An intelligent vehicle trajectory tracking and stability control system and method based on adaptive model predictive control

Abstract

The application discloses an intelligent automobile track tracking and stability control system and method based on adaptive model predictive control, proposes an adaptive preview error model, an adaptive forgetting factor recursive least square estimator and an integrated controller, in view of the problem that a conventional preview model only changes a preview distance according to a vehicle speed, considers the influence of a road surface adhesion coefficient on the intelligent automobile, designs two preview distance switching modes based on the vehicle speed and the road surface adhesion coefficient, and makes switching soft constraints at the switching points of the vehicle speed and the road surface adhesion coefficient, so that the switching mode is prevented from being repeatedly switched, and the system stability is improved; in view of the variable road conditions that the intelligent automobile may actually face, the tire side stiffness and the road surface adhesion coefficient are estimated on line, an adaptive forgetting factor is introduced to coordinate the balance between the convergence speed and the identification error, the precision of the prediction model is effectively improved, and the stability of the vehicle is improved based on the adaptive adjustment of the control amount constraint of the road surface adhesion coefficient.

Description

Technical Field

[0001] This invention relates to the field of intelligent vehicle control technology, and in particular to an intelligent vehicle trajectory tracking and stability control system and method based on adaptive model predictive control. Background Technology

[0002] With the rapid development of sensor technology, in-vehicle computers, and artificial intelligence, autonomous driving technology has become a global research hotspot in the past decade. Autonomous driving integrates perception, planning, and motion control, with trajectory tracking control being a key technology. The main purpose of trajectory tracking is to accurately track a reference trajectory by eliminating tracking deviations. Trajectory tracking control methods mainly include feedforward feedback control, proportional-integral-derivative control, and sliding mode control. Among these, model predictive control, with its predictive characteristics, ability to handle multi-objective optimization and constrained problems, and strong robustness, is widely used.

[0003] Currently, model predictive control generally uses fixed model parameters. However, due to the complex and varied actual operating conditions of intelligent vehicles, influenced by factors such as road curvature, road surface adhesion coefficient, tire lateral stiffness, and vehicle speed, this reduces model accuracy. Furthermore, using fixed constraints is detrimental to the control of intelligent vehicles, leading to a decline in vehicle trajectory tracking capabilities. In addition, conventional aiming error models based on speed changes do not consider variations in the road surface adhesion coefficient. Different road conditions have different requirements for aiming distance, thus necessitating improvements in the adaptive control capabilities of intelligent vehicles. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes an intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control. It mainly comprises four parts: an adaptive preview error model, an adaptive forgetting factor recursive least squares estimator, a lateral controller, and a torque distribution controller.

[0005] The adaptive anti-aiming error model comprehensively considers the different requirements of road curvature, road surface adhesion coefficient, and vehicle speed on anti-aiming distance, and designs switching modes and soft constraints to construct an adaptive anti-aiming error model. A vehicle physical model is also constructed through some simplifications and assumptions. These two models are combined as the prediction model for the model predictive controller, and the control quantity is obtained by solving this model.

[0006] Adaptive Forgetting Factor Recursive Least Squares Estimator: In real-world applications of intelligent vehicles, the road adhesion coefficient and tire side stiffness vary constantly with different operating conditions. Therefore, an adaptive forgetting factor recursive least squares estimator is used to estimate tire side stiffness and road adhesion coefficient. An adaptive forgetting factor is introduced to balance convergence speed and identification error. Accurate tire side stiffness estimation helps improve the accuracy of the model predictive controller (MMC) model, while estimating the road adhesion coefficient allows for real-time adjustments to control constraints, improving the MMC's tracking performance and safety.

[0007] Lateral controller: A model predictive controller is used for lateral control. Its function is to collect the vehicle's state variables and, based on the established predictive model, perform optimal solutions while satisfying the design objective function and constraints. The solution determines the front wheel steering angle acting on the actual vehicle to minimize the error between the actual vehicle trajectory and the reference trajectory. At the same time, the additional yaw moment is solved as the expected value and output to the torque distribution control for torque distribution to achieve stability control.

[0008] Torque distribution controller: The additional yaw moment and longitudinal force output by the controller are optimally distributed to the torque while meeting the design objective function and constraints. The influence of tire slip ratio is also taken into account for further optimization, and then applied to the actual vehicle to achieve stability control and assist the vehicle's trajectory tracking, thereby reducing trajectory tracking errors.

[0009] Furthermore, the vehicle physical model proposed in this invention, which is also the vehicle dynamics model, makes the following assumptions: Ignoring the vehicle's vertical, roll, and pitch motions, the vehicle is simplified to a two-degree-of-freedom dynamic model, with the vehicle only moving within the xoy plane. The vehicle is front-wheel steering, and the vehicle's coordinate system lies within a plane symmetrical to the vehicle's left and right sides. The origin of the vehicle's center of mass is O, the x-axis is the vehicle's longitudinal axis with its positive direction pointing towards the front, the y-axis points laterally and its positive direction follows the right-hand rule, and the z-axis is vertically upward. Therefore, according to Newton's second law, rotational equilibrium and force equilibrium equations are established at the vehicle's center of mass, yielding the following expression:

[0010]

[0011] Where m is the vehicle mass, V x Let β be the longitudinal velocity of the vehicle's center of mass in the vehicle's coordinate system, β be the sideslip angle of the vehicle's center of mass, and γ be the yaw rate of the vehicle. z Let l be the moment of inertia of the vehicle about the z-axis. f and l r F represents the distance from the vehicle's center of gravity to the front and rear axles, respectively. yfl F yfr F yrl F yrrThese are the lateral forces acting on the four wheels of the vehicle, M and M respectively. z To add yaw moment.

[0012] Based on the above assumptions, we can conclude that the tire lateral force is directly proportional to the tire slip angle, as shown in the following expression:

[0013]

[0014]

[0015] Among them, F yf and F yr C represents the resultant lateral forces acting on the wheels of the front and rear axles of the vehicle. f and C r α represents the lateral stiffness of the front and rear wheels of the vehicle, respectively. f and α r These are the slip angles of the front and rear wheels of the vehicle, δ, respectively. f This refers to the steering angle of the front wheels.

[0016] The expression for the two-degree-of-freedom model is obtained as follows:

[0017]

[0018] In general, β and The value is relatively small, close to 0, so the vehicle yaw angle can be considered to be approximately equal to the heading angle.

[0019] The pre-aiming error model expression is as follows:

[0020]

[0021] in, The desired heading angle of the aiming point. The vehicle's current heading angle. Let e ​​be the heading angle deviation of the aiming point, and let e be the difference between the desired heading angle and the vehicle's current heading angle. d For lateral deviation, e d0 L is the distance between the extended line of the aiming point and the current vehicle's center of mass along the y-axis of the vehicle coordinate system. p This is the pre-aiming distance.

[0022] From the above formula, we can derive:

[0023]

[0024] Where κ is the road curvature of the aiming point.

[0025] The decision module collects information on road curvature, road surface adhesion, and vehicle speed. Taking into account the controller's computational burden, stability, and safety, it designs two aiming distance switching modes based on the road surface adhesion coefficient and vehicle speed, respectively.

[0026] Based on real vehicle test data, the road surface adhesion coefficient is divided into three types: dry road surface with a road surface adhesion coefficient of 0.7-1, wet road surface with a road surface adhesion coefficient of 0.5-0.7, and icy / snowy road surface with a road surface adhesion coefficient of 0.3-0.5.

[0027] On dry roads, intelligent vehicles exhibit good tracking performance and control capabilities. To prevent excessive computational burden on the controller, a speed-based pre-aiming distance mode is adopted, expressed as follows:

[0028]

[0029] Among them, L pmin The minimum aiming distance is set to 6m, L pmax The maximum aiming distance is set to 20m, V min and V max The minimum and maximum speeds are designed to be 6 m / s and 20 m / s respectively. p The aiming time is set to 1 second.

[0030] On wet and icy roads, stability and safety are even more critical. The intelligent vehicle's control capabilities decrease, and even at low speeds, it must consider road curvature at long lead-in distances to react early. Therefore, a lead-in distance model based on the road adhesion coefficient is adopted, expressed as follows:

[0031]

[0032] Among them, L p1 and L p2 These are two aiming distances for the switching mode, with values ​​set to 20m and 23m respectively.

[0033] To prevent the frequent switching of the aiming distance mode from affecting the control, boundary fuzzy control is established at the road adhesion coefficient boundary, forming a soft constraint of ±0.1 on the road adhesion coefficient; boundary fuzzy control is also established at the vehicle speed boundary, forming a soft constraint of ±2m / s on the vehicle speed. Once the soft constraints are formed, the aiming distance mode can only be switched after these soft constraints are exceeded.

[0034] Combining the two-degree-of-freedom dynamic model and the aiming error model, the prediction equation of the model predictive controller can be obtained, as shown in the following expression:

[0035]

[0036] An adaptive forgetting factor recursive least squares estimator is used to estimate tire lateral stiffness and road adhesion coefficient, respectively. The formula for the recursive least squares method with forgetting factor is as follows:

[0037] z(k) = h T (k)θ(k)+e(k)

[0038]

[0039]

[0040] Where z(k) is the system output at time k, h(k) is the system input, θ(k) is the parameter to be identified, e(k) is the measurement noise, K(k) is the algorithm gain, P(k) is the covariance matrix, and λ m It is a forgetting factor.

[0041] In the estimation of tire lateral stiffness, z(k) represents F yf and F yr h(k) are respectively α f and α r θ(k) are C f and C r The tire lateral force and slip angle are input as known quantities to the estimator, and then the estimated value of the slip stiffness is obtained from the estimated quantities.

[0042] When the tire is in a low slip ratio range, the road adhesion rate and slip ratio are approximately proportional, so the following expression can be obtained:

[0043]

[0044] Among them, F x For the longitudinal force of the tire, F z For the vertical force of the tire, k r denoted as the slope of the adhesion-slip ratio curve in the low slip ratio range, and s as the tire slip ratio.

[0045] The slip ratio is defined as follows:

[0046]

[0047] Where R is the wheel radius, ω is the wheel rolling angular velocity, and v is the velocity of the wheel center. In the estimation of the road surface adhesion coefficient, h(k) is s, θ(k) is k r After calculating the slope of the adhesion rate-slip rate curve using the tire longitudinal force, vertical force, and tire slip ratio as known quantities, the road adhesion coefficient is calculated using the following formula:

[0048] μ = k r s mp

[0049] Where μ is the road surface adhesion coefficient, s m denoted as the maximum tire slip ratio within the linear region, and p is the ratio of the maximum road adhesion coefficient to the peak road adhesion coefficient within the linear region.

[0050] The forgetting factor is used to assign weights to old and new data, and is typically set to 0.98. However, when the identification parameter error is small, introducing the forgetting factor can increase the error of the online identification parameters. Conversely, when the online identification error is large, the forgetting factor needs to be optimized to enable faster convergence and reduce the identification error. Therefore, the forgetting factor should be designed to adapt to the error. To meet these requirements, the following expression is proposed for calculating the adaptive forgetting factor:

[0051] λ(k)=λ min +(1-λ min )h ε(k)

[0052]

[0053] Where λ(k) is the forgetting factor at time k, λ min Let h be the minimum value of the forgetting factor, and h be the sensitivity coefficient, representing the sensitivity of the forgetting factor to errors. e(k) is the error at time k. base This serves as a reference for acceptable error.

[0054] Replace λ with λ(k) m The final expression for the adaptive forgetting factor recursive least squares method is as follows:

[0055]

[0056] The lateral controller employs a model predictive controller, expressing the prediction equations in state equation form:

[0057]

[0058] in, Let x be the rate of change of the system state variable, y be the system state variable, u be the control input, w be the disturbance variable, and A be the system output variable. c B c D c C c The coefficient matrix is ​​calculated as follows:

[0059]

[0060] u = [δ f M z ] T

[0061] w = κ

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] Discretizing the state equations yields the following expression:

[0068]

[0069] Among them, A=I+A c T s B = B c T s D = D c T s T s This is the controller sampling time.

[0070] To facilitate the control and constraint of the control increment, the state variables and control variables are combined as new system state variables, resulting in a new state equation, expressed as follows:

[0071]

[0072] in, The new coefficient matrix is ​​calculated as follows:

[0073]

[0074] The prediction equations for the future state of the vehicle and the system output are as follows:

[0075]

[0076] In the above formula,

[0077] ΔU(k)=[Δu(k),Δu(k+1),...Δu(k+N c -1)] T

[0078] W(k) = [w(k), w(k+1), ..., w(k+N)] c -1)] T

[0079]

[0080]

[0081]

[0082] Where, N p For the model predictive controller prediction time domain, N c For the model predictive controller, control time domain.

[0083] To ensure that the lateral controller can accurately track the trajectory and maintain stability, the following objective function is established:

[0084]

[0085] Among them, Y ref (k) represents the expected value of the system output at time k, Y ref (k)-Y(k) represents the system output error, Q and R are the weights of the error and control increment, respectively, ρ is the weighting coefficient, and ε is the relaxation factor.

[0086] The controller constraints are designed as follows:

[0087] δ fmin ≤δ f ≤δ fmax Δδ fmin ≤Δδ≤Δδ max

[0088] M zmin ≤M z ≤M zmax ΔM zmin ≤ΔM z ≤ΔM zmax

[0089] Where, δ fmin and δ fmax M represents the minimum and maximum values ​​of the front wheel steering angle, respectively. zmin and M zmax These are the minimum and maximum values ​​of the additional yaw moment, Δδ, respectively. fmin and Δδ max These are the minimum and maximum values ​​of the front wheel steering angle increment, ΔM. zmin and ΔM zmax These are the minimum and maximum values ​​of the additional yaw moment increment, respectively.

[0090] The final objective function and constraint expressions are as follows:

[0091]

[0092] Wherein, ΔU min and ΔU maxThese represent the minimum and maximum values ​​of the control increment, U. min and U max These are the minimum and maximum values ​​of the control quantity, respectively.

[0093] The lateral controller obtains the optimal front wheel steering angle and additional yaw moment based on the objective function and constraints. The control quantity constraints and control increment constraints in this invention can be changed according to the road adhesion coefficient estimated by the adaptive forgetting factor recursive least squares method. The road surface is dry, and the constraint design is U. min U max ΔU min ΔU max The road surface is wet and slippery; the constraint has been updated to 0.8U. min 0.8U max 0.7ΔU min 0.7ΔU max The road surface is icy and snowy, and the constraint has been updated to 0.5U. min 0.5U max 0.4ΔU min 0.4ΔU max .

[0094] To consider vehicle stability and the impact of tire slip ratio while tracking trajectory, this invention proposes a torque distribution controller. The objective function is designed considering three points: First, the sum of the torques of each wheel must equal the total torque required to track the longitudinal velocity. The total torque is the torque required to maintain the current longitudinal velocity and is obtained from the error between the desired and actual longitudinal velocities. Second, the driving force of each wheel should satisfy the additional yaw moment provided by the model predictive controller. Finally, the low energy consumption requirement during intelligent vehicle operation is considered. Therefore, the objective function for optimal torque distribution is designed as follows:

[0095]

[0096] Where HT-V represents the total torque and additional yaw moment that need to be satisfied, σ and Q1 are their weighting factors, and T is the matrix form of the torques of the four wheels. min and T max To satisfy the minimum and maximum torque values ​​of the tire friction elliptic limit, the matrix expressions for H, T, V, and R1 are calculated as follows:

[0097]

[0098]

[0099]

[0100] Where d is the wheel track.

[0101] The objective function is transformed into a quadratic programming problem, and the torque of each wheel is solved. The slip ratio is then used to adjust the final torque output. As the slip ratio changes, the longitudinal force of the wheel exhibits a stable region that increases from a small value to a large value, and an unstable region that gradually decreases from its peak value. Based on this characteristic, the optimal wheel slip ratio is estimated, as expressed below:

[0102]

[0103] Among them, F x s(k) and s(k) are the longitudinal force and slip ratio of the wheel at time k after discretization, respectively, and ΔF x Δs is the difference between the current time and the previous time, when ΔF x When s is approximately equal to 0 and Δs is greater than 0, d The optimal wheel slip ratio.

[0104] The expression for the desired wheel rolling angular velocity, derived from the optimal wheel slip ratio, is as follows:

[0105]

[0106] Where, ω d Let the desired wheel rolling angular velocity be denoted by . Torque is adjusted using sliding mode control. The design expression and reaching law of the sliding surface are as follows:

[0107]

[0108] Among them, s ω For sliding surface, Sat(s) is the derivative of the sliding surface. ω Let ) be the saturation function, and its design is as follows:

[0109]

[0110] Here, Δ is a relatively small design parameter.

[0111] In the design of the reaching law, decreasing the coefficient ε can reduce system chattering, but it will cause the system to tend towards stability and reduce speed. Finally, the torque related to the wheel slip ratio can be considered, as expressed below:

[0112] T d =J w [ω d -ε ω sat(s ω )]+T

[0113] Among them, T d J is the final wheel torque acting on the intelligent vehicle. w Let ε be the moment of inertia of the wheel. ω A coefficient that is greater than 0.

[0114] The beneficial effects of this invention are:

[0115] 1. The adaptive anti-aiming error model proposed in this invention addresses the problem of conventional anti-aiming models only changing the anti-aiming distance based on vehicle speed. It considers the impact of road surface adhesion coefficient on intelligent vehicles and designs two anti-aiming distance switching modes: one based on vehicle speed and the other on road surface adhesion coefficient. These modes are incorporated into the model's predictive controller equations and soft constraints are applied at the switching points between vehicle speed and road surface adhesion coefficient to avoid repeated mode switching and improve system stability. This model is applicable to trajectory tracking at different vehicle speeds and considers the additional anti-aiming distance requirements of intelligent vehicles on low-adhesion surfaces, in addition to vehicle speed, thus improving the safety of intelligent vehicles.

[0116] 2. The adaptive forgetting factor recursive least squares estimator proposed in this invention estimates tire lateral stiffness and road adhesion coefficient online for the ever-changing road conditions that intelligent vehicles may face. It introduces an adaptive forgetting factor to balance the convergence speed and identification error, effectively improving the accuracy of the prediction model. Furthermore, it updates the constraints of control quantity and control increment as the road adhesion coefficient changes, significantly improving the adaptive trajectory tracking capability and safety of intelligent vehicles under various operating conditions.

[0117] 3. The torque distribution controller proposed in this invention provides a new torque distribution strategy for four-wheeled intelligent vehicles and tire characteristics. It adjusts the torque output according to the slip ratio, which improves vehicle stability while ensuring the tracking accuracy of intelligent vehicles compared to the conventional average torque distribution strategy. Attached Figure Description

[0118] Figure 1 This is a two-degree-of-freedom dynamic model for the vehicle.

[0119] Figure 2 An adaptive aiming error model;

[0120] Figure 3 This is a flowchart of the intelligent vehicle trajectory tracking and stability control method based on adaptive model predictive control according to the present invention. Detailed Implementation

[0121] The invention will now be further described with reference to the accompanying drawings.

[0122] Figure 1This is a two-degree-of-freedom dynamics model of a vehicle. Vertical, roll, and pitch motions are neglected; the vehicle only moves within the xoy plane. The vehicle is front-wheel steering, and the vehicle's coordinate system lies in a plane symmetrical to the vehicle's left and right sides. The origin, O, is the vehicle's center of mass. The x-axis is the vehicle's longitudinal axis, with its positive direction pointing towards the front of the vehicle. The y-axis points laterally, with its positive direction following the right-hand rule. The z-axis points vertically upwards. Therefore, according to Newton's second law, rotational and force equilibrium equations are established at the vehicle's center of mass, yielding the following expression:

[0123]

[0124] Where m is the vehicle mass, V x Let β be the longitudinal velocity of the vehicle's center of mass in the vehicle's coordinate system, β be the sideslip angle of the vehicle's center of mass, and γ be the yaw rate of the vehicle. z Let l be the moment of inertia of the vehicle about the z-axis. f and l r F represents the distance from the vehicle's center of gravity to the front and rear axles, respectively. yfl F yfr F yrl F yrr These are the lateral forces acting on the four wheels of the vehicle, fl for the left front wheel, fr for the right front wheel, rl for the left rear wheel, rr for the right rear wheel, and M. z To add yaw moment.

[0125] Based on the above assumptions, we can consider the tire lateral force to be directly proportional to the tire slip angle, resulting in the following expression:

[0126]

[0127]

[0128] Among them, F yf and F yr These are the resultant lateral forces of the wheels acting on the front and rear axles of the vehicle, C. f and C r α represents the lateral stiffness of the front and rear wheels of the vehicle, respectively. f and α r These are the slip angles of the front and rear wheels of the vehicle, δ, respectively. f This refers to the steering angle of the front wheels.

[0129] The expression for the two-degree-of-freedom model is obtained as follows:

[0130]

[0131] Figure 2 For the aiming error model, since in general, the centroid sideslip angle β and its derivative... Since the value is relatively small, close to 0, the vehicle yaw angle can be considered approximately equal to the heading angle. Therefore, the expression for the aiming error model is as follows:

[0132]

[0133] in, The desired heading angle of the aiming point. The vehicle's current heading angle. Let e ​​be the heading angle deviation of the aiming point, and let e be the difference between the desired heading angle and the vehicle's current heading angle. d For lateral deviation, e d0 L is the distance between the extended line of the aiming point and the current vehicle's center of mass along the y-axis of the vehicle coordinate system. p Pre-aiming distance

[0134] From the above formula, we can derive:

[0135]

[0136] Where κ is the road curvature of the aiming point.

[0137] Combining the two-degree-of-freedom dynamic model and the aiming error model, the prediction equation of the model predictive controller can be obtained, as shown in the following expression:

[0138]

[0139] Figure 3 This is a flowchart of a trajectory tracking and stability control method for intelligent vehicles based on adaptive model predictive control. When the intelligent vehicle performs trajectory tracking, the adaptive forgetting factor recursive least squares estimator first calculates the wheel lateral stiffness and road adhesion coefficient online based on relevant information collected by the vehicle's sensors, and updates the prediction model, control variables, and control increment constraints in real time. Then, the adaptive preview error model receives the reference trajectory and road adhesion coefficient information from the upper-level trajectory planning module, determines the preview distance through the decision module, and calculates the lateral error, preview point heading error, and preview point curvature, which are then transmitted to the model predictive controller. The model predictive controller then obtains the front wheel steering angle and additional yaw moment through optimal solution. The longitudinal controller compares the difference between the desired longitudinal speed and the actual speed to calculate the vehicle's longitudinal force. Finally, the torque distribution controller distributes torque, considering the influence of wheel slip ratio, and adjusts the torque of each wheel to obtain the final wheel torque, which, together with the front wheel steering angle, controls the intelligent vehicle for trajectory tracking and stability control.

[0140] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. All equivalent methods or modifications that do not depart from the technology of the present invention should be included within the scope of protection of the present invention.

Claims

1. An intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control, characterized in that, include: Adaptive preview error model, adaptive forgetting factor recursive least squares estimator, lateral controller, torque distribution controller; The adaptive anti-aiming error model comprehensively considers the different requirements of road curvature, road surface adhesion coefficient and vehicle speed on anti-aiming distance, designs switching modes and soft constraints, and constructs an adaptive anti-aiming error model. Two aiming distance switching modes based on road surface adhesion coefficient and vehicle speed were designed respectively. Boundary fuzzy control was established at the boundary of road surface adhesion coefficient to form a soft constraint of ±0.1 on the road surface adhesion coefficient; boundary fuzzy control was established at the boundary of vehicle speed to form a soft constraint of ±2m / s on the vehicle speed. Once a soft constraint is formed, it must be overcome before the aiming distance mode can be switched. Adaptive forgetting factor recursive least squares estimator: used to accurately estimate tire lateral stiffness and road adhesion coefficient, and introduces an adaptive forgetting factor to balance convergence speed and identification error; Lateral controller: A model predictive controller is used for lateral control. The model predictive controller uses an adaptive anticipation error model and a two-degree-of-freedom vehicle model as prediction models. The control quantity is obtained by solving this model. Its function is to collect the state quantity of the vehicle. Based on the established prediction model, the optimal solution is performed under the condition of satisfying the design objective function and constraints. The front wheel steering angle is calculated to act on the actual vehicle, so as to minimize the error between the actual driving trajectory and the reference trajectory. At the same time, the additional yaw moment is calculated as the expected value and output to the torque distribution controller for torque distribution to achieve stability control. The lateral controller adopts a model predictive controller, and the prediction equation is written in the form of a state equation: in, Let x be the rate of change of the system state variable, y be the system state variable, u be the control input, and w be the disturbance variable. For a matrix, the specific calculation is as follows: Discretizing the state equations yields the following expression: in, , , ; Combining the state variables and control variables as new system state variables yields a new state equation, expressed as follows: in, The new matrix is ​​calculated as follows: ， ， ， The prediction equations for the future state of the vehicle and the system output are as follows: In the above formula, Establish the following objective function: in, This represents the expected value of the system output at time k. This represents the system output error, where Q and R are the weights of the error and control increment, respectively. These are the weighting coefficients. It is a relaxation factor; The lateral controller constraint design is as follows: in, and These are the minimum and maximum values ​​of the front wheel steering angle, respectively. and These are the minimum and maximum values ​​of the additional yaw moment, respectively. and These are the minimum and maximum values ​​of the front wheel steering angle increment, respectively. and These are the minimum and maximum values ​​of the additional yaw moment increment, respectively; The final objective function and constraint expressions are as follows: in, and These represent the minimum and maximum values ​​of the control increment, respectively. and These are the minimum and maximum values ​​of the control quantity, respectively. The lateral controller solves for the optimal front wheel steering angle and additional yaw moment based on the objective function and constraints; the torque distribution controller optimizes the distribution of the additional yaw moment and longitudinal force output by the lateral controller under the condition of satisfying the design objective function and constraints, and takes into account the influence of tire slip ratio, and applies the optimized torque to the actual vehicle to achieve stability control and assist the vehicle's trajectory tracking. The objective function of the torque distribution controller is calculated as follows: in, This indicates the total torque and additional yaw moment that need to be satisfied. and Its weighting factor, It is a matrix representation of the torques of the four wheels. and To satisfy the minimum and maximum torque values ​​of the tire friction elliptic limit, H, T, V, The matrix expression is calculated as follows: Where d is the wheel track; The objective function is transformed into a quadratic programming problem, and the torque of each wheel is solved. The slip ratio is then used to adjust the final torque output. As the slip ratio changes, the longitudinal force of the wheel exhibits a stable region that increases from a small value to a large value, and an unstable region that gradually decreases from its peak value. Based on this characteristic, the optimal wheel slip ratio is estimated, as expressed below: in, and These represent the longitudinal force and slip ratio of the wheel at time k after discretization. and The difference between the current time and the previous time is when Approximately equal to 0 and When greater than 0, The optimal wheel slip ratio; The expression for the desired wheel rolling angular velocity, derived from the optimal wheel slip ratio, is as follows: in, To determine the desired wheel rolling angular velocity, sliding mode control is used to adjust the torque. The design expression and reaching law of the sliding surface are as follows: In the design of the reaching law, the coefficient Reducing the torque can decrease system chattering, but it will cause the system to tend to stabilize and reduce speed. Ultimately, the torque related to wheel slip ratio can be considered, as expressed below: in, For the wheel torque that ultimately acts on the intelligent vehicle, Let be the moment of inertia of the wheel.

2. The intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control according to claim 1, characterized in that, The two-degree-of-freedom model of the vehicle: Assuming the vehicle is front-wheel steering, the vehicle's coordinate system lies in a plane symmetrical to the vehicle's left and right sides. The origin, O, is the vehicle's center of mass. The x-axis is the vehicle's longitudinal axis, with its positive direction pointing towards the front of the vehicle. The y-axis points towards the side of the vehicle, with its positive direction following the right-hand rule. The z-axis points vertically upward. According to Newton's second law, the rotational equilibrium and force equilibrium equations are established at the vehicle's center of mass, yielding the following expression: in, For vehicle quality, Let be the longitudinal velocity of the center of mass in the vehicle body coordinate system. The sideslip angle is the angle at the vehicle's center of gravity. Let yaw rate be the vehicle's angular velocity. Let be the moment of inertia of the vehicle about the z-axis. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. These are the lateral forces acting on the four wheels of the vehicle. To add yaw moment; The lateral force of a tire is directly proportional to the tire slip angle, as shown in the following expression: in, and These are the resultant lateral forces acting on the wheels of the front and rear axles of the vehicle, respectively. and These are the lateral stiffness of the front and rear wheels of the vehicle, respectively. and These are the slip angles of the front and rear wheels of the vehicle, respectively. The steering angle of the front wheels; The expression for the two-degree-of-freedom model is obtained as follows: in and When the value is close to 0, the vehicle yaw angle is approximately equal to the heading angle.

3. The intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control according to claim 1, characterized in that, The pre-aiming error model expression is as follows: in, The desired heading angle of the aiming point. The vehicle's current heading angle. Here, represents the heading angle deviation of the aiming point, and represents the difference between the desired heading angle and the vehicle's current heading angle. This is the lateral deviation. This represents the distance between the extended line of the pre-aiming point and the current vehicle's center of mass along the y-axis of the vehicle coordinate system. Pre-aiming distance; From the above formula, we can obtain: in The road curvature is the target point.

4. The intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control according to claim 1, characterized in that, The adaptive anti-aiming error model includes two anti-aiming distance switching modes: one based on the road surface adhesion coefficient and the other based on vehicle speed. The road surface adhesion coefficient is divided into three types: dry road surface, wet and slippery road surface, and icy and snowy road surface; On dry roads, a speed-based aiming distance mode is used, expressed as follows: in, To minimize the aiming distance, For maximum aiming distance, and These are the minimum speed and the maximum speed, respectively. Pre-aiming time; For wet and slippery roads and icy roads, a pre-aiming distance mode based on the road adhesion coefficient is adopted, as shown in the following expression: in, and They are set to 20m and 23m respectively.

5. The intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control according to claim 1, characterized in that, The prediction equation of the model predictive controller is as follows: 。 6. The intelligent vehicle trajectory tracking and stability control system based on adaptive model predictive control according to claim 1, characterized in that, The adaptive forgetting factor recursive least squares estimator: The formula for recursive least squares with a forgetting factor is as follows: in, This is the system output at time k. For system input, The parameters to be identified. To measure noise, For algorithm gain, Let covariance matrix be the variance matrix. Forgetting factor; In the estimation of tire lateral stiffness, They are respectively and , They are respectively and , They are respectively and The tire lateral force and slip angle are input as known quantities to the estimator, and then the estimated value of the slip stiffness is obtained from the estimated quantities. When the tire is in a low slip ratio range, the road adhesion rate and slip ratio are approximately proportional, so the following expression can be obtained: in, For the longitudinal force of the tire, The vertical force of the tire. This represents the slope of the adhesion-slip ratio curve in the low slip ratio range. This refers to the tire slip ratio; The slip ratio is defined as follows: in, For the wheel radius, The angular velocity of the wheel. Let be the speed at the wheel center, used in estimating the road surface adhesion coefficient. , for , for After calculating the slope of the adhesion rate-slip rate curve using the tire longitudinal force, vertical force, and tire slip ratio as known quantities, the road adhesion coefficient is calculated using the following formula: in, The road surface adhesion coefficient, denoted as the maximum tire slip ratio within the linear region, and p is the ratio coefficient between the maximum road adhesion coefficient and the peak road adhesion coefficient within the linear region. The forgetting factor is used to assign weights to the old and new data. It is designed to adapt to changes in error. The specific calculation expression is as follows: in, Let k be the forgetting factor at time k. Let h be the minimum value of the forgetting factor, and h be the sensitivity coefficient, representing the sensitivity of the forgetting factor to errors. Let k be the error at time k. This serves as a reference for permissible errors; use Alternative The final expression for the adaptive forgetting factor recursive least squares method is as follows: 。 7. A method for an intelligent vehicle trajectory tracking and stability control system based on the adaptive model predictive control described in claim 1, characterized in that, When an intelligent vehicle performs trajectory tracking, the adaptive forgetting factor recursive least squares estimator first calculates the wheel lateral stiffness and road adhesion coefficient online based on relevant information collected by the sensors on the intelligent vehicle, and updates the prediction model, control quantity, and control increment constraints in real time. Then, the adaptive aiming error model receives the reference trajectory and road adhesion coefficient information from the estimator provided by the upper-level trajectory planning module, determines the aiming distance through the decision module, calculates the lateral error, aiming point heading error, and aiming point curvature, and transmits them to the model predictive controller. The model predictive controller obtains the front wheel steering angle and additional yaw moment through optimal solution. The longitudinal controller compares the difference between the expected longitudinal vehicle speed and the actual vehicle speed, calculates the vehicle's longitudinal force, and transmits it to the torque distribution controller. Finally, the torque distribution controller performs torque distribution, considers the influence of wheel slip ratio, adjusts the torque of each wheel to obtain the final wheel torque, and controls the intelligent vehicle for trajectory tracking and stability control together with the front wheel steering angle.

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