Vehicle lateral stability control methods, products, controllers, and vehicles considering time delays

Abstract

This invention belongs to the field of vehicle control, specifically relating to a vehicle lateral stability control method, product, controller, and vehicle considering time delay. The method first introduces a Smith predictor into the control loop to feedforward compensate for the time delay, effectively transforming the time-delayed lateral dynamics model into a time-delay-free internal nominal model. Then, the residual time delay is explicitly incorporated as a bounded uncertainty parameter into the tuning process. The feasible region is solved using semi-discretization, and the optimal feedback gain matrix is ​​obtained through Pareto front analysis and optimal point selection. Finally, the pre-tuned optimal feedback gain matrix and the predicted state vector output by the Smith predictor are combined to form the front wheel steering angle control command. This invention can simultaneously improve the convergence speed and steady-state accuracy of the vehicle's lateral position and heading angle errors, and has provable robust stability margins, solving the technical challenge of existing solutions in balancing tracking accuracy and robustness under time-varying and time-delay conditions.

Description

Technical Field

[0001] This invention belongs to the field of vehicle control, specifically relating to a vehicle lateral stability control method that takes time delay into account, and the corresponding computer program product, vehicle lateral stability controller and autonomous vehicle. Background Technology

[0002] Lateral control is crucial for the driving safety of intelligent vehicles. In typical scenarios such as lane keeping and emergency obstacle avoidance, the vehicle needs to adjust the front wheel angle in real time via the steering actuator to accurately track the desired trajectory. However, there is an unavoidable time lag between the vehicle's sensor data acquisition and the steering motor response. This lag, typically ranging from 200 to 400 ms, is accumulated from multiple stages including perception fusion, localization planning, control calculations, bus scheduling, and EPS mechanical response. This lag reduces the system's phase margin, amplifies tracking errors, and in severe cases, can even cause steering oscillations or instability, especially at high speeds or high curvature, directly threatening vehicle safety. Therefore, ensuring the accuracy and stability of lateral tracking under conditions with large and varying time lags is of great significance for the successful implementation of intelligent driving functions.

[0003] Traditionally, lateral control in intelligent vehicles often employs geometric tracking or LQR methods designed based on time-delay-free models. Therefore, as time delay increases, the tracking error amplifies significantly or even oscillates. To address this issue, engineers have proposed robust LQR methods based on time-delay models. However, these schemes are forced to reduce gain due to the conservative nature of the stability region, leading to decreased control bandwidth and larger steady-state errors. Model predictive control (MPC) has also been used to solve lateral stability control problems. While it can achieve high accuracy when the time delay is accurately constant, it has high computational overhead and is extremely sensitive to time delay deviations, easily experiencing catastrophic degradation under time-varying time delays. Furthermore, Smith predictors compensate for time delays through internal nominal modulus compensation, allowing for higher feedback gain. However, its performance depends on the consistency between the nominal and true time delays. Existing tuning methods do not incorporate the worst-case scenario of residual time delays into design constraints and often employ single-objective optimization, relying on empirical trial and error, making it difficult to balance dynamic convergence speed, steady-state accuracy, and time-varying time delay robustness.

[0004] In summary, existing intelligent vehicle lateral control technologies suffer from insufficient stability margins when facing large and time-varying time-delay conditions. LQR-type methods tuned using time-delay-free models offer insufficient stability margins, while robust LQR methods based on time-delay stability criteria sacrifice control bandwidth due to conservatism. MPC schemes incur high computational overhead and are extremely sensitive to time-delay deviations, while Smith predictor schemes fail to incorporate the worst-case scenario of residual time delays into tuning constraints, lack provable robustness, and have difficult-to-reproduce tuning processes. Therefore, achieving near-MPC tracking accuracy, provable robustness to time-varying time delays, and a reproducible tuning process under automotive-grade low-computational constraints remains a long-standing technical challenge in this field. Summary of the Invention

[0005] To address the challenge of balancing tracking accuracy and robust stability in existing intelligent vehicle lateral control schemes under time-varying and time-delay conditions, this invention provides a vehicle lateral stability control method that considers time delay, along with corresponding computer program products, a vehicle lateral stability controller, and an autonomous vehicle.

[0006] This invention is achieved using the following technical solution: A vehicle lateral stability control method considering time delay includes the following steps: A state-space equation for a vehicle control system with time delay is constructed using a two-degree-of-freedom vehicle model to realize path tracking; and a curvature feedforward equation is generated when the vehicle is tracking a preset path in steady state.

[0007] Design a Smith predictor for a vehicle control system with time delay; and construct a residual time delay model for the vehicle closed-loop control.

[0008] The stability of the residual time delay model is determined by a semi-discretization method, and a set of candidate gains that satisfy the stability constraints is obtained by scanning.

[0009] The feedback gain matrix K is parameterized as (p1, p2), where p1 represents the lateral position error gain and p2 represents the heading error gain. A bi-objective optimization model is constructed that minimizes both the discrete closed-loop spectrum radius and the steady-state lateral error of the residual time delay model.

[0010] The candidate gain set is used as the feasible set of the bi-objective optimization model, and it is Pareto-tuned. Then, the Knee inflection point that minimizes the marginal benefit of the bi-objective optimization is selected. ; thereby generating the optimal feedback gain .

[0011] Within any control cycle, obtain the predicted state vector estimated by the Smith predictor. Then calculate the vehicle's turning angle using the following formula. : ; In the above formula, This represents the curvature of the current tracking path calculated based on the curvature feedforward equation. The feedforward component below.

[0012] The present invention also includes a computer program product comprising a computer program that, when executed by a processor, implements the vehicle lateral stability control method considering time delay as described above, and then generates vehicle steering control commands that can simultaneously satisfy vehicle stability and minimize lateral error based on the real-time state of the vehicle and the output of the Simth predictor.

[0013] The present invention also includes a vehicle lateral stability controller, which includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the vehicle lateral stability control method considering time delay as described above, and then generates a vehicle steering control command that can simultaneously satisfy vehicle stability and minimize lateral error based on the real-time state of the vehicle and the output of the Simth predictor.

[0014] The vehicle lateral stability controller includes an offline planner and an online optimizer.

[0015] The offline planner is used for: A state-space equation for a vehicle control system with time delay is constructed using a two-degree-of-freedom vehicle model to realize path tracking; and a curvature feedforward equation is generated when the vehicle is tracking a preset path in steady state.

[0016] Design a Smith predictor for a vehicle control system with time delay; and construct a residual time delay model for the vehicle closed-loop control.

[0017] The stability of the residual time delay model is determined by a semi-discretization method, and a set of candidate gains that satisfy the stability constraints is obtained by scanning.

[0018] The feedback gain matrix K is parameterized as (p1, p2), where p1 represents the lateral position error gain and p2 represents the heading error gain. A bi-objective optimization model is constructed that minimizes both the discrete closed-loop spectrum radius and the steady-state lateral error of the residual time delay model.

[0019] The candidate gain set is used as the feasible set S of the bi-objective optimization model, and Pareto tuning is performed on it; then, the Knee inflection point that minimizes the marginal benefit of the bi-objective optimization is selected. ; thereby generating the optimal feedback gain .

[0020] The online optimizer is used to: obtain the predicted state vector estimated by the Smith predictor within any control cycle. Then calculate the vehicle turning angle using the following formula. : ; In the above formula, This represents the curvature of the current tracking path calculated based on the curvature feedforward equation. The feedforward component below.

[0021] The present invention also includes an autonomous vehicle that employs the vehicle lateral stability controller as described above.

[0022] The technical solution provided by this invention has the following beneficial effects: This invention introduces a Smith predictor into the control loop to feedforward compensate for time delays, effectively transforming the time-delayed lateral dynamics model into a time-delay-free internal nominal model. Based on this, the residual time delay is explicitly incorporated as a bounded uncertainty parameter into the tuning process. The feasible region is solved using semi-discretization to obtain the feedback gain combination, ultimately forming the front wheel steering angle control law. This scheme not only removes the main time delay from the closed loop, eliminating the assumption that time delay is negligible when tuning the gain, but also explicitly incorporates the worst-case scenario of the residual time delay into the design constraints, eliminating the assumption that the actual time delay is always equal to a constant time delay to guarantee performance. Therefore, compared to the traditional LQR method that tunes the gain based on a time-delay-free model and the MPC time delay compensation method, which is highly sensitive to time delay values ​​in the predictive model, this invention significantly improves the convergence speed and steady-state accuracy of lateral position error and heading angle error under conditions where vehicle speed, bus load, and actuator response cause fluctuations in actual time delay, and possesses provable robust stability margins.

[0023] In practical applications, this invention transforms the computationally intensive robust tuning process into offline selection. In the offline stage, dynamic convergence speed, steady-state tracking accuracy, and residual time delay robustness margin are optimized. Stability constraint boundaries are obtained through semi-discretization, and a fixed feedback gain combination is obtained in one step through multi-objective optimization. The online stage only retains the state recursion of the Smith predictor and a single matrix-vector multiplication, with single-step computational overhead on the order of microseconds. Furthermore, the tuning inputs, constraints, Pareto front, and final point selection are all completely recorded in data form. This allows the invention to operate stably on mainstream automotive-grade MCUs at control frequencies of 100Hz and above, while ensuring consistent performance and reproducibility of tuning results across different engineers and vehicle models. It overcomes the problems of high computational cost, experience-dependent tuning processes, and difficulty in reproducibility associated with existing high-precision time delay compensation methods.

[0024] The Pareto front weight tuning method proposed in this invention transforms the parameter matrix tuning problem from the traditional trial-and-error parameter tuning by engineers into a front-end solution of a multi-objective optimization problem, giving the weight selection clear physical meaning and traceability. When vehicle parameters (wheelbase, mass, tire lateral stiffness) change or the driving scenario switches from low speed to high speed, the corresponding compromise point can be directly selected on the generated Pareto front, significantly shortening the calibration cycle and enhancing the practical value of this solution for different types of vehicles. Attached Figure Description

[0025] Figure 1 This is a flowchart of the steps of the vehicle lateral stability control method considering time delay provided in Embodiment 1 of the present invention.

[0026] Figure 2 This is a visualization of the Pareto front design and optimal point selection process in Embodiment 1 of the present invention.

[0027] Figure 3 In Embodiment 1 of this invention, the Pareto set is returned. A visual representation of the parametric plane process.

[0028] Figure 4 This is a schematic diagram of the working principle of the vehicle lateral stability controller provided in Embodiment 2 of the present invention.

[0029] Figure 5 These are the actual time delay curves for the three operating conditions in the simulation experiment.

[0030] Figure 6 This is a comparison chart of the vehicle path tracking trajectories of the present invention and two control group schemes in three scenarios during simulation experiments.

[0031] Figure 7 The simulation experiment shows a comparison of the single-step CPU time of the present invention and two control group schemes in three scenarios. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0033] Example 1

[0034] This embodiment provides a novel vehicle lateral stability control method that considers time delay. On one hand, this method introduces a Smith predictor into the control loop to feedforward compensate for the time delay, effectively transforming the time-delayed lateral dynamics model into a time-delay-free internal nominal model. On the other hand, the residual time delay is explicitly incorporated as a bounded uncertainty parameter into the tuning process. The feasible region is solved using semi-discretization to obtain the feedback gain combination, ultimately forming the front wheel steering angle control law.

[0035] Based on the above strategy, the technical solution provided in this embodiment can both remove the main time delay from the closed loop and no longer tune the gain based on the premise that the time delay is negligible; and explicitly incorporate the worst-case scenario of the residual time delay into the design constraints, no longer guaranteeing performance based on the premise that the actual time delay is always equal to the constant time delay. This method solves the technical problem that existing intelligent vehicle lateral control methods are unable to balance tracking accuracy and robust stability under time-varying time delay conditions.

[0036] Specifically, such as Figure 1 As shown, this embodiment provides a vehicle lateral stability control method that considers time delay, including the following steps: I. Vehicle Lateral Time-Delay Dynamics Modeling A state-space equation for a vehicle control system with time delay is constructed using a two-degree-of-freedom vehicle model to realize path tracking; and a curvature feedforward equation is generated when the vehicle is tracking a preset path in steady state.

[0037] In a typical scenario of lane keeping and path tracking for autonomous driving of passenger vehicles, the lateral acceleration 'a' of the vehicle in the normal driving range in this embodiment is... y satisfy: Longitudinal vehicle speed V x satisfy: To achieve a balance between modeling accuracy and real-time computational cost, the following settings can be made for the constructed vehicle dynamics model: (1) longitudinal vehicle speed V x (1) The vehicle is approximately constant within a control cycle, and the longitudinal and lateral motions are decoupled. (2) The vehicle is considered a rigid body, and the roll, pitch and vertical motions are ignored. The center of gravity of the vehicle is located at the geometric center of the sprung mass. (3) The tires work in the linear region, and the lateral force is proportional to the slip angle.

[0038] Based on the above assumptions, this embodiment models the vehicle as a two-degree-of-freedom vehicle model and constructs a tracking error model for the vehicle, which includes the following details: Define a vehicle coordinate system that moves with the vehicle, with the X-axis pointing towards the front of the vehicle and the Y-axis pointing towards the left side of the vehicle. Let the vehicle's longitudinal velocity and lateral velocity be V0 and V1, respectively. x and V y yaw rate and yaw acceleration For vehicle state variables; F yf F yr These are the forces on the front and rear tires of the vehicle, respectively. Let be the steering angle of the vehicle's front wheels; from Newton's second law and the angular momentum theorem, we get: ;

[0039] Where m is the total vehicle mass, J z Let a be the moment of inertia of yaw about the vertical axis, and let a and b be the distances from the vehicle's center of mass to the front and rear axles, respectively.

[0040] Then the front wheel slip angle α of the vehicle f and rear wheel slip angle a r Satisfy the following formula: ;

[0041] Substituting the above formula into the linear tire model , and to Make a small angle approximation (i.e.: ), sorted out as follows:

[0042] Among them, Cf and C r This represents the equivalent lateral stiffness of the front and rear wheels.

[0043] Based on this, a lateral position error e relative to the reference path is introduced. y and heading angle error When the curvature of the reference path is The reference yaw rate is : At that time, the vehicle's tracking error model can be expressed as: ;

[0044] In the above formula, and e y and The first derivative.

[0045] In a vehicle control system with time delay, the state vector is taken. The control input is : ,in, There is a time delay in the control system, and the disturbance input is : The state-space equation for path tracking can be obtained as follows: ; Among them, A, B and C w These are the system state matrix, control input matrix, and disturbance input matrix, which respectively satisfy the following equation:

[0046]

[0047] Based on the state-space equation for vehicle path tracking described above, when the vehicle travels at speed V... x Steady-state tracking curvature is When the circular path is (i.e.) ),Will and Substituting the steady-state solution, we can obtain the expression for the curvature feedforward equation as follows: ;

[0048] In the above formula, the first term For Ackermann geometric feedforward; second term This is the dynamic compensation term, corresponding to the additional turning angle required for steady-state tracking of the curve; where g represents gravitational acceleration; K v For insufficient turning gradient, and satisfying the following equation:

[0049] II. Smith Predictor Design and Residual Delay Closed-Loop Model Establishment

[0050] In this embodiment, the nominal model and the delayed nominal model inside the designed Smith predictor are as follows: ; in, The front wheel steering angle command output by the controller at time t is sent to the actuator and, after a real time delay... The control commands applied to the vehicle, i.e., the actual control commands received by the vehicle, are ; For nominal time delay (in this embodiment) ), The actual time delay includes unknown disturbances; the residual time delay is defined as... ; Represents the nominal state vector in the nominal model The first derivative; Represents the time-delay state vector in the nominal delay model. The first derivative.

[0051] In the Smith predictor, the predicted state vector is estimated based on the state increment. The process is as follows: nominal vehicles in the past State increment generated within seconds due to receiving new instructions for: ; The first derivative of its state increment is And satisfy the following formula: ; Furthermore, based on the current true state x(t), past values ​​are superimposed... The nominal but not yet reflected state increments in actual vehicles, thus forming an understanding of the actual vehicle's passage. Predicted state vector of the vehicle state : ; right The instantaneous rate of change of the predicted state vector is obtained by taking the derivative. Satisfy the following formula: ; In the above formula, Let x(t) be the first derivative. When When the model is a perfect match, the term within the square brackets in the above equation is always zero, and the predicted state vector output by the Simth predictor is... It meets the requirements of a standard linear system without time delay.

[0052] The process of designing a feedback control law to achieve nominal closed-loop control based on the output of the Simth predictor is as follows: Suppose the controller outputs the predicted state vector. The feedback format is as follows: ; in, This is the feedback gain matrix to be designed.

[0053] (1) When the model is a perfect match and At this point, let the disturbance input w be always equal to 0; perform homogeneous analysis to obtain: ; That is, the nominal closed-loop dynamics are completely unaffected by time delay, which is equivalent to a time-delay-free dynamic. Pole assignment problem.

[0054] (2) When the model has residual time delay, such as When w is always equal to 0, then we have: ; Depend on It can be seen that, under the assumption of perfect model matching, the nominal model has the same dynamics as the real vehicle, and Therefore = As can be seen from the working principle of the Smith predictor, the nominal quantity is in the interval... The cumulative increment is exactly equal to the actual vehicle speed in the interval. The state change on (missing one) (synchronous translation), thus: Substituting these values, we obtain the following residual time-delay closed-loop homogeneous equation: ; Therefore, Smith's nominal compensation has no residual bias; the effect of time delay on robustness margin is determined solely by the residual time delay. Decision, not full time delay .

[0055] III. Residual Delay Stability Analysis and Gain Set Generation Based on Semi-Discretization

[0056] To accurately characterize the true stability boundary on the parameter plane, this embodiment employs a semi-discretization method to perform Floquet stability determination on the differential equations of the residual time delay model of the closed-loop control, and in... A set of candidate gains satisfying stability constraints is obtained by scanning the plane; the specific process is as follows: (1) Residual closed-loop homogeneous equation As analyzed above, the residual closed-loop homogeneous equation of the vehicle residual system is: ; in, For the instantaneous coefficients of the residual system, , For the time delay term coefficients of the residual system, .

[0057] Based on this, the residual time-delay grid in this embodiment Recorded as: The number of grid points is denoted as The j-th grid point is denoted as The semi-discretization step size h is set to h = 0.005s, which is related to the control period T. s =10ms decoupling to ensure time delay resolution as small as 5ms.

[0058] (2) Finding the integral term using the exact solution of the subinterval and the augmented matrix method

[0059] The continuous time axis is uniformly divided into sub-intervals. ,remember The delay term will be applied to the i-th sub-interval. Treated as piecewise constants .in, Let be the discrete delay section number corresponding to the j-th grid, and satisfy: ; In the above formula, `round` is the rounding function; then when When h=5ms .

[0060] The exact solution of the delayed differential equation on this subinterval is:

[0061] Among them, the state transition matrix Sub-interval mapping coefficients Integral term .

[0062] Because the transverse dynamics contain zero eigenvalues ​​(pure integral of the position channel). Irreversible It is difficult to calculate directly. Therefore, an augmented matrix is ​​constructed. for: ; in These are the n-order identity matrix and the zero matrix, respectively. For Take matrix exponent as follows: ; Then a single call obtains synchronous results. To avoid numerical oddities.

[0063] (3) Single-period transfer matrix for three residual time delay cases

[0064] Construct extended state for: The extended state single-step mapping matrix at substep size h is constructed as follows: To make the next state... Based on residual time delay The symbol can be categorized into the following three cases: (i):When If this exactly matches Smith's equation, then the residual closed-loop homogeneous equation degenerates into the following ordinary differential equation: ; at this time The extended state degenerates into Substep size mapping matrix for: .

[0065] (ii): When ,at this time Translation based on extended state Solving for: ; in, for The skeleton matrix that is independent of the candidate gain. for The sparse correction matrix of the injected candidate feedback satisfies the following equation: ; (iii): Smith overcompensation Mathematically rigorous The model corresponds to a predictive DDE, whose single-period transfer matrix suffers from an infinite-dimensional functional projection problem. To ensure the conservatism of the design, this embodiment uses a worst-case approximation: it is treated as... Delayed DDE processing is constructed similarly according to (ii). , that is to say and obtain the corresponding .

[0066] (4) Residual time delay stability margin

[0067] By semi-discretization theory, the extended state mapping matrix over substep h The spectral radius completely determines the asymptotic stability of the closed loop under the residual time delay. The discrete closed-loop spectral radius of the j-th residual time delay grid point is defined as... : ; Define the discrete stability margin of the j-th grid point for: ; By the semi-discretization stability theorem, the residual time delay The necessary and sufficient condition for the lower closed-loop asymptotic stability is: ; in, Represents the minimum discrete stability margin. It is a closed-loop system for all Criteria for robust stability.

[0068] IV. Constructing a dual-objective optimization model and implementing Pareto front analysis and optimal point selection

[0069] In this embodiment, the feedback gain matrix K is parameterized as (p1, p2), where p1 represents the lateral position error gain and p2 represents the heading error gain; thus, the four-dimensional feedback tuning problem is reduced to a two-dimensional parameter search. Based on this, the Smith predictor calculates the nominal time delay... After internal control cancellation, the effective time delay of the closed-loop system degenerates into a residual time delay. The control gain can be significantly amplified; however, it must also be ensured that: the closed loop remains stable for all residual time delays; and the steady-state lateral error is minimized under constant reference curvature. These two objectives conflict with each other. Therefore, this embodiment constructs a bi-objective optimization model that minimizes both the discrete closed-loop spectral radius and the steady-state lateral error of the residual time delay model, as expressed below: ; Among them, the first optimization objective In The discrete closed-loop spectrum radius under the worst-case residual time delay; the second optimization objective. In Let Ω represent the steady-state lateral error of the ideal Smith equivalent time-delay closed loop with respect to the reference curvature; Ω represents the feasible region of the feedback gain matrix. The two optimization objectives are explained in detail below: (1) Spectral radius target: By utilizing Smith to compensate for the amplification space caused by the main time lag, the scanning range is significantly larger than that without Smith. Assuming... The number of candidate parameter points for p1 is ; The number of candidate parameter points for p2 is Then the total candidate points For each candidate Spectral radius is taken from residual time-delay grid The maximum value in the range is used as the robustness index for that point, i.e.: ; in, It represents the discrete closed-loop spectrum radius of the j-th residual time-delay grid point.

[0070] (2) Steady-state lateral error target: Under the ideal Smith assumption, since the nominal time delay has been canceled out, the steady-state behavior is equivalent to a time-delay-free closed loop. At this point, for a constant curvature reference... ,make Solving for the problem, we get: ; in, This represents the first component of the steady-state vector (i.e., the lateral position error); only when... Calculations are only performed at certain times to ensure that the statistical samples are all within the stability region; when season And directly eliminate the candidate point.

[0071] Based on this, this embodiment uses the candidate gain set as the feasible set S of the bi-objective optimization model and performs Pareto tuning on it; then, it selects the Knee inflection point that minimizes the marginal benefit of the bi-objective optimization. ; thereby generating the optimal feedback gain The process includes: (1) To avoid the critical point where the spectral radius is exactly close to 1 from participating in the sorting, an adaptive threshold is used: Select the smallest value from {0.02, 0.01, 0.005, 0.002, 1e-4}. , making The number of points is no less than 30, and this value is recorded as follows. .

[0072] The feasible set S contains all parameter points that satisfy the following two conditions. : ; (2) Perform Pareto non-dominated sorting on the points in S: Let the target vector of point i be . Then i is the Pareto front. If and only if:

[0073] (3) Selecting the optimal point on the Pareto front: To eliminate the dimensional differences between the two objectives, the frontier point is linearly normalized:

[0074] in, and For each of the leading edge points k and The normalized value; and for The minimum and maximum values; and They are respectively The minimum and maximum values. Superscript This indicates that extrema exist only on the Pareto front point set. Take the inner set, not the entire feasible set. ; Click on the front edge Sort in ascending order, therefore ;end represents the index of the leading edge's ending point.

[0075] (4) Construct the unit direction vector of the line connecting the beginning and end of the front edge. for:

[0076] Then the perpendicular distance d from the k-th leading edge point to the unit direction vector is... k for: ; in, Let be a two-dimensional vector pointing from the first point of the front edge to the kth point of the front edge; .

[0077] Therefore, the optimal point is where the marginal benefit of performance is lowest. for: ; in, The function represents finding the position where the maximum value is reached (the optimal solution); it automatically selects the point that best balances the two objectives, because simply optimizing in either direction will significantly worsen the other objective. Ultimately, it will... Map back to the (p1,p2) parameter plane; output the optimal point. Corresponding gain parameters The feedback gain matrix is ​​the final recommended choice.

[0078] Specifically, in this embodiment, a visualization of the process of selecting the optimal point that satisfies the dual objective optimization based on the Pareto front is shown below. Figure 2As shown in the figure. The gray scatter points represent the feasible set S, the blue solid line represents the Pareto front obtained by non-dominated sorting, and the pink square represents the fastest convergence (…). The blue diamond represents the point with the lowest gain, and the green triangle in the middle represents the automatically selected optimal point. There is a significant trade-off between the two targets in the figure. This embodiment can automatically locate the optimal point with the lowest marginal benefit.

[0079] Furthermore, the Pareto set was shot back. Visualization of the parametric plane process, such as Figure 3 As shown in the figure, the black solid line represents... The stable boundary, represented by the black dashed line. Contour lines, the blue area represents the Pareto set, and the green triangle represents the automatically selected optimal point. , which serves as the feedback gain matrix for the final output.

[0080] 5. Based on the pre-tuned feedback gain matrix K, the vehicle is controlled online.

[0081] In this embodiment, within any control cycle, the predicted state vector estimated by the Smith predictor is first obtained. In the Simth predictor, the predicted state vector is... The forecasting methods include: (1) Combined with the controller output u c (t) and the nominal model in the following Simth predictor derive the nominal state vector. : .

[0082] (2) Read the time-delayed state vector from the historical buffer. : .

[0083] (3) Based on the current state x(t) of the vehicle, the predicted state vector of the current control cycle is estimated by the following formula. : .

[0084] Then calculate the vehicle turning angle using the following formula. : ; The above equation includes two terms: Ackermann geometric feedforward and understeer gradient compensation, where, This represents the curvature of the current tracking path calculated based on the curvature feedforward equation. The feedforward component below.

[0085] In this embodiment, the actual cornering command issued by the controller... For feedback components With curvature feedforward components The sum of these values ​​ensures that the closed-loop system converges asymptotically with respect to the spectral radius even under the worst-case residual time delay.

[0086] In practical applications, The controller uses the known curvature feedforward equation based on the real-time state of the vehicle and the reference curvature of the target path. Dynamically updated. This can be obtained through pre-planning in an offline state. This can be obtained directly from the output of the Simth predictor.

[0087] It is important to emphasize that steps one through four in the solution provided in this embodiment can be completed offline beforehand. Step five, however, is implemented online. Specifically, in the offline stage, the optimization objectives are dynamic convergence speed, steady-state tracking accuracy, and residual time delay robustness margin. The stability constraint boundary is obtained through semi-discretization, and the fixed feedback gain combination is obtained in one step through multi-objective optimization. The online stage only retains the state recursion of the Smith predictor's internal model and a single matrix and vector multiplication. The computational cost per step is on the order of microseconds, and the tuned inputs, constraints, Pareto front, and final point selection are all recorded completely in data form.

[0088] Based on this, since this embodiment transforms online real-time solution into offline single-stage tuning and online fixed-gain execution, and transforms the parameter weight selection problem, which originally relied on repeated trial and error based on engineer experience, into a multi-objective optimization problem with a clear objective function and feasible region, compared to the MPC scheme that requires online QP solution for each control cycle, and the traditional scheme that relies on experience trial and error and can generally only be tuned for a single index, this embodiment can operate stably on mainstream automotive-grade MCUs at a control frequency of 100Hz and above. At the same time, it ensures that the tuning results of different engineers and different vehicle models have consistent performance and reproducibility, thereby solving the technical problems of high computational cost, reliance on experience, and difficulty in reproducing existing high-precision time delay compensation methods.

[0089] Example 2

[0090] The vehicle lateral stability control method considering time delay provided in Example 1 is essentially a data processing method. In order to better apply this scheme, this example further provides a computer program product, a vehicle lateral stability controller, and an autonomous vehicle.

[0091] The computer program product provided in this embodiment includes a computer program. When the computer program is executed by the processor, it implements the vehicle lateral stability control method considering time delay as in Embodiment 1, and then generates a vehicle steering control command that can simultaneously satisfy vehicle stability and minimize lateral error based on the real-time state of the vehicle and the output of the Simth predictor.

[0092] The vehicle lateral stability controller provided in this embodiment includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the vehicle lateral stability control method considering time delay as in Embodiment 1, and then generates a vehicle steering control command that can simultaneously satisfy vehicle stability and minimize lateral error based on the real-time state of the vehicle and the output of the Simth predictor.

[0093] The vehicle lateral stability controller includes an offline planner and an online optimizer. For example... Figure 4 As shown, the offline planner executes all data processing tasks in the aforementioned offline phase. The online optimizer handles all data processing tasks in the aforementioned online phase.

[0094] The autonomous vehicle provided in this embodiment uses the vehicle lateral stability controller as described above.

[0095] The product provided in this embodiment can be implemented in various ways and applied to multiple scenarios, including L2+ / L3 level autonomous driving vehicles and commercial vehicle platooning. In practical applications, the product can be embedded in existing vehicles as a standalone lateral stability controller or integrated into the vehicle's ADAS domain controller or VCU as a software module. For existing vehicles, the upgrade can be completed simply by flashing the control algorithm into the domain controller as a software package and reading vehicle status information via the CAN / CAN-FD bus, without any modification to the vehicle's original hardware. For new vehicles not yet manufactured, the relevant solution's program can be directly burned into the domain controller firmware during the production line stage, and vehicle-specific calibration can be completed using the Pareto weight tuning process provided in this embodiment. Regardless of the method used, the product provided in this embodiment can significantly reduce the lateral tracking error of vehicles under conditions of communication and execution delays, and greatly reduce the computational power required by the control algorithm for automotive-grade MCUs.

[0096] Furthermore, it is important to emphasize that the Pareto front weight tuning method proposed in this embodiment transforms the parameter matrix tuning problem from the traditional trial-and-error parameter tuning by engineers into a front-end solution for a multi-objective optimization problem, giving the weight selection clear physical meaning and traceability. When vehicle parameters (wheelbase, mass, tire lateral stiffness) change or the driving scenario switches from low speed to high speed, the corresponding compromise point can be directly selected on the generated Pareto front, significantly shortening the calibration cycle.

[0097] Simulation Experiment

[0098] To verify the performance of the vehicle lateral stability control method considering time delay provided by this invention, technicians simulated relevant schemes and tested their performance. The experimental details are as follows: I. Simulation Conditions This experiment uses the Simulink / CarSim joint platform to simulate and test the relevant solutions. The parameters of the experimental vehicle under the simulation conditions are as follows: Table 1: Parameters of Example Vehicles

[0099] II. Comparative Experiment

[0100] 2.1 Path tracking accuracy and robustness

[0101] To systematically verify the robustness of the technical solution provided by this invention under real communication / execution time delays, this experiment constructs three typical operating conditions: Scenario 1: Steady time delay ; Scenario 2: Time-varying delay ; Scenario 3: Time-varying and time-delayed .

[0102] The actual time delay curves for the three operating conditions are as follows: Figure 5 As shown.

[0103] Next, under the dual-line-shifting reference trajectory, the technical solution provided by this invention (denoted as Proposed) is compared with the following two baseline methods as a control group: (a) Traditional time-delay compensation (LQR): The feedback law is directly tuned using A and B as the nominal models. Where P is The symmetric positive definite solution. The weight matrix is ​​taken as... Corresponding in sequence , The equivalent Q and R magnitudes corresponding to the best advantage of this invention are consistent to ensure comparability.

[0104] (b) State augmented time delay (denoted as MPC): Augmented delay number of segments , the past The step control quantity is incorporated into the augmented state, and the number of steps in the prediction time domain is taken as follows. (Predicted duration) ,cover (And reserve 200ms look-ahead) to control the number of time-domain steps. , where n is the dimension of the original state.

[0105] The vehicle path tracking trajectories of this invention and two control group schemes in three scenarios are as follows: Figure 6 As shown in the figure. Analysis of the data in the figure reveals that: In scenario 1, all three can track, but LQR shows a significant tracking lag at X>20m because it does not compensate for the 300ms delay. The maximum lateral deviation of MPC and the technical solution provided by this invention is ≤0.1m.

[0106] In scenario 2, due to the mismatch between the internal time delay model and the time-varying time delay, MPC exhibits continuous low-frequency residual oscillations at X>90m; while the maximum lateral deviation of the solution provided by this invention is ≤0.1m.

[0107] In scenario 3, the MPC oscillation amplitude further increases to the meter level and shows a divergent trend, while the present invention still maintains a maximum lateral deviation of ≤0.1m, verifying the robust stability of the present invention.

[0108] 2.2 CPU computing power consumption

[0109] This experiment further compared the single-step CPU time (logarithmic scale) of the present invention and two control group schemes in three scenarios, and the experimental data obtained are as follows: Figure 7 As shown in the figure, analysis of the data reveals that, for single-step CPU time, LQR ≈ 0.8 μs / step, MPC ≈ 700~1100 μs / step, and the present invention ≈ 1.5 μs / step. Therefore, the CPU computing power consumption of the present invention is reduced by approximately 2~3 orders of magnitude compared to MPC, and is on par with LQR. This means that the present invention can be directly deployed in automotive-grade ECUs (typically with a clock frequency of 200MHz and a control cycle of 5~10ms).

[0110] Based on the data from the above comparative experiments, it can be seen that the present invention has higher tracking accuracy and stronger time-delay robustness compared to the prior art. Under dual-track reference trajectories, it is particularly effective for steady time delays. Time-varying and time-delay and Under three typical operating conditions, the lateral tracking error of this invention can be stably converged to within 0.1m; traditional LQR... Significant tracking errors occur under these conditions. Traditional state-augmented time-delay MPCs also exhibit persistent low-frequency residual oscillations due to the mismatch between the internal nominal model and the actual time delay under time-varying time-delay conditions. This invention provides a feedback law in analytical form, with a single-step control cycle CPU time of only about 1.5μs, which is about 3 to 4 orders of magnitude lower than that of traditional state-augmented time-delay MPCs (N=50, single-step time 2.5~4ms). It can operate stably at a frequency of 100kHz on mainstream automotive-grade MCUs while retaining sufficient computing power margin to be compatible with other ADAS functions.

[0111] III. Calibration Verification for Different Vehicle Models

[0112] This experiment further replaced the vehicle parameters with those of a typical light commercial vehicle, and the tuning process still output a feasible optimal solution without modifying the algorithm. This demonstrates that the present invention has consistent applicability to both passenger cars and commercial vehicles.

[0113] In summary, this invention addresses the long-standing engineering challenge of directional drive vehicles (DWD) where tracking accuracy deteriorates due to communication and execution time delays, while computational limitations persist and are difficult to balance. It proposes a vehicle lateral stability control method based on a combination of Pareto front weight tuning and analytical feedback time delay compensation. This approach ensures both lateral tracking accuracy and time delay robustness while reducing the real-time computational overhead of the control algorithm to a level comparable to classical LQR. This overcomes the limitation of existing high-precision time delay compensation algorithms being difficult to deploy in real-time on automotive-grade MCUs, demonstrating significant engineering practical value and industrialization prospects.

[0114] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A vehicle lateral stability control method considering time delay, characterized in that, It includes: A state-space equation for path tracking is constructed using a two-degree-of-freedom vehicle model to build a vehicle control system with time delay. It also generates the curvature feedforward equation for the vehicle's steady-state tracking of the preset path; Design a Smith predictor for a vehicle control system with time delay, and construct a residual time delay model for the vehicle closed-loop control. The stability of the residual time delay model is determined by a semi-discretization method, and a set of candidate gains that satisfy the stability constraints is obtained by scanning. The feedback gain matrix K is parameterized as (p1, p2), where p1 represents the lateral position error gain and p2 represents the heading error gain. A bi-objective optimization model is constructed that minimizes both the discrete closed-loop spectrum radius and the steady-state lateral error of the residual time delay model. The candidate gain set is used as the feasible set of the bi-objective optimization model, and it is Pareto-tuned. Then, the Knee inflection point that minimizes the marginal benefit of the bi-objective optimization is selected. ; thereby generating the optimal feedback gain ; Within any control cycle, obtain the predicted state vector estimated by the Smith predictor. Then calculate the vehicle turning angle using the following formula. : ； in, This represents the curvature of the current tracking path calculated based on the curvature feedforward equation. The feedforward component below.

2. The vehicle lateral stability control method considering time delay as described in claim 1, characterized in that: The state-space equation for path tracking in a vehicle control system with time delay is: ； In the above formula, x(t) represents the vehicle's state vector at time t; This represents the first derivative of x(t); Indicates the system's control input; The time delay of the control system is represented by w(t); the disturbance input of the system is represented by A, B, and C. w These are the system state matrix, control input matrix, and disturbance input matrix, respectively.

3. The vehicle lateral stability control method considering time delay as described in claim 2, characterized in that: The expression for the curvature feedforward equation is: ； In the above formula, a and b are the distances from the vehicle's center of gravity to the front and rear axles, respectively; V x Represents longitudinal vehicle speed; g represents gravitational acceleration; K v The gradient is insufficient for steering.

4. The vehicle lateral stability control method considering time delay as described in claim 3, characterized in that, The expression for the residual time delay model is: ； In the above formula, K represents the feedback gain matrix to be designed; This indicates the residual time delay.

5. The vehicle lateral stability control method considering time delay as described in claim 4, characterized in that: The bi-objective optimization model is expressed as follows: ； ； ； In the above formula, Indicate the optimization objective; N is the discrete closed-loop spectrum radius under the worst-case residual time delay; j This represents the total number of residual time-delay grid points; Represents the discrete closed-loop spectral radius of the j-th residual time-delay grid point; Ω represents the steady-state lateral error of the ideal Smith equivalent time-delay-free closed loop relative to the reference curvature; Ω represents the feasible region of the feedback gain matrix.

6. The vehicle lateral stability control method considering time delay as described in claim 5, characterized in that: The optimal feedback gain The generation methods include: The parameter points in the feasible set S are pre-screened based on the preset spectral radius threshold and the transverse error threshold. Perform Pareto nondominated sorting on the parameter points in the filtered S; Linear normalization is applied to the leading edge points to eliminate dimensions, and a unit direction vector is constructed connecting the beginning and end of the leading edge. ; And calculate the perpendicular distance d from any k-th parameter point to the unit direction vector. k ; The Knee point with the lowest marginal benefit of performance is identified using the following formula. : ； Will Mapping back to the (p1,p2) parameter plane yields the corresponding optimal feedback gain. : .

7. The vehicle lateral stability control method considering time delay as described in claim 1, characterized in that: Within any control period; the predicted state vector The forecasting methods include: (1) Combined with the controller output u c (t) and the nominal model in the following Simth predictor derive the nominal state vector. : ； (2) Read the time-delayed state vector from the historical buffer. : ; (3) Based on the current state x(t) of the vehicle, the predicted state vector of the current control cycle is estimated by the following formula. : 。 8. A computer program product comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the vehicle lateral stability control method considering time delay as described in any one of claims 1-7, and then generates a vehicle steering control command that can simultaneously satisfy vehicle stability and minimize lateral error based on the real-time state of the vehicle and the output of the Simth predictor.

9. A vehicle lateral stability controller, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the vehicle lateral stability control method considering time delay as described in any one of claims 1-7, and then generates a vehicle steering control command that can simultaneously satisfy vehicle stability and minimize lateral error based on the real-time state of the vehicle and the output of the Simth predictor. The vehicle lateral stability controller includes an offline planner and an online optimizer. The offline planner is used for: A state-space equation for a vehicle control system with time delay is constructed using a two-degree-of-freedom vehicle model to realize path tracking; and a curvature feedforward equation is generated when the vehicle is tracking a preset path in steady state. Design a Smith predictor for a vehicle control system with time delay, and construct a residual time delay model for the vehicle closed-loop control. The stability of the residual time delay model is determined by a semi-discretization method, and a set of candidate gains that satisfy the stability constraints is obtained by scanning. The feedback gain matrix K is parameterized as (p1, p2), where p1 represents the lateral position error gain and p2 is the heading error gain; a bi-objective optimization model is constructed that minimizes both the discrete closed-loop spectrum radius and the steady-state lateral error of the residual time delay model. The candidate gain set is used as the feasible set of the bi-objective optimization model, and it is Pareto tuned; then, the Knee inflection point that minimizes the marginal benefit of the bi-objective optimization is selected. ; thereby generating the optimal feedback gain ; The online optimizer is used to: obtain the predicted state vector estimated by the Smith predictor within any control cycle. Then calculate the vehicle turning angle using the following formula. : ； in, This represents the curvature of the current tracking path calculated based on the curvature feedforward equation. The feedforward component below.

10. An autonomous vehicle, characterized in that: It employs the vehicle lateral stability controller as described in claim 9.

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