A vehicle limit control method based on hybrid-order koopman tensor decomposition and CBF fusion

Abstract

This invention relates to the field of vehicle control technology, specifically to a vehicle limit control method based on hybrid-order Koopman tensor decomposition and CBF fusion. The method involves acquiring the motion state of the target vehicle and estimating its motion state at the next moment. Based on the motion state at the next moment, the tire forces of the target vehicle are determined. The state vector of the target vehicle is determined according to the motion state at the next moment and the tire forces, and a control input vector is defined. Based on the state vector and the control input vector, a first-order linear Koopman model, a second-order bilinear Koopman model, and a third-order higher-order Koopman model are constructed. The weights of each Koopman model are determined based on a comprehensive index of the severity of the target vehicle's operating conditions. The prediction results of each Koopman model are calculated, and a fused prediction result is determined based on the weights of each Koopman model. A nominal controller is constructed based on the affine form of the fused prediction result. The nominal controller is solved to determine the control input vector at the current moment for controlling the target vehicle.

Description

Technical Field

[0001] This specification relates to the field of vehicle control technology, and in particular to a vehicle limit control method that combines hybrid-order Koopman tensor decomposition and CBF. Background Technology

[0002] In the field of vehicle dynamics control, especially under extreme conditions such as high-speed emergency obstacle avoidance, braking on icy and snowy roads, and extreme steering in continuous curves, the tire operating point often enters the nonlinear saturation region, resulting in vehicle dynamics exhibiting strong nonlinearity, time-varying characteristics, and uncertainty. To address this challenge, existing control methods are mainly divided into two categories: one is nonlinear methods based on physical models, such as using the Pacejka tire model combined with nonlinear model predictive control (MPC). Although this method is theoretically mature, its control accuracy is highly dependent on the accurate calibration of model parameters, and the real-time computational burden of solving nonlinear optimization problems online is heavy, making it difficult to widely apply on embedded platforms; the other is the data-driven Koopman operator method, which approximates the nonlinear system by elevating it to a high-dimensional linear space, and has the advantage of high computational efficiency.

[0003] However, current vehicle control methods based on the Koopman operator generally employ a first-order linear approximation. When tire forces enter the saturation region and the force-slip relationship exhibits significant higher-order nonlinear characteristics, the error of the single-order linear approximation increases rapidly. Although theoretically, the approximation quality can be improved by increasing the spatial dimension, the number of model parameters increases with the square of the dimension, which can easily lead to the curse of dimensionality and limit the effectiveness of practical applications.

[0004] Therefore, this specification provides a vehicle limit control method that combines hybrid-order Koopman tensor decomposition with CBF. Summary of the Invention

[0005] This specification provides a vehicle limit control method that combines hybrid-order Koopman tensor decomposition with CBF (Continuous Bragg Flow Factor) to address the aforementioned problems in the prior art.

[0006] The following technical solution is adopted in this specification:

[0007] This specification provides a vehicle limit control method that combines hybrid-order Koopman tensor decomposition with CBF fusion, including:

[0008] S1. Obtain the motion state of the target vehicle, the motion state including the longitudinal velocity, lateral velocity, yaw rate, heading angle, and position coordinates of the target vehicle;

[0009] S2. Determine the motion state of the target vehicle at the next moment based on the motion state and the IMU data of the target vehicle;

[0010] S3. Based on the preset tire force relaxation model, tire force observation model and the motion state of the target vehicle at the next moment, determine the tire force, wheel slip angle and wheel normal load of the target vehicle;

[0011] S4. Based on the motion state of the target vehicle at the next moment and the forces of each tire of the target vehicle, determine the state vector of the target vehicle and define the control input vector;

[0012] S5. Based on the state vector and the control input vector, construct a first-order linear Koopman model, a second-order bilinear Koopman model, and a third-order higher-order Koopman model;

[0013] S6. Determine the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle, and determine the comprehensive index of the severity of the working condition based on the tire utilization rate index, sideslip angle index, and lateral acceleration index.

[0014] S7. Determine the weights of each Koopman model based on the comprehensive index of the severity of the working condition and the preset weight formula of each Koopman model;

[0015] S8. Calculate the prediction results of each Koopman model, and determine the fusion prediction result based on the weights of each Koopman model.

[0016] S9. Determine the affine form of the fusion prediction result;

[0017] S10. Construct a nominal controller based on the affine form of the fusion prediction results;

[0018] S11. Solve for the nominal controller, determine the control input vector at the current moment, and control the target vehicle according to the control input vector at the current moment.

[0019] Based on the aforementioned technical means, this solution introduces a hybrid-order Koopman model, which solves the problem of inaccuracy of traditional linear models when vehicles are in extreme motion (when tires enter the nonlinear region). By introducing higher-order terms, it can more accurately capture the saturation characteristics of tire forces and the strong coupling relationship between yaw and lateral forces, thereby providing a more physically realistic prediction model under extreme conditions such as drifting and fishtailing.

[0020] Furthermore, the IMU data includes longitudinal acceleration, lateral acceleration, and yaw acceleration;

[0021] The calculation expression for determining the motion state of the target vehicle at the next moment in S2 is as follows:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] in, The longitudinal velocity; The lateral velocity; The yaw rate is the stated angular velocity. The heading angle is mentioned; () represents the position coordinates of the target vehicle; The longitudinal acceleration; The lateral acceleration is mentioned. The yaw acceleration is given. Indicates the current moment. Indicates the next moment; The sampling period represents... and The time interval between them.

[0029] Furthermore, the tire forces of the target vehicle include the longitudinal force and lateral force of each tire;

[0030] The calculation expression for the tire force relaxation model described in S3 is as follows:

[0031]

[0032]

[0033] The tire force observation model is as follows:

[0034]

[0035]

[0036]

[0037]

[0038] The formula for calculating the wheel slip angles of the target vehicle is as follows:

[0039]

[0040]

[0041]

[0042]

[0043] The calculation expression for the normal load of each wheel of the target vehicle is as follows:

[0044]

[0045]

[0046]

[0047]

[0048] in, Let be the longitudinal force and the lateral force of the i-th tire, respectively. These represent the front left, front right, rear left, and rear right tires, respectively. All are relaxation time constants; This is a rough estimate of the steady-state force based on a simplified tire model; Let be the differentials of the longitudinal force and the lateral force of the i-th tire, respectively; For the first i The rotational angular acceleration of each tire; This refers to the front wheel steering angle; These are the front and rear wheelbases, respectively. The wheelbase is the distance between the wheels. For the moment of inertia of the wheel, The radius of the wheel's rolling motion. For the moment of inertia of yaw rotation, For the overall vehicle weight; This represents the driving / braking torque for each wheel; a positive value indicates driving, and a negative value indicates braking. The wheel slip angles of the target vehicle are defined as follows: These are the longitudinal velocity, lateral velocity, and yaw rate of the target vehicle at the next moment, respectively. The normal loads on each wheel of the target vehicle are denoted as . , For the height of the center of mass, It is the acceleration due to gravity. The longitudinal acceleration and lateral acceleration are from the IMU data.

[0049] Furthermore, the computational expression for the first-order linear Koopman model in S5 is as follows:

[0050]

[0051] The computational expression for the second-order bilinear Koopman model is:

[0052]

[0053] The computational expression for the third-order higher-order Koopman model is:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] in, Let this be the state vector of the target vehicle; This is the control input vector for the target vehicle. This is the control input vector of the target vehicle at the current moment; Based on the state vector at the current time The state vector after increasing its dimensionality; , , It was identified and determined using a first-order linear Koopman model; The parameters of the linear part in the second-order bilinear Koopman model are determined through identification using the second-order bilinear Koopman model. The control input vector of the target vehicle at the current moment. The j-th control input, for The corresponding bilinear coupling matrix is ​​determined by dimensionality reduction through Tucker decomposition; These are the independent linear parameters in the third-order higher-order Koopman model, identified and determined through the third-order higher-order Koopman model. The third-order coupling term is the CP decomposition form of the third-order higher-order Koopman model. These are the state pairs extracted from the state vector. The third-order coupling term is represented as a third-order tensor in the form of a tensor-vector product. Indicates along the first Tensor-vector product of modes; for R is the rank of CP. This is the output factor vector when the CP rank is r. Let r be the state pair factor vector when CP rank is r. Let r be the control factor vector when CP rank is r. Let r be the scaling factor when CP rank is r. This represents the outer product of vectors.

[0061] Furthermore, in S6, the calculation expressions for the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle are determined as follows:

[0062]

[0063]

[0064]

[0065] The formula for calculating the comprehensive index of operating condition severity is as follows:

[0066]

[0067] in, These are the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle, respectively. These are the squares of the longitudinal force and the squares of the lateral force of the i-th tire, respectively. This is the preset road surface adhesion coefficient; Let be the normal load on the i-th tire of the target vehicle; Let be the slip angle of the i-th tire of the target vehicle; Let be the peak slip angle of the i-th tire of the target vehicle; ; These are the preset weight coefficients. .

[0068] Furthermore, the S7 specifically includes:

[0069] The comprehensive index of the severity of the working condition is filtered;

[0070] Substitute the filtered comprehensive index of the severity of the working condition into the preset weight formula of each Koopman model to determine the initial weight of each Koopman model.

[0071] The initial weights of each Koopman model are normalized to determine the weights of each Koopman model.

[0072] The calculation expression for the filtering process is:

[0073]

[0074] in, This is a comprehensive index of the severity of the operating condition after filtering at the current moment; This is a comprehensive index of the severity of the operating condition after filtering at the previous moment; These are the preset filter coefficients; This is a comprehensive indicator of the severity of the current operating condition.

[0075] The default weight formulas for each Koopman model are as follows:

[0076]

[0077]

[0078]

[0079] in, These are the initial weights of the first-order linear Koopman model at the current time. These are the initial weights of the second-order bilinear Koopman model at the current time. These are the initial weights of the third-order higher-order Koopman model at the current moment; For the Sigmoid function, For each preset switching threshold, These are the preset transition slopes;

[0080] The calculation expression for normalization is:

[0081]

[0082] in, The weights are assigned to each Koopman model.

[0083] Furthermore, the calculation expression for the fused prediction result in S8 is as follows:

[0084]

[0085] in, The prediction results for each Koopman model are shown below. For fusion prediction results;

[0086] The affine form of the calculation expression for the fusion prediction result described in S9 is as follows:

[0087]

[0088]

[0089]

[0090]

[0091] in, When i is 1, 2, or 3 respectively, They are respectively , , ; When i is 1, 2, or 3 respectively, They are respectively , , ; middle hour They are respectively .

[0092] Furthermore, S10 specifically includes:

[0093] Based on the affine form of the fusion prediction results, a nominal controller is constructed using the LQR control algorithm.

[0094] Furthermore, S10 specifically includes:

[0095] Based on the affine form of the fusion prediction results, an MPC controller based on the fusion prediction results is constructed as the nominal controller.

[0096] Furthermore, in S11, the nominal controller is solved to determine the control input vector at the current moment, specifically including:

[0097] Solve for the nominal controller to determine the predicted control input vector;

[0098] Define the safety set and barrier function, determine the discrete-time CBF constraint conditions, and affine the discrete-time CBF constraint conditions;

[0099] Based on the affine discrete-time CBF constraint, the predicted control input vector is corrected to determine the control input vector at the current time.

[0100] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects:

[0101] This solution introduces a hybrid-order Koopman model, which solves the problem of inaccuracy of traditional linear models when vehicles are in extreme motion (when tires enter the nonlinear region). By introducing higher-order terms, it can more accurately capture the saturation characteristics of tire forces and the strong coupling relationship between yaw and lateral forces, thus providing a more physically realistic prediction model under extreme conditions such as drifting and fishtailing. Attached Figure Description

[0102] The accompanying drawings, which are included to provide a further understanding of this specification and form part of this specification, illustrate exemplary embodiments and are used to explain this specification, but do not constitute an undue limitation thereof. In the drawings:

[0103] Figure 1 A flowchart illustrating a vehicle limit control method that combines hybrid-order Koopman tensor decomposition and CBF fusion, provided as an embodiment of this specification.

[0104] Figure 2 This specification provides a corresponding Figure 1 A schematic diagram of the structure of an electronic device. Detailed Implementation

[0105] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this specification will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0106] In embodiments of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0107] The technical solutions provided in the various embodiments of this specification are described in detail below with reference to the accompanying drawings.

[0108] Figure 1 A flowchart illustrating a vehicle limit control method based on hybrid-order Koopman tensor decomposition and CBF fusion, provided for embodiments of this specification, includes the following steps:

[0109] S1: Obtain the motion state of the target vehicle, which includes the longitudinal velocity, lateral velocity, yaw rate, heading angle, and position coordinates of the target vehicle.

[0110] S2: Determine the motion state of the target vehicle at the next moment based on the motion state and the IMU data of the target vehicle.

[0111] This specification describes the process of vehicle limit control involving hybrid-order Koopman tensor decomposition and CBF fusion. In the embodiments described herein, this process can be executed by a core vehicle computing device, such as a domain controller with an Electronic Control Unit (ECU). However, this specification does not limit the type of device or platform used to implement this hybrid-order Koopman tensor decomposition and CBF fusion process. For ease of description, an automotive-grade central domain controller will be used as the execution entity in the following description.

[0112] In one or more embodiments of this specification, the central domain controller is capable of acquiring motion state data characterizing the motion state of the target vehicle itself, wherein the motion state includes the longitudinal velocity of the target vehicle. Lateral velocity yaw rate Heading angle The location coordinates of the target vehicle ( (This may be location data recorded by positioning devices in the target vehicle, such as Global Positioning System (GPS)).

[0113] Furthermore, the central domain controller can determine motion state data representing the motion state of the target vehicle at the next moment based on the acquired motion state data and the IMU data recorded by the inertial measurement unit (IMU) in the target vehicle.

[0114] Specifically, the IMU data includes the target vehicle's longitudinal acceleration, lateral acceleration, and yaw rate.

[0115] The calculation expression for determining the motion state data characterizing the target vehicle's motion state at the next moment is:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] in, This represents the longitudinal velocity. This represents the lateral velocity. ω represents the yaw rate. This is the heading angle. ( ) represents the position coordinates of the target vehicle. This is the longitudinal acceleration. This is lateral acceleration. This is the yaw acceleration. Indicates the current moment. The expression for calculating each of the above motion states represents the motion state at the next moment, with the left side of the equals sign representing the motion state at the next moment and the right side representing the motion state at the current moment. The preset sampling period, which can be set to 10ms in this manual, means that motion state data is acquired every 10ms to perform steps S1 and thereafter. express and The time interval between them.

[0123] S3: Based on the preset tire force relaxation model, tire force observation model and the motion state of the target vehicle at the next moment, determine the tire force, wheel slip angle and wheel normal load of the target vehicle.

[0124] In one or more embodiments of this specification, the central domain controller can determine the tire forces, wheel slip angles, and wheel normal loads of the target vehicle based on a preset tire force relaxation model, tire force observation model, and the target vehicle's motion state at the next moment. The tire forces of the target vehicle include the longitudinal force and lateral force of each tire.

[0125] The calculation expression for the tire force relaxation model is as follows:

[0126]

[0127]

[0128] The tire force observation model is as follows:

[0129]

[0130]

[0131]

[0132]

[0133] The formula for calculating the slip angle of each wheel of the target vehicle is as follows:

[0134]

[0135]

[0136]

[0137]

[0138] The formula for calculating the normal loads on each wheel of the target vehicle is as follows:

[0139]

[0140]

[0141]

[0142]

[0143] in, Let be the longitudinal force and the lateral force of the i-th tire, respectively. These represent the front left, front right, rear left, and rear right tires, respectively. All are preset relaxation time constants, ranging from 0.02 to 0.05 s. This is a rough estimate of the steady-state force based on a simplified tire model. Let be the differentials of the longitudinal force and the lateral force of the i-th tire, respectively. These are the derivatives of the longitudinal velocity, lateral velocity, and yaw rate, respectively. For the first i The rotational angular acceleration of each tire reflects the inertial effect of the wheel rotating around its axle. It can be measured at extremely high frequencies by wheel speed sensors and other related sensors. Then, its rate of change can be calculated numerically in the controller. The front wheel steering angle is zero, and the rear wheel steering angle is zero. These are the front and rear wheelbases, respectively, and their sum is the wheelbase L of the target vehicle. The wheelbase is the distance between the wheels. For the moment of inertia of the wheel, The radius of the wheel's rolling motion. For the moment of inertia of yaw rotation, For the overall vehicle weight. This represents the drive / braking torque for each wheel; positive values ​​indicate drive, and negative values ​​indicate braking. For the wheel slip angles of the target vehicle, . These are the longitudinal velocity, lateral velocity, and yaw rate of the target vehicle at the next moment (calculated from S2). The normal loads on each wheel of the target vehicle are... , For the height of the center of mass, It is the acceleration due to gravity. These are the longitudinal and lateral accelerations in the IMU data.

[0144] It's worth noting that the process of determining the tire forces of the target vehicle within each sampling period can be done using the following established practice: A tire force relaxation model is used to predict the prior estimate of the tire forces at the current time step from the previous time step, while simultaneously calculating the prior covariance. Then, the observations at the current time step (the "observations" calculated by the tire force observation model are actually calculated using motion states on the left side of the equation and tire forces on the right side, with the difference between the two serving as the residual) are used to correct the prior estimate, obtaining the posterior estimate, and updating the covariance matrix. The final output is the estimated value of each tire force and its covariance (representing the uncertainty of the estimate). These tire force estimates will be used in subsequent steps.

[0145] S4: Determine the state vector of the target vehicle based on the motion state of the target vehicle at the next moment and the forces of each tire of the target vehicle, and define the control input vector.

[0146] S5: Based on the state vector and the control input vector, construct a first-order linear Koopman model, a second-order bilinear Koopman model, and a third-order higher-order Koopman model.

[0147] In one or more embodiments of this specification, the central domain controller can determine the state vector of the target vehicle and define the control input vector based on the target vehicle's motion state at the next moment and the forces of each tire of the target vehicle.

[0148] The state vector of the target vehicle The expression is:

[0149]

[0150] Control input vector The expression is:

[0151]

[0152] In this specification, training data covering the entire working condition range is generated from a high-fidelity multibody dynamics simulation platform (such as CarSim, IPG CarMaker). The training data can be obtained by roughly following steps (1) to (4) to obtain a training dataset covering the entire working condition range. .

[0153] (1) Training data may include the following scenarios:

[0154] Straight-line braking scenario: initial speed 40~200 km / h, road surface adhesion coefficient μ∈{0.2,0.4,0.6,0.8,1.0}.

[0155] Steady-state / transient steering scenarios: vehicle speed 60~160 km / h, steering wheel angle 0°~360°.

[0156] Sine sweep steering scenario: frequency 0.2~3.0 Hz, amplitude 30°~180°.

[0157] Double lane change / slalom scenario: according to ISO 3888 standard, vehicle speed 60~140 km / h.

[0158] Random combination excitation scenario: Pseudo-random signals are applied simultaneously to steering, braking, and drive inputs.

[0159] Driving conditions: Full acceleration on roads with different coefficients of adhesion.

[0160] μ-split road surface scenario: Braking and steering under different adhesion coefficients of the left and right wheels.

[0161] (2) Based on the sampling period The joint state is recorded in ms (100 Hz). and control input The time series.

[0162] (3) Data preprocessing: outlier removal (3σ criterion), low-pass filtering (4th-order Butterworth filter with a 30 Hz cutoff frequency), zero-mean unit variance standardization, and recording of standardized parameters for online use.

[0163] (4) Data partitioning: The training set, validation set and test set are divided into three sets according to a ratio of 70% / 15% / 15%.

[0164] Next, the central domain controller constructs an observation function based on the state vector and control input vector. Based on the observation function, the dimension of the state vector is increased, and based on this, a first-order linear Koopman model, a second-order bilinear Koopman model, and a third-order higher-order Koopman model are constructed.

[0165] Specifically, multiple types of composite observation function sets can be designed. The observation functions can be divided into identity observation functions, second-order cross polynomial observation functions, radial basis function (RBF) observation functions, and tire force-specific nonlinear observation functions.

[0166] Category 1 – Identical Observation Functions (14 in total):

[0167]

[0168] Ensure that the lifting vector contains all components of the original state vector. This can be achieved through a projection matrix. From the state of improvement Restore to its original state: This facilitates the design of subsequent controllers (state estimates can be directly obtained).

[0169] The second category – second-order cross-polynomial observation functions (approximately 50):

[0170]

[0171] Introducing product terms between state components can capture nonlinear interactions. The set of state pairs indexes is selected based on the physical meaning of vehicle dynamics, including, for example (Affects lateral force) (The longitudinal force multiplied by itself may reflect a saturation trend.) (The effect of longitudinal velocity on lateral force) (Coupling of tire friction ellipse), etc. Physical filtering is used to retain only meaningful intersections, avoiding excessive dimensionality.

[0172] The third category – Radial Basis Function (RBF) observation functions (approximately 30):

[0173]

[0174] RBF is a typical local kernel function that can model different regions of the state space using local linearization. K-means clustering is performed on the training data, and the center density and width are adjusted according to the performance indicators of each cluster. According to the center The average distance to the nearest neighbor is set. By allocating more center points in extreme operating conditions (such as high sideslip angles and large slip ratios) (approximately 60% of the centers come from these regions), the nonlinear behavior under extreme conditions can be characterized more precisely.

[0175] Category 4 – Nonlinear observation functions specifically for tire forces (approximately 12):

[0176]

[0177]

[0178]

[0179] in Mimicking the tire's lateral force with the slip angle (include These four wheels exhibit an S-shaped characteristic in terms of lateral force variation. Capture the saturation behavior of the combined tire force. Describe the saturation characteristics of the sideslip angle. These are the preset design parameters. This is the nominal adhesion coefficient.

[0180] Ultimately, elevate the dimension. State promotion mapping , That is, based on the state vector at the current moment The state vector after increasing the dimensionality.

[0181] Therefore, the computational expression for the first-order linear Koopman model is:

[0182]

[0183] in , , It can be identified and determined through a first-order linear Koopman model. . This is the control input vector for the target vehicle at the current moment.

[0184] One method for identifying a first-order linear Koopman model is to construct a boosting state matrix from the training data: Next time step matrix Control input matrix Constructing an augmented regression matrix Solving using Tikhonov regularized least squares: ,in The regularization parameter is selected through cross-validation. The number of parameters in the first-order linear Koopman model is... .

[0185] The computational expression for the second-order bilinear Koopman model is:

[0186]

[0187] in These are the parameters of the linear part in the second-order bilinear Koopman model, which can be identified and determined through the second-order bilinear Koopman model. To control the input vector The j-th control input. for The corresponding bilinear coupling matrix can be determined through Tucker decomposition and dimensionality reduction. matrices Stacked as third-order bilinear coupled tensors The bilinear term can be expressed as: ,in Indicates along the first Tensor-vector product of modalities.

[0188] Physical meaning: Bilinear terms capture the multiplicative coupling between state and control. For example, the equivalent lateral stiffness of a tire varies with operating conditions, causing the gain of the steering angle input on the yaw moment to be non-constant, but rather related to the current state (such as lateral acceleration and tire force). This gain variation can be approximated by bilinear terms. Direct storage... While using a single parameter is feasible, it could lead to overfitting and computational burden. Therefore, tensor decomposition dimensionality reduction, specifically Tucker decomposition dimensionality reduction, is employed.

[0189] Tucker decomposition and dimensionality reduction:

[0190] right Perform Tucker decomposition:

[0191]

[0192] in:

[0193] For the core tensor;

[0194] To output the mode factor matrix;

[0195] This is the state mode factor matrix;

[0196] For the control mode factor matrix;

[0197] Let the Tucker rank be for each mode (e.g., take...) ).

[0198] Parameter compression effect:

[0199] by For example:

[0200] Number of undecomposed parameters:

[0201] Number of parameters after decomposition:

[0202] Compression ratio: approximately 17:1

[0203] Online computing acceleration:

[0204] During prediction, a small-scale tensor product is first performed in the factor space, and then projected back to the original space. Utilizing the properties of Tucker decomposition, the bilinear terms can be calculated and decomposed into:

[0205]

[0206] Total computational load from Down to .

[0207] The identification algorithm for the second-order bilinear Koopman model can be based on Higher-order Singular Value Decomposition (HOSVD) initialization followed by iterative optimization using Alternating Least Squares (ALS). Identification steps:

[0208] 1. Direct Least Squares Initialization: Ignore Tucker decomposition and directly perform least squares (without regularization) on the bilinear model to obtain the initial tensor. This step may have many parameters, but it is only to provide the initial structure.

[0209] 2. HOSVD Initialization Factor Matrix: For Perform singular value decomposition (SVD) along each mode, and take the first... The left singular vectors are used as The initial value.

[0210] 3. ALS Alternating Least Squares Iterative Optimization: With other variables fixed, the following four sub-steps are executed alternately, updating in turn. .

[0211] Sub-step 1: Fix ,right (together) Solve for regularized least squares.

[0212] Sub-step 2: Fix ,right Solve for regularized least squares.

[0213] Sub-step 3: Fix ,right Solve for regularized least squares.

[0214] Sub-step 4: Fix all factor matrices and apply the core tensor The least squares solution is obtained after vectorization.

[0215] Each sub-step becomes linear least squares, which has an analytical solution.

[0216] The convergence condition for iterative optimization is that iteration continues until the objective function changes very little (e.g., ...). (like ()) or reach the maximum number of iterations (e.g., 100 times).

[0217] The computational expression for the third-order higher-order Koopman model is:

[0218]

[0219] in, These are the independent linear parameters in the third-order higher-order Koopman model, which can be identified and determined through the third-order higher-order Koopman model. The third term is... It is a third-order coupling term in the CP decomposition form of a third-order high-order Koopman model. These are the state pairs extracted from the state vector. The selection of state pairs is based on physical meaning to avoid the curse of dimensionality. The state pair selection strategy is to choose physically meaningful crossover pairs from the original 14-dimensional state vector.

[0220] Crossover between motion states ( ): 21 pairs in total.

[0221] The interaction between motion state and tire force ( ): A total of 48 pairs.

[0222] The total logarithm is .therefore .

[0223] Therefore, what was originally needed to be stored One parameter.

[0224] Then, CP decomposition and dimensionality reduction are performed:

[0225] The third-order coupling term can be expressed in tensor-vector product form:

[0226]

[0227] Among them, the third-order tensor elements Indicates the first The first boost status output, the first The state pair, the first The third-order coupling coefficients between the control inputs Indicates along the first Modal tensor-vector product. CP decomposition is essentially a low-rank approximation of this tensor:

[0228]

[0229] in, Let r be the CP rank. When the CP rank is r, For the output factor vector, For state-factor vectors, For the control factor vector, This is the scaling factor. This represents the vector outer product. The number of parameters after CP decomposition is... .Pick The number of parameters is Compared to undecomposed Compression ratio approximately 10:1.

[0230] The calculation of third-order terms can be decomposed into: scalar-vector product:

[0231]

[0232] The computational workload is approximately This is the second multiplication and addition.

[0233] Third-order high-order Koopman model identification algorithm - multi-initialization CP-ALS:

[0234] (a) Multiple random initializations: Randomly initialize the factor vector , conducted Independent initialization.

[0235] (b) Execute ALS iteration after each initialization:

[0236] Sub-step 1: Fix ,right (together) Solve the least squares problem.

[0237] Sub-step 2: Fix ,right Solve the least squares problem

[0238] Sub-step 3: Fix ,right Solve the least squares problem

[0239] Update: Update And normalize each factor vector (to avoid numerical instability).

[0240] (c) Select the optimal result: Select the one with the smallest final objective function value from all initialization results, that is, select the model with the smallest verification error from multiple initializations.

[0241] (d) CP rank selection: from the smallest rank (e.g.) Gradually increase the rank value, evaluate the prediction accuracy gain on the validation set, and select the rank value at the inflection point where the accuracy gain significantly decreases (e.g., ...). ).

[0242] In this manual, the predictive performance of the first-order (first-order linear Koopman model), second-order (second-order bilinear Koopman model), and third-order (third-order higher-order Koopman model) models can be evaluated on the test set to verify their advantages under different operating conditions. The prediction evaluation is shown in Table 1 below.

[0243] Table 1 Prediction and Evaluation Table

[0244]

[0245] The evaluations in Table 1 above refer to assessing the predictive performance of first-order, second-order, and third-order models on the test set with different numbers of prediction steps, and are abbreviated as "evaluation". The evaluation metrics include: position prediction, yaw rate prediction, and tire force prediction.

[0246] S6: Determine the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle, and determine the comprehensive index of the severity of the working condition based on the tire utilization rate index, sideslip angle index, and lateral acceleration index.

[0247] In one or more embodiments of this specification, the central domain controller can determine the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle, and determine a comprehensive index of the severity of the operating condition based on the tire utilization rate index, sideslip angle index, and lateral acceleration index.

[0248] The calculation expressions for the target vehicle's tire utilization rate, sideslip angle, and lateral acceleration are determined as follows:

[0249]

[0250]

[0251]

[0252] The formula for calculating the comprehensive index of operating condition severity is as follows:

[0253]

[0254] in, These are the tire utilization rate, sideslip angle, and lateral acceleration indicators of the target vehicle. These are the squares of the longitudinal force and the squares of the lateral force of the i-th tire, respectively. This is the preset road surface adhesion coefficient. Let be the normal load of the i-th tire of the target vehicle. Let be the slip angle of the i-th tire of the target vehicle. The preset peak slip angle for the i-th tire of the target vehicle (the slip angle corresponding to the peak of the tire lateral force), typically about 6° to 10°, depends on tire characteristics and road conditions. . These are the preset weight coefficients. ,like .

[0255] S7: Determine the weights of each Koopman model based on the comprehensive index of the severity of the working condition and the preset weight formula of each Koopman model.

[0256] In one or more embodiments of this specification, the central domain controller can determine the weights of each Koopman model based on a comprehensive index of the severity of the operating conditions and a preset weight formula for each Koopman model.

[0257] Specifically, the central domain controller filters the comprehensive index of operational condition severity. Then, the filtered comprehensive index is substituted into the preset weight formula of each Koopman model to determine the initial weights of each model. Finally, the initial weights of each Koopman model are normalized to determine the final weights of each model.

[0258] The calculation expression for filtering is:

[0259]

[0260] in, This is a comprehensive index of the severity of the operating condition after filtering at the current moment. This is a comprehensive index of the severity of the operating conditions after filtering at the previous moment. These are the preset filter coefficients. . This is a comprehensive indicator of the severity of the current operating conditions.

[0261] The default weight formulas for each Koopman model are as follows:

[0262]

[0263]

[0264]

[0265] in, These are the initial weights of the first-order linear Koopman model at the current time. These are the initial weights of the second-order bilinear Koopman model at the current time. These are the initial weights of the third-order higher-order Koopman model at the current moment. For the Sigmoid function, For each preset switching threshold, For each preset transition slope, satisfying , Typical parameter values, for example: .

[0266] The calculation expression for normalization is:

[0267]

[0268] in, The weights for each Koopman model are as follows: For the weights of the first-order linear Koopman model, For the weights of the second-order bilinear Koopman model, These are the weights of the third-order higher-order Koopman model. Of course, here... In fact It is simply abbreviated as .

[0269] S8: Calculate the prediction results of each Koopman model and determine the fusion prediction result based on the weights of each Koopman model.

[0270] S9: Determine the affine form of the fusion prediction result.

[0271] In one or more embodiments of this specification, the central domain controller calculates the prediction results of each Koopman model, i.e. And according to the weights of each Koopman model, The fusion prediction results are determined. Based on the fusion prediction results, the affine form of the fusion prediction results is determined.

[0272] The calculation expression for the fusion prediction result is as follows:

[0273]

[0274] in, The results are the predictions for each Koopman model. This is the result of the fusion prediction.

[0275] Since the linear part of each Koopman model contains Therefore, an effective state transition matrix can be defined. It is a weighted average of the linear components of the three Koopman models, with the weights determined by the operating conditions. Note that the nonlinear terms in the second-order and third-order Koopman models are ignored here (because they are not directly related to the linear components). (linear terms), but will be handled separately later:

[0276]

[0277] in, When i is 1, 2, or 3 respectively, They are respectively , , .

[0278] In order to express the fusion prediction results as a function of the control input Affine form (i.e. ), can include all explicit elements The items were separated and merged into a single item. The coefficient matrix of the product. Note that the nonlinear terms in the second-order and third-order Koopman models may depend on... and The product of , but after simplification, can be written as In the form of.

[0279] A point-by-point analysis of the contributions of the three Koopman models:

[0280] First-order linear Koopman model: Contributed to Part: Contributed to Part: .

[0281] Second-order bilinear Koopman model: .

[0282] Linear part: Into (multiplied by) ).

[0283] Linear input items: Into (multiplied by) ).

[0284] Bilinear terms: It can be written in matrix form: Each component multiplied by a matrix then acts on This is equivalent to That is, one Matrix multiplication Each column of the matrix is Therefore, the bilinear term contributes to Part of Note that this matrix depends on the current .

[0285] Third-order higher-order Koopman model: .

[0286] Linear part: Into (multiplied by) ).

[0287] Linear input items: Into (multiplied by) ).

[0288] Third-order terms: This can also be rearranged into a matrix form. Note that for each... , It is a scalar multiplied by a vector Later obtained .and It is dependent on The scalar. Therefore, the entire third-order term can be written as:

[0289]

[0290] That is, one Matrix multiplication Each row and column of this matrix is ​​composed of , and Composed of various elements, it obviously depends on... This matrix is... Multiply by the part that follows.

[0291] Combining all the above contributions yields the affine form of the final fusion prediction result:

[0292]

[0293] in:

[0294]

[0295]

[0296] in, When i is 1, 2, or 3 respectively, They are respectively , , ; middle hour They are respectively .

[0297] Notice: The first term is a weighted sum of the three linear input terms of the Koopman model, independent of... The second term comes from the bilinear term of the second-order Koopman model, which depends on... The third term, derived from the CP decomposition of the third-order Koopman model, also depends on... .therefore, It is a state-dependent efficient input matrix, which needs to be adjusted according to the current boost state in each control cycle. Comprehensive index of the severity of working conditions Recalculate.

[0298] S10: Construct a nominal controller based on the affine form of the fusion prediction result.

[0299] In one or more embodiments of this specification, a nominal controller can be constructed based on an affine form of the fused prediction results.

[0300] Specifically, a nominal controller can be designed to generate control inputs that track the reference trajectory based on the affine form of the fused prediction results. A linear quadratic regulator (LQR) control algorithm can be used to construct the nominal controller.

[0301] The steps are as follows: using the effective state transition matrix and effective input matrix The LQR gain is obtained by solving the discrete algebraic Riccati equation (DARE).

[0302] Riccati equations:

[0303]

[0304] in For the positive definite solution of the Riccati equation (using...) Representing the Riccati solution to distinguish it from the projection matrix LQR gain: The state weight matrix is... To control the weight matrix. and It is aimed at the current situation The effective matrix (ignoring this for now) right The dependency of this matrix is ​​considered as a constant matrix.

[0305] Solve Then, the optimal feedback gain matrix It is given by the following formula:

[0306]

[0307] Online solution of the Riccati equation (especially in high-dimensional forms) The computational load is enormous, which cannot meet the real-time requirements of vehicle control (typically a control cycle of 10ms). Therefore, a strategy of offline pre-calculation + online interpolation is needed, i.e., gain scheduling. Gain calculation strategy:

[0308] (a) Offline phase: Comprehensive index of the severity of the working condition Uniform sampling is performed within the range [0,1], for example, by taking uniform sampling points. For each sampling point Determine the comprehensive index of the severity of this working condition. The effective matrix under and (Here we need to...) The state dependency in the equation is approximated, for example, by taking the value under typical conditions or its linear part. Then, the DARE is solved to obtain the corresponding LQR gain. Store these gain matrices This forms a lookup table.

[0309] (b) Online Phase: In each control cycle, the severity index of the operating condition after filtering at the current moment is used as the basis for calculation. Find two adjacent sampling points in the lookup table. and The current gain is calculated using linear interpolation:

[0310]

[0311] Get the current gain Then, the nominal control law, i.e., the nominal controller, can be characterized as:

[0312]

[0313] in This is an enhanced representation of a pre-defined reference trajectory. These are pre-defined feedforward terms (such as steady-state steering angle and driving torque calculated based on the curvature of the reference trajectory).

[0314] Of course, in this specification, for scenarios that require handling constraints or multi-step prediction optimization, in addition to using the LQR control method, an MPC controller based on the fusion prediction results can also be constructed as the nominal controller based on the affine form of the fusion prediction results, that is, a model predictive control scheme can be adopted.

[0315] Specifically, given the current time Given the state vector after dimensional boosting at the current moment. And the lifting representation of the reference trajectory ( MPC solves the following optimization problem:

[0316]

[0317]

[0318]

[0319]

[0320] Where H is the prediction time domain (typically 10~20 steps), indicating how many steps to predict forward. This is the projection matrix used to improve the state from 106 dimensions. Extract the first 14 dimensions of the lifting vector (original state) ). This is the state tracking weight matrix. To control the input weight matrix. To control the incremental weight matrix. To control the increment, initially , This refers to the actual control input applied to the target vehicle at the previous moment. It only includes actuator constraints—preset upper and lower limits of the control amplitude. and control increment upper and lower limits These are physical limitations (such as maximum steering angle and maximum braking torque) that must be met.

[0321] It is worth noting that the MPC controller design does not include safety constraints (safety constraints are represented by discrete-time CBF constraints in subsequent steps). This separate design has the following advantages:

[0322] (a) The QP subproblem of MPC is always feasible (including only actuator constraints).

[0323] (b) Safety guarantees are independent of the nominal controller form—CBF provides consistent safety guarantees regardless of whether LQR or MPC is used as the nominal controller.

[0324] (c) Transparency: When the system is far from the safety boundary, CBF does not modify the nominal control, and the performance optimization of the nominal controller is not affected.

[0325] Because the prediction model in MPC is The prediction model is linear, the objective function is quadratic convex, and the constraints are linear. The MPC problem is a standard convex quadratic programming (QP) problem. The optimal control sequence is then obtained by solving the MPC controller. Extract the first element of the sequence This serves as the control input vector. Then, at the next time step, the MPC (rolling time domain) is resolved based on the new state.

[0326] S11: Solve the nominal controller to determine the control input vector at the current moment, and control the target vehicle according to the control input vector at the current moment.

[0327] In one or more embodiments of this specification, after the nominal controller is constructed, the nominal controller can be solved to determine the control input vector at the current moment, and the target vehicle can be controlled according to the control input vector at the current moment.

[0328] Specifically, the nominal controller is solved to determine the predicted control input vector. The safety set and barrier function are defined, and the discrete-time CBF constraints are determined and affinedized. Based on the affined discrete-time CBF constraints, the predicted control input vector is corrected to determine the control input vector at the current time step for controlling the target vehicle.

[0329] Among them, the security set is defined. The barrier function is shown in Table 2 below.

[0330] Table 2 Definitions of various barrier functions

[0331]

[0332] in:

[0333] Lateral stability – centroid sideslip angle constraint

[0334] centroid side slip angle :

[0335]

[0336] when (e.g., at 5 m / s) Clamp to This avoids the singularity of the sideslip angle definition at low speeds.

[0337] Side slip angle safety threshold (Designed for adaptive operation):

[0338]

[0339] in The preset reference side slip angle threshold (typical value 5°~8°). This is a preset reference speed. This design provides stricter constraints under high-speed and low-adhesion conditions. Road surface adhesion coefficient. The lower the speed, the smaller the allowable sideslip angle (low-friction surfaces are more prone to sideslip). The higher the speed, the smaller the allowable sideslip angle (higher speeds are more sensitive to lateral disturbances).

[0340] Yaw stability – Yaw angular velocity deviation constraint

[0341]

[0342] In the formula, ω represents the yaw rate. The maximum permissible yaw rate deviation is usually set to a constant (e.g., 0.1~0.2 rad / s). The steady-state yaw rate is given by the steering dynamics formula:

[0343]

[0344] in Wheelbase The understeering coefficient is defined as:

[0345]

[0346] The unit is s² / m, which makes It has the dimension of length. This refers to the lateral stiffness of the front and rear axles.

[0347] Anti-rollover – Load transfer rate constraint

[0348]

[0349] Typical threshold To prevent rollover. LTR (Load Transfer Ratio): describes the degree of load unevenness between the left and right wheels of a vehicle. Equivalent approximation for the whole vehicle:

[0350]

[0351] Collision Avoidance - Distance Constraints to Obstacles

[0352]

[0353] In the formula, =(X,Y): The vehicle's current global position (from its motion state). Location of the obstacle (can be provided by the sensing module). The preset safe distance can be set according to vehicle speed, reaction time, etc.

[0354] Friction limit – the forces of each tire within the friction circle.

[0355]

[0356] In the formula, It is the product of the current road surface adhesion coefficient and the normal load of each wheel, i.e., the radius of the friction circle (maximum allowable resultant force).

[0357] Map the security functions, i.e., the barrier functions, to the boosting space:

[0358]

[0359] Furthermore, since the Koopman model is an approximate model, yes The approximate predicted value.

[0360] The positive invariance condition of the discrete-time control barrier function (DCBF), i.e., the discrete-time CBF constraint condition, can be:

[0361]

[0362] in, The preset attenuation rate parameter, . It is the current boosted state (known). Is to exert control The predicted state at the next time step (using the fused prediction results within the above framework). (As a prediction).

[0363] Attenuation rate parameter selection guide: The smaller the size, the earlier the safety intervention and the more conservative the constraints. The larger, the more allowed The larger the single-step descent, the more delayed the safety intervention. Recommended value range: This condition guarantees that as long as the initial state is within the safe set ( If each step of the control input satisfies the DCBF condition, then the state will never leave the safe set—that is, the safe set has positive invariance.

[0364] Substituting the affine form of the fused prediction results into the DCBF conditions, at the nominal control point... (A first-order Taylor expansion is performed at the nominal controller, such as LQR or MPC):

[0365]

[0366] in It is the predicted state at the next moment after nominal control is applied. yes With respect to the gradient of the control input vector (row vector, dimension 1×m), Calculate the value at the given location.

[0367] because, ,and ,therefore, right The gradient can be obtained using the chain rule:

[0368]

[0369] Substituting the Taylor expansion into the DCBF conditions and rearranging, we obtain the following about Affine constraints:

[0370]

[0371]

[0372]

[0373] Then we get information about Affine inequalities:

[0374]

[0375] Each security constraint is a barrier function. This corresponds to a linear inequality like this. Here , .

[0376] Summarized into a set of constraints ,in For the total number of safety constraints ( correspond to ).

[0377] In this specification, directly applying the CBF condition using the fused prediction results may lead to a violation of safety constraints in the actual state due to prediction errors. Therefore, robust handling of this uncertainty is necessary to ensure that the real system remains safe even under worst-case error conditions. Considering the prediction error of the fused prediction results, let the upper bound of the error be:

[0378]

[0379] This represents the true next-time state vector corresponding to the fused prediction results. Upper bound of the error. To determine offline from the validation set residual statistics, establish A lookup table to the upper bound of the error. Typically, Follow The error increases slightly (the model error is slightly larger under extreme conditions).

[0380] Even if the upper bound of the state prediction error is determined... We also need to know how this error will affect the safety function. The value of is determined because the CBF condition directly constrains the value of the safety function, not the state itself. Therefore, the Lipschitz constant of the safety function is introduced. .

[0381]

[0382] in It is the state space that the target vehicle can potentially reach (usually limited by the range covered by the training data). The Lipschitz constant measures the function. The upper limit of the rate of change.

[0383] Therefore, the CBF constraint can be modified using the upper bound of the error and the Lipschitz constant, so that the real system still satisfies the original DCBF condition even if there is a worst-case error.

[0384] To tighten constraints and ensure robust safety, the new robust CBF constraint should be:

[0385]

[0386] Alternatively, it can be:

[0387]

[0388] Thus, it is only necessary to reserve an additional amount in the margin required to satisfy the prediction. This provides a margin to account for potential decreases in the true value. Thus, as long as this stricter constraint holds, it guarantees that even with the worst-case error, the true state still satisfies the original CBF condition.

[0389] Next, the control input vector predicted by the nominal controller can be corrected, which can be achieved by solving a quadratic programming problem (QP).

[0390] Construct a minimum modified quadratic programming problem:

[0391]

[0392]

[0393]

[0394] in This is the predetermined correction cost weight matrix.

[0395] Weighting design strategy: Take a larger value (e.g., 100): retain the nominal steering, since the steering system has limited bandwidth. Choose a smaller value (e.g., 1): Safety intervention is prioritized through braking torque distribution because the braking system responds quickly.

[0396] QP size: a decision variable Dimension, number of constraints The problem is strictly convex and extremely small in size, and can be solved in less than 0.5ms using solvers such as Operator Splitting Quadratic Program (OSQP) and qpOASES.

[0397] Transparency property: When CBF constraint is not activated ( (If the value is much greater than zero, the constraint has no effect), the optimal solution for QP is... —That is, the safety projection layer does not make any modifications to the nominal control and does not affect tracking performance. Only near the safety boundary are CBF constraints activated and minimal modifications applied.

[0398] In one or more embodiments of this specification, in extreme cases (such as when multiple security constraints are activated simultaneously and conflict with each other), secure projection QP may not be feasible. A two-level degradation strategy is designed:

[0399] Level 1 – Constraint Relaxation:

[0400] Introducing nonnegative relaxation variables :

[0401]

[0402] Modify the objective function as follows:

[0403]

[0404] Penalty weight Set according to security priority:

[0405] Collision Avoidance : (Highest priority, least likely to relax)

[0406] Anti-rollover :

[0407] Lateral / Yaw Stability :

[0408] Tire friction circle : (Brief over-limit driving is permitted because the tires have a certain overload capacity.)

[0409] Level Two – Emergency Braking:

[0410] If QP is still not feasible after relaxation or the minimum relaxation amount exceeds the threshold, switch to emergency full braking mode:

[0411]

[0412] That is, the steering angle is reduced to zero, and the maximum braking torque is applied to all four wheels. This is the preset maximum braking torque (a negative value indicates braking). This is a conservative but safe strategy: full braking can reduce the vehicle speed as quickly as possible, while straight driving (steering to zero) avoids further steering disturbances, thus minimizing the possibility of a collision or loss of control. It also triggers a warning and logs the information.

[0413] In one or more embodiments of this specification, a sliding window incremental update mechanism is introduced to adapt to long-term parameter drift such as changes in road conditions and tire wear:

[0414] (1) Data caching:

[0415] Maintenance length is A circular buffer (e.g., 1000 samples, corresponding to 10 seconds of data) stores the most recent data. Each cycle data.

[0416] (2) Fast update of first-order model:

[0417] Every For each cycle (e.g., 100 cycles, or 1 second), recursive least squares (RLS) is used to... Perform incremental correction:

[0418]

[0419]

[0420]

[0421] in , which is the preset forgetting factor. , . P is a pre-defined covariance matrix that represents the uncertainty of the current parameter estimates. Initially, since the parameters are uncertain, P will be set to be relatively large. It is the prediction error: how much the state at the next moment calculated using the old parameters differs from the state at the actual measured moment.

[0422] (3) Low-frequency fine-tuning of high-order models:

[0423] At relatively long intervals (e.g., 60 seconds), perform a small number of ALS iterations to fine-tune the Tucker factor and CP factor (e.g., 3-5 iterations), using data within a sliding window.

[0424] (4) Update security checks:

[0425] After the update, in the most recent Evaluate the single-step prediction RMSE on a sample:

[0426] If the RMSE after the update exceeds 1.2 times that before the update, revert to the parameters before the update.

[0427] If there are more than 3 consecutive regressions, the forgetting factor will be... Increase by 0.01 to reduce update sensitivity.

[0428] Record update logs for later analysis.

[0429] This manual provides an example of high-speed emergency obstacle avoidance. Scenario description: A vehicle is traveling at 120 km / h (33.3 m / s) when a stationary obstacle suddenly appears 50 m ahead, requiring an emergency lane change to avoid it. The road surface adhesion coefficient μ = 0.85.

[0430] Control process:

[0431] (1) Initial stage ( s):

[0432] The driver / system has not yet started operation. Operating parameters. fusion weight First-order models dominate, resulting in low computational load.

[0433] (2) Emergency turning phase ( s):

[0434] Large steering angle input causes tire force to rise rapidly, with the front wheel slip angle reaching 8°~10° and tire force utilization rate reaching over 0.85.

[0435] Operating conditions The fusion weight changed from 0.1 to 0.85. It decreased from 0.92 to 0.08. Rise to 0.32. Rise to 0.60.

[0436] The third-order model dominates, accurately predicting tire force saturation behavior and peak characteristics of the force-slip curve.

[0437] (3) CBF safety projection function:

[0438] The nominal MPC output steering angle will cause the predicted centroid sideslip angle to reach 12°, exceeding the safety threshold. CBF constraint activation.

[0439] Safety projection QP automatically executes: reduces steering angle increment by approximately 15%. Applies an additional 300 N·m braking torque to the inner rear wheel (left rear wheel), generating an auxiliary yaw moment.

[0440] Complete obstacle avoidance trajectory tracking while ensuring the side deflection angle is safe.

[0441] (4) Correction phase ( s):

[0442] As the vehicle straightens, tire pressure decreases. The weights smoothly decrease from 0.85 to 0.15, and the fused weights smoothly revert to first-order dominance. The Sigmoid function ensures that the weight switching is seamless.

[0443] Performance Evaluation: Based on tests conducted using the CarSim co-simulation platform, the state prediction accuracy in the extreme phase is significantly improved compared to the first-order Koopman+MPC method. Position prediction RMSE (20 steps / 200ms): Approximately 0.35m for the first-order method, approximately 0.08m for the method described in this invention. Yaw rate RMSE: Approximately 3.2° / s for the first-order method, approximately 0.7° / s for the method described in this invention. Safety constraint satisfaction rate: Approximately 88% for the first-order method, exceeding 99% for the method described in this invention.

[0444] The embodiments provided in this manual are: braking on low-adhesion surfaces.

[0445] Scene description: Icy and snowy road surface ( The vehicle must be able to brake at 80 km / h in an emergency, with the shortest possible braking distance while maintaining vehicle stability.

[0446] Control process and effects:

[0447] (1) Advantages of tire force prediction:

[0448] The joint state space allows the model to directly predict the saturation trend of longitudinal forces in each wheel. When the longitudinal force of a certain wheel approaches... At approximately 1800 N, the model predicts that its growth rate will decline sharply.

[0449] Based on this prediction, nominal MPC adjusts the braking force distribution in advance, transferring braking torque to wheels with remaining capacity to prevent any wheels from locking up.

[0450] (2) Friction circle CBF constraint effect:

[0451] Tire force friction circle constraint Friction circle radius under low adhesion conditions Significantly reduced (from approximately 4500 N on a dry surface to approximately 1800 N).

[0452] CBF automatically limits total braking force to prevent requests for braking torque exceeding the adhesion limit.

[0453] (3) Yaw stabilizing effect of CBF:

[0454] Even slight differences in the adhesion conditions of the left and right wheels (such as uneven snow distribution) can cause yaw moment during braking.

[0455] When the predicted yaw rate deviates When approaching the threshold, Constraint activation triggers CBF to automatically intervene in differential braking correction: reducing braking force on the high-adhesion side or increasing braking force on the low-adhesion side.

[0456] Performance:

[0457] The braking distance is reduced by about 8% compared to the unoptimized ABS, with no wheel lock-up throughout the braking process, and the yaw rate deviation is controlled within 2° / s.

[0458] The examples provided in this manual: Extreme steering on continuous curves

[0459] Scenario description: Passing through a series of curves at near-maximum speed (lateral acceleration of approximately 0.9g) in the S-curve of the track.

[0460] Control process and effects:

[0461] (1) Dynamic adjustment of fusion weights:

[0462] Operating conditions The curvature fluctuates periodically with the curve (it rises at the curve entrance and falls on the straight section).

[0463] The fusion weights are rapidly adjusted at the entrance / exit of curves, and the Sigmoid function ensures a smooth transition without uncontrolled jumps.

[0464] (2) Foresight in predicting tire force state:

[0465] Tire force state prediction enables nominal MPC to anticipate load transfer trends in curves in advance.

[0466] MPC (Modular Controlled Load Transfer) manages load transfer in advance: it increases the front axle load by applying slight braking before entering a curve, and optimizes the distribution of braking force between the inside and outside of the curve.

[0467] (3) Multi-constraint coordination:

[0468] Side slip angle Yaw rate and rollover The three CBF constraints are approaching the activation boundary simultaneously.

[0469] Safety projection QP automatically seeks the optimal correction that satisfies all constraints—typically manifested as: slightly reducing vehicle speed (reducing regenerative braking), fine-tuning steering angle, and optimizing left and right braking force distribution.

[0470] Performance:

[0471] The lap time is improved by about 3% compared to the conservative safety control strategy, all safety constraints are met throughout the race, and the peak load transfer rate is controlled within 0.75 (below the rollover threshold of 0.8).

[0472] In summary, the beneficial technical effects are as follows:

[0473] The accuracy of extreme condition modeling has been significantly improved.

[0474] Hybrid tensor decomposition methods overcome the accuracy bottleneck of first-order linear Koopman decomposition: Second-order bilinear model: captures the multiplicative coupling between state and control (the condition-dependent nature of tire equivalent stiffness). Third-order CP model: describes the peak and decay behavior of the force-slip curve in the tire force saturation region.

[0475] In a 20-step (200ms) prediction for a high-speed obstacle avoidance scenario: Position RMSE decreased from approximately 0.35m in the first-order method to approximately 0.08m. Yaw rate RMSE decreased from approximately 3.2° / s to approximately 0.7° / s. Prediction accuracy improved by approximately 4-5 times. Tensor decomposition (Tucker decomposition compression ratio 17:1, CP decomposition compression ratio 10:1) makes the number of parameters in the high-order model controllable and real-time computation feasible.

[0476] Formal security assurance

[0477] CBF safe projection provides a stronger safety guarantee mechanism than MPC hard constraints: by controlling the positive invariance theory of the barrier function, the invariance of the safe set is mathematically guaranteed. Robust CBF correction guarantees that safety constraints still hold even when the model prediction has bounded errors. The safe projection QP is extremely small (5-dimensional decision variables, approximately 18 constraints), with a solution time of less than 0.5ms. When constraints are not activated, the safety layer makes zero correction to the nominal control, without affecting normal tracking performance. Differentiated relaxation penalties are used to prioritize safety constraints.

[0478] Full-condition adaptive coverage

[0479] Adaptive order fusion enables on-demand scheduling of "simple models for simple working conditions and complex models for extreme working conditions": ensuring that the weights are infinitely differentiable. This eliminates control jumps caused by hard switching. The fusion prediction accuracy is 20%~30% higher than using any single-order model. Under normal operating conditions, the operation mode, which primarily uses a first-order model, significantly reduces the average computational load.

[0480] Reduce dependence on physical model parameters

[0481] The augmented joint state space of tire forces offers the following advantages: The Koopman model learns the dynamic evolution of tire forces directly from data, eliminating the need to calibrate complex tire model parameters such as Pacejka. It naturally incorporates the time delay characteristic of tire force establishment, which traditional algebraic models cannot describe. Tire forces, as state variables, can be directly constrained in the CBF (Circuit-Coefficient of Performance), achieving safety limits on the friction circle.

[0482] The online RLS / ALS incremental update mechanism enables the model to adapt to tire wear and road surface changes, resulting in strong long-term robustness.

[0483] System-level synergistic effects

[0484] The four core innovations of this invention support each other and produce a synergistic effect: tire force augmentation provides physically meaningful state variables for high-order Koopman models, improving modeling quality. Hybrid-order modeling provides candidate models with different accuracy-efficiency trade-offs for adaptive fusion. Adaptive fusion provides a prediction model with guaranteed accuracy and affine structure for the CBF layer. CBF safety projection utilizes the affine structure of the fused model to achieve efficient safety constraint processing. The overall system achieves superior comprehensive performance compared to existing technologies in terms of modeling accuracy, computational efficiency, and safety assurance.

[0485] This specification also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A vehicle limit control method combining hybrid-order Koopman tensor decomposition and CBF is provided.

[0486] This instruction manual also provides Figure 2 The diagram shows a schematic structural representation of the electronic device. Figure 2 As shown, at the hardware level, this electronic device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above. Figure 1 A vehicle limit control method combining hybrid-order Koopman tensor decomposition and CBF is provided.

[0487] Of course, in addition to software implementation, this specification does not exclude other implementation methods, such as logic devices or a combination of hardware and software. In other words, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0488] In the 1990s, improvements to a technology could be clearly distinguished as either hardware improvements (e.g., improvements to the circuit structure of diodes, transistors, switches, etc.) or software improvements (improvements to the methodology). However, with technological advancements, many methodological improvements today can be considered direct improvements to the hardware circuit structure. Designers almost always obtain the corresponding hardware circuit structure by programming the improved methodology into the hardware circuit. Therefore, it cannot be said that a methodological improvement cannot be implemented using hardware physical modules. For example, a Programmable Logic Device (PLD) (such as a Field Programmable Gate Array (FPGA)) is such an integrated circuit whose logic function is determined by the user programming the device. Designers can program and "integrate" a digital system onto a PLD themselves, without needing chip manufacturers to design and manufacture dedicated integrated circuit chips. Furthermore, nowadays, instead of manually manufacturing integrated circuit chips, this programming is mostly implemented using "logic compiler" software. Similar to the software compiler used in program development, the original code before compilation must also be written in a specific programming language, called a Hardware Description Language (HDL). There are many HDLs, such as ABEL (Advanced Boolean Expression Language), AHDL (Altera Hardware Description Language), Confluence, CUPL (Cornell University Programming Language), HDCal, JHDL (Java Hardware Description Language), Lava, Lola, MyHDL, PALASM, and RHDL (Ruby Hardware Description Language). Currently, the most commonly used are VHDL (Very-High-Speed ​​Integrated Circuit Hardware Description Language) and Verilog. Those skilled in the art should also understand that by simply performing some logic programming on the method flow using one of these hardware description languages ​​and programming it into an integrated circuit, the hardware circuit implementing the logical method flow can be easily obtained.

[0489] The controller can be implemented in any suitable manner. For example, it can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code form, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included therein for implementing various functions can also be considered as structures within the hardware component. Alternatively, the means for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0490] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0491] For ease of description, the above devices are described in terms of function, divided into various units. Of course, in implementing this specification, the functions of each unit can be implemented in one or more software and / or hardware components.

[0492] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0493] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0494] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0495] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0496] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0497] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0498] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic or disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0499] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0500] Those skilled in the art will understand that the embodiments of this specification can be provided as methods, systems, or computer program products. Therefore, this specification may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this specification may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0501] This specification can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This specification can also be practiced in distributed computing environments, where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0502] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0503] The above description is merely an embodiment of this specification and is not intended to limit this specification. Various modifications and variations can be made to this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of the claims of this specification.

Claims

1. A vehicle limit control method of hybrid order Koopman tensor decomposition and CBF fusion, characterized in that, include: S1. Obtain the motion state of the target vehicle, the motion state including the longitudinal velocity, lateral velocity, yaw rate, heading angle, and position coordinates of the target vehicle; S2. Determine the motion state of the target vehicle at the next moment based on the motion state and the IMU data of the target vehicle; S3. Based on the preset tire force relaxation model, tire force observation model and the motion state of the target vehicle at the next moment, determine the tire force, wheel slip angle and wheel normal load of the target vehicle; S4. Based on the motion state of the target vehicle at the next moment and the forces of each tire of the target vehicle, determine the state vector of the target vehicle and define the control input vector; S5. Based on the state vector and the control input vector, construct a first-order linear Koopman model, a second-order bilinear Koopman model, and a third-order higher-order Koopman model; S6. Determine the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle, and determine the comprehensive index of the severity of the working condition based on the tire utilization rate index, sideslip angle index, and lateral acceleration index. S7. Determine the weights of each Koopman model based on the comprehensive index of the severity of the working condition and the preset weight formula of each Koopman model; S8. Calculate the prediction results of each Koopman model, and determine the fusion prediction result based on the weights of each Koopman model. S9. Determine the affine form of the fusion prediction result; S10. Construct a nominal controller based on the affine form of the fusion prediction results; S11. Solve for the nominal controller, determine the control input vector at the current moment, and control the target vehicle according to the control input vector at the current moment.

2. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 1, characterized in that, The IMU data includes longitudinal acceleration, lateral acceleration, and yaw acceleration; The calculation expression for determining the motion state of the target vehicle at the next moment in S2 is as follows: in, The longitudinal velocity; The lateral velocity; The yaw rate is the stated angular velocity. The heading angle is mentioned; () represents the position coordinates of the target vehicle; The longitudinal acceleration; The lateral acceleration is mentioned. The yaw acceleration is given. Indicates the current moment. Indicates the next moment; The sampling period represents... and The time interval between them.

3. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 2, characterized in that... The tire forces of the target vehicle include the longitudinal force and lateral force of each tire; The calculation expression for the tire force relaxation model described in S3 is as follows: The tire force observation model is as follows: The formula for calculating the wheel slip angles of the target vehicle is as follows: The calculation expression for the normal load of each wheel of the target vehicle is as follows: in, Let be the longitudinal force and the lateral force of the i-th tire, respectively. These represent the front left, front right, rear left, and rear right tires, respectively. All are relaxation time constants; This is a rough estimate of the steady-state force based on a simplified tire model; Let be the differentials of the longitudinal force and the lateral force of the i-th tire, respectively; For the first i The rotational angular acceleration of each tire; This refers to the front wheel steering angle; These are the front and rear wheelbases, respectively. The wheelbase is the distance between the wheels. For the moment of inertia of the wheel, The radius of the wheel's rolling motion. For the moment of inertia of yaw rotation, For the overall vehicle weight; This represents the driving / braking torque for each wheel; a positive value indicates driving, and a negative value indicates braking. The wheel slip angles of the target vehicle are defined as follows: These are the longitudinal velocity, lateral velocity, and yaw rate of the target vehicle at the next moment, respectively. The normal loads on each wheel of the target vehicle are denoted as . , For the height of the center of mass, It is the acceleration due to gravity. The longitudinal acceleration and lateral acceleration are from the IMU data.

4. The vehicle limit control method fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 3, characterized in that, The computational expression for the first-order linear Koopman model in S5 is as follows: The computational expression for the second-order bilinear Koopman model is: The computational expression for the third-order higher-order Koopman model is: in, Let this be the state vector of the target vehicle; This is the control input vector for the target vehicle. This is the control input vector of the target vehicle at the current moment; Based on the state vector at the current time The state vector after increasing the dimensionality; , , It was identified and determined using a first-order linear Koopman model; The parameters of the linear part in the second-order bilinear Koopman model are determined through identification using the second-order bilinear Koopman model. The control input vector of the target vehicle at the current moment. The j-th control input, for The corresponding bilinear coupling matrix is ​​determined by dimensionality reduction through Tucker decomposition; These are the independent linear parameters in the third-order higher-order Koopman model, identified and determined through the third-order higher-order Koopman model. The third-order coupling term is the CP decomposition form of the third-order higher-order Koopman model. These are the state pairs extracted from the state vector. The third-order coupling term is represented as a third-order tensor in the form of a tensor-vector product. Indicates along the first Tensor-vector product of modes; for R is the rank of CP. This is the output factor vector when the CP rank is r. Let r be the state pair factor vector when CP rank is r. Let r be the control factor vector when CP rank is r. The scaling factor is the CP rank r. This represents the outer product of vectors.

5. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 4, characterized in that... The calculation expressions for the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle determined in S6 are as follows: The formula for calculating the comprehensive index of operating condition severity is as follows: in, These are the tire utilization rate index, sideslip angle index, and lateral acceleration index of the target vehicle, respectively. These are the squares of the longitudinal force and the squares of the lateral force of the i-th tire, respectively. This is the preset road surface adhesion coefficient; Let be the normal load on the i-th tire of the target vehicle; Let be the slip angle of the i-th tire of the target vehicle; Let be the peak slip angle of the i-th tire of the target vehicle; ; These are the preset weight coefficients. .

6. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 5, characterized in that... S7 specifically includes: The comprehensive index of the severity of the working condition is filtered; Substitute the filtered comprehensive index of the severity of the working condition into the preset weight formula of each Koopman model to determine the initial weight of each Koopman model. The initial weights of each Koopman model are normalized to determine the weights of each Koopman model. The calculation expression for the filtering process is: in, This is a comprehensive index of the severity of the operating condition after filtering at the current moment; This is a comprehensive index of the severity of the operating condition after filtering at the previous moment; These are the preset filter coefficients; This is a comprehensive indicator of the severity of the current operating condition. The default weight formulas for each Koopman model are as follows: in, These are the initial weights of the first-order linear Koopman model at the current time. These are the initial weights of the second-order bilinear Koopman model at the current time. These are the initial weights of the third-order higher-order Koopman model at the current moment; For the Sigmoid function, For each preset switching threshold, These are the preset transition slopes; The calculation expression for normalization is: in, The weights are assigned to each Koopman model.

7. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 6, characterized in that... The calculation expression for the fusion prediction result in S8 is as follows: in, The prediction results for each Koopman model are shown below. For fusion prediction results; The affine form of the calculation expression for the fusion prediction result described in S9 is as follows: in, When i is 1, 2, or 3 respectively, They are respectively , , ; When i is 1, 2, or 3 respectively, They are respectively , , ; middle hour They are respectively .

8. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 7, characterized in that... S10 specifically includes: Based on the affine form of the fusion prediction results, a nominal controller is constructed using the LQR control algorithm.

9. The vehicle limit control method based on the fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 7, characterized in that... S10 specifically includes: Based on the affine form of the fusion prediction results, an MPC controller based on the fusion prediction results is constructed as the nominal controller.

10. A vehicle limit control method fusion of hybrid-order Koopman tensor decomposition and CBF as described in claim 8 or 9, characterized in that, S11 solves for the nominal controller to determine the control input vector at the current moment, specifically including: Solve for the nominal controller to determine the predicted control input vector; Define the safety set and barrier function, determine the discrete-time CBF constraint conditions, and affine the discrete-time CBF constraint conditions; Based on the affine discrete-time CBF constraint, the predicted control input vector is corrected to determine the control input vector at the current time.

Images