Vehicle roll-pitch cooperative control method based on genetic algorithm optimized cupper model

Abstract

The application discloses a vehicle lateral and vertical cooperative control method based on genetic algorithm optimization of Kupmann model and belongs to the technical field of vehicle safety control.The application aims to cooperatively optimize vehicle lateral stability and vertical posture response under a model predictive control framework, and four-wheel target longitudinal slip rates are converted into corresponding wheel driving / braking torque through a genetic algorithm optimization of Kupmann model based on a bottom-layer slip rate tracking controller.The application firstly constructs a controlled object model, establishes a vehicle lateral and vertical coupling dynamics model and a road disturbance model, then constructs a genetic algorithm optimization based Kupmann linear prediction model, designs a model predictive control cooperative stability controller based on genetic algorithm optimization Kupmann operator, and finally converts the target slip rates of the wheels into corresponding wheel driving / braking torque.The application realizes the cooperative action of tire force distribution, roll suppression and dynamic vertical load adjustment, so as to improve the lateral and vertical cooperative stability performance of the vehicle under a low adhesion uneven road surface environment.

Description

Technical Field

[0001] This invention belongs to the field of vehicle safety control technology. Background Technology

[0002] Active safety control systems for vehicles are crucial for improving vehicle stability and safety. However, existing methods often focus on a single direction of motion or a single control objective, neglecting the coupling relationships within vehicle dynamics and making it difficult to achieve synergistic improvements in stability performance under complex road conditions. In highly disturbed environments such as low-adhesion, uneven road surfaces, tire adhesion deteriorates, and road roughness excitation intensifies, causing vehicle dynamics to exhibit strong nonlinearity and strong coupling characteristics. This places higher demands on the accuracy of vehicle dynamics modeling, collaborative control performance, and real-time computational efficiency. Currently, the following problems still exist regarding vehicle lateral-vertical cooperative stability control methods: 1. In low-adhesion, uneven road surface environments, the low-adhesion road surface and the uneven excitation together increase the difficulty of vehicle dynamics modeling. Existing vehicle dynamics models are unable to accurately represent tire nonlinearity and lateral-to-vertical coupling relationships, resulting in insufficient model accuracy; while using high-precision nonlinear models has problems such as complex modeling, difficulty in parameter identification, large computational load, and insufficient adaptability to operating conditions, making it difficult to balance modeling accuracy, real-time performance, and generalization ability.

[0003] 2. Some studies employ data-driven linearization modeling, mapping complex nonlinear vehicle dynamics to a high-dimensional linear space to reduce the difficulty of control solutions. However, such methods typically rely on large amounts of data for model training, and the construction of the observation space depends on empirical design. This results in low model training and update efficiency, making it difficult to quickly adapt to changes in complex operating conditions, thus limiting their engineering application capabilities.

[0004] 3. Most existing cooperative control methods design lateral control and vertical control separately, or only achieve the superposition of control effects through hierarchical coordination. It is difficult to integrate the lateral-vertical coupling state, tire adhesion constraints and control input constraints into the same control framework, resulting in insufficient coordination between lateral stability control and vertical attitude control, making it difficult to fully improve the lateral-vertical cooperative stability performance of vehicles in low-adhesion uneven road surface environments. Summary of the Invention

[0005] The purpose of this invention is to collaboratively optimize the lateral stability and vertical attitude response of a vehicle within a model predictive control framework. The target longitudinal slip ratio of the four wheels is converted into the corresponding wheel drive / braking torque by the underlying slip ratio tracking controller. This is a vehicle lateral-vertical collaborative control method based on a genetic algorithm-optimized Koopman model.

[0006] The steps of this invention are: S1. Constructing the controlled object model: Constructing a controlled object model of a four-wheel independent drive vehicle under low-adhesion uneven road surface conditions to simulate the dynamic response of the vehicle to yaw rate, lateral velocity, roll angle and tire vertical load under low adhesion coefficient and random road surface elevation excitation. S2. Establish vehicle lateral-vertical coupling dynamics model and road disturbance model: Use the filtered white noise method to generate random vertical excitation of low-adhesion uneven road surface, and determine the time lag relationship when the front and rear wheels pass through the same road surface position according to the vehicle wheelbase and longitudinal speed to obtain the four-wheel road surface elevation input; establish an eight-degree-of-freedom lateral-vertical coupling dynamics model of the vehicle to describe the coupling relationship between the lateral motion, yaw motion, body roll motion and vertical motion of the vehicle under low-adhesion and uneven road surface conditions; S3. Construct a Koopman linear prediction model optimized by a genetic algorithm: Collect closed-loop operation data of vehicles under typical working conditions on uneven roads with low adhesion, and construct a training sample set; Based on the Koopman operator theory, introduce an observation function to map the eight-degree-of-freedom lateral-vertical coupling dynamic model described in step S2 to a high-dimensional linear space; Use a genetic algorithm to iteratively optimize the type and / or parameter combination of the observation function, with prediction accuracy and model complexity as optimization objectives, determine the optimal observation function and its optimal parameter combination, and construct a high-precision, low-complexity Koopman linear prediction model; S4. Design a model predictive control cooperative stability controller based on genetic algorithm optimization of the Koopman operator: Based on the Koopman linear prediction model described in step S3, construct a multi-objective optimization problem within the model predictive control framework. The optimization objectives of the multi-objective optimization problem include yaw rate tracking, lateral velocity suppression, roll angle suppression, and dynamic vertical load fluctuation suppression. Vehicle state safety constraints and actuator saturation constraints are introduced into the multi-objective optimization problem. Through rolling optimization, the target longitudinal slip ratio and active suspension force of the four wheels are output. S5. Bottom-level execution control: The target longitudinal slip ratio of the four wheels obtained in step S4 is output to the bottom-level slip ratio tracking controller, which converts the target slip ratio of each wheel into the driving / braking torque of the corresponding wheel.

[0007] To simulate random vertical excitation on a low-adhesion, uneven road surface, this invention uses a filtered white noise method in Simulink to generate road surface elevation inputs at each wheel location and outputs them to the IMP_ZGND port of CarSim; road surface excitation. With unit white noise The first-order differential equation between them is satisfied: (1) in, The lower cutoff frequency is the spatial frequency. For reference spatial frequency, This is the road surface roughness coefficient. For the longitudinal speed of the vehicle, Units of white noise; Considering the time lag in the excitation of the front and rear wheels on the same road surface, the road surface input for the rear wheel can be expressed as: (2) in, for Input the road surface elevation for the side and rear wheels. for Side front wheel time delay The subsequent road surface elevation input, For the time lag, This refers to the vehicle's wheelbase.

[0008] The vehicle side-vertical coupling dynamic model of this invention: Dynamic vertical force Based on the vertical displacement of unsprung mass and road surface elevation excitation The calculation yielded: (10) in, for The equivalent vertical stiffness of the wheel's tire. for The tire's equivalent vertical damping coefficient; Tire vertical load consists of static vertical load and dynamic vertical load. The static vertical load is distributed as follows: (17) in, The static vertical load is on the left front wheel. The static vertical load is on the right front wheel. The static vertical load is on the left rear wheel. The static vertical load is on the right rear wheel. For the overall vehicle quality, It is the acceleration due to gravity. This is the distance from the vehicle's center of gravity to the rear axle. This is the distance from the vehicle's center of gravity to the front axle. The vertical load on the tire is obtained from equation (18): (18) in, for The static vertical load on the wheel.

[0009] This invention is based on the Koopman linear prediction model optimized by a genetic algorithm: (38) in, for The upgraded state vector at time step 1. This is the Koopman up-dimensional state transition matrix. for The upgraded state vector at time step 1. The control input matrix is ​​obtained through genetic algorithm optimization. for The control input vector at time t, The perturbation input matrix is ​​obtained through optimization using a genetic algorithm. for The perturbation input vector at time t.

[0010] This invention is a model predictive control cooperative stable controller based on genetic algorithm optimization of the Koopman operator: (54) in, To control the optimal control sequence in the time domain. In order to be in The transpose of the optimal control input vector at the current time obtained from time prediction. In order to be in Time prediction The transpose of the time-optimal control input vector. In order to be in The transpose of the optimal control input vector for the control time-domain terminal obtained from the time-domain prediction. To control the length of the time domain.

[0011] The longitudinal slip ratio and active suspension force of the four-wheel target in this invention are: (55) in, Let be the optimal control input vector at time k. Let k be the longitudinal slip ratio of the left front wheel target. Let k be the longitudinal slip ratio of the right front wheel target. Let k be the longitudinal slip ratio of the left rear wheel target. Let k be the longitudinal slip ratio of the right rear wheel target. Let k be the optimal vertical control force of the left front wheel active suspension. Let k be the optimal vertical control force of the right front wheel active suspension. Let k be the optimal vertical control force of the left rear wheel active suspension. The optimal vertical control force of the right rear wheel active suspension at time k is given.

[0012] The positive effects of this invention are as follows: 1. To address the challenge of balancing accuracy and real-time performance in modeling vehicle lateral-vertical coupling dynamics on uneven, low-adhesion road surfaces, this method utilizes the Koopman operator to map the vehicle's lateral-vertical coupling nonlinear system to a high-dimensional linear space. This constructs a linear prediction model capable of characterizing the coupling relationships between multiple states, including lateral velocity, yaw rate, roll angle, and tire vertical load. This model preserves the nonlinear dynamic characteristics of the vehicle's lateral-vertical coupling while reducing the complexity of subsequent online optimization by the controller, thus achieving a balance between modeling accuracy and real-time control requirements. 2. To address the issues of traditional Koopman modeling, such as the reliance on empirically designed observation functions, excessive redundant features, and insufficient adaptability to complex working conditions, this method introduces a genetic algorithm to adaptively optimize the parameters and combinations of Koopman observation functions. By automatically selecting effective observation functions and optimizing the coupling representation relationship between state, control input, and road disturbance, the model's predictive ability for strong nonlinearity and strongly coupled dynamics under low adhesion and uneven road surfaces is improved. Simultaneously, the computational burden caused by ineffective dimensionality-upgrading features is reduced, thus improving the efficiency of model training and updating. 3. To address the shortcomings of existing methods for co-optimizing lateral and vertical control, this method designs an MPC controller based on a genetic algorithm-optimized Koopman prediction model. It integrates control objectives such as lateral stability, yaw response, roll suppression, and dynamic vertical load fluctuations, and comprehensively incorporates safety state constraints and actuator constraints. By simultaneously solving multiple control variables through rolling optimization, it achieves the synergistic effect of tire force distribution, roll suppression, and dynamic vertical load adjustment, thereby improving the vehicle's lateral and vertical coordinated stability performance on low-adhesion, uneven road surfaces. Attached Figure Description

[0013] Figure 1 This is a structural block diagram of the vehicle side-vertical cooperative stability control (GAK-MPC) method based on genetic algorithm optimization of the Koopman model as described in this invention; Figure 2 This is a schematic diagram of the modeling process for optimizing Koopman based on genetic algorithms as described in this invention; Figure 3 This is a schematic diagram of the vehicle side-vertical coupling dynamics model described in this invention; wherein, (a) is a top view and (b) is a rear view; Figure 4 This is the convergence curve of the identification error of the genetic algorithm described in this invention; Figure 5 The figure shows the verification results of the GA-Koopman model of vehicle lateral and vertical dynamics under known working conditions described in this invention; where (a) is the lateral velocity, (b) is the yaw rate, (c) is the vertical displacement, (d) is the roll angle, (e) is the dynamic vertical load, and (f) is the suspension dynamic deflection. Figure 6The figure shows the verification results of the GA-Koopman model of vehicle lateral and vertical dynamics under unknown working conditions described in this invention; where (a) is the lateral velocity, (b) is the yaw rate, (c) is the vertical displacement, and (d) is the roll angle. Figure 7 This is a comparison diagram of the response of the GAK-MPC controller under the dual-track shifting condition and the uncontrolled condition described in this invention; where (a) is the lateral velocity, (b) is the yaw rate, (c) is the roll angle, and (d) is the load transfer rate. Figure 8 This is a control response diagram of the GAK-MPC controller output under the dual lane change condition described in this invention; where (a) is the longitudinal slip ratio and (b) is the active suspension force. Figure 9 This is a comparison diagram of the response of GAK-MPC and NMPC control strategies under the dual lane change condition described in this invention; where (a) is the lateral velocity, (b) is the yaw rate, (c) is the roll angle, and (d) is the load transfer rate. Figure 10 This is a comparison chart of the single-step solution time of the GAK-MPC controller and NMPC described in this invention. Detailed Implementation

[0014] This invention relates to a vehicle lateral-vertical cooperative stability control method based on a genetic algorithm-optimized Koopman model. More specifically, this invention addresses the problem of decreased vehicle stability margin under strongly coupled lateral-vertical dynamics conditions. It utilizes the Koopman model to linearly characterize the nonlinear lateral-vertical coupled dynamics and optimizes the observation function and its parameter combination through a genetic algorithm, proposing a lateral-vertical cooperative stability control method that combines modeling accuracy and computational efficiency.

[0015] This invention primarily addresses the vehicle lateral-vertical coordinated stability control problem under complex road conditions such as slippery and rugged terrain. It proposes a vehicle lateral-vertical coordinated stability control method based on a genetic algorithm-optimized Koopman operator. This method uses the Koopman operator to perform an up-dimensional linear representation of the vehicle's lateral-vertical coupled nonlinear model, and utilizes a genetic algorithm to optimize the observation function and its parameter combinations, constructing a high-precision, low-complexity linear prediction model. Furthermore, within the model predictive control framework, it collaboratively optimizes the vehicle's lateral stability and vertical attitude response, solving for the target longitudinal slip ratios of the four wheels and the active suspension forces. The target longitudinal slip ratios of the four wheels are converted into corresponding wheel drive / braking torques by a bottom-level slip ratio tracking controller, thereby improving the vehicle's lateral-vertical coordinated stability and active safety performance.

[0016] The vehicle side-vertical cooperative stability control method based on genetic algorithm optimization of the Koopman model includes the following steps: Step 1: Construct a controlled object model of a four-wheel independent drive vehicle under low-adhesion uneven road surface conditions. This model can realistically reflect the dynamic response of the vehicle under key states such as yaw rate, lateral velocity, roll angle, and tire vertical load under low-adhesion and random road surface excitation, and can be used to verify the effectiveness of the control strategy.

[0017] Step 2: Establish the vehicle lateral-vertical coupled dynamics model and road disturbance model. A random vertical excitation for a low-adhesion, uneven road surface is generated using a filtered white noise method. The time lag relationship between the front and rear wheels when they pass the same road surface position is determined based on the vehicle's wheelbase and longitudinal speed, thus obtaining the four-wheel road surface elevation input. An eight-degree-of-freedom lateral-vertical coupled dynamics model is established to describe the coupling relationship between the vehicle's lateral motion, yaw motion, body roll motion, and vertical motion under low-adhesion and uneven road surface conditions.

[0018] Step 3: Establish a linear prediction model for lateral-vertical coupling based on a genetic algorithm-optimized Koopman operator. Addressing the challenges of strong nonlinearity and complex online solution for vehicle lateral-vertical coupling systems on low-adhesion, uneven road surfaces, closed-loop operating data under typical conditions are collected to construct training samples. The Koopman operator is then used to map the nonlinear dynamics of vehicle lateral-vertical coupling to a high-dimensional linear space. Furthermore, a genetic algorithm is employed to optimize the Koopman observation function and its parameter combinations, resulting in a linear prediction model that balances prediction accuracy and computational efficiency, providing a foundation for subsequent model predictive control.

[0019] Step 4: Design a vehicle lateral and vertical cooperative stability controller (GAK-MPC) based on the model and under the model predictive control architecture. Based on the Koopman linear prediction model, a multi-objective optimization problem is constructed, including yaw rate tracking, lateral velocity suppression, roll angle suppression, and dynamic vertical load fluctuation suppression. Taking into account vehicle state safety constraints and actuator saturation constraints, the target longitudinal slip ratio of the four wheels and the active suspension force are obtained through rolling optimization. The target longitudinal slip ratio of the four wheels is converted into the corresponding wheel drive / braking torque by the underlying slip ratio tracking controller, realizing the coordinated improvement of vehicle lateral and vertical stability performance.

[0020] From a functional perspective, the method proposed in this invention mainly includes: a controlled object model for a four-wheel independently driven electric vehicle, a vehicle lateral-vertical coupling dynamics model considering road disturbances, a Koopman linear prediction model optimized by a genetic algorithm, and a vehicle lateral-vertical cooperative stability controller within the model prediction framework. The function of each part is described in detail below: A four-wheel independent drive vehicle simulation model based on the CarSim platform is used to simulate a real controlled object, providing dynamic response information of the vehicle under low-adhesion uneven road surface conditions. The model receives input signals such as wheel drive / braking torque and active suspension force, as well as road disturbance excitations, and outputs state variables such as vehicle lateral velocity, yaw rate, vertical displacement, roll angle, and tire vertical load to reflect the influence of control actions on lateral, yaw, vertical, and roll motions.

[0021] A vehicle lateral-vertical coupled dynamics model considering road surface disturbances is used to characterize the coupled dynamic relationship between the vehicle's lateral motion, vertical motion, and body attitude under complex road conditions. The road surface disturbance model generates random road surface elevation inputs and their rates of change at each wheel using a filtered white noise method, reflecting the impact of uneven road surfaces on tire vertical loads and changes in vehicle attitude. The lateral-vertical coupled dynamics model employs an eight-degree-of-freedom vehicle dynamics model and considers composite slip characteristics in tire force calculations to describe the coupling relationship between the vehicle's lateral response, vertical response, roll attitude, and tire forces under low adhesion and uneven road surface conditions, providing a dynamic foundation for the subsequent establishment of the Koopman linear prediction model.

[0022] The Koopman linear prediction model optimized by a genetic algorithm was obtained through data-driven identification. This model uses the Koopman operator to map the vehicle's lateral-vertical coupled nonlinear system to a high-dimensional linear space, and then utilizes a genetic algorithm to optimize the observation function parameters, thereby establishing a linear prediction model that combines prediction accuracy and real-time solution efficiency. This model is used to predict future state variables such as lateral velocity, yaw rate, roll angle, and tire vertical load in the time domain, providing a foundation for subsequent controllers that characterizes the lateral-vertical coupling properties and facilitates online optimization.

[0023] The vehicle side-vertical cooperative stability controller (GAK-MPC) under the model prediction framework aims to ensure vehicle side-vertical cooperative stability. It optimizes the solution by considering safety constraints and actuator saturation constraints, resulting in the control variables being the target longitudinal slip ratio of the four wheels and the active suspension force. The target longitudinal slip ratio of the four wheels is converted into the corresponding wheel drive / braking torque by the underlying slip ratio tracking controller, while the active suspension force is directly input to the active suspension actuator for vehicle attitude adjustment.

[0024] The block diagram of the vehicle side-vertical cooperative stability control (GAK-MPC) based on the genetic algorithm-optimized Koopman model of this invention is as follows: Figure 1 As shown in the diagram, the GAK-MPC controller outputs the target longitudinal slip ratio of the four wheels and the active suspension force based on the vehicle status. It then uses a PID controller to track the target slip ratio, converting the target longitudinal slip ratio of the four wheels into corresponding wheel drive / braking torque. Finally, through the adjustment of the active suspension force and wheel drive / braking torque, it achieves coordinated control of the vehicle's lateral and vertical motion.

[0025] The process of constructing a linear prediction model based on genetic algorithm optimization of Koopman is as follows: Figure 2 As shown, the process includes parameter search, observation function dictionary construction, Koopman matrix identification, model prediction error evaluation, and fitness feedback update. The genetic algorithm updates the observation function parameter population by performing selection, crossover, and mutation operations based on the fitness evaluation results, repeating the closed-loop optimization process of "parameter generation—dictionary construction—matrix identification—model prediction—error evaluation." When the fitness function meets the convergence condition or reaches the maximum number of iterations, the optimal observation function parameters are output, and the Koopman observation function dictionary and the final linear prediction model are reconstructed.

[0026] This embodiment provides a co-simulation model based on the above principles and operating process, and its construction and operation process are as follows: 1. Selection of co-simulation software This embodiment employs a co-simulation approach using MATLAB / Simulink and CarSim to build a control system verification platform. CarSim is used to construct a high-fidelity vehicle dynamics model and a low-adhesion, uneven road surface simulation environment to simulate the actual motion response of a four-wheel independently driven vehicle under low-adhesion, uneven road conditions. MATLAB / Simulink is used to build the genetic algorithm optimization module for the Koopman module, the GAK-MPC controller module, and the underlying actuator tracking module. Through the co-simulation of these two software programs, real-time calculation and verification of the control algorithm can be achieved while ensuring the accuracy of the vehicle dynamics simulation.

[0027] 2. Co-simulation settings When performing co-simulation with MATLAB / Simulink and CarSim, vehicle parameters, road adhesion conditions, and dual lane change driving conditions are first set in CarSim. Then, the CarSim vehicle model is sent to the designated Simulink model, allowing the vehicle model to participate as the controlled object in the closed-loop simulation of the control system. The Simulink controller module reads the vehicle state output by CarSim at each sampling time. Based on this, the GAK-MPC controller outputs the target longitudinal slip ratio and active suspension force for all four wheels. The target longitudinal slip ratio is converted into corresponding wheel drive / braking torque by the underlying slip ratio tracking controller. Simultaneously, a road excitation model is built in Simulink, generating four-wheel road inputs. The wheel drive / braking torque, active suspension force, and road excitation are then input into the CarSim vehicle model to achieve closed-loop co-simulation of the controlled vehicle. If the vehicle parameters, road parameters, or driving condition settings in CarSim are modified, the corresponding Simulink co-simulation interface needs to be regenerated or updated to ensure consistent communication between the simulation model and the controller.

[0028] 3. Construction of a four-wheel independent drive electric vehicle model The CarSim electric vehicle model mainly consists of systems such as the body, drivetrain, steering system, braking system, tires, suspension, aerodynamics, and operating condition configuration. A four-wheel independent drive electric vehicle is selected as the controlled object, and an active suspension system is configured. The vehicle's longitudinal drive is implemented by four hub motors. In the CarSim / Simulink co-simulation, the four-wheel drive / braking torques are applied through the IMP_MYUSM_L1, IMP_MYUSM_R1, IMP_MYUSM_L2, and IMP_MYUSM_R2 interfaces, respectively; the four-wheel active suspension forces are applied through the IMP_FS_L1, IMP_FS_R1, IMP_FS_L2, and IMP_FS_R2 interfaces, respectively. The electric vehicle parameters are shown in Table 1.

[0029] Table 1 Vehicle Parameter Settings

[0030] The following describes the specific steps of the control method of the present invention: Step 1: Obtain the controlled vehicle model and random road surface disturbances using the CarSim / Simulink co-simulation platform: The controlled vehicle model is used to simulate a real controlled object of a vehicle under low-adhesion, uneven road conditions. Its main function is to use the driving / braking torque of the four wheels and the active suspension force as control inputs to change the lateral, yaw, vertical, and roll motion states of the vehicle, and output state information in real time. Random road surface disturbances are used to simulate the vertical excitation caused by uneven road surfaces, which, together with the low-adhesion conditions, constitute a complex road operating environment.

[0031] To simulate random vertical excitation on a low-adhesion, uneven road surface, a filtered white noise method was used in Simulink to generate the road surface elevation input at each wheel, and the output was sent to the IMP_ZGND port of CarSim; road surface excitation. With unit white noise The first-order differential equation between them is satisfied: (1) in, The lower cutoff frequency is the spatial frequency. For reference spatial frequency, This is the road surface roughness coefficient. For the longitudinal speed of the vehicle, The unit is white noise.

[0032] Considering the time lag in the excitation of the front and rear wheels on the same road surface, the road surface input for the rear wheel can be expressed as: (2) in, For the time lag, This refers to the vehicle's wheelbase.

[0033] Step 2: Establishment of the vehicle's lateral-vertical coupling dynamics model: The eight-degree-of-freedom vehicle body dynamics model is established as follows: (3) (4) (5) (6) (7) in, For the front wheel steering angle, For lateral velocity, For longitudinal velocity, The yaw rate is angular velocity. For the longitudinal force of the tire, This refers to the lateral force of the tire. This is the additional yaw moment generated by the difference in longitudinal forces between the left and right tires. The vertical load on each tire. This refers to the total force generated at a single wheel by an independent suspension actuator unit. The roll angle is... This represents the vertical displacement of the center of mass.

[0034] Forces of each independent suspension It is mainly affected by linear elastic force, nonlinear elastic force, linear damping force and active suspension force, and the specific formula is as follows: (8) In the formula The term represents the vertical relative displacement between the sprung mass and the unsprung mass, reflecting the real-time dynamic deflection of the suspension.

[0035] Vertical displacement of the sprung mass Vertical displacement from the center of mass and roll angle The derivation leads to: (9).

[0036] Dynamic vertical force Based on the vertical displacement of unsprung mass and road surface elevation excitation The calculation yielded: (10).

[0037] Finally, a tire nonlinear model is established. On low-adhesion surfaces, tires easily enter the nonlinear saturation region; therefore, this method uses the nonlinear Burckhardt tire model. To comprehensively reflect the tire's composite slip characteristics, this tire model introduces a synthetic slip ratio. To calculate the total friction coefficient, the synthetic slip ratio is defined for any wheel. expression: (11) in This refers to the tire slip angle.

[0038] The slip angles of the four tires are as follows: (12).

[0039] Total friction coefficient The calculation formula is: (13) In the formula, These are empirical parameters fitted for different road surfaces.

[0040] According to the principle of friction circle decomposition, the longitudinal force of the tire... and lateral force It can be represented as: (14) (15) (16) In the formula, the tire vertical load consists of static vertical load and dynamic vertical load.

[0041] The static vertical load distribution is as follows: (17).

[0042] Therefore, the vertical load on the tire can be obtained from equation (18): (18).

[0043] Step 3: Optimize the Koopman linear prediction model using a genetic algorithm: Based on the Koopman concept, a linear prediction model is constructed, and the eight-degree-of-freedom lateral-vertical coupling dynamic model is expressed as a discrete-time nonlinear function in the following form: (19) in, Let k be the system state vector at time k. To control the input vector, This represents the external disturbance vector.

[0044] To construct the Koopman linear prediction model, a dictionary vector of parameterized observation functions is first defined. Using the original system state as the base term, this, along with the nonlinear function constructed from the system state vector, control input vector, and external disturbance vector, forms the Koopman boosted state vector. The boosted state at time k is defined as: (20) in To improve the mapping, the observation function Indicates the first A nonlinear observation function.

[0045] To address the nonlinear coupling relationships among state variables, control inputs, and external disturbances in a vehicle dynamics system, an observation function based on a weighted activation function is constructed, and the first element in the observation function dictionary is defined. One adaptive observation function: (twenty one) in, The state quantity is coupled with the weight vector. To control the input coupling weight vector, This is the external perturbation coupling weight vector; The activation bias determines the center position of the nonlinear function's action; This is the kurtosis factor, used to adjust the slope of the nonlinear activation function.

[0046] The first The state coupling weights, control input coupling weights, external perturbation coupling weights, activation biases, and kurtosis factors in each observation function are feature parameters of that function. These parameters, acting as a gene in the genetic algorithm, are defined as follows: (twenty two).

[0047] By concatenating the parameters of all observation functions, a complete chromosome is obtained: (twenty three).

[0048] For a given Construct the lifting state based on its corresponding observation function parameters. Construct a data matrix using the data from the training set: (twenty four) (25) (26) (27).

[0049] Construct the augmented regression matrix and the Koopman parameter matrix to be identified: (28) (29) in, To improve the spatial state matrix, To control the input matrix, This is the perturbation input matrix.

[0050] A Koopman lifting dynamics structure based on input affine is used in the lifting space: (30).

[0051] To ensure numerical stability and improve robustness to noise, the Tikhonov regularized least squares method is used for the solution: (31) in is the regularization coefficient.

[0052] Its analytical solution is: (32) right By performing block extraction, the currently given parameters can be obtained. Koopman parameter matrix below .

[0053] To avoid the problem of large long-term prediction drift in the prediction time domain that may result from optimizing only the single-step prediction error, a multi-step prediction error is used to construct the fitness function of the genetic algorithm. For any starting time in the validation set... Using the currently given parameters The corresponding Koopman linear prediction model is used for Step-by-step open-loop rolling prediction yields the predicted boosted state sequence: (33).

[0054] because The former Dimension refers to the original state. The predicted value of the original state can be directly restored by selecting the matrix: (34).

[0055] Based on the multi-step prediction error of the validation set, define individual The multi-step prediction error cost function is: (35) in, The set of starting points for the validation set. This is a weight matrix used to balance different state dimensions.

[0056] Finally, the fitness function of the genetic algorithm is defined as: (36).

[0057] Genetic algorithms minimize The population is iteratively updated to achieve the objective. Once the genetic algorithm satisfies the maximum update generation or fitness convergence condition, the optimal observation function parameters are output. .based on Reconstruct the final Koopman lifting map: (37).

[0058] By re-identifying the final Koopman linear prediction model using the training data, we obtain: (38) Thus, the lateral-vertical coupled Koopman linear prediction model for subsequent GAK-MPC controller design is obtained.

[0059] The following are the model validation results involved in this invention: The accuracy of the lateral coupling linear prediction model based on the genetic algorithm optimization of Koopman established in step three is verified. By verifying the convergence performance of the genetic algorithm, the model fitting ability under known working conditions, and the model generalization ability under unknown working conditions, it is determined whether the identified Koopman linear prediction model can provide a reliable prediction model basis for the subsequent GAK-MPC controller.

[0060] Figure 4 This verifies the convergence of identification errors during the optimization process of the genetic algorithm. (By...) Figure 4 It can be seen that as the number of evolutionary iterations increases, the optimal individual error and the population average error gradually decrease and eventually tend to stabilize. This indicates that the real number encoding strategy and the segmented random evaluation mechanism can effectively complete the optimization of high-dimensional observation function parameters and obtain a convergent and stable combination of Koopman observation function parameters.

[0061] Figure 5To verify the fitting ability of the GA-Koopman model under known operating conditions, closed-loop simulation data with the same distribution as the training set was selected as test data. The CarSim output results were used as a benchmark for comparison. Multi-step open-loop prediction was performed using a Koopman linear prediction model constructed with optimal observation function parameters. The prediction results show that during double lane change steering, the predicted curve and the simulation output curve maintain good consistency, with no obvious long-term drift. The model can effectively reproduce the changing trends of key state variables such as vehicle lateral velocity, yaw rate, vertical displacement, roll angle, dynamic vertical load, and suspension deflection, indicating that the model has good fitting accuracy under known operating conditions.

[0062] Figure 6 This document presents the validation results of the GA-Koopman model's generalization ability under unknown conditions. To test the model's predictive ability under unseen input conditions, a data sequence not used in training was constructed, and the corresponding front wheel steering angle and road surface roughness disturbance were used as external inputs to the model. The results show that, under unknown input sequences, the GA-Koopman model can still track the dynamic evolution trends of vehicle lateral velocity, yaw rate, vertical displacement, and roll angle. Although some state variables exhibit amplitude deviations during long-term open-loop prediction, the prediction results remain consistent with the CarSim output in terms of phase and trend, without divergence, indicating that the model has good generalization ability and open-loop prediction stability.

[0063] Step 4: Design of a vehicle side-vertical cooperative stability controller based on genetic algorithm optimization of the Koopman model The linear prediction model based on the genetic algorithm to optimize Koopman has been established in the above steps. Therefore, the original nonlinear solution problem can be further transformed into a standard QP problem based on the linear prediction model. The state vector of the boosting space is defined as: (39) in, Let be the state vector of the original system. For the control input of the original system, This is the disturbance input to the original system.

[0064] To construct a comprehensive control objective that includes lateral stability, yaw response, roll attitude, and tire load fluctuation, the system output vector is defined as: (40).

[0065] The state equation and output equation of the control system in the lifting space are as follows: (41) in This is the output matrix obtained through derivation.

[0066] Set the prediction time domain as Control time domain is .exist Time, define the prediction time domain The state sequence, output sequence, and interference sequence within the sequence are as follows: (42).

[0067] Define the prediction time domain Control sequence within for: (43).

[0068] Therefore, the output sequence in the prediction time domain can be represented as a linear function of the current state sequence, the future control sequence, and the future disturbance sequence: (44) in They are The prediction matrix is ​​obtained by recursion within the prediction time domain.

[0069] Set the control reference output as follows: (45) in The ideal yaw rate.

[0070] Construct a reference output sequence in the prediction time domain : (46).

[0071] At each sampling time, the following optimization objective function is constructed: (47) in, To output the weight matrix, To control the input weight matrix, To control the incremental weight matrix, To control the input increment.

[0072] The optimization problem must simultaneously consider both the physical constraints of the control input and the safety constraints of the vehicle state. For the control input, the target longitudinal slip ratio of the four wheels and the active suspension force must satisfy the following: (48) (49) in, This represents the maximum permissible value for longitudinal slip ratio. This represents the maximum permissible value of the active suspension force.

[0073] For the vehicle's safety boundary conditions, the lateral velocity, body roll angle, and suspension dynamic deflection respectively satisfy the following: (50) (51) (52) in, These correspond to the limit values ​​of each physical quantity under low-adhesion road surface conditions.

[0074] Therefore, the lateral-sagging cooperative stability control problem can be expressed as a standard quadratic programming problem: (53).

[0075] Solving the above quadratic programming problem yields the optimal control sequence: (54).

[0076] Based on the rolling optimization principle of model predictive control, only the first control input in the above optimal control sequence is considered. Applying this to the controlled vehicle, we can obtain the longitudinal slip ratio of the four wheels and the four active suspension forces at the current sampling moment: (55) The longitudinal slip ratio of the four wheels is input to the underlying slip ratio tracking controller, which then calculates the driving / braking torque of the four wheels and applies it to the controlled object. The four active suspension forces are directly input to the active suspension actuator, thereby achieving coordinated control of the vehicle's lateral speed, yaw rate, body roll angle and dynamic vertical load.

[0077] Simulation tests were conducted under ISO dual-track shifting conditions, with the adhesion coefficient set to [value missing]. The road surface unevenness level is C, and the initial speed is set to... The simulation parameters are shown in Table 2.

[0078] Table 2 Simulation parameters of GAK-MPC controller

[0079] Figure 7 (a) Comparison of vehicle lateral speed response. It can be seen that after adopting GAK-MPC control, the peak lateral speed is reduced compared to when there is no controller. Suppressed at approximately Within this range, the controller can effectively reduce the risk of vehicle sideslip. Figure 7(b) Comparison of yaw rate response: After adopting GAK-MPC control, the peak yaw rate decreased from that without a controller. Suppressed at approximately Within the specified range, this indicates that the controller can suppress yaw instability while ensuring vehicle steering response. Figure 7 (c) Comparison of vehicle roll angle response. After using GAK-MPC control, the peak roll angle changed from that without a controller. Reduced to approximately Within a certain range, the oscillation amplitude also decreased significantly, indicating that the active suspension force of the control quantity can effectively improve the vehicle's attitude stability. Figure 7 (d) Comparison of load transfer rate response. After adopting GAK-MPC control, most of the fluctuations in load transfer rate are limited to a small range. Although there are still instantaneous fluctuations caused by road impact in some areas, the overall load transfer degree is significantly lower than that in the uncontrolled state. It can alleviate the load transfer between the left and right wheels and retain more sufficient adhesion margin for the tire lateral force to exert.

[0080] Figure 8 The control output results of the GAK-MPC controller are given. Figure 8 (a) Comparison of reference and actual values ​​of longitudinal slip ratio for the four wheels. Figure 8 (b) shows the active suspension force output of the controller. Figure 8 As can be seen, the actual slip ratio in CarSim can follow the target slip ratio output by the controller quite well, indicating that the underlying slip ratio tracking controller can effectively execute the control commands of GAK-MPC and improve vehicle yaw and lateral stability by adjusting the longitudinal force of the tires; the active suspension force can be adjusted in real time according to the vehicle state to suppress body roll and dynamic vertical load fluctuations. Both sets of control quantities are limited within the set physical constraints, indicating that the controller described in this invention can achieve coordinated control of lateral and vertical motion while satisfying actuator constraints.

[0081] To further verify the side-sag coordinated stability control effect of the GAK-MPC control strategy described in this invention under low-adhesion uneven road surface conditions, the NMPC control strategy and the GAK-MPC control strategy described in this invention were compared and analyzed under the same double lane change condition. Figure 9 The comparison of vehicle key state response curves is presented, among which, Figure 9 (a) represents the lateral velocity. Figure 9 (b) represents the yaw rate. Figure 9 (c) is the vehicle body roll angle. Figure 9 (d) represents the load transfer rate. (From...) Figure 9 It can be seen that after adopting NMPC and GAK-MPC control, the vehicle's lateral speed, yaw rate, body roll angle and load transfer rate are all effectively suppressed.

[0082] To further quantitatively evaluate the control effects of different control strategies, this embodiment calculated the root mean square error (RMSE) of key vehicle response indicators under each control strategy, and the statistical results are shown in Table 3. As shown in Table 3, compared to the uncontrolled condition, the vehicle dynamic response is significantly improved after adopting the GAK-MPC control strategy described in this invention. The peak lateral velocity is reduced by 55.8%, and the peak load transfer rate remains within the safe threshold range, indicating that this control strategy can effectively reduce the risk of lateral instability and rollover under low-adhesion uneven road conditions. Furthermore, compared to the NMPC control strategy, the GAK-MPC control strategy described in this invention achieves similar control effects in indicators such as lateral velocity, yaw rate, and load transfer rate. The difference between the lateral velocity RMSE and NMPC is approximately... The RMSE index of LTR is slightly lower than that of NMPC. These results indicate that the GAK-MPC control strategy based on the genetic algorithm-optimized Koopman linear prediction model can maintain good lateral-vertical coordinated control performance while reducing the complexity of nonlinear optimization solutions.

[0083] Table 3 Comparison of quantitative indicators under different control strategies

[0084] Figure 10 A comparison of the single-step solution time between NMPC and the GAK-MPC control strategy described in this invention is presented, and Table 4 further provides the corresponding computation time statistics. Figure 10 As shown in Table 4, NMPC, due to its requirement for online solution of high-dimensional nonconvex nonlinear optimization problems, exhibits significant fluctuations in single-step solution time and a clear computational peak; its average single-step solution time is... The peak reached The current methods are insufficient to meet the control cycle requirements of real-time vehicle dynamics control. In contrast, the GAK-MPC control strategy described in this invention transforms the original nonlinear predictive control problem into a quadratic programming problem by constructing a Koopman linear prediction model optimized by a genetic algorithm, significantly reducing the complexity of online optimization. Statistical results show that the average single-step solution time of GAK-MPC is only [missing information]. It reduces the time by approximately 340 times compared to NMPC; its peak solution time is... The time frame remains within the allowable range for real-time vehicle control. The control method described in this invention significantly reduces the online computational burden on the onboard control unit while maintaining lateral-vertical coordinated stability control, thereby improving the real-time performance of the control algorithm in actual vehicle control systems.

[0085] Table 4 Comparison of solution times for vehicle side-vertical cooperative stability controller 。

Claims

1. A vehicle side-vertical cooperative control method based on genetic algorithm optimization of the Koopman model, characterized in that: The steps are as follows: S1. Constructing the controlled object model: Constructing a controlled object model of a four-wheel independent drive vehicle under low-adhesion uneven road surface conditions to simulate the dynamic response of the vehicle to yaw rate, lateral velocity, roll angle and tire vertical load under low adhesion coefficient and random road surface elevation excitation. S2. Establish vehicle lateral-vertical coupling dynamics model and road disturbance model: Use the filtered white noise method to generate random vertical excitation of low-adhesion uneven road surface, and determine the time lag relationship when the front and rear wheels pass through the same road surface position according to the vehicle wheelbase and longitudinal speed to obtain the four-wheel road surface elevation input; establish an eight-degree-of-freedom lateral-vertical coupling dynamics model of the vehicle to describe the coupling relationship between the lateral motion, yaw motion, body roll motion and vertical motion of the vehicle under low-adhesion and uneven road surface conditions; S3. Construct a Koopman linear prediction model optimized by a genetic algorithm: Collect closed-loop operation data of vehicles under typical working conditions on uneven roads with low adhesion, and construct a training sample set; Based on the Koopman operator theory, introduce an observation function to map the eight-degree-of-freedom lateral-vertical coupling dynamic model described in step S2 to a high-dimensional linear space; Use a genetic algorithm to iteratively optimize the type and / or parameter combination of the observation function, with prediction accuracy and model complexity as optimization objectives, determine the optimal observation function and its optimal parameter combination, and construct a high-precision, low-complexity Koopman linear prediction model; S4. Design a model predictive control cooperative stability controller based on genetic algorithm optimization of the Koopman operator: Based on the Koopman linear prediction model described in step S3, construct a multi-objective optimization problem within the model predictive control framework. The optimization objectives of the multi-objective optimization problem include yaw rate tracking, lateral velocity suppression, roll angle suppression, and dynamic vertical load fluctuation suppression. Vehicle state safety constraints and actuator saturation constraints are introduced into the multi-objective optimization problem. The rolling optimization solution outputs the target longitudinal slip ratio and active suspension force for all four wheels. S5. Bottom-level execution control: The target longitudinal slip ratio of the four wheels obtained in step S4 is output to the bottom-level slip ratio tracking controller, which converts the target slip ratio of each wheel into the driving / braking torque of the corresponding wheel.

2. The vehicle side-vertical cooperative control method based on genetic algorithm optimization of the Koopman model according to claim 1, characterized in that: To simulate random vertical excitation on a low-adhesion, uneven road surface, a filtered white noise method was used in Simulink to generate the road surface elevation input at each wheel and output it to the IMP_ZGND port of CarSim. Road surface excitation With unit white noise The first-order differential equation between them is satisfied: （1） in, The lower cutoff frequency is the spatial frequency. For reference spatial frequency, This is the road surface roughness coefficient. For the longitudinal speed of the vehicle, Units of white noise; Considering the time lag in the excitation of the front and rear wheels on the same road surface, the road surface input for the rear wheel can be expressed as: （2） in, for Input the road surface elevation for the side and rear wheels. for Side front wheel time delay The subsequent road surface elevation input, For the time lag, This refers to the vehicle's wheelbase.

3. The vehicle side-vertical cooperative control method based on genetic algorithm optimization of the Koopman model according to claim 1, characterized in that: Vehicle lateral-vertical coupling dynamics model: Dynamic vertical force Based on the vertical displacement of unsprung mass and road surface elevation excitation The calculation yielded: （10） in, for The equivalent vertical stiffness of the wheel's tire. for The tire's equivalent vertical damping coefficient; Tire vertical load consists of static vertical load and dynamic vertical load. The static vertical load is distributed as follows: （17） in, The static vertical load is on the left front wheel. The static vertical load is on the right front wheel. The static vertical load is on the left rear wheel. The static vertical load is on the right rear wheel. For the overall vehicle quality, It is the acceleration due to gravity. This is the distance from the vehicle's center of gravity to the rear axle. This is the distance from the vehicle's center of gravity to the front axle. The vertical load on the tire is obtained from equation (18): （18） in, for The static vertical load on the wheel.

4. The vehicle side-vertical cooperative control method based on genetic algorithm optimization of the Koopman model according to claim 1, characterized in that: Koopman linear prediction model optimized by genetic algorithm: （38） in, for The upgraded state vector at time step 1. This is the Koopman up-dimensional state transition matrix. for The upgraded state vector at time step [time]. The control input matrix is ​​obtained through genetic algorithm optimization. for The control input vector at time t, The perturbation input matrix is ​​obtained through optimization using a genetic algorithm. for The perturbation input vector at time t.

5. The vehicle side-vertical cooperative control method based on genetic algorithm optimization of the Koopman model according to claim 1, characterized in that: Model predictive control and cooperative stable controller based on genetic algorithm optimization of Koopman operator: （54） in, To control the optimal control sequence in the time domain. In order to be in The transpose of the optimal control input vector at the current time obtained from the time-to-time prediction. In order to be in Time prediction The transpose of the time-optimal control input vector. In order to be in The transpose of the optimal control input vector for the control time-domain terminal obtained from the time-domain prediction. To control the length of the time domain.

6. The vehicle side-vertical cooperative control method based on genetic algorithm optimization of the Koopman model according to claim 1, characterized in that: The target longitudinal slip ratio and active suspension force for the four wheels are: （55） in, Let be the optimal control input vector at time k. Let k be the longitudinal slip ratio of the left front wheel target. Let k be the longitudinal slip ratio of the right front wheel target. Let k be the longitudinal slip ratio of the left rear wheel target. Let k be the longitudinal slip ratio of the right rear wheel target. Let k be the optimal vertical control force of the left front wheel active suspension. Let k be the optimal vertical control force of the right front wheel active suspension. Let k be the optimal vertical control force of the left rear wheel active suspension. The optimal vertical control force of the right rear wheel active suspension at time k is given.

Images