A physics-inspired data-driven approach to vehicle lateral dynamics modeling
Through a physics-inspired data-driven approach, a linear variable parameter system model is established to separate time-varying vehicle parameters, which solves the adaptability and robustness problems of traditional vehicle lateral dynamics models under complex conditions and achieves accurate simulation and prediction of vehicle dynamic behavior.
Patent Information
- Application Number
- CN202310886521.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-19
- Publication Date
- 2025-09-30
- Estimated Expiration
- 2043-07-19
AI Technical Summary
Existing vehicle lateral dynamics modeling methods lack adaptability and robustness under complex and changeable actual road conditions. Traditional methods rely on Newton's laws of motion and cannot effectively handle time-varying vehicle parameters, leading to safety hazards.
A physics-inspired data-driven approach is adopted to establish a data-driven vehicle lateral dynamics model through a variable tire stiffness model, a linear variable parameter system, discretization and the Kronecker product operator. This method separates the time-varying vehicle parameters from the measurable parameters and simplifies the model structure.
It achieves accurate simulation and prediction of vehicle dynamics behavior under various driving conditions, improves the adaptability and robustness of the model, and reduces data requirements and computational complexity.
Smart Images
Figure CN117010085B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of autonomous driving technology, and specifically provides a data-driven vehicle lateral dynamics modeling method based on physics inspiration. Background Art
[0002] Vehicle lateral dynamics is an important component of vehicle dynamics, involving steering, braking, acceleration, and other behaviors. Traditional vehicle lateral dynamics modeling methods are primarily based on classical mechanics and control theory, and all employ dynamic modeling methods based on Newton's laws of motion. While these methods provide accurate model predictions, their adaptability and robustness to complex and changing real-world road conditions and vehicle behaviors need to be improved.
[0003] With the development of data-driven technology, more and more researchers have begun to use data-driven methods to model vehicle lateral dynamics. However, existing data-driven methods have certain problems in terms of physical consistency, model interpretability, and model prediction performance.
[0004] The existing technologies are distinguished as follows:
[0005] Technical comparison with patent CN114684199A "A mechanism analysis-data driven vehicle dynamics series hybrid model, intelligent vehicle trajectory tracking control method and controller";
[0006] 1. Patent CN114684199A focuses on using both mechanism analysis and data to establish a hybrid vehicle dynamics model, while our approach focuses on deriving a purely data-driven vehicle dynamics model based on mechanism.
[0007] Second, the model obtained by patent CN114684199A relies on complex nonlinear tire and vehicle dynamics models, while our method does not rely on tire models and is only based on a small amount of online measurement data.
[0008] 3. Patent CN114684199A requires the use of LSTM as the backbone network and combines it with a fully connected neural network to work, while our method does not require the design of a neural network.
[0009] Fourth, patent CN114684199A requires the collection of multi-operating condition data to pre-train a large number of weight parameters of the neural network, while our solution does not require training.
[0010] 5. Patent CN114684199A requires measurement of tire longitudinal force, while our method does not require tire longitudinal force.
[0011] Technical comparison with patent CN115303289A "A deep Gaussian vehicle dynamics model, training method, intelligent vehicle trajectory tracking control method and terminal device method";
[0012] 1. Patent CN115303289A involves complex models such as multi-layer feedforward neural networks and deep Gaussian models, which require a large amount of initial data for weight parameter training. Our method does not rely on neural networks, but is based only on a linear variable parameter data-driven model derived from vehicle dynamics mechanisms.
[0013] Second, the system of patent CN115303289A involves up to 10 online state parameter inputs, while our method only requires 4 online state parameters as model inputs.
[0014] 3. Patent CN115303289A uses a strongly nonlinear tire model, and this model relies on a large number of experimental parameters for model calibration. Our method does not rely on the tire model and is ultimately presented in the form of a linear model with a simple structure and easy control.
[0015] Technical comparison with patent CN113657036A "Vehicle dynamics simulation implementation method based on neural network and physical model".
[0016] 1. Patent CN113657036A focuses on designing a hybrid vehicle dynamics model that combines a parameter model and a dynamics model. The main idea is divided into two steps: first, customized experiments, parameter collection, and identification of specific unknown parameters; second, combining parameter identification with the vehicle dynamics model to obtain a physical law-data driven hybrid model. Our method starts from the mechanism and only derives a purely data-driven model.
[0017] Second, patent CN113657036A relies on neural networks to identify vehicle dynamics models, while our method does not involve neural networks.
[0018] 3. Patent CN113657036A involves the calculation of vehicle cornering stiffness. These two quantities are highly nonlinear and time-varying in actual operation, making calculation difficult. Our method derives a linear variable parameter model, separates the highly nonlinear parameters from the system state parameters, and characterizes the nonlinear time-varying parameters through data.
[0019] Fourth, patent CN113657036A requires special customization of different vehicle operation scenarios and the collection of a large amount of data to calibrate the weight parameters of the neural network. Our method does not require complex vehicle operation scenarios, and the data requirement is far less than the above method.
[0020] To address the shortcomings of existing technologies, this paper proposes a physics-inspired, data-driven vehicle lateral dynamics modeling method. This method leverages the advantages of physics-inspired methods to provide model interpretability and physical consistency, while also leveraging the advantages of data-driven techniques to provide model adaptability and robustness. Summary of the Invention
[0021] In order to solve the problem that many vehicle parameters, such as vehicle mass, tire longitudinal stiffness, lateral stiffness, and vehicle center of mass position, may be time-varying in actual operation, resulting in inaccuracy of the dynamic model based on Newton's law, especially when the vehicle operates in the nonlinear region of the tire, which poses a huge hidden danger to the vehicle's operating safety, the present invention proposes a physics-inspired data-driven vehicle lateral dynamics modeling method to solve the problem of inaccuracy of traditional vehicle lateral dynamics models due to time-varying vehicle-related parameters under complex motion conditions.
[0022] To achieve the above object, the technical solution adopted by the present invention is:
[0023] A physics-inspired, data-driven approach to vehicle lateral dynamics modeling, including:
[0024] 1) A tire force model with variable tire stiffness is proposed, and a vehicle lateral dynamics model is established;
[0025] 2) Convert the above model into a linear variable parameter system model;
[0026] 3) Discretize the above system;
[0027] 4) By introducing the Kronecker product operator, the above discrete system is further simplified and the data matrix is defined as:
[0028] 5) Based on the data, the initial system correlation matrix is obtained using the physical rules of the linear variable parameter lateral dynamics model;
[0029] 6) Obtain a data-driven dynamics model based on the physical rules of vehicle lateral motion.
[0030] As a further improvement of the present invention, the tire force model in step 1) is specifically as follows:
[0031] The nonlinear terms are lumped into the tire stiffness to preserve the linear relationship between tire force and slip rate / sideslip angle, as shown in the following formula:
[0032]
[0033] As a further improvement of the present invention, the linear variable parameter system model in step 2) is specifically as follows:
[0034] The adjustment parameter is ρ, and the model and specific parameter expressions are shown in the following formula:
[0035]
[0036]
[0037] A(ρ)=A0+A1ρ1+A2ρ2+A3ρ3
[0038] B(p)=B0+B1ρ1+B2ρ2+B3ρ3
[0039]
[0040]
[0041]
[0042] Note that in the above formulas, A1, B0, and B3 are all time-varying vehicle-related system parameters, which are separated from the adjustment parameter ρ.
[0043] As a further improvement of the present invention, the specific steps of discretization of the system in step 3) are as follows:
[0044] The discrete time step is T s , the continuous system can be transformed into the following system:
[0045] x k+1 =A k (ρ k )x k +B k (ρ k ) u k
[0046]
[0047]
[0048] As a further improvement of the present invention, the Kronecker product operator is introduced in step 4), the above discrete system is further simplified, and a data matrix is defined. The specific steps are as follows:
[0049] By introducing the Kronecker product operator, the above discrete system is further simplified:
[0050]
[0051] Assume that a set of data can be collected The data length is n d , define the following data matrix:
[0052]
[0053]
[0054]
[0055]
[0056]
[0057] As a further improvement of the present invention, the step 5) is based on the data and utilizes the physical rules of the linear variable parameter lateral dynamics model to obtain the initial system correlation matrix, which is specifically as follows;
[0058] Based on the data and using the physical rules of the linear variable parameter lateral dynamics model, the following relationship is obtained:
[0059]
[0060] Based on the data, the initial system correlation matrix is obtained:
[0061]
[0062] As a further improvement of the present invention, the step 6) obtains a data-driven dynamics model based on the physical rules of vehicle lateral motion, specifically as follows:
[0063]
[0064] Compared with the prior art, the present invention has the following advantages and beneficial effects:
[0065] The advantage of this invention lies in the development of a novel, physics-inspired, data-driven vehicle lateral dynamics modeling method. This method incorporates a novel tire force model expression. Using a linear variable parameter system model, it cleverly separates vehicle-related time-varying parameters from measurable parameters related to vehicle motion. This model, based solely on vehicle motion data and independent of time-varying vehicle-related parameters, provides a data-driven vehicle lateral dynamics model. This model accurately, rapidly, and effectively captures vehicle dynamics and motion characteristics across the full range of vehicle / tire operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0066] Figure 1 The technical route of the present invention;
[0067] Figure 2 Schematic diagram of bicycle model;
[0068] Figure 3 Signals required for the data-driven model: (a) front wheel steering angle; (b) longitudinal speed; (c) front wheel slip ratio;
[0069] Figure 4 Data-driven model validation: (a) lateral velocity; (b) yaw angle;
[0070] Figure 5 Corner sweep and speed change conditions: (a) front wheel steering angle; (b) longitudinal speed; (c) front wheel slip rate;
[0071] Figure 6 Data-driven model verification for corner sweep and variable speed conditions: (a) lateral velocity; (b) yaw angle;
[0072] Figure 7 Double lane-changing conditions: (a) front wheel steering angle; (b) longitudinal speed; (c) front wheel slip rate;
[0073] Figure 8 Data-driven model validation for dual lane-changing conditions: (a) lateral velocity; (b) yaw angle. DETAILED DESCRIPTION
[0074] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:
[0075] The present invention discloses a data-driven vehicle lateral dynamics modeling method based on physics inspiration, and its technical route is as follows: Figure 1 As shown, the specific implementation is as follows:
[0076] Figure 2 This is a schematic diagram of a bicycle model. According to Newton's laws of mechanics, the traditional vehicle lateral dynamics model can be described by the following formula:
[0077]
[0078] Traditional linear tire force models assume constant tire stiffness and a linear relationship between tire force and slip rate / slip angle, oversimplifying tire motion conditions. Traditional nonlinear tire force models require pre-collection of data for nonlinear model identification, lack adaptability to operating conditions, and are expensive to acquire. Unlike traditional tire force models, this paper proposes a novel tire force model that lumps nonlinear terms into tire stiffness, preserving the linear relationship between tire force and slip rate / slip angle, as shown in the following formula:
[0079]
[0080] The above model is transformed into a linear variable parameter system model, where the adjustment parameter is ρ. The model and specific parameter expressions are shown in the following formula:
[0081]
[0082]
[0083] A(ρ)=A0+A1ρ1+A2ρ2+A3ρ3
[0084] B(ρ)=B0+B1ρ1+B2ρ2+B3ρ3
[0085]
[0086]
[0087]
[0088] Note that in the above formulas, A1, B0, and B3 are all time-varying vehicle-related system parameters, which are separated from the adjustment parameter ρ.
[0089] Discretize the above system, and the discrete time step is T s , the continuous system can be transformed into the following system:
[0090] x k+1 =A k (ρ k )x k +B k (ρ k )u k
[0091]
[0092]
[0093] By introducing the Kronecker product operator, the above discrete system can be further simplified:
[0094]
[0095] Assume that a set of data can be collected The data length is n d , define the following data matrix:
[0096]
[0097]
[0098]
[0099]
[0100]
[0101] Based on the data and using the physical rules of the linear variable parameter lateral dynamics model, the following relationship can be obtained:
[0102]
[0103] Therefore, based on the data, the initial system correlation matrix can be obtained:
[0104]
[0105] To this end, the data-driven dynamics model based on the physical rules of vehicle lateral motion can be derived as follows:
[0106]
[0107] Based on the above data-driven vehicle lateral dynamics model, we can obtain the vehicle lateral dynamics state verification results.
[0108] The results are presented under various operating conditions, including conventional path following, corner sweeping and variable speed, and double lane change.
[0109] Under normal path tracking conditions, we obtain the measured front wheel steering angle, longitudinal velocity, and front wheel slip ratio and plot the results on Figure 3 In which, the front wheel angle is the input of the proposed data-driven system, and the longitudinal speed and the front wheel slip ratio together constitute the adjustment parameter vector. The vehicle lateral speed and yaw angle are verified by the data-driven model and the measured values. The results are shown in Figure 4 The predicted results of the proposed model are very close to the actual measured values, which proves the accuracy and reliability of the model in conventional path tracking conditions.
[0110] Under the corner sweep and speed change conditions, we plot the measured vehicle system steering angle, longitudinal speed, and front wheel slip rate on Figure 5 In. Figure 6 In
[15] , we also validated the model for lateral velocity and yaw angle, and the results showed that the model’s prediction results were equally accurate under corner sweep and variable speed conditions.
[0111] Finally, we also tested the model under the double lane change condition. We plotted the front wheel steering angle, longitudinal speed, and front wheel slip ratio of the model on Figure 7 middle. Figure 8 The verification results of the model's lateral velocity and yaw angle are shown in Figure 2. Figure 7 and Figure 8 As can be seen from the figure, the proposed model also performs well in the double lane change condition, and its prediction results are very close to the actual measured values. This demonstrates the accuracy and reliability of the model in complex driving scenarios.
[0112] Overall, the data-driven vehicle lateral dynamics model described above enables us to effectively simulate and predict the vehicle's dynamic behavior under various driving conditions. These validation results not only demonstrate the model's accuracy and reliability but also provide an important reference for future vehicle control and design.
[0113] The above descriptions are only some embodiments of the present invention and are not intended to limit the present invention in any other form. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection required by the present invention.
Claims
1. A physics-inspired data-driven vehicle lateral dynamics modeling method, characterized by: include: 1) A tire force model with variable tire stiffness is proposed, and a vehicle lateral dynamics model is established; 2) Convert the above model into a linear variable parameter system model; The linear variable parameter system model in step 2) is specifically as follows; The adjustment parameters are , the model and specific parameter expressions are shown in the following formula: ； ； Note that in the above formula, , , are all time-varying vehicle-related system parameters, which are related to the adjustment parameters separate from each other; 3) Discretize the above system; The specific steps of discretization of the system in step 3) are as follows: The discrete time step is , the continuous system can be transformed into the following system: ； ； 4) By introducing the Kronecker product operator, the above discrete system is further simplified and the data matrix is defined as: 5) Based on the data, the initial system correlation matrix is obtained using the physical rules of the linear variable parameter lateral dynamics model; 6) Obtain a data-driven dynamics model based on the physical rules of vehicle lateral motion.
2. The physics-inspired data-driven vehicle lateral dynamics modeling method according to claim 1, characterized in that: The tire force model in step 1) is specifically as follows: The nonlinear terms are lumped into the tire stiffness to preserve the linear relationship between tire force and slip rate / sideslip angle, as shown in the following formula: ； Among them, i represents f or r, indicating the front wheel or rear wheel, j represents x or y, indicating the longitudinal or lateral direction, represents the corresponding tire stiffness, represents the tire slip rate, Indicates the effective radius of the tire, Indicates the tire rotation speed, represents the vehicle longitudinal velocity, Indicates the tire slip angle, represents the front wheel steering angle, represents the lateral velocity of the vehicle, Indicates the distance from the front axle to the rear axle and the center of mass, represents the vehicle's yaw rate. The traditional vehicle lateral dynamics model can be described by the following formula: ； in Indicates the vehicle mass, represents the vehicle's moment of inertia around the z-axis.
3. The physics-inspired data-driven vehicle lateral dynamics modeling method according to claim 1, characterized in that: Step 4) introduces the Kronecker product operator, further simplifies the above discrete system, and defines the data matrix. The specific steps are as follows: By introducing the Kronecker product operator, the above discrete system is further simplified: ； Assume that a set of data can be collected , the data length is , define the following data matrix: 。 4. The physics-inspired data-driven vehicle lateral dynamics modeling method according to claim 1, characterized in that: In step 5), based on the data, the physical rules of the linear variable parameter lateral dynamics model are used to obtain the initial system correlation matrix, which is as follows; Based on the data and using the physical rules of the linear variable parameter lateral dynamics model, the following relationship is obtained: ； Based on the data, the initial system correlation matrix is obtained: 。 5. The physics-inspired data-driven vehicle lateral dynamics modeling method according to claim 1, characterized in that: The step 6) obtains a data-driven dynamics model based on the physical rules of vehicle lateral motion, specifically as follows: 。