A body posture control method based on a koopman operator

Abstract

The present application is suitable for the field of vehicle dynamics modeling and control technology, and provides a vehicle body posture control method based on Koopman operator, which establishes a linear equation to describe the nonlinear link in the vehicle posture control process by selecting a suitable observation function, and applies the established linear equation in the subsequent controller design, effectively solving the problem that the current vehicle body posture controller does not consider the nonlinear link, and the proposed observation function establishment method also provides an important reference for the application of Koopman operator in vehicle body posture control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of vehicle dynamics modeling and control, and particularly relates to a vehicle body posture control method based on a Koopman operator. BACKGROUND

[0002] The current vehicle performance requirements are increasingly strict and diversified, and the automobile industry is developing towards intelligentization and electrification. Intelligent chassis has become one of the core components of future vehicles. Among them, vehicle posture control technology plays a very important role in ensuring the ride comfort and handling stability of vehicles, and has attracted widespread attention. However, there are multiple nonlinear links in the actual vehicle body posture control process, which brings challenges to the controller design. Therefore, considering the nonlinear links under the premise of ensuring the solving efficiency has become the research key point of the vehicle posture controller.

[0003] However, the current vehicle body posture control method has the following shortcomings:

[0004] (1) The nonlinear links are not considered, and a linear model is usually used instead of a nonlinear model, and the nonlinear elements in the vehicle body posture control and the vehicle body motion of the active suspension are ignored.

[0005] (2) The posture control method based on Koopman is not studied enough, and the related research focuses on single vehicle body roll or pitch motion, ignoring the mutual coupling effect of vehicle body motion, and the actual control effect is affected. SUMMARY

[0006] The purpose of the embodiment of the application is to provide a vehicle body posture control method based on a Koopman operator, which aims to solve the problems proposed in the background technology.

[0007] The embodiment of the application is implemented in the following way: a vehicle body posture control method based on a Koopman operator includes the following steps:

[0008] Step 1: Select the step length, collect the vehicle running data of the specified time length, including the vehicle body vertical height , vehicle body roll angle , vehicle body pitch angle , four unsprung mass displacements , vehicle body vertical velocity , vehicle body roll angle velocity , vehicle body pitch angle velocity , four unsprung mass velocities , four suspension active forces Simulation data. Among them, the running data should include the suspension active force applied and the suspension active force not applied. The data is divided into rows according to the type and columns according to the time stamp, and is recorded as .

[0009] Step 2: The part of the data set of the active force of the suspension is recorded as the data set , and the other part is recorded as the data set , the observation function is selected to upgrade the data set , and the upgraded data set is obtained; the data set and the data set are recombined into an augmented data set .

[0010] Step 3: The augmented data set is divided into a training data set and a validation data set , wherein the length of the training data set is . The extended dynamic mode decomposition (EDMD) is used to fit the training data set , and the state transition matrix and the action matrix of the upgraded linear system are obtained. After that, the fitting effect is checked on the validation data set .

[0011] Step 4: The cost function and the constraint condition of the model predictive controller are designed for the upgraded linear system, and the Riccati equation is solved or a solver is directly used to solve to realize the body posture control.

[0012] Further technical solutions, in the step 1, simulation is used to obtain vehicle operation data, specifically including the following steps:

[0013] First, a nonlinear body posture model is established as follows:

[0014] ;

[0015] wherein, is the vehicle state at the th step, is the active action force applied by the active suspension at the th step; then, the simulation step size is set, the time length is set, and the initial condition sampling range is set, wherein the displacement unit is , the angle unit is , the angular velocity unit is , the speed unit is , and the force unit is :

[0016] ;

[0017] ;

[0018] The main action power peak size range is set to At the input, the main action power size keeps a period cycle, each cycle is divided into eight stages with a time length of 0.2s, respectively representing the front left, front right, rear right and rear left suspension main action power;

[0019] In the determined sampling range, uniform sampling is performed, and then the initial conditions of the simulation are determined, and after starting the simulation, the simulation data including the body vertical height , body roll angle , body pitch angle , four unsprung mass displacements , body vertical velocity , body roll angle velocity , body pitch angle velocity , four unsprung mass velocities , four suspension main action powers are collected; the data is divided into rows according to the type and columns according to the timestamp, and is recorded as .

[0020] Further technical solutions, in the step 2, three order observation functions are selected:

[0021] ;

[0022] Wherein, , , , represents the transpose of the matrix.

[0023] Further technical solutions, in the step 3, the fitting process of the training data set is as follows:

[0024] The first length part of the training data set is divided into , and the last length part is divided into , to obtain the augmented transition matrix , wherein represents the pseudo-inverse of the matrix. The four rows from bottom to top are the action matrix , and the remaining part is the state transition matrix ; thus the state space equation of the upgraded linear system is obtained:

[0025] ;

[0026] The state transition matrix of the linear system in the higher dimension is obtained The action matrix Wherein represents the state vector of the step The action vector of the step represents the state vector of the step The action vector of the step .

[0027] Further technical solutions, the step 4 includes the following specific steps:

[0028] The objective function of the controller is designed as:

[0029] ;

[0030] Wherein, , , , Respectively represent the vertical acceleration of the vehicle body, the pitch angle acceleration, the roll angle acceleration and the acceleration of the four unsprung masses, , , , , , , , And The weight coefficients of the controller objective function about the vertical displacement of the vehicle body, the pitch angle, the roll angle, the displacement of the four unsprung masses, the vertical acceleration of the vehicle body, the pitch angle acceleration, the roll angle acceleration, the acceleration of the four unsprung masses and the active action force are in turn;

[0031] The constraint conditions include:

[0032] State transition equation constraint: ;

[0033] Actuator limit inequality constraint: .

[0034] Further technical solutions, in the step 4, , , , , , , , , , , , , , , , , , , , .

[0035] The embodiment of the present application provides a vehicle body posture control method based on a Koopman operator, based on the Koopman operator theory, on the basis of a large amount of vehicle operation data, a nonlinear vehicle body posture model is upgraded and a linear vehicle body posture model is obtained, and then a controller is designed for the linear model to control the vehicle body posture. In the process of establishing the linear model, the nonlinear properties of the vehicle model are retained, and compared with the model-based method, the modeling process is simplified, and higher solving efficiency can be realized in the controller design process while sacrificing smaller control accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 A functional architecture diagram of the vehicle body posture control method based on the Koopman operator is provided for the embodiment of the present application.

[0037] Figure 2 A flowchart of the vehicle body posture control method based on the Koopman operator is provided for the embodiment of the present application.

[0038] Figure 3 The method for applying a main action force when collecting data;

[0039] Figure 4 The test results of the center of mass height time history curve of part of the samples for modeling the vehicle body posture dynamics using the Koopman operator;

[0040] Figure 5 The test results of the roll angle time history curve of part of the samples for modeling the vehicle body posture dynamics using the Koopman operator;

[0041] Figure 6 The test results of the left front unsprung mass displacement time history curve of part of the samples for modeling the vehicle body posture dynamics using the Koopman operator. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0043] The specific implementation of the present application is described in detail below in combination with specific embodiments.

[0044] As Figure 1 and 2As shown, an embodiment of the present invention provides a vehicle body attitude control method based on the Koopman operator, which includes the following steps:

[0045] Step 1: First, establish the nonlinear vehicle body attitude model as shown below:

[0046] ;

[0047] in, It is the first The vehicle status at the step, It is an active suspension in the first The active motion force applied by the step. Then, the simulation step size is set. Length of time Set the initial sampling range, where the displacement unit is... The unit of angle is The unit of angular velocity is The unit of speed is The unit of force is :

[0048] ;

[0049] ;

[0050] Set the peak value range of the active driving force to... During input, the magnitude of the active motion maintains a cyclical pattern, with each cycle consisting of eight 0.2-second phases. The detailed process is as follows: Figure 3 As shown, where These represent the main suspension action power for the front left, front right, rear right, and rear left, respectively.

[0051] Uniform sampling is performed within a defined sampling range. Then, the initial conditions for the simulation are determined. After the simulation begins, the vertical height of the vehicle body at each moment is collected. Body roll angle Vehicle pitch angle Four unsprung mass displacements Vertical speed of vehicle body Body roll rate Vehicle pitch rate Four unsprung mass velocities Four suspension active power The simulation data includes this. The data is divided into rows by data type and columns by timestamp, denoted as... .

[0052] Step 2: Transfer the dataset The active motion force of the middle suspension is denoted as the dataset. , other parts are recorded as dataset , select 3 order observation function:

[0053] ;

[0054] wherein, , , , represent the transpose of the matrix;

[0055] The data set is upgraded to obtain the upgraded data set . The data set and the data set are recombined into the augmented data set .

[0056] Step 3: The augmented data set is divided into the training data set and the verification data set , wherein the length of the training data set is . The part of the training data set with the length of is divided into , and the part with the length of is divided into , to obtain the augmented transition matrix , wherein represents the pseudo-inverse of the matrix. The bottom four rows are the action matrix , and the remaining part is the state transition matrix . Thus, the state space equation of the upgraded linear system is obtained as follows:

[0057] ;

[0058] wherein, represents the upgraded state vector of the th step, represents the action vector of the th step, . The state transition matrix and the action matrix of the upgraded linear system are obtained, and the fitting effect is checked on the verification data set , wherein the time history curves of the body center of mass height, roll angle and left front spring mass displacement of three samples are shown in Figure 4 , Figure 5 , Figure 6 respectively, and it is confirmed that the short-term fitting effect is good.

[0059] Step 4: Design the cost function and constraint condition of the model predictive controller for the linear system after dimensionality increasing, and solve the Riccati equation or directly use a solver to realize the vehicle body posture control.

[0060] The objective function of the controller is designed as:

[0061]

[0062] The weight coefficients of the controller objective function about the vertical displacement of the vehicle body, the pitch angle, the roll angle, the displacement of the four unsprung masses, the vertical acceleration of the vehicle body, the pitch angle acceleration, the roll angle acceleration, the acceleration of the four unsprung masses and the active actuator are respectively:

[0063] The constraint conditions include:

[0064] The state transition equality constraint is:

[0065] The actuator limit inequality constraint is:

[0066]

[0067] As a preferred embodiment of the present application, in the step 1, the specific method for obtaining the vehicle operation data by simulation is as follows:

[0068] 1) Determine the limit values of each state variable that may appear in the driving conditions;

[0069] 2) Randomly and uniformly sample each state variable and combine them as the initial conditions of the simulation;

[0070] 3) First, simulate under the condition of no active actuator;

[0071] 4) Introduce the active actuator, introduce the active actuator in the above various conditions for simulation, and the selection of the active actuator should cover common conditions.

[0072] As a preferred embodiment of the present application, in the step 2, the observation function selection method is as follows:​​​​​​​​​​​​​​​​​​

[0073] 1) First, based on the body attitude angle get the corresponding rotation matrix, as follows:

[0074] ;

[0075] 2) Then, based on the body attitude angular velocity get its skew-symmetric matrix, as follows:

[0076] ;

[0077] 3) get order matrix , the final selection of observation function as follows:

[0078] .

[0079] The above only for the preferred embodiments of the present application, and not to limit the present application, any modification, equivalent replacement and improvement within the spirit and principles of the present application, etc., should be included in the scope of protection of the present application.

Claims

1. A body posture control method based on a Koopman operator, characterized by, The method comprises the following steps: Step 1: Choose the step length, collect the vehicle running data for a specified length of time, including the body vertical height , body roll angle , body pitch angle , four unsprung mass displacement , body vertical velocity , body roll angle velocity , body pitch angle velocity , four unsprung mass velocity , four suspension main actuator force Simulation data within the simulation data, ; wherein the running data should include the suspension main actuator force applied and not applied; the data is divided by type, and by time stamp, and is recorded as ; Step 2: The data set is recorded as the data set , and the other part is recorded as the data set . The observation function is selected to upgrade the data set to obtain the upgraded data set . The data set and the data set are recombined into the augmented data set ; Step 3: Augmenting the dataset into a training dataset and a validation dataset , where the training dataset has length ; fitting the training dataset using an extended dynamic mode decomposition, resulting in a state transition matrix and an action matrix , and then checking the fit on the validation dataset ; Step 4: the cost function and constraint condition of the model predictive controller for the linear system design model after dimension lifting are designed, and the body posture control is realized by solving Riccati equation or directly using a solver; In the step 1, simulation is used to obtain vehicle operation data, and the specific steps include the following steps: First, a nonlinear body posture model as shown in the following formula is established: ； wherein, is the first step vehicle state, is the active suspension active force applied in the first step; then, a simulation step size is set, a time length is set, an initial condition sampling range is set, wherein the displacement unit is , the angle unit is , the angular velocity unit is , the speed unit is , and the force unit is : ； ； The main action power peak value size range is set as At the input time, the main action power size keeps a period cycle, each cycle is divided into eight stages with a time length of 0.2s, Respectively represent the front left, front right, rear right and rear left suspension main action power; Uniformly sampling in the determined sampling range, then determining the initial conditions of the simulation, starting the simulation and collecting the data including the vertical height of the vehicle body , the roll angle of the vehicle body , the pitch angle of the vehicle body , the displacement of the four unsprung masses , the vertical velocity of the vehicle body , the roll angular velocity of the vehicle body , the pitch angular velocity of the vehicle body , the velocity of the four unsprung masses , the four suspension active forces The simulation data inside; the data is divided by type, and the time stamp is divided by column, recorded as ; In the step 1, a 3-order observation function is selected: ； wherein , , , denotes the transpose of a matrix.

2. The Koopman operator-based body posture control method according to claim 1, characterized by, In the step 3, the training data set The fitting process is as follows: The training data set is divided into two parts, the first part with length of and the second part with length of . The second part is divided into two parts, the first part with length of and the second part with length of . The augmented transition matrix is obtained as , where represents the pseudo-inverse of the matrix; The last four rows from bottom to top are the action matrix , and the remaining part is the state transition matrix ; thus the state space equation of the linear system after dimensionality increasing is obtained as ； The state transition matrix of the linear system in higher dimension is obtained with the action matrix where represents the state vector of the first step in higher dimension, represents the action vector of the first step, .

3. The Koopman operator-based body pose control method according to claim 1, characterized in that, The step 4 comprises the following specific steps: The objective function of the controller is designed as: ； wherein, , , , respectively represent the vertical acceleration of the vehicle body, the pitch angle acceleration, the roll angle acceleration and the acceleration of the four unsprung masses; , , , , , , , and are the weight coefficients of the vertical displacement of the vehicle body, the pitch angle, the roll angle, the displacement of the four unsprung masses, the vertical acceleration of the vehicle body, the pitch angle acceleration, the roll angle acceleration, the acceleration of the four unsprung masses and the active suspension force in the controller target function, respectively. The constraint condition comprises: State transition equation constraints: ; Actuation force limit inequality constraint: .

4. The Koopman operator-based body posture control method according to claim 3, characterized by, In step 4, , , , , , , , , , , .

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