A vehicle adaptive trajectory tracking control method and system considering steering delay

Abstract

The application discloses a vehicle adaptive trajectory tracking control method and system considering steering delay, relates to the technical field of intelligent vehicle motion control, and is used for solving the technical problems of large tracking error, uneven control and low stability existing in the prior art. The vehicle adaptive trajectory tracking control method considering steering delay comprises the following steps: acquiring a current state of a vehicle, a reference trajectory and a road adhesion coefficient; establishing a lateral dynamics model and a trajectory tracking error model, and introducing a first-order inertia link to represent steering delay; constructing an augmented prediction model, taking a reference curvature as an external drive, and incorporating steering actuator dynamics into a state space; establishing an objective function and a constraint of model predictive control; adjusting a prediction time domain according to a longitudinal vehicle speed, respectively constructing normalization factors according to the adhesion coefficient and the reference curvature, and adjusting an output error weight matrix and a control increment weight matrix; and obtaining a current front wheel steering angle instruction based on model predictive control.

Description

Technical Field

[0001] This invention relates to the field of intelligent vehicle motion control technology, and more specifically, to a vehicle adaptive trajectory tracking control method and system that takes into account steering delay. Background Technology

[0002] In the field of intelligent vehicle motion control, trajectory tracking control is one of the core technologies for achieving autonomous navigation and safe driving. Existing trajectory tracking control methods are usually based on vehicle kinematics or dynamics models, combined with strategies such as model predictive control, sliding mode control, and linear quadratic regulators to enable the vehicle to accurately track the desired path. Among them, model predictive control is widely used in vehicle lateral control because it can explicitly handle system constraints and predict future states. Meanwhile, to adapt to different driving conditions, some methods have begun to consider the impact of road adhesion coefficient on vehicle dynamics and have conducted simulation verification under different adhesion conditions. In addition, some studies have attempted to introduce reference trajectory curvature information to improve cornering performance, or to use a dual-loop PID (Proportional-Integral-Derivative) structure to achieve longitudinal speed control.

[0003] Existing trajectory tracking control methods still have the following shortcomings. First, when a vehicle moves from a high-adhesion surface to a low-adhesion or abruptly changed surface, the available lateral force boundary of the tires changes drastically. If the controller still uses fixed weights and prediction parameters, it is easy to cause overly aggressive control input, uneven changes in front wheel steering angle, and increased sideslip angle, thereby reducing vehicle attitude stability and trajectory tracking accuracy. Second, when the vehicle is traveling on a curve with large curvature or a path with continuously changing curvature, the controller lacks the ability to predict changes in curvature ahead, resulting in a significant increase in trajectory tracking error, especially at the entrance and exit of curves, where hysteresis or overshoot is likely to occur. Third, traditional trajectory tracking control models usually assume that the front wheel steering angle output by the controller can be applied to the vehicle's front wheels instantaneously, without fully considering the dynamic hysteresis characteristics of the steering actuator. In high-speed continuous obstacle avoidance, curve following, or low-adhesion conditions, ignoring steering hysteresis will reduce the consistency between the prediction model and the actual vehicle response, causing problems such as increased trajectory tracking error, lag in steering response, and local control spikes. Summary of the Invention

[0004] The purpose of this invention is to provide a vehicle adaptive trajectory tracking control method and system that considers steering delay, to solve the technical problems of large tracking errors, uneven control, and low stability caused by fixed control parameters, insufficient adhesion adaptability, and dynamic steering lag in existing technologies under conditions of variable adhesion road surfaces, continuous curvature changes, and steering delay. In view of this, this invention achieves this through the following solution.

[0005] In a first aspect, the present invention provides a vehicle adaptive trajectory tracking control method that takes into account steering delay, comprising: Obtain the vehicle's current status, reference trajectory, and road surface adhesion coefficient; A lateral dynamics model and a trajectory tracking error model are established, and a first-order inertial element is introduced to characterize the steering delay, describing the dynamic response between the front wheel steering angle command and the actual steering angle. An augmented prediction model is constructed, with the reference curvature as the external driver, and the steering actuator is dynamically incorporated into the state space; Establish the objective function and constraints for model predictive control. The objective function includes the weighted sum of output error, control increment and slack variables. The constraints include control increment limit, rotation angle amplitude limit, rotation angle change rate limit, output limit and centroid sideslip angle limit based on adhesion coefficient correction. The prediction time domain is adjusted based on the longitudinal vehicle speed, and normalization factors are constructed based on the adhesion coefficient and reference curvature, respectively, to adjust the output error weight matrix and the control increment weight matrix. The current front wheel steering angle command is obtained based on model predictive control; where: The lateral dynamics model is based on a two-degree-of-freedom single-track model and is used to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the driving matrix multiplied by the reference trajectory curvature. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle from the previous moment.

[0006] Compared with existing technologies, the vehicle adaptive trajectory tracking control method of the present invention, which considers steering delay, firstly establishes a lateral dynamics and trajectory tracking error model and introduces a first-order inertial element to characterize the steering delay. This enables the controller to describe the dynamic response lag between the front wheel steering angle command and the actual steering angle, thereby incorporating the true characteristics of the steering actuator into the prediction process and effectively avoiding increased tracking error and control command mismatch caused by ignoring lag. Secondly, by constructing an augmented prediction model with reference curvature as the external drive and dynamically incorporating the steering actuator into the state space, the controller can perceive changes in curve curvature in advance and predict the actuator response, significantly improving the predictive ability and control accuracy of curve following. Furthermore, the method established by the present invention... The model predictive control objective function not only includes a weighted sum of output error and control increment, but also introduces relaxation variables to enhance optimization feasibility. The constraints include a centroid sideslip angle limit based on the adhesion coefficient correction, which automatically tightens the sideslip angle boundary on low-adhesion surfaces to prevent vehicle instability. Furthermore, this invention adaptively adjusts the prediction time domain based on longitudinal vehicle speed and constructs normalization factors based on the adhesion coefficient and reference curvature to dynamically adjust the output error weight matrix and control increment weight matrix. This allows the controller to automatically balance tracking accuracy and control smoothness under different vehicle speeds, adhesion levels, and curvature conditions. Finally, the current front wheel steering angle command is obtained based on the model predictive control solution, achieving real-time optimal tracking of the lateral trajectory. Through the above technical solutions of this invention, the technical problems of large tracking errors, uneven control, and low stability caused by fixed control parameters, insufficient adhesion adaptability, and dynamic steering lag in existing technologies under varying adhesion surfaces, continuous curvature changes, and steering delays are solved.

[0007] Furthermore, the vehicle adaptive trajectory tracking control method of the present invention, which takes into account steering delay, also includes longitudinal cooperative control; The longitudinal coordinated control adopts a series proportional-integral-derivative structure. The outer loop proportional-integral-derivative controller generates a corrected reference speed based on the deviation between the desired longitudinal position and the actual longitudinal position. The inner loop proportional-integral-derivative controller generates longitudinal driving force or braking force based on the deviation between the corrected reference speed and the actual longitudinal speed.

[0008] Furthermore, in the vehicle adaptive trajectory tracking control method considering steering delay of the present invention, the state equation of the lateral dynamics model includes: The total mass of the vehicle multiplied by the lateral acceleration equals the sum of the lateral forces on the front and rear wheels; The yaw moment of inertia multiplied by the yaw angular acceleration equals the front wheel lateral force multiplied by the front wheelbase minus the rear wheel lateral force multiplied by the rear wheelbase. Furthermore, under the linear tire assumption, the lateral forces of the front and rear wheels are equal to the corresponding lateral stiffness multiplied by the lateral slip angle.

[0009] Furthermore, in the vehicle adaptive trajectory tracking control method of the present invention that considers steering delay, the error vector in the trajectory tracking error model includes lateral error, lateral error rate of change, heading error, and heading error rate of change.

[0010] Furthermore, in the vehicle adaptive trajectory tracking control method considering steering delay of the present invention, in the augmented prediction model: The augmented state vector at the next moment is equal to the discrete state matrix multiplied by the augmented state vector at the current moment, plus the input matrix multiplied by the current feedback control increment, plus the external input matrix multiplied by the current external input vector consisting of the reference curvature driving term and the reference heading angle change rate.

[0011] Furthermore, in the vehicle adaptive trajectory tracking control method of the present invention that considers steering delay, the objective function includes: The weighted sum of the squares of the output error vectors at each prediction time point in the prediction time domain is added to the weighted sum of the squares of the control increment vectors at each time point in the control time domain, and then the square of the slack variable is multiplied by the penalty coefficient.

[0012] Furthermore, in the vehicle adaptive trajectory tracking control method of the present invention that considers steering delay, the centroid sideslip angle limiting based on adhesion coefficient correction is: The absolute value of the centroid sideslip angle is less than or equal to an upper limit function that monotonically increases with the road surface adhesion coefficient. This upper limit function increases accordingly when the adhesion is high.

[0013] Furthermore, in the vehicle adaptive trajectory tracking control method of the present invention that considers steering delay, the method of adjusting the prediction time domain according to the longitudinal vehicle speed is as follows: Based on the optimized selection results of the prediction time domain at different vehicle speeds, the prediction time domain is adaptively adjusted online.

[0014] Furthermore, in the vehicle adaptive trajectory tracking control method of the present invention that considers steering delay, the normalization factor includes an attachment normalization factor and a curvature normalization factor. The adhesion normalization factor is obtained by applying a saturation function to the estimated value of the road surface adhesion coefficient and then limiting the amplitude; the curvature normalization factor is obtained by dividing the absolute value of the curvature of the reference trajectory by a preset curvature benchmark value and then limiting the amplitude to the minimum value. The adjustment of the output error weight matrix and the control increment weight matrix is ​​achieved by designing the lateral error weight, heading error weight, and control increment weight as functions that change linearly or nonlinearly with the attachment normalization factor and curvature normalization factor, respectively.

[0015] Secondly, the present invention provides a vehicle adaptive trajectory tracking control system that takes into account steering delay, comprising: The information acquisition module is used to acquire the vehicle's current status, reference trajectory, and road surface adhesion coefficient; The dynamics modeling module is used to establish the lateral dynamics model and the trajectory tracking error model, and introduces a first-order inertial element to characterize the steering delay and describe the dynamic response between the front wheel steering angle command and the actual steering angle. The lateral dynamics model is based on a two-degree-of-freedom single-track model and is used to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the drive matrix multiplied by the curvature of the reference trajectory. The prediction model building module is used to build an augmented prediction model, which uses the reference curvature as an external drive and dynamically incorporates the steering actuator into the state space. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle of the previous moment. The optimization problem establishment module is used to establish the objective function and constraints of model predictive control. The objective function includes the weighted sum of output error, control increment and slack variables. The constraints include control increment limit, rotation angle amplitude limit, rotation angle change rate limit, output limit and centroid sideslip angle limit based on adhesion coefficient correction. The parameter adaptive module is used to adjust the prediction time domain according to the longitudinal vehicle speed, construct normalization factors according to the adhesion coefficient and reference curvature respectively, and adjust the output error weight matrix and control increment weight matrix. The control variable solving module is used to obtain the current front wheel steering angle command based on model predictive control.

[0016] Compared with the prior art, the beneficial effects of the vehicle adaptive trajectory tracking control system considering steering delay of the present invention are the same as those of the vehicle adaptive trajectory tracking control method considering steering delay described in the above technical solution, and will not be repeated here. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart illustrating the vehicle adaptive trajectory tracking control method considering steering delay according to the present invention. Figure 2 This is a schematic diagram of the framework of a vehicle adaptive trajectory tracking control system according to the present invention; Figure 3 This is a schematic diagram of the lateral dynamics model of the vehicle in this invention; Figure 4 This is a schematic diagram of the trajectory tracking error model in this invention; Figure 5 This is a schematic diagram of the longitudinal collaborative control in this invention; Figure 6 This is a schematic diagram of the trajectory tracking simulation results under high adhesion conditions. Figure 6 (a) is a schematic diagram of the horizontal position. Figure 6 (b) is a schematic diagram of lateral tracking error. Figure 6 (c) is a schematic diagram of heading angle error. Figure 6 (d) is a schematic diagram of the centroid sideslip angle. Figure 6 (e) is a schematic diagram of lateral acceleration. Figure 6 (f) is a schematic diagram of the front wheel steering angle. Figure 6 (g) is a schematic diagram of the longitudinal velocity. Figure 6 (h) is a schematic diagram of longitudinal error; Figure 7 This is a schematic diagram of the simulation results of trajectory tracking under low adhesion conditions in this invention. Figure 7 (a) is a schematic diagram of the horizontal position. Figure 7 (b) is a schematic diagram of lateral tracking error. Figure 7 (c) is a schematic diagram of heading angle error. Figure 7 (d) is a schematic diagram of lateral acceleration. Figure 7 (e) is a schematic diagram of the centroid sideslip angle. Figure 7 (f) is a schematic diagram of the front wheel steering angle. Figure 7 (g) is a schematic diagram of the longitudinal velocity. Figure 7 (h) is a schematic diagram of longitudinal error. Detailed Implementation

[0018] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present 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 of the present invention and are not intended to limit the present invention.

[0019] It should be noted that when a component is referred to as being "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as being "connected to" another component, it can be directly connected to or indirectly connected to that other component.

[0020] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. "Several" means one or more, unless otherwise explicitly specified.

[0021] Existing trajectory tracking control methods still have the following shortcomings. First, when a vehicle moves from a high-adhesion surface to a low-adhesion or abruptly changed surface, the available lateral force boundary of the tires changes drastically. If the controller still uses fixed weights and prediction parameters, it is easy to cause overly aggressive control input, uneven changes in front wheel steering angle, and increased sideslip angle, thereby reducing vehicle attitude stability and trajectory tracking accuracy. Second, when the vehicle is traveling on a curve with large curvature or a path with continuously changing curvature, the controller lacks the ability to predict changes in curvature ahead, resulting in a significant increase in trajectory tracking error, especially at the entrance and exit of curves, where hysteresis or overshoot is likely to occur. Third, traditional trajectory tracking control models usually assume that the front wheel steering angle output by the controller can be applied to the vehicle's front wheels instantaneously, without fully considering the dynamic hysteresis characteristics of the steering actuator. In high-speed continuous obstacle avoidance, curve following, or low-adhesion conditions, ignoring steering hysteresis will reduce the consistency between the prediction model and the actual vehicle response, causing problems such as increased trajectory tracking error, lag in steering response, and local control spikes.

[0022] To address the above technical problems, this invention provides a vehicle adaptive trajectory tracking control method that considers steering delay, comprising: Obtain the vehicle's current status, reference trajectory, and road surface adhesion coefficient; A lateral dynamics model and a trajectory tracking error model are established, and a first-order inertial element is introduced to characterize the steering delay, describing the dynamic response between the front wheel steering angle command and the actual steering angle. An augmented prediction model is constructed, with the reference curvature as the external driver, and the steering actuator is dynamically incorporated into the state space; Establish the objective function and constraints for model predictive control. The objective function includes the weighted sum of output error, control increment, and slack variables. The constraints include control increment limit, rotation angle amplitude limit, rotation angle rate of change limit, output limit, and centroid sideslip angle limit based on adhesion coefficient correction. The prediction time domain is adjusted based on the longitudinal vehicle speed, and normalization factors are constructed based on the adhesion coefficient and reference curvature, respectively, to adjust the output error weight matrix and the control increment weight matrix. The current front wheel steering angle command is obtained based on model predictive control; where: The lateral dynamics model is based on a two-degree-of-freedom single-track model and is used to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the driving matrix multiplied by the reference trajectory curvature. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle from the previous moment.

[0023] In the above-mentioned technical solution, the vehicle adaptive trajectory tracking control method of the present invention, which considers steering delay, firstly establishes a lateral dynamics and trajectory tracking error model and introduces a first-order inertial element to characterize the steering delay. This enables the controller to describe the dynamic response lag between the front wheel steering angle command and the actual steering angle, thereby incorporating the true characteristics of the steering actuator into the prediction process and effectively avoiding the increase in tracking error and control command mismatch caused by ignoring lag. Secondly, by constructing an augmented prediction model with reference curvature as the external drive and dynamically incorporating the steering actuator into the state space, the controller can perceive changes in curve curvature in advance and predict the actuator response, significantly improving the prediction capability and control accuracy of curve following. Furthermore, the present invention... The established model predictive control objective function not only includes a weighted sum of output error and control increment, but also introduces relaxation variables to enhance optimization feasibility. The constraints include a centroid sideslip angle limit based on the adhesion coefficient correction, which automatically tightens the sideslip angle boundary on low-adhesion surfaces to prevent vehicle instability. Furthermore, this invention adaptively adjusts the prediction time domain based on longitudinal vehicle speed and constructs normalization factors based on the adhesion coefficient and reference curvature to dynamically adjust the output error weight matrix and control increment weight matrix. This allows the controller to automatically balance tracking accuracy and control smoothness under different vehicle speeds, adhesion levels, and curvature conditions. Finally, the current front wheel steering angle command is obtained based on model predictive control, achieving real-time optimal tracking of the lateral trajectory. Through the above technical solutions of this invention, the technical problems of large tracking errors, uneven control, and low stability caused by fixed control parameters, insufficient adhesion adaptability, and dynamic steering lag in existing technologies under varying adhesion surfaces, continuous curvature changes, and steering delays are solved.

[0024] To better understand the present invention, the following specific embodiments further illustrate the content of the present invention, but the content of the present invention is not limited to the following embodiments.

[0025] Example 1 This embodiment provides a vehicle adaptive trajectory tracking control method that considers steering delay, including: Step 1: Obtain the vehicle's current status, reference trajectory, and road surface adhesion coefficient; Step 2: Establish the lateral dynamics model and the trajectory tracking error model, and introduce a first-order inertial element to characterize the steering delay and describe the dynamic response between the front wheel steering angle command and the actual steering angle. The lateral dynamics model is established based on a two-degree-of-freedom single-track model to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the drive matrix multiplied by the curvature of the reference trajectory. Step 3: Construct an augmented prediction model, using the reference curvature as an external drive and dynamically incorporating the steering actuator into the state space. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle from the previous moment. Step 4: Establish the objective function and constraints for model predictive control. The objective function includes the weighted sum of output error, control increment, and slack variables. The constraints include control increment limit, angle amplitude limit, angle change rate limit, output limit, and centroid sideslip angle limit based on adhesion coefficient correction. Step 5: Adjust the prediction time domain according to the longitudinal vehicle speed, construct normalization factors according to the adhesion coefficient and reference curvature respectively, and adjust the output error weight matrix and control increment weight matrix. Step 6: Obtain the current front wheel steering angle command based on model predictive control.

[0026] Example 2 In a first aspect, this embodiment provides a vehicle adaptive trajectory tracking control method that considers steering delay, including: Step 1: Obtain the vehicle's current state, reference trajectory, and road surface adhesion coefficient. The current state includes longitudinal speed, lateral speed, yaw rate, heading angle, lateral position, and actual front wheel turning angle. The reference trajectory includes reference position, reference heading angle, reference curvature, and reference speed.

[0027] Step 2: Establish the lateral dynamics model and the trajectory tracking error model, and introduce a first-order inertial element to characterize the steering delay and describe the dynamic response between the front wheel steering angle command and the actual steering angle. The transverse dynamics model is based on a two-degree-of-freedom single-track model, and its state equations include: The total vehicle mass multiplied by the lateral acceleration equals the sum of the lateral forces of the front and rear wheels; the yaw moment of inertia multiplied by the yaw angular acceleration equals the front wheel lateral force multiplied by the front wheelbase minus the rear wheel lateral force multiplied by the rear wheelbase; and under the linear tire assumption, the front and rear wheel lateral forces are respectively equal to the corresponding lateral stiffness multiplied by the lateral slip angle. The error vector in the trajectory tracking error model includes lateral error, lateral error rate of change, heading error, and heading error rate of change. Its continuous-time error state equation is: The first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the drive matrix multiplied by the reference trajectory curvature.

[0028] Step 3: Construct an augmented prediction model, using the reference curvature as an external driver and dynamically incorporating the steering actuator into the state space; The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle of the previous moment. The augmented state vector at the next moment is equal to the discrete state matrix multiplied by the augmented state vector at the current moment, plus the input matrix multiplied by the current feedback control increment, plus the external input matrix multiplied by the current external input vector consisting of the reference curvature driving term and the reference heading angle change rate.

[0029] Step 4: Establish the objective function and constraints for model predictive control. The objective function includes the weighted sum of output error, control increment, and slack variables. The constraints include control increment limit, angle amplitude limit, angle change rate limit, output limit, and centroid sideslip angle limit based on adhesion coefficient correction. The objective function can be: the weighted sum of the squares of the output error vectors at each prediction time in the prediction time domain, plus the weighted sum of the squares of the control increment vectors at each time in the control time domain, plus the square of the slack variable multiplied by the penalty coefficient; the centroid sideslip angle limit based on the adhesion coefficient correction is: the absolute value of the centroid sideslip angle is less than or equal to an upper limit function that monotonically increases with the road adhesion coefficient, and the value of the upper limit function increases accordingly at high adhesion.

[0030] Step 5: Adjust the prediction time domain according to the longitudinal vehicle speed, construct normalization factors according to the adhesion coefficient and reference curvature respectively, and adjust the output error weight matrix and control increment weight matrix. The method for adjusting the prediction time domain based on longitudinal vehicle speed is as follows: Based on the optimized selection results of the prediction time domain at different vehicle speeds, the prediction time domain is adaptively adjusted online. Normalization factors include adhesion normalization factor and curvature normalization factor. The adhesion normalization factor is obtained by applying a saturation function to the estimated road adhesion coefficient and then limiting it. The curvature normalization factor is obtained by dividing the absolute value of the reference trajectory curvature by a preset curvature benchmark value and then limiting it to a minimum value. The adjustment of the output error weight matrix and the control increment weight matrix is ​​achieved by designing the lateral error weight, heading error weight, and control increment weight as functions that change linearly or nonlinearly with the adhesion normalization factor and the curvature normalization factor, respectively.

[0031] Step 6: Obtain the current front wheel steering angle command based on model predictive control.

[0032] Step 7, perform longitudinal coordinated control; the longitudinal coordinated control adopts a series proportional-integral-derivative structure, the outer loop proportional-integral-derivative controller generates a corrected reference speed based on the deviation between the desired longitudinal position and the actual longitudinal position, and the inner loop proportional-integral-derivative controller generates longitudinal driving force or braking force based on the deviation between the corrected reference speed and the actual longitudinal speed.

[0033] Secondly, this embodiment provides a vehicle adaptive trajectory tracking control system that takes into account steering delay, including: The information acquisition module is used to acquire the vehicle's current status, reference trajectory, and road surface adhesion coefficient; The dynamics modeling module is used to establish the lateral dynamics model and the trajectory tracking error model, and introduces a first-order inertial element to characterize the steering delay and describe the dynamic response between the front wheel steering angle command and the actual steering angle. The lateral dynamics model is based on a two-degree-of-freedom single-track model and is used to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the drive matrix multiplied by the curvature of the reference trajectory. The prediction model building module is used to build an augmented prediction model, which uses the reference curvature as an external drive and dynamically incorporates the steering actuator into the state space. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle of the previous moment. The optimization problem establishment module is used to establish the objective function and constraints of model predictive control. The objective function includes the weighted sum of output error, control increment and slack variables. The constraints include control increment limit, rotation angle magnitude limit, rotation angle rate of change limit, output limit and centroid sideslip angle limit based on adhesion coefficient correction. The parameter adaptive module is used to adjust the prediction time domain according to the longitudinal vehicle speed, construct normalization factors according to the adhesion coefficient and reference curvature respectively, and adjust the output error weight matrix and control increment weight matrix. The control variable solving module is used to obtain the current front wheel steering angle command based on model predictive control.

[0034] Example 3 Please see Figure 1 This embodiment further illustrates the vehicle adaptive trajectory tracking control method considering steering delay of the present invention based on Embodiment 2 described above. Figure 3 and Figure 4 middle, For a fixed coordinate system on the ground, For the vehicle coordinate system, For the longitudinal direction of the vehicle body, The vehicle body is horizontal; For vehicle yaw angle, For heading angle; Indicates the vehicle's yaw rate; Indicates the vehicle's sideslip angle; and These are the lateral forces acting on the front and rear wheels in the tire coordinate system, respectively. These are the front and rear wheel slip angles, respectively. Indicates the distance from the center of mass to the front and rear axles; Indicates the longitudinal and lateral speeds of the vehicle. The resultant velocity of the vehicle's center of gravity; The steering angle of the front wheels; These represent the speeds at the front and rear wheels, respectively. For reference, the matching point on the online platform; The tangential direction of the reference line. These are the reference line normal and tangential unit vectors, respectively. The heading angle is the reference line. These are the tangential unit vector and the normal unit vector in the direction of vehicle velocity, respectively; This refers to the lateral deviation of the vehicle relative to the reference line; specifically: S100, such as Figure 3 As shown, this embodiment establishes the vehicle's lateral dynamics based on a two-degree-of-freedom single-track model, expressed as follows: ; in, Indicates the overall vehicle weight. Indicates lateral acceleration. Indicates longitudinal velocity. Indicates yaw rate. Indicates the lateral force on the front wheel. Indicates the actual steering angle of the front wheels. Indicates the lateral force on the rear wheel. This represents the moment of inertia about the z-axis of the center of mass. Indicates yaw acceleration. This indicates the distance from the center of gravity to the front axle. This indicates the distance from the center of mass to the rear axle.

[0035] Furthermore, under the linear tire assumption, for the front wheel lateral force... and rear wheel lateral force ,have: ; in, Indicates the front wheel lateral stiffness. Indicates the front wheel slip angle. Indicates lateral velocity. This indicates the distance from the center of gravity to the front axle. Indicates yaw rate. Indicates the actual steering angle of the front wheels. Indicates longitudinal velocity. Indicates the rear wheel lateral stiffness. Indicates the rear wheel slip angle. This indicates the distance from the center of mass to the rear axle.

[0036] Furthermore, substituting into the vehicle's lateral dynamics equations yields the state equations: .

[0037] S200, Establish the trajectory tracking error model; based on the aforementioned state equations, please refer to... Figure 4 Selecting lateral error Horizontal error change rate Heading error Rate of change of heading error The error vector is formed as follows: The error state equation is then expressed as: ; in, This represents the first derivative of the error vector with respect to time. Represents the system matrix. Represents the error vector. Represents the input matrix, Indicates the actual steering angle of the front wheels. Represents the driving matrix, This represents the rate of change of the reference heading angle; this formula reflects the relationship between the evolution of the vehicle's lateral error, the front wheel steering angle input, and the change in the curvature of the reference trajectory, and is the basis for subsequent predictive controller modeling.

[0038] In actual vehicle operation, the steering command output by the controller cannot be instantaneously applied to the front wheels. The steering actuator typically exhibits a certain dynamic lag. The target front wheel steering angle output by the controller. Given the actual steering angle of the vehicle's front wheels, the dynamics of the steering system can be represented using a first-order inertial element as follows: ;in, Indicates the time constant of the steering system. This represents the Laplace operator.

[0039] Discretizing the equation, and assuming the control period is T, we have: ; in, This indicates the actual steering angle of the front wheels at the next moment. This indicates the actual steering angle of the front wheels at the current moment. This represents the target front wheel steering angle output by the controller at the current moment; this formula allows the actuator to be dynamically and explicitly incorporated into the prediction model, improving the consistency between the controller's prediction results and the actual vehicle steering response.

[0040] S400, constructing an augmented predictive model considering curvature drive and actuator dynamics; specifically, to simultaneously describe the timing characteristics of trajectory tracking error, steering actuator dynamic response, and feedback control quantity, an augmented predictive model is further constructed. First, the total front wheel steering angle command is decomposed into a curvature feedforward term and a feedback correction term, i.e.: ; The curvature feedforward term at the current moment is represented as: ; in, This represents the distance from the center of gravity to the front axle. This represents the distance from the center of mass to the rear axle. This represents the curvature of the reference trajectory at the current moment. Represents the velocity gain coefficient. Indicates longitudinal velocity. This represents the feedback correction item at the current moment.

[0041] Furthermore, the continuous-time error state equation of the system has been established in step S200. To facilitate subsequent rolling optimization, it is discretized using the forward Euler method, resulting in: ; in, This represents the error vector at the next time step. This represents the error vector at the current moment. This indicates the actual steering angle of the front wheels at the current moment. This represents the rate of change of the reference heading angle at the current moment; Discrete system matrix ; It is the identity matrix. To control the cycle, For continuous system matrices; for discrete input matrices , For continuous input matrices, discrete driving matrices , It is a continuous driving matrix.

[0042] Furthermore, to integrate the trajectory tracking error, actual front wheel steering angle, and feedback control input into the model predictive control framework, the augmented state vector is constructed as follows: ; in, Represents the augmented state vector. Indicates the discrete time step index. This represents the transpose of the error vector at the current time. This indicates the actual steering angle of the front wheels at the current moment. Indicates the previous moment (the first moment) Feedback correction of the rotation angle (each control cycle).

[0043] Furthermore, considering the steering actuator dynamics and the reference curvature driving term, it can be written as the following augmented discrete state-space model: ; ; ; in, Indicates the next moment (the...) The augmented state vector (in control cycles), Indicates the current time (the nth time) The augmented state vector (in control cycles), This represents the augmented state matrix (6×6). This represents the input matrix (6×1). This represents the feedback control increment, which is the difference between the feedback correction angle at the current moment and the feedback correction angle at the previous moment. External driving terms; augmented state matrix and input matrix middle, Represents the matrix of a discrete system. Represents a discrete input matrix. This represents a coefficient related to the steering time constant and control cycle.

[0044] Furthermore, the system output vector is defined as: ; The output equation can then be written as: ; ; in, Indicates the first The system output vector for each control cycle Indicates the first The lateral error of each control cycle Indicates the first The rate of change of the lateral error over each control cycle Indicates the first The heading error per control cycle Indicates the first Rate of change of heading error per control cycle Indicates the previous moment (the first moment) Feedback correction angle (each control cycle) Indicates the output matrix. Indicates the first The augmented state vector for each control cycle; through the above method, the augmented prediction model can simultaneously characterize the evolution of trajectory tracking error, steering actuator hysteresis, and historical information of control quantities, providing a unified prediction model foundation for the establishment of the subsequent model prediction control objective function and the rolling optimization solution.

[0045] S500, establish the objective function for model predictive control; specifically, in the prediction time domain, establish an objective function that takes into account trajectory tracking error, control increment smoothness, and the feasibility of soft constraints, expressed as: ; in, Represents the objective function value. This represents the prediction output error vector. express transpose, This represents the output error weight matrix. This represents the control increment vector. express transpose, This represents the control increment weight matrix. Indicates the penalty coefficient. The expression represents a slack variable; this formula embodies the design concept of this invention, which ensures trajectory tracking accuracy while taking into account both control smoothness and the solvability of the optimization problem.

[0046] S600, establish constraints; specifically: The control increment constraint is: ; The total front wheel steering angle amplitude constraint is: , ; The constraint for the total front wheel steering angle change rate is: , ; The control output constraints are: ; The centroid sideslip angle constraint is: ; in, This indicates the lower limit of the control increment. Indicates the current time (the nth time) The control increment vector (each control cycle) This indicates the upper limit of the control increment. This indicates the lower limit of the total front wheel steering angle command. Indicates the first Total front wheel steering angle command for each control cycle This indicates the upper limit of the total front wheel steering angle command. This represents the step index within the prediction time domain. Indicates control of the time domain. This indicates the lower limit of the change in the front wheel steering angle command at adjacent times. This represents the difference in corner commands between two adjacent control cycles. This indicates the upper limit of the change in front wheel steering angle command between adjacent time points. This indicates the lower limit of the output quantity. This represents the system output vector at the current moment. Indicates the upper limit of the output quantity. Indicates the centroid sideslip angle. Indicates the road surface adhesion coefficient. It represents the acceleration due to gravity.

[0047] S700, based on the selection results of the optimal prediction time domain at different vehicle speeds, performs online adaptive adjustment of the prediction time domain, as shown below: ; in, Indicates the prediction time domain, This represents the rounding function. This represents the vehicle's longitudinal speed. Simultaneously, an adhesion normalization factor and a curvature normalization factor are introduced to adaptively adjust the controller weight matrix. The adhesion normalization factor and the curvature normalization factor are respectively: ; ; Based on this, the output weight matrix and the comprehensive control weight matrix are adjusted, as shown below: ; in, Indicates the attachment normalization factor. Represents the saturation function. This represents an estimated value of the road surface adhesion coefficient. Represents the curvature normalization factor. Describes the minimum value function. Indicates the curvature of the reference trajectory. This represents the preset curvature reference value. This represents the output error weight matrix. Represents a diagonal matrix. Indicates lateral error The weighting coefficients, Indicates the rate of change of lateral error The weighting coefficients, Indicates heading error The weighting coefficients, Indicates the rate of change of heading error The weighting coefficients, Indicates feedback correction of the turning angle The weighting coefficients.

[0048] Furthermore, to enable the weight matrix to adaptively adjust online according to changes in road surface adhesion conditions and reference trajectory curvature, this embodiment designs the weights of each output term as follows: ; ; ; ; ; in, Indicates the basic weight of the lateral position error. This represents the adjustment coefficient for the curvature's weight on the lateral error. This represents a road curvature-related factor, reflecting the degree of curvature of the reference path. This represents the adjustment coefficient for the adhesion coefficient on the weight of the lateral error. This represents the adhesion coefficient correction factor under low adhesion conditions. The basic weight representing the rate of change of the lateral error. Indicates the basic weight of the heading angle error. This represents the adjustment coefficient for the curvature's weighting of the heading angle error. This represents the adjustment coefficient for the adhesion coefficient on the weighting of the heading angle error. Indicates the basic weight of the rate of change of heading angle error. This represents the adjustment coefficient for the weighting of the rate of change of curvature with respect to the heading angle error. This represents the adjustment coefficient for the weighting of the rate of change of the heading angle error by the adhesion coefficient. This indicates the basic weights of the control input. This represents the adjustment coefficient of curvature on the weight of the control input. This represents the adjustment coefficient of the adhesion coefficient on the weight of the control input. Through the above method, the present invention can adjust the predictive controller parameters online according to changes in vehicle speed, adhesion level, and curvature, thereby improving adaptability under different operating conditions.

[0049] S800 performs longitudinal dual-loop PID coordinated control; the control block diagram of the dual-loop PID longitudinal tracking controller in this embodiment is as follows. Figure 5 As shown. Specifically, the outer-loop PID uses the deviation between the desired longitudinal position and the actual longitudinal position of the vehicle as input to achieve closed-loop position control; the inner-loop PID performs closed-loop speed control based on the error between the vehicle's reference speed and the actual speed. To meet the real-time requirements of longitudinal control, this embodiment directly maps the desired acceleration to the accelerator pedal opening or braking pressure based on the offline calibration results of the electric vehicle's drive and braking system, without considering brake energy recovery.

[0050] Further, please refer to Figure 2 The lateral controller employs a dual-channel structure of "curvature feedforward + MPC feedback". The feedforward channel generates a nominal steering angle based on the reference trajectory curvature and vehicle speed to compensate for the vehicle's steady-state steering requirements on curved paths. The feedback channel constructs an augmented prediction model based on trajectory tracking error and actuator state, and outputs feedback corrections through rolling optimization. To enhance the consistency between the model and the actual vehicle response, the controller further incorporates first-order dynamics of the steering actuator. Furthermore, considering the varying tolerances of the vehicle to control input amplitude, rate of change, and yaw dynamics under different adhesion coefficients, this embodiment performs online scheduling of the prediction time domain and objective function weights based on vehicle speed, adhesion coefficient estimates, and path curvature, thereby enabling the controller to adapt to different operating conditions.

[0051] Furthermore, the simulation results of continuous obstacle avoidance under high adhesion coefficient conditions are as follows: Figure 6 As shown. Figure 6(a) illustrates the vehicle's lateral position trajectory, with three control methods employed: Adaptive Model Predictive Control (AMPC), AMPC without steering delay, and Model Predictive Control (MPC). As can be seen, all three methods successfully track the reference trajectory and avoid both static obstacles (black rectangles) and dynamic obstacles (gray grid rectangles) on the road. AMPC exhibits the highest degree of alignment between the actual lateral position and the reference trajectory, following the planner's output trajectory well in both main lateral obstacle avoidance phases. AMPC without steering delay shows some lag in sections with rapid lateral position changes. The MPC method shows relatively significant trajectory deviation, especially during the lateral position adjustment phase of continuous obstacle avoidance, where its trajectory alignment is weaker than the other two methods. Figure 6 (b) shows the variation of lateral tracking error with longitudinal displacement. It can be seen that the errors of all three methods fluctuate to some extent during obstacle avoidance, but the amplitudes differ. AMPC's maximum absolute lateral error is approximately 0.06m, gradually converging to near 0 after a longitudinal displacement of approximately 190m, demonstrating its high-precision tracking capability under high-adhesion, high-speed obstacle avoidance conditions. AMPC, without considering steering delay, has a maximum error of approximately 0.17m, showing similar overall performance, but with slightly larger error fluctuations during the second lateral obstacle avoidance and trajectory return phases. In contrast, the conventional MPC method has a peak error of approximately 0.23m, with significant error oscillations during multiple lateral adjustments. Therefore, introducing an adaptive adjustment mechanism and dynamic modeling of the steering actuator can significantly reduce lateral error and improve later-stage convergence performance. Figure 6 (c) to Figure 6 (e) shows the changes in heading angle error (i.e., the aforementioned heading error), centroid sideslip angle, and lateral acceleration. Under high adhesion conditions, none of the three methods showed sustained divergence or abnormal fluctuations. According to constraint calculations, when the road adhesion coefficient is 0.85, the centroid sideslip angle constraint boundary is ±9.47°. Figure 6 (d) shows that the peak sideslip angles of all three methods are significantly lower than this boundary, indicating that the vehicle did not experience significant sideslip during obstacle avoidance. AMPC maintains the vehicle's attitude response within a reasonable range while ensuring a small lateral error, demonstrating that the designed controller can balance path tracking accuracy and vehicle stability. Figure 6 (f) shows the change in front wheel steering angle with longitudinal displacement. The AMPC method, which does not consider steering lag, exhibits significant abrupt changes in local areas, while the AMPC method shows a more continuous change in front wheel steering angle. This indicates that by incorporating the first-order dynamic characteristics of the steering actuator into the prediction model, the controller can anticipate the impact of steering response lag on vehicle motion, thereby improving the smoothness of local steering input. Figure 6 (g) and Figure 6(h) illustrates the changes in longitudinal speed and longitudinal error with longitudinal displacement, showing that the dual-loop PID longitudinal controller can track the reference speed well. The speed gradually decreases from 120 km / h to approximately 100 km / h, and the maximum longitudinal error is approximately 0.15 m, stabilizing around -0.03 m in the later stages. This indicates good coordination between longitudinal and lateral control, and the vehicle does not experience significant longitudinal tracking degradation due to lateral control actions during continuous obstacle avoidance. In summary, in high-adhesion continuous obstacle avoidance scenarios, the AMPC method has a smaller lateral tracking error compared to conventional MPC. Compared to AMPC without considering steering delay, its front wheel steering angle input is smoother, demonstrating the role of dynamic modeling of the steering actuator in improving control input smoothness and overall control coordination, while simultaneously balancing lateral trajectory tracking accuracy and vehicle attitude stability.

[0052] Furthermore, the simulation results of continuous obstacle avoidance under low adhesion coefficient conditions are as follows: Figure 7 As shown. Figure 7 (a) shows the lateral position trajectory. The reference trajectory includes two obvious lateral obstacle avoidance adjustments: the first segment has a peak lateral displacement of approximately 3.1m, and the second segment has approximately 3.6m, after which the vehicle gradually returns to the lane. All three methods can complete the obstacle avoidance task, but AMPC and AMPC without considering delay have a higher degree of fit with the reference trajectory, while conventional MPC has a larger deviation during the obstacle avoidance and return-to-center phases. Figure 7 (b) The variation of lateral tracking error with longitudinal displacement is shown. The AMPC error ranges from approximately -0.06 to 0.045 m, with a maximum of approximately 0.06 m. The conventional MPC error ranges more widely, from approximately -0.09 to 0.085 m, with a maximum of approximately 0.09 m. AMPC reduces the maximum error by approximately 33% compared to MPC, and the adaptive adjustment mechanism improves the tracking accuracy of low-adhesion trajectories. Steering delay has a limited impact on the overall error amplitude, but it can improve the smoothness of steering input in local sections. Figure 7 (c) to Figure 7 (e) shows the changes in heading angle error, lateral acceleration, and centroid sideslip angle. Under low adhesion, the vehicle is more sensitive to control inputs. The peak centroid sideslip angle is approximately 1.8°, which is less than ±3.37° of the constraint boundary. The response is continuous, and there is no obvious sideslip instability, indicating that AMPC maintains good vehicle attitude stability while maintaining lateral tracking accuracy. Figure 7 (f) shows the change in front wheel steering angle with longitudinal displacement. AMPC changes smoothly, generally ranging from -1.1° to 1.2°. AMPC, which does not consider steering delay, exhibits local spikes. Conventional MPC has a small amplitude and insufficient response, resulting in a larger lateral error. AMPC demonstrates better steering smoothness. Figure 7 (g) and Figure 7(h) shows the changes in longitudinal speed and longitudinal error with longitudinal displacement, respectively. The vehicle speed can track the reference speed well, without significant overshoot or oscillation, and decreases in stages to balance low-adhesion safety and traffic efficiency. The maximum longitudinal error is approximately 0.12m, indicating good coordination between lateral and longitudinal control. In summary, under low-adhesion conditions, AMPC achieves a good balance between lateral error, front wheel steering angle smoothness, and vehicle attitude stability, and performs better than conventional MPC and AMPC methods that do not consider steering delay.

[0053] In the description of the above embodiments, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0054] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A vehicle adaptive trajectory tracking control method considering steering delay, characterized in that, include: Obtain the vehicle's current status, reference trajectory, and road surface adhesion coefficient; A lateral dynamics model and a trajectory tracking error model are established, and a first-order inertial element is introduced to characterize the steering delay, describing the dynamic response between the front wheel steering angle command and the actual steering angle. An augmented prediction model is constructed, with the reference curvature as the external driver, and the steering actuator is dynamically incorporated into the state space; Establish the objective function and constraints for model predictive control. The objective function includes the weighted sum of output error, control increment and slack variables. The constraints include control increment limit, rotation angle amplitude limit, rotation angle change rate limit, output limit and centroid sideslip angle limit based on adhesion coefficient correction. The prediction time domain is adjusted based on the longitudinal vehicle speed, and normalization factors are constructed based on the adhesion coefficient and reference curvature, respectively, to adjust the output error weight matrix and the control increment weight matrix. The current front wheel steering angle command is obtained based on model predictive control; where: The lateral dynamics model is based on a two-degree-of-freedom single-track model and is used to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the drive matrix multiplied by the reference trajectory curvature. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle from the previous moment. The normalization factor includes the attached normalization factor. curvature normalization factor ; indicates as: ， ； The adjustment of the output error weight matrix and the control increment weight matrix is ​​achieved by adjusting the horizontal error weights respectively. Horizontal error rate of change weight Heading error weights Weight of heading error change rate and control incremental weights The design is implemented as a function that varies with the attachment normalization factor and the curvature normalization factor, expressed as: ； ； ； ； ； in, This represents an estimated value of the road surface adhesion coefficient. Indicates the curvature of the reference trajectory. This represents the preset curvature reference value. , , , , These are the basic weight coefficients for each weight item. , , , , , , and These are the adjustment coefficients for each weighted term, representing either curvature or adhesion coefficient. This indicates the preset exponent parameter.

2. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 1, characterized in that, It also includes vertical collaborative control; The longitudinal coordinated control adopts a series proportional-integral-derivative structure. The outer loop proportional-integral-derivative controller generates a corrected reference speed based on the deviation between the desired longitudinal position and the actual longitudinal position. The inner loop proportional-integral-derivative controller generates longitudinal driving force or braking force based on the deviation between the corrected reference speed and the actual longitudinal speed.

3. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 1, characterized in that, The state equations of the transverse dynamics model include: The total mass of the vehicle multiplied by the lateral acceleration equals the sum of the lateral forces on the front and rear wheels; The yaw moment of inertia multiplied by the yaw angular acceleration equals the front wheel lateral force multiplied by the front wheelbase minus the rear wheel lateral force multiplied by the rear wheelbase. Furthermore, under the linear tire assumption, the lateral forces of the front and rear wheels are equal to the corresponding lateral stiffness multiplied by the lateral slip angle.

4. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 1, characterized in that, The error vector in the trajectory tracking error model includes lateral error, lateral error rate of change, heading error, and heading error rate of change.

5. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 4, characterized in that, In the augmented prediction model: The augmented state vector at the next moment is equal to the discrete state matrix multiplied by the augmented state vector at the current moment, plus the input matrix multiplied by the current feedback control increment, plus the external input matrix multiplied by the current external input vector consisting of the reference curvature driving term and the reference heading angle change rate.

6. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 1, characterized in that, The objective function includes: The weighted sum of the squares of the output error vectors at each prediction time point in the prediction time domain is added to the weighted sum of the squares of the control increment vectors at each time point in the control time domain, and then the square of the slack variable is multiplied by the penalty coefficient.

7. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 1, characterized in that, The centroid sideslip angle limiting based on the adhesion coefficient correction is: The absolute value of the centroid sideslip angle is less than or equal to an upper limit function that monotonically increases with the road surface adhesion coefficient. This upper limit function increases accordingly when the adhesion is high.

8. The vehicle adaptive trajectory tracking control method considering steering delay according to claim 1, characterized in that, The method for adjusting the prediction time domain based on longitudinal vehicle speed is as follows: Based on the optimized selection results of the prediction time domain at different vehicle speeds, the prediction time domain is adaptively adjusted online.

9. A vehicle adaptive trajectory tracking control system that considers steering delay, characterized in that, The vehicle adaptive trajectory tracking control method considering steering delay, as described in any one of claims 1 to 8, comprises: The information acquisition module is used to acquire the vehicle's current status, reference trajectory, and road surface adhesion coefficient; The dynamics modeling module is used to establish the lateral dynamics model and the trajectory tracking error model, and introduces a first-order inertial element to characterize the steering delay and describe the dynamic response between the front wheel steering angle command and the actual steering angle. The lateral dynamics model is based on a two-degree-of-freedom single-track model and is used to describe the relationship between the vehicle's lateral acceleration and yaw acceleration and the lateral forces of the front and rear wheels. The continuous-time error state equation of the trajectory tracking error model is: the first derivative of the error vector is equal to the sum of the system matrix multiplied by the error vector, the input matrix multiplied by the actual front wheel steering angle, and the drive matrix multiplied by the curvature of the reference trajectory. The prediction model building module is used to build an augmented prediction model, which uses the reference curvature as an external drive and dynamically incorporates the steering actuator into the state space. The augmented prediction model is constructed by discretizing the continuous-time error state equation using the forward Euler method and introducing an augmented state vector that includes the error vector, the actual front wheel steering angle, and the feedback correction steering angle of the previous moment. The optimization problem establishment module is used to establish the objective function and constraints of model predictive control. The objective function includes the weighted sum of output error, control increment and slack variables. The constraints include control increment limit, rotation angle amplitude limit, rotation angle change rate limit, output limit and centroid sideslip angle limit based on adhesion coefficient correction. The parameter adaptive module is used to adjust the prediction time domain according to the longitudinal vehicle speed, construct normalization factors according to the adhesion coefficient and reference curvature respectively, and adjust the output error weight matrix and control increment weight matrix. The control variable solving module is used to obtain the current front wheel steering angle command based on model predictive control.

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