Vehicle body attitude control method based on Koopman operator

Abstract

The invention is applicable to the technical field of vehicle dynamics modeling and control, and provides a Koopman operator-based vehicle body attitude control method, which comprises the following steps of: establishing a linear equation by selecting a proper observation function to describe a nonlinear link in a vehicle attitude control process, and applying the established linear equation to subsequent controller design, so that the vehicle attitude control accuracy is improved. The problem that an existing vehicle body attitude controller is insufficient in consideration of nonlinear links is effectively solved, and meanwhile, the provided observation function establishing method also provides important reference for application of a Koopman operator in the aspect of vehicle body attitude control.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle dynamics modeling and control, and in particular relates to a vehicle body posture control method based on a Koopman operator. Background Art

[0002] Vehicle performance requirements are becoming increasingly stringent and diverse, and the automotive industry is continuously moving towards intelligent and electrified driving. Intelligent chassis are becoming a core component of future vehicles. Vehicle posture control technology plays a crucial role in ensuring ride comfort and handling stability, and has garnered widespread attention. However, the practical process of vehicle posture control involves multiple nonlinearities, which poses challenges to controller design. Therefore, considering these nonlinearities while ensuring efficient solution performance has become a key research topic in vehicle posture controllers.

[0003] However, the current methods for vehicle posture control have the following shortcomings: (1) Insufficient consideration of nonlinear links. Linear models are usually used instead of nonlinear models, while ignoring the nonlinear elements in active suspension and body motion in body posture control.

[0004] (2) There is insufficient research on Koopman-based attitude control methods. Related studies focus on single body roll or pitch motion, ignoring the mutual coupling of body motion, which affects the actual control effect. Summary of the Invention

[0005] The purpose of the embodiments of the present invention is to provide a vehicle body posture control method based on the Koopman operator, aiming to solve the problems raised in the above background technology.

[0006] The embodiment of the present invention is implemented as follows: a vehicle body posture control method based on Koopman operator includes the following steps: Step 1: Select the step length to collect vehicle operation data for a specified time period, including the vertical height of the vehicle body. , body roll angle , vehicle pitch angle , four unsprung mass displacements , vehicle body vertical speed , body roll angular velocity , vehicle pitch angular velocity , four unsprung mass velocities , four suspension active forces The simulation data including the following. Among them, the operation data should include both the application of the active suspension motion power and the non-application of the active suspension motion power. The data is divided into rows according to the type and columns according to the timestamp, recorded as .

[0007] Step 2: Dataset The part of the active dynamic force of the suspension is recorded as the data set , and the rest is recorded as data set , select the observation function to transform the data set Dimensionality upgrade to obtain the dataset after dimension upgrade ; The dataset and datasets Reorganize into augmented dataset .

[0008] Step 3: Augment the dataset Divide into training data sets and validation dataset , where the length of the training dataset is . Use Extended Dynamic Mode Decomposition (EDMD) on the training dataset Perform fitting to obtain the state transfer matrix of the dimensional linear system and action matrix After that, in the validation dataset Check the fitting effect.

[0009] Step 4: Design the cost function and constraints of the model predictive controller for the upgraded linear system, and achieve vehicle posture control by solving the Riccati equation or directly using a solver.

[0010] A further technical solution, in step 1, uses simulation to obtain vehicle operation data, specifically including the following steps: First, establish the nonlinear body posture model as shown below: ; in, It is The vehicle status of the step, Is the active suspension Then, set the simulation step size. , time length , set the initial condition sampling range, where the displacement unit is , the angle unit is , the unit of angular velocity is , the speed unit is The unit of force is : ; ; Set the peak power range of the main action to , when input, the main action power size keeps cycle, each cycle is divided into eight stages of 0.2s, Represent the active suspension motion forces of the left front, right front, right rear and left rear respectively; Sample evenly within the determined sampling range, then determine the initial conditions for the simulation, and collect the vertical height of the vehicle body at each moment after starting the simulation. , body roll angle , vehicle pitch angle , four unsprung mass displacements , vehicle body vertical speed , body roll angular velocity , vehicle pitch angular velocity , four unsprung mass velocities , four suspension active forces The simulation data including the data is divided into rows according to the type and columns according to the timestamp, recorded as .

[0011] A further technical solution is to select a third-order observation function in step 2: ; in, , , , Represents the transpose of a matrix.

[0012] A further technical solution is that in step 3, the training data set The fitting process is as follows: Before training the dataset The length is divided into , will be after The length is divided into , and obtain the augmented transfer matrix ,in Represents the pseudoinverse of a matrix. The four rows from bottom to top are the action matrix , the rest is the state transfer matrix ; So far, the state space equation of the linear system after dimensionality increase is: ; The state transfer matrix of the linear system after dimensionality increase can be obtained and action matrix ,in Representative The dimension-increasing state vector of the step, Representative The action vector of the step, .

[0013] Further technical solution, said step 4 includes the following specific steps: The objective function of the designed controller is: ; in, , , , Represent the vertical acceleration, pitch angular acceleration, roll angular acceleration and acceleration of the four unsprung masses of the vehicle body respectively; 、 、 、 、 、 、 、 and These are the weight coefficients of the controller objective function for the vehicle body vertical displacement, pitch angle, roll angle, displacement of the four unsprung masses, vehicle body vertical acceleration, pitch angle acceleration, roll angle acceleration, acceleration of the four unsprung masses, and active motion force; Constraints include: State transition equality constraints: ; Actuator force limit inequality constraints: .

[0014] A further technical solution is that in step 4, , , , , , , , , , , , , , , , , , , , .

[0015] An embodiment of the invention provides a vehicle posture control method based on the Koopman operator. Based on Koopman operator theory and a large amount of vehicle operation data, the nonlinear vehicle posture model is upgraded to a linear model. A vehicle posture controller is then designed for the linear model. While the linear model is established, the nonlinear nature of the vehicle model is preserved. Compared to model-based methods, the modeling process is simplified, resulting in higher solution efficiency and less control accuracy during controller design. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A functional architecture diagram of a vehicle body posture control method based on a Koopman operator provided in an embodiment of the present invention; Figure 2 A flow chart of a vehicle body posture control method based on a Koopman operator provided in an embodiment of the present invention; Figure 3 Methods for applying active motion force when collecting data; Figure 4 The test results of the time history curve of the center of mass height of some samples using the Koopman operator to model the vehicle body posture dynamics; Figure 5 The test results of the roll angle time history curve of some samples using the Koopman operator to model the vehicle body posture dynamics; Figure 6 The test results of the time history curve of the left front unsprung mass displacement of some samples using the Koopman operator to model the vehicle body posture dynamics. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0018] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0019] like Figure 1 and 2 As shown, a vehicle body posture control method based on the Koopman operator is provided in one embodiment of the present invention, comprising the following steps: Step 1: First, establish a nonlinear vehicle body posture model as shown below: ; in, It is The vehicle status of the step, Is the active suspension Then, set the simulation step size , time length , set the initial condition sampling range, where the displacement unit is , the angle unit is , the unit of angular velocity is , the speed unit is The unit of force is : ; ; Set the peak power range of the main action to , when input, the main action power size keeps cycle, each cycle is divided into eight stages of 0.2s, the detailed process is as follows Figure 3 As shown, They represent the active suspension dynamics of the left front, right front, right rear and left rear respectively.

[0020] Sample evenly within the determined sampling range, then determine the initial conditions for the simulation, and collect the vertical height of the vehicle body at each moment after starting the simulation. , body roll angle , vehicle pitch angle , four unsprung mass displacements , vehicle body vertical speed , body roll angular velocity , vehicle pitch angular velocity , four unsprung mass velocities , four suspension active forces The data is divided into rows according to type and columns according to timestamp, recorded as .

[0021] Step 2: Dataset The part of the active dynamic force of the suspension is recorded as the data set , and the rest is recorded as data set , select the third-order observation function: ; in, , , , Represents the transpose of a matrix; The dataset Dimensionality upgrade to obtain the dataset after dimension upgrade . and datasets Reorganize into augmented dataset .

[0022] Step 3: Augment the dataset Divide into training data sets and validation dataset , where the length of the training dataset is . Prepend the training dataset The length is divided into , will be after The length is divided into , and obtain the augmented transfer matrix ,in Represents the pseudoinverse of a matrix. The four rows from bottom to top are the action matrix , the rest is the state transfer matrix The state space equation of the linear system after dimensionality increase is: ; in, Representative The dimension-increasing state vector of the step, Representative The action vector of the step, . Get the state transfer matrix of the linear system after dimensionality increase and action matrix After that, in the validation dataset The fitting results are shown in the figure. The time history curves of the vehicle center of mass height, roll angle, and left front unsprung mass displacement of the three samples are shown in the figure. Figure 4 、 Figure 5 、 Figure 6 As shown, it is confirmed that the short-term fitting effect is good.

[0023] Step 4: Design the cost function and constraints of the model predictive controller for the upgraded linear system, and achieve vehicle posture control by solving the Riccati equation or directly using a solver.

[0024] The objective function of the designed controller is: ; in, , , , Represent the vertical acceleration, pitch angular acceleration, roll angular acceleration and acceleration of the four unsprung masses of the vehicle body, 、 、 、 、 、 、 、 and These are the weight coefficients of the controller objective function for the vehicle body vertical displacement, pitch angle, roll angle, displacement of the four unsprung masses, vehicle body vertical acceleration, pitch angle acceleration, roll angle acceleration, acceleration of the four unsprung masses, and active motion force; Constraints include: State transition equality constraints: ; Actuator force limit inequality constraints: .

[0025] A further technical solution is that in step 4, , , , , , , , , , , , , , , , , , , , .

[0026] As a preferred embodiment of the present invention, in step 1, the specific method of using simulation to obtain vehicle operation data is: 1) Determine the possible limit values ​​of each state quantity in driving conditions; 2) Randomly and uniformly sample each state variable and combine them as the initial conditions of the simulation; 3) First, simulate without active motion power; 4) Introduce the main action power. Introduce the main action power into the above working conditions for simulation. The selection of the main action power should cover common working conditions.

[0027] As a preferred embodiment of the present invention, in step 2, the observation function is selected as follows: 1) First, based on the vehicle body posture angle Get the corresponding rotation matrix as follows: ; 2) Then based on the vehicle body angular velocity Get its antisymmetric matrix as follows: ; 3) Get Matrix of order , the final observation function is selected as follows: .

[0028] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A vehicle body posture control method based on Koopman operator, characterized in that: The following steps are involved: Step 1: Select the step length to collect vehicle operation data for a specified time period, including the vertical height of the vehicle body. , body roll angle , vehicle pitch angle , four unsprung mass displacements , vehicle body vertical speed , body roll angular velocity , vehicle pitch angular velocity , four unsprung mass velocities , four suspension active forces The simulation data including the following: Among them, the operation data should include the two types of suspension active motion power and the two types of suspension active motion power; the data are divided into rows according to type and columns according to timestamp, recorded as ; Step 2: Dataset The part of the active dynamic force of the suspension is recorded as the data set , and the rest is recorded as data set , select the observation function to transform the data set Dimensionality upgrade to obtain the dataset after dimension upgrade ; The dataset and datasets Reorganize into augmented dataset ; Step 3: Augment the dataset Divide into training data sets and validation dataset , where the length of the training dataset is ; Using extended dynamic pattern decomposition to train the dataset Perform fitting to obtain the state transfer matrix of the dimensional linear system and action matrix After that, in the validation dataset Check the fitting effect on the top; Step 4: Design the cost function and constraints of the model predictive controller for the upgraded linear system, and achieve vehicle posture control by solving the Riccati equation or directly using a solver.

2. The vehicle body posture control method based on Koopman operator according to claim 1, characterized in that: In step 1, simulation is used to obtain vehicle operation data, which specifically includes the following steps: First, establish the nonlinear body posture model as shown below: ； in, It is The vehicle status of the step, Is the active suspension Then, set the simulation step size. , time length , set the initial condition sampling range, where the displacement unit is , the angle unit is , the unit of angular velocity is , the speed unit is The unit of force is : ； ； Set the peak power range of the main action to , when input, the main action power size keeps cycle, each cycle is divided into eight stages of 0.2s, Represent the active suspension motion forces of the left front, right front, right rear and left rear respectively; Sample evenly within the determined sampling range, then determine the initial conditions for the simulation, and collect the vertical height of the vehicle body at each moment after starting the simulation. , body roll angle , vehicle pitch angle , four unsprung mass displacements , vehicle body vertical speed , body roll angular velocity , vehicle pitch angular velocity , four unsprung mass velocities , four suspension active forces The simulation data including the data is divided into rows according to the type and columns according to the timestamp, recorded as .

3. The vehicle body posture control method based on Koopman operator according to claim 2, characterized in that: In step 1, a third-order observation function is selected: ； in, , , , Represents the transpose of a matrix.

4. The vehicle body posture control method based on Koopman operator according to claim 1, characterized in that: In step 3, the training data set The fitting process is as follows: Before training the dataset The length is divided into , will be after The length is divided into , and obtain the augmented transfer matrix ,in represents the pseudo-inverse of the matrix; The four rows from bottom to top are the action matrix , the rest is the state transfer matrix ; So far, the state space equation of the linear system after dimensionality increase is: ； The state transfer matrix of the linear system after dimensionality increase can be obtained and action matrix ,in Representative The dimension-increasing state vector of the step, Representative The action vector of the step, .

5. The vehicle body posture control method based on Koopman operator according to claim 1, characterized in that: The step 4 includes the following specific steps: The objective function of the designed controller is: ； in, , , , Represent the vertical acceleration, pitch angular acceleration, roll angular acceleration and acceleration of the four unsprung masses of the vehicle body respectively; 、 、 、 、 、 、 、 and These are the weight coefficients of the controller objective function for the vehicle body vertical displacement, pitch angle, roll angle, displacement of the four unsprung masses, vehicle body vertical acceleration, pitch angle acceleration, roll angle acceleration, acceleration of the four unsprung masses, and active motion force; Constraints include: State transition equality constraints: ; Actuator force limit inequality constraints: .

6. The vehicle body posture control method based on Koopman operator according to claim 5, characterized in that: In step 4, , , , , , , , , , , , , , , , , , , , .

Images