamics modeling device based on a simplified tire model, comprising: The first building module is used to construct a dual-track vehicle dynamics model based on a simplified tire model and a vehicle dynamics model. The simplified tire model can describe the loss of tire lateral force due to tire force saturation within a large longitudinal force output range. When there is no longitudinal force output, the simplified tire model degenerates into the corresponding tire model for the pure lateral bias condition. The second construction module is used to construct a Frenet coordinate system kinematic model based on the situation where the heading angle and velocity angle are inconsistent under large sideslip angles. The third building module is used to construct a tire load transfer model based on the dynamic response of the tire load approximated by the first-order response. The fourth construction module is used to determine the state-space equations of the dual-rail vehicle based on the dual-rail vehicle dynamics model, the Frenet coordinate system kinematic model, and the tire load transfer model.

[0014] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for modeling the dynamics of a dual-track vehicle based on a simplified tire model.

[0015] The present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described dual-track vehicle dynamics modeling method based on a simplified tire model.

[0016] The above-mentioned at least one technical solution adopted in this invention can achieve the following beneficial effects: In this invention, to reduce model complexity and reasonably represent tire force saturation relationships, a simplified tire model is proposed. This simplified tire model can describe the loss of tire lateral force due to tire force saturation within a large longitudinal force output range. When there is no longitudinal force output, the simplified tire model degenerates into the corresponding tire model for pure sideslip conditions. Furthermore, an error-free Frenet coordinate system kinematic model suitable for large sideslip angles is constructed, and a first-order response approximation is performed on the lateral and longitudinal tire load transfer models. Thus, a dual-track vehicle state-space equation is constructed. This state-space model can accurately predict the vehicle's response to control commands in the future. This method simplifies model complexity while maintaining high prediction accuracy. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0018] Figure 1 A schematic diagram of a method for modeling the dynamics of a dual-track vehicle based on a simplified tire model, provided by the present invention; Figure 2 A schematic diagram of a modeling method for vehicle dynamics trajectory tracking provided by the present invention; Figure 3 A schematic diagram showing the planning results of a lap speed simulation planning algorithm for a vehicle model proposed in this invention. Figure 4 A schematic diagram of the simulation results of a model predictive control algorithm for a vehicle model proposed in this invention; Figure 5 A schematic diagram of a computer device for implementing a dual-track vehicle dynamics modeling method based on a simplified tire model, provided by the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0020] In the past era of internal combustion engines, wheel torque output was not a focus. Most of the complex tire models studied were designed to establish the relationship between lateral and longitudinal slip ratios and tire forces, which brought difficulties to the longitudinal dynamic control of wheels.

[0021] Based on this, this invention, combining the characteristic of electric vehicles that can directly and accurately output wheel torque and the need to characterize tire force saturation under lateral and longitudinal coupling conditions, proposes a simplified dual-track vehicle dynamics modeling method for tire models. The aim is to represent the most complex passenger vehicle system currently available—four-wheel independently driven electric vehicles—with as few parameters and a simpler model as possible. The modeling method provided by this invention can be applied to trajectory tracking problems; however, the vehicle dynamics modeling portion is universal and does not need to be bound to the trajectory tracking model.

[0022] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] Figure 1 This is a schematic diagram of a dual-track vehicle dynamics modeling method based on a simplified tire model according to the present invention, which specifically includes the following steps: S101. Based on the simplified tire model and the vehicle dynamics model, a dual-track vehicle dynamics model is constructed. The simplified tire model can describe the loss of tire lateral force due to tire force saturation within a large longitudinal force output range. When there is no longitudinal force output, the simplified tire model degenerates into the corresponding tire model for the pure lateral slip condition.

[0024] The simplified tire model is a simplified tire saturation force model. This simplified tire model describes tire lateral behavior that depends on the slip ratio, but simplifies longitudinal force to tire force. Compared to commonly used combined slip model methods, it avoids the need to control the tire's longitudinal slip ratio. Furthermore, this model can describe the loss of tire lateral force due to tire force saturation over a relatively large range of longitudinal force outputs. When there is no longitudinal force output, the tire model degenerates into the tire model corresponding to the pure sideslip condition. The simplified tire model is as follows:

[0025] (1); in, To account for tire lateral forces at tire force saturation; The tire lateral force calculated for a given pure sideslip condition is the tire lateral force obtained by ignoring the longitudinal slip ratio of the tire under the current tire sideslip angle. This refers to the longitudinal force of the tire; This refers to the vertical load on the tire; This is the adhesion coefficient of the road surface.

[0026] For a given pure sideslip condition, the tire lateral force model calculates the tire lateral force under the current tire sideslip angle, neglecting the influence of the tire's longitudinal slip ratio. For a given longitudinal force input to the tire and tire vertical load The tire lateral force considering tire force saturation is calculated based on formula (1). .

[0027] Optionally, the Magic Tire Formula can be used as the tire lateral force model for pure skewness conditions. The tire lateral force model for pure skewness conditions is as follows: (2); in, These are the parameters for the Magic Tire formula; It represents the lateral slip ratio; subscript and These represent the front and rear wheels, respectively, with subscripts 1 and 2 indicating the left and right wheels, respectively; the lateral slip ratios of the four wheels are expressed as: (3); in, The speed at the vehicle's center of gravity; It is the sideslip angle of the vehicle's center of gravity, that is, the angle between the velocity direction and the heading of the vehicle; The yaw rate of the vehicle; These are the distances from the vehicle's center of gravity to the front axle, the rear axle, and the center of the left and right tires, respectively. Indicates the front wheel steering angle.

[0028] Optionally, the vehicle body dynamics model is: (4); (5); (6); in, The speed at the vehicle's center of gravity; It is the sideslip angle of the vehicle's center of gravity, that is, the angle between the velocity direction and the heading of the vehicle; The yaw rate of the vehicle; For the quality of the vehicle; For the execution office to bypass Moment of inertia of the shaft; These are the distances from the vehicle's center of gravity to the front axle, the rear axle, and the center of the left and right tires, respectively. Indicates the front wheel steering angle; Indicates tire force, subscript Indicates the longitudinal and lateral directions respectively, subscripts These represent the front and rear wheels, respectively, with subscripts. Represent the left and right wheels respectively; for any variable , This variable The derivative with respect to time.

[0029] The simplified tire model and the vehicle body dynamics model are combined to obtain the dual-track vehicle dynamics model, which includes the equations (1)-(6) combined.

[0030] S102. Based on the situation where the heading angle and velocity angle of the vehicle are inconsistent under large sideslip angles, a Frenet coordinate system kinematic model is constructed.

[0031] This invention uses the Frenet coordinate system to describe the vehicle dynamics modeling problem. Considering the inconsistency between the heading angle and velocity angle under large sideslip angles, a Frenet coordinate system kinematic model is constructed. The Frenet coordinate system kinematic model is as follows: (7); in, This represents the vertical movement distance; for The derivative with respect to time; The speed at the vehicle's center of gravity; This refers to lateral error; for The derivative with respect to time; This represents the error between the vehicle speed direction and the Frenet coordinate system direction. for The derivative with respect to time; For the present The corresponding path curvature; The sideslip angle is the vehicle's center of gravity. for The derivative with respect to time. Note that compared to the commonly used formula for heading error, the formula used in this invention has one more variable. When the vehicle's sideslip angle is very small Therefore, the commonly used formula can be considered accurate, but when the vehicle's sideslip angle changes significantly, It should not be overlooked that only the formulas used in this invention are precise.

[0032] S103. Based on the first-order response approximating the dynamic response of the tire load, a tire load transfer model is constructed.

[0033] The tire load transfer model is as follows: (8); (9); (10); (11); in, For the vertical load of the tire, subscript and These represent the front wheel and the rear wheel, respectively, with subscripts 1 and 2 representing the left wheel and the right wheel, respectively. For the quality of the vehicle; These are the distances from the vehicle's center of gravity to the rear axle and the distances to the centers of the left and right tires, respectively. This is the distance between the front and rear axles of the vehicle. The height of the vehicle's center of gravity; It is the acceleration due to gravity; and These are the vehicle's steady-state accelerations along the x-axis and y-axis, respectively. and The calculation formula is: (12); (13); (14); (15); in, and These are the vehicle's pseudo-accelerations along the x and y axes, respectively. The speed at the vehicle's center of gravity; for The derivative with respect to time; The sideslip angle is the vehicle's center of gravity. for The derivative with respect to time; The yaw rate of the vehicle; It is the approximate characteristic time of the approximate first-order response from pseudo-acceleration to stable acceleration.

[0034] This invention approximates the first-order response of the lateral and longitudinal tire load transfer models and calculates the four-wheel load based on the current load transfer pseudo-acceleration.

[0035] S104. Based on the dual-track vehicle dynamics model, Frenet coordinate system kinematics model, and tire load transfer model, determine the state-space equations of the dual-track vehicle.

[0036] The state-space equation for a dual-track vehicle is: (16); in, State variables , The speed at the vehicle's center of gravity; The sideslip angle is the vehicle's center of gravity. The yaw rate of the vehicle; It represents the lateral slip ratio; This refers to lateral error; This represents the error between the vehicle speed direction and the Frenet coordinate system direction. and These are the vehicle's steady-state accelerations along the x-axis and y-axis, respectively. for The derivative with respect to time; This represents the equations formed by the dual-track vehicle dynamics model, the Frenet coordinate system kinematic model, and the tire load transfer model. To control the amount , Indicates the front wheel steering angle. These represent the longitudinal tire forces of the vehicle's left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. In some cases, this can be adjusted... Scaling should be done appropriately.

[0037] In one embodiment, the trajectory tracking problem of a dual-track vehicle dynamics model can be solved by using the dual-track vehicle state-space equation.

[0038] The dual-track vehicle dynamics modeling method based on a simplified tire model provided in this invention simultaneously considers wheel steering angle control input and four-wheel torque distribution control input, rather than using a hierarchical approach where the upper layer considers wheel steering angle and desired yaw moment, and the lower layer considers four-wheel torque distribution. Compared to traditional hierarchical methods, the method presented in this invention can consider tire load transfer and tire force saturation, thus achieving higher accuracy.

[0039] In the method of this invention, the tire force modeling parameters based on the pure sideslip condition can well fit the real model under this condition. Furthermore, by adjusting the ground adhesion coefficient estimation and combining it with the tire force saturation model of this invention, a high-precision characterization of the tire's lateral and longitudinal coupling characteristics can be achieved. Therefore, it is considered applicable to any adhesion condition. In addition, the "simplified tire model" referred to in this invention means a simplification compared to the combined slip tire model, while the model proposed in this invention has slightly increased complexity compared to the pure sideslip tire model.

[0040] The dual-track vehicle dynamics modeling method based on a simplified tire model provided by this invention is a vehicle dynamics mechanism model obtained by trajectory tracking motion control of common four-wheel Ackerman steering vehicles on flat roads, such as... Figure 2 As shown, the specific construction methods include: 1. Establish a vehicle body dynamics model based on vehicle physical parameters, and establish a simplified tire model based on the pure tire sideslip condition.

[0041] 2. By combining the vehicle body dynamics model and the simplified tire model, a complete dual-track vehicle dynamics model is obtained, and a Frenet coordinate system kinematic model for trajectory tracking is derived from the dual-track vehicle dynamics model.

[0042] 3. Based on the current vehicle body dynamics model, derive the quasi-static tire load transfer situation, and use the first-order response model to approximate the dynamic response of the tire load to obtain the tire load transfer model.

[0043] 4. Finally, the state-space equations for the dual-track vehicle are obtained. ,in State variables , To control the amount .

[0044] In one embodiment, the optimal control problem is obtained by using the state-space equations of the dual-track vehicle. The optimal control problem is then described as a general nonlinear programming problem using the shooting method or the spectral method, and solved using a nonlinear solver. Figure 3 and Figure 4 The two examples showcase trajectory tracking control based on the state-space equations of a dual-track vehicle proposed in this invention. Both are model predictive control methods. Figure 3 This displays a visualization of the solution results for a single model predictive control. Figure 4 The image shown illustrates the performance of a model predictive controller in a simulation test. The specific implementation of the predictive control method based on the state-space equations of a dual-track vehicle provided by this invention is as follows:

[0045] In the prediction time domain Establish optimization variables in the middle: And design the cost function. And the upper and lower bounds of the state variables: Upper and lower bounds of the control quantity: To establish the following optimal control problem: (17); in, This is the system state quantity measured at the current moment. This problem can be solved using a general nonlinear programming solver, and the first control variable obtained after the solution... The model predictive controller is used as the output of the control system at the current moment, and is measured and output repeatedly in the next control cycle. This process is repeated until the design of the model predictive controller is completed.

[0046] It is worth noting that, in order to highlight the applicability of the proposed method under the condition of large vehicle sideslip angle, the ground-tire model parameters in the two application examples above are set to the parameters corresponding to the gravel road surface. Under these parameters, it can be proven that the occurrence of large sideslip angle is the optimal solution for the shortest time problem. Large sideslip angle generally leads to a large lateral slip ratio of the tire. At this time, the tire is in a strong nonlinear lateral and longitudinal coupling condition. The successful application of the model proposed in this invention proves that the model proposed in this invention can accurately characterize the dynamic characteristics of the vehicle under highly nonlinear conditions.

[0047] This invention provides a dual-track vehicle dynamics modeling method based on a simplified tire model, designed to adapt to the planning and control strategies of four-wheel independent drive vehicles with integrated control. The method employs a dual-track model and includes a first-order approximation of load transfer between the four wheels, while also incorporating steering and four-wheel torque distribution control. Furthermore, to reduce model complexity and reasonably represent tire force saturation relationships, a simplified tire model is proposed. Then, an error-free Frenet coordinate system kinematic model suitable for large slip angles is presented. Finally, the state-space equations for the dual-track vehicle considering load transfer and tire saturation in the trajectory tracking problem of a four-wheel independent drive vehicle are obtained, including eight degrees of freedom and five control variables.

[0048] When applying the dual-track vehicle dynamics modeling method based on a simplified tire model provided by this invention, it is not necessary to... Figure 1 The steps shown are executed in sequence. The specific execution order of each step can be determined as needed, and this invention does not impose any restrictions on it.

[0049] The above describes a method for modeling the dynamics of a dual-rail vehicle based on a simplified tire model, provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding device for modeling the dynamics of a dual-rail vehicle based on a simplified tire model, the device comprising: The first building module is used to construct a dual-track vehicle dynamics model based on a simplified tire model and a vehicle dynamics model. The simplified tire model can describe the loss of tire lateral force due to tire force saturation within a large longitudinal force output range. When there is no longitudinal force output, the simplified tire model degenerates into the corresponding tire model for the pure lateral bias condition. The second construction module is used to construct a Frenet coordinate system kinematic model based on the situation where the heading angle and velocity angle are inconsistent under large sideslip angles. The third building module is used to construct a tire load transfer model based on the dynamic response of the tire load approximated by the first-order response. The fourth construction module is used to determine the state-space equations of the dual-rail vehicle based on the dual-rail vehicle dynamics model, the Frenet coordinate system kinematic model, and the tire load transfer model.

[0050] Specific limitations regarding the dual-rail vehicle dynamics modeling device based on a simplified tire model can be found in the limitations of the dual-rail vehicle dynamics modeling method based on a simplified tire model mentioned above, and will not be repeated here. Each module in the aforementioned dual-rail vehicle dynamics modeling device based on a simplified tire model can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0051] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A method for modeling the dynamics of dual-track vehicles based on a simplified tire model is provided.

[0052] The present invention also provides Figure 5 The schematic diagram of the computer device shown is as follows: Figure 5As shown, at the hardware level, this computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above. Figure 1 A method for modeling the dynamics of dual-track vehicles based on a simplified tire model is provided.

[0053] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0054] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

Claims

1. A method for modeling the dynamics of a dual-track vehicle based on a simplified tire model, characterized in that, include: A dual-track vehicle dynamics model is constructed based on a simplified tire model and vehicle body dynamics model. The simplified tire model can describe the loss of lateral force due to tire force saturation within a large longitudinal force output range. When there is no longitudinal force output, the simplified tire model degenerates into the corresponding tire model for pure lateral slip conditions. Based on the situation where the heading angle and velocity angle of a vehicle are inconsistent under large sideslip angles, a kinematic model in the Frenet coordinate system is constructed. A tire load transfer model is constructed based on the first-order response approximating the dynamic response of the tire load. Based on the dynamics model of the dual-rail vehicle, the kinematic model of the Frenet coordinate system, and the tire load transfer model, the state-space equations of the dual-rail vehicle are determined.

2. The method according to claim 1, characterized in that, The simplified tire model is as follows: ； in, To account for tire lateral forces at tire force saturation; The tire lateral force model calculated for a given pure sideslip condition, ignoring the longitudinal slip ratio of the tire under the current tire sideslip angle; This refers to the longitudinal force of the tire; This refers to the vertical load on the tire; This is the adhesion coefficient of the road surface.

3. The method according to claim 2, characterized in that, The tire lateral force model under pure yaw conditions is as follows: ； in, These are the parameters for the Magic Tire formula; Lateral slip ratio; subscript and These represent the front and rear wheels, respectively, with subscripts 1 and 2 indicating the left and right wheels, respectively; the lateral slip ratios of the four wheels are expressed as: ； in, The speed at the vehicle's center of gravity; It is the sideslip angle of the vehicle's center of gravity, that is, the angle between the velocity direction and the heading of the vehicle; The yaw rate of the vehicle; These are the distances from the vehicle's center of gravity to the front axle, the rear axle, and the center of the left and right tires, respectively. Indicates the steering angle of the front wheels.

4. The method according to claim 1, characterized in that, The vehicle body dynamics model is as follows: ； ； ； in, The speed at the vehicle's center of gravity; It is the sideslip angle of the vehicle's center of gravity, that is, the angle between the velocity direction and the heading of the vehicle; The yaw rate of the vehicle; For the quality of the vehicle; For the execution office to bypass Moment of inertia of the shaft; These are the distances from the vehicle's center of gravity to the front axle, the rear axle, and the center of the left and right tires, respectively. Indicates the front wheel steering angle; Indicates tire force, subscript Indicates the longitudinal and lateral directions respectively, subscripts These represent the front and rear wheels, respectively, with subscripts. Represent the left and right wheels respectively; for any variable , This variable The derivative with respect to time.

5. The method according to claim 1, characterized in that, The kinematic model of the Frenet coordinate system is as follows: ； in, This represents the vertical movement distance; for The derivative with respect to time; The speed at the vehicle's center of gravity; This refers to lateral error; for The derivative with respect to time; This represents the error between the vehicle speed direction and the Frenet coordinate system direction. for The derivative with respect to time; For the present The corresponding path curvature; The sideslip angle is the center of gravity of the vehicle. for The derivative with respect to time.

6. The method according to claim 1, characterized in that, The tire load transfer model is as follows: ； ； ； ； in, For the vertical load of the tire, subscript and These represent the front wheel and the rear wheel, respectively, with subscripts 1 and 2 representing the left wheel and the right wheel, respectively. For the quality of the vehicle; These are the distances from the vehicle's center of gravity to the rear axle and the distances to the centers of the left and right tires, respectively. This is the distance between the front and rear axles of the vehicle. The height of the vehicle's center of gravity; It is the acceleration due to gravity; and These are the vehicle's steady-state accelerations along the x-axis and y-axis, respectively. and The calculation formula is: ； ； ； ； in, and These are the vehicle's pseudo-accelerations along the x and y axes, respectively. The speed at the vehicle's center of gravity; for The derivative with respect to time; The sideslip angle is the center of gravity of the vehicle. for The derivative with respect to time; The yaw rate of the vehicle; It is the approximate characteristic time of the approximate first-order response from pseudo-acceleration to stable acceleration.

7. The method according to claim 1, characterized in that, The state-space equation for a dual-track vehicle is: ； in, State variables , The speed at the vehicle's center of gravity; The sideslip angle is the center of gravity of the vehicle. The yaw rate of the vehicle; Lateral slip ratio; This refers to lateral error; This represents the error between the vehicle speed direction and the Frenet coordinate system direction. and These are the vehicle's steady-state accelerations along the x-axis and y-axis, respectively. for The derivative with respect to time; This represents the equations formed by the dual-track vehicle dynamics model, the Frenet coordinate system kinematic model, and the tire load transfer model. To control the amount , Indicates the front wheel steering angle. These represent the longitudinal tire forces of the vehicle's left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

8. The method according to claim 1, characterized in that, The method further includes: The vehicle trajectory is tracked using a dual-track vehicle state-space equation.

Images