Intelligent automobile path tracking and yaw stability adaptive cooperative control method based on security set constraint

Abstract

The invention discloses an intelligent automobile path tracking and yaw stability self-adaptive cooperative control method based on safety set constraint. The method comprises the following steps: step 1) establishing a vehicle dynamics model and a vehicle path tracking model considering active yaw moment; 2) constructing a self-adaptive cooperative control prediction output equation; 3) constructing a safety set of the side slip angle and the yaw velocity; 4) outputting an output variable, a control increment and a self-adaptive weight matrix of control input by utilizing a self-adaptive multi-target coordination strategy; 5) constructing and solving a quadratic programming optimization problem to obtain an optimal control input parameter; 7, the optimal front wheel steering angle and the additional torque of each tire are transmitted to a vehicle running mechanism, and execution of a control instruction is completed. While the tracking precision is ensured, the dynamic behavior of the vehicle is restrained in advance, active and smooth stability management is achieved, and the comprehensive performance and the safety level of the vehicle in a complex scene are improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent vehicle motion control, specifically to an adaptive cooperative control method for intelligent vehicle path tracking and yaw stability based on safety set constraints. Background Technology

[0002] Path tracking and yaw stability control are two key issues in the field of intelligent vehicle motion control, directly affecting vehicle driving safety and performance. Path tracking control aims to enable the vehicle to travel accurately and smoothly along a predetermined trajectory, suitable for normal driving conditions; while yaw stability control focuses on maintaining vehicle attitude stability under extreme conditions (such as high-speed cornering, low-friction surfaces, etc.), preventing instability, and ensuring vehicle handling safety. In existing research, path tracking control and yaw stability control are usually designed as relatively independent subsystems, or simply coupled through weight coordination. However, in complex and ever-changing real-world driving scenarios, there is an inherent conflict between the two objectives: in pursuit of higher path tracking accuracy, control commands may cause the vehicle to move to the dynamic boundary, thereby compromising yaw stability; conversely, overemphasizing stability intervention may significantly reduce the accuracy and smoothness of trajectory tracking. This contradiction is particularly prominent when the vehicle is at its dynamic limits or when road conditions change drastically, posing a serious challenge to the overall performance and safety of intelligent vehicles. Furthermore, traditional yaw stability control often employs rule-based or threshold-based reactive constraint strategies, which are only activated and corrected after the vehicle's state (such as yaw rate, sideslip angle, etc.) reaches a preset safety boundary. This method is a "remedial" control, which suffers from response lag, making it difficult to adjust the vehicle's attitude smoothly and promptly. Moreover, the system is often already in a suboptimal state when control intervenes, affecting not only ride comfort but also potentially failing to completely avoid instability risks due to the late intervention. Summary of the Invention

[0003] The purpose of this invention is to provide an adaptive cooperative control method for path tracking and yaw stability of intelligent vehicles based on safety set constraints, comprising the following steps:

[0004] Step 1) Establish a vehicle dynamics model and a vehicle path tracking model that consider active yaw moment;

[0005] Step 2) Based on the vehicle dynamics model and path tracking model, construct an adaptive cooperative control predictive output equation that considers the path tracking and yaw stability of the intelligent vehicle;

[0006] Step 3) Construct a safety set for the sideslip angle and yaw rate of the center of mass;

[0007] Step 4) Construct an adaptive multi-objective coordination strategy based on the tire slip angle saturation level, and use the adaptive multi-objective coordination strategy to output the adaptive weight matrix of output variables, control increments, and control inputs. , and ;

[0008] Step 5) Based on the adaptive cooperative control, predict the output equation, the safety set of the center of mass sideslip angle and yaw rate, and the adaptive weight matrix. , and The quadratic programming optimization problem is constructed and solved to obtain the optimal control input parameters, including the optimal front wheel steering angle and the vehicle's active yaw moment.

[0009] Step 6) Distribute the active yaw moment of the entire vehicle to obtain the additional torque of each tire. ; Optimal front wheel steering angle and additional torque of each tire The data is transmitted to the vehicle's control mechanism to complete the execution of control commands.

[0010] Furthermore, in step 1), the vehicle dynamics model considering the active yaw moment is shown below:

[0011] (1)

[0012] The lateral forces on the front and rear wheels are shown below:

[0013] (2)

[0014] Front wheel slip angle and rear wheel slip angle As shown below:

[0015] (3)

[0016] Furthermore, in step 1), the vehicle path tracking model is as follows:

[0017] (4)

[0018] Furthermore, in step 2), the predicted output equation for the intelligent vehicle's path tracking and yaw stability adaptive cooperative control is shown below:

[0019] (5)

[0020] Furthermore, in step 2), the steps for constructing the predictive output equation for the adaptive cooperative control of intelligent vehicle path tracking and yaw stability include:

[0021] Step 2.1) Construct the state-space equations, i.e.:

[0022] (6)

[0023] Step 2.2) Discretize the state-space equations to obtain:

[0024] (7)

[0025] Step 2.3) Augment the state variables to obtain:

[0026] (8)

[0027] Step 2.4) Based on the augmented state variables, construct the augmented state space, i.e.:

[0028] (9)

[0029] Step 2.5) Based on the augmented state space, in the prediction time domain... Control Time Domain The predictive output equations for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles are constructed below.

[0030] Furthermore, in step 3), the safety sets for the sideslip angle and yaw rate are as follows:

[0031] (10)

[0032] Furthermore, in step 3), the safety sets for the centroid sideslip angle and yaw rate include the upper boundary safety set and the lower boundary safety set;

[0033] The steps for constructing the upper boundary safety set include:

[0034] Step 3.1) Determine the safety boundaries for the sideslip angle and yaw rate, i.e.:

[0035] (11)

[0036] Step 3.2) Based on constraint variables Build a secure set ,Right now:

[0037]

[0038] (12)

[0039]

[0040] Among them, the control barrier function The constraints are as follows:

[0041] (13)

[0042] Step 3.3) Let For including constant coefficients A linear function, constructing a safety set constraint, namely:

[0043] (14)

[0044] Step 3.4) Construct discrete-time safety set constraints, namely:

[0045] (15)

[0046] Step 3.5) Construction The upper boundary control barrier function of the time-stability index is:

[0047] (16)

[0048] Step 3.6) Construct an expression for the safe set that satisfies the upper boundary. ;

[0049] Step 3.7) Construct the constraints of the upper boundary control barrier function during the prediction process, namely:

[0050] (17)

[0051] Step 3.8) Construct the upper boundary safety set constraints in the prediction time domain, i.e.:

[0052] (18)

[0053] Step 3.9) Based on the upper boundary control barrier function, update the upper boundary safety set constraints to obtain:

[0054] (19)

[0055] Step 3.10) Rewrite the updated upper boundary safety set constraints in compact form, resulting in:

[0056] (20)

[0057] In the formula, , ,

[0058] ;

[0059] Step 3.12) Construct control output and ,Right now:

[0060] (twenty one)

[0061]

[0062] Step 3.11) Based on control output and The compact form of the upper bound safety set constraint is updated to the final upper bound safety set, i.e.:

[0063] (twenty two)

[0064] Lower boundary safety set passes The lower boundary control barrier function at time t is determined;

[0065] The lower boundary control barrier function is shown below:

[0066] (twenty three)

[0067] Furthermore, in step 4), the adaptive multi-objective coordination strategy based on the tire slip angle saturation level is as follows:

[0068] (twenty four)

[0069] Among them, the reference centroid sideslip angle and reference yaw rate As shown below:

[0070] (25)

[0071] The adaptive weights are shown below:

[0072]

[0073] (26)

[0074]

[0075] Adaptive coefficients that are directly and inversely proportional to the tire slip angle , As shown below:

[0076] (27)

[0077] Among them, tire saturation slip angle As shown below:

[0078] (28)

[0079] Among them, the saturation sideslip angle of the left or right front wheel during longitudinal slip is considered. As shown below:

[0080] (29)

[0081] Furthermore, in step 5), the steps for constructing and solving the quadratic programming optimization problem include:

[0082] Step 5.1) Construction The control sequence expression in the time domain is:

[0083] (30)

[0084] In the formula, , ,

[0085] ;

[0086] Step 5.2) Combining the safety set of the centroid sideslip angle and yaw rate, and the adaptive multi-objective coordination strategy, the control problem is expressed as a quadratic programming optimization problem with inequality constraints, namely:

[0087] (31)

[0088]

[0089]

[0090] Step 5.3) Solve the quadratic programming optimization problem to obtain the optimal control increment sequence; set the first element of the optimal control increment sequence... As the actual control increment, it is added to the control quantity at the previous moment. ,get Optimal control input at time 1 ,Right now:

[0091] (32)

[0092] Furthermore, in step 6), the additional torque of each tire... As shown below:

[0093] (33)

[0094] Vertical loads of left front, right front, left rear, and right rear tires , , , As shown below:

[0095] (34)

[0096] The technical effects of this invention are undeniable. This invention proposes an adaptive cooperative control method for path tracking and yaw stability based on safety set constraints. This method actively weakens the vehicle's instability tendency and constrains the vehicle's dynamic behavior in advance by using safety set constraints based on the control obstacle function, thereby enhancing the vehicle's yaw stability. Through an adaptive multi-objective coordination strategy, it achieves smooth coordination of control objectives under different operating conditions, enhances the multi-condition adaptability of the cooperative control method, and realizes the synergistic improvement of path tracking and yaw stability. Attached Figure Description

[0097] Figure 1 The overall architecture of the predictive controller is determined by the collaborative model; Figure 2 This is a two-degree-of-freedom vehicle dynamics model; Figure 3 For path tracking models; Figure 4 For comparison of safety set constraints and direct constraints. Figure 5 Tire side slip characteristic curve and region division; Figure 6 The relationship between the adaptive coefficient and the tire slip angle; Figure 7 For path tracking results and control input in scenario A Figure 8 Results of yaw stability control for scenario A Figure 9 For SSC-AMPC in scenario A, the tire slip angle and adaptive coefficient are... Figure 10 For path tracking results and control input in scenario B Figure 11 Results of yaw stability control for scenario B Figure 12 The tire slip angle and adaptive coefficient of SSC-AMPC in scenario B. Detailed Implementation

[0098] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0099] Example 1:

[0100] See Figures 1 to 6 An adaptive cooperative control method for path tracking and yaw stability of intelligent vehicles based on safety set constraints includes the following steps:

[0101] Step 1) Establish a vehicle dynamics model and a vehicle path tracking model that consider active yaw moment;

[0102] Step 2) Based on the vehicle dynamics model and path tracking model, construct an adaptive cooperative control predictive output equation that considers the path tracking and yaw stability of the intelligent vehicle;

[0103] Step 3) Construct a safety set for the sideslip angle and yaw rate of the center of mass;

[0104] Step 4) Construct an adaptive multi-objective coordination strategy based on the tire slip angle saturation level, and use the adaptive multi-objective coordination strategy to output the adaptive weight matrix of output variables, control increments, and control inputs. , and ;

[0105] Step 5) Based on the adaptive cooperative control, predict the output equation, the safety set of the center of mass sideslip angle and yaw rate, and the adaptive weight matrix. , and The quadratic programming optimization problem is constructed and solved to obtain the optimal control input parameters, including the optimal front wheel steering angle and the vehicle's active yaw moment.

[0106] Step 6) Distribute the active yaw moment of the entire vehicle to obtain the additional torque of each tire. ; Optimal front wheel steering angle and additional torque of each tire The data is transmitted to the vehicle's control mechanism to complete the execution of control commands.

[0107] Example 2:

[0108] The method for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles based on safety set constraints is the same as in Example 1. Further, in step 1), the vehicle dynamics model considering the active yaw moment is shown below:

[0109] (1)

[0110] In the formula, For vehicle quality; and These are the vehicle's longitudinal and lateral speeds, respectively. This refers to the yaw rate; This is the moment of inertia of yaw rotation; and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. For active yaw moment; and These are the lateral forces on the front and rear wheels, respectively.

[0111] The lateral forces on the front and rear wheels are shown below:

[0112] (2)

[0113] In the formula, and These are the lateral stiffness of the front and rear wheels, respectively.

[0114] Front wheel slip angle and rear wheel slip angle As shown below:

[0115] (3)

[0116] In the formula, This refers to the steering angle of the front wheels.

[0117] Example 3:

[0118] The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints has the same technical content as any one of Examples 1-2. Further, in step 1), the vehicle path tracking model is as follows:

[0119] (4)

[0120] In the formula, Let be the path curvature at the orthogonal projection point of the vehicle's center of mass onto the reference path; This is the lateral distance error between the current position of the vehicle's center of gravity and its orthogonal projection point on the reference path; The actual heading angle of the vehicle Tangent angle at the orthogonal projection point of the vehicle's center of gravity on the reference path The heading angle error between them.

[0121] Example 4:

[0122] The method for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles based on safety set constraints has the same technical content as any one of embodiments 1-3. Further, in step 2), the predicted output equation for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles is as follows:

[0123] (5)

[0124] In the formula, the predicted output The mapping matrix from state to output Control input increment sequence ,

[0125] Additional variable matrix Dynamic influence matrix ,

[0126] Interference effect matrix C is the output matrix; A is the state transition matrix; B is the input matrix; E is the disturbance distribution matrix.

[0127] Example 5:

[0128] The method for adaptive cooperative control of intelligent vehicle path tracking and yaw stability based on safety set constraints has the same technical content as any one of embodiments 1-4. Further, in step 2), the step of constructing the predictive output equation for adaptive cooperative control of intelligent vehicle path tracking and yaw stability includes:

[0129] Step 2.1) Construct the state-space equations, i.e.:

[0130] (6)

[0131] In the formula, the state variable Control input Additional variables Output variables ;

[0132] , , , ;

[0133] Step 2.2) Discretize the state-space equations to obtain:

[0134] (7)

[0135] In the formula, , , , , It is the identity matrix. The discrete time step;

[0136] Step 2.3) Augment the state variables to obtain:

[0137] (8)

[0138] Step 2.4) Based on the augmented state variables, construct the augmented state space, i.e.:

[0139] (9)

[0140] In the formula, , , , , ;

[0141] Step 2.5) Based on the augmented state space, in the prediction time domain... Control Time Domain The predictive output equations for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles are constructed below.

[0142] Example 6:

[0143] The method for adaptive cooperative control of intelligent vehicle path tracking and yaw stability based on safety set constraints is the same as any one of embodiments 1-5. Further, in step 3), the safety sets for the centroid sideslip angle and yaw rate are as follows:

[0144] (10)

[0145] In the formula, ,

[0146] .

[0147] Example 7:

[0148] The method for adaptive and cooperative control of intelligent vehicle path tracking and yaw stability based on safety set constraints has the same technical content as any one of embodiments 1-6. Further, in step 3), the safety set for the centroid sideslip angle and yaw rate includes the upper boundary safety set and the lower boundary safety set.

[0149] The steps for constructing the upper boundary safety set include:

[0150] Step 3.1) Determine the safety boundaries for the sideslip angle and yaw rate, i.e.:

[0151] (11)

[0152] In the formula, , , , , The road surface adhesion coefficient;

[0153] Step 3.2) Based on constraint variables Build a secure set ,Right now:

[0154]

[0155] (12)

[0156]

[0157] In the formula, For the control barrier function; Represents the boundary of the safe set; Indicates the interior of the safe set;

[0158] Among them, the control barrier function The constraints are as follows:

[0159] (13)

[0160] Step 3.3) Let For including constant coefficients A linear function, constructing a safety set constraint, namely:

[0161] (14)

[0162] In the formula, and Represent Time and Time-control barrier function The value;

[0163] Step 3.4) Construct discrete-time safety set constraints, namely:

[0164] (15)

[0165] In the formula, For inclusion and scalar;

[0166] Step 3.5) Construction The upper boundary control barrier function of the time-stability index is:

[0167] (16)

[0168] Step 3.6) Construct an expression for the safe set that satisfies the upper boundary. ;

[0169] Step 3.7) Construct the constraints of the upper boundary control barrier function during the prediction process, namely:

[0170] (17)

[0171] Step 3.8) Construct the upper boundary safety set constraints in the prediction time domain, i.e.:

[0172] (18)

[0173] Step 3.9) Based on the upper boundary control barrier function, update the upper boundary safety set constraints to obtain:

[0174] (19)

[0175] In the formula, ;

[0176] Step 3.10) Rewrite the updated upper boundary safety set constraints in compact form, resulting in:

[0177] (20)

[0178] In the formula, , ,

[0179] ;

[0180] Step 3.12) Construct control output and ,Right now:

[0181] (twenty one)

[0182]

[0183] Step 3.11) Based on control output and The compact form of the upper bound safety set constraint is updated to the final upper bound safety set, i.e.:

[0184] (twenty two)

[0185] Lower boundary safety set passes The lower boundary control barrier function at time t is determined;

[0186] The lower boundary control barrier function is shown below:

[0187] (twenty three)

[0188] In the formula, , This is the lower bound for the sideslip angle and yaw rate of the center of mass.

[0189] Example 8:

[0190] The method for adaptive cooperative control of intelligent vehicle path tracking and yaw stability based on safety set constraints is the same as any one of embodiments 1-7. Further, in step 4), the adaptive multi-objective coordination strategy based on the tire slip angle saturation degree is as follows:

[0191] (twenty four)

[0192] In the formula, the reference value of the output variable is... , , and These are the adaptive weight matrices for the output variable, control increment, and control input, respectively.

[0193] Among them, the reference centroid sideslip angle and reference yaw rate As shown below:

[0194] (25)

[0195] In the formula, , ;

[0196] The adaptive weights are shown below:

[0197]

[0198] (26)

[0199]

[0200] In the formula, ~ , , , , These are the initial weights;

[0201] Adaptive coefficients that are directly and inversely proportional to the tire slip angle , As shown below:

[0202] (27)

[0203] Among them, tire saturation slip angle As shown below:

[0204] (28)

[0205] In the formula, and These are the saturation sideslip angles of the left and right front wheels, respectively.

[0206] Among them, the saturation sideslip angle of the left or right front wheel during longitudinal slip is considered. As shown below:

[0207] (29)

[0208] In the formula, For the vertical load of the left or right front wheel. The slip ratio of the left front wheel or the right front wheel. Let j be the longitudinal slip stiffness of the front wheel; j = l, r.

[0209] Example 9:

[0210] The method for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles based on safety set constraints has the same technical content as any one of embodiments 1-8. Further, in step 5), the steps for constructing and solving the quadratic programming optimization problem include:

[0211] Step 5.1) Construction The control sequence expression in the time domain is:

[0212] (30)

[0213] In the formula, , ,

[0214] ;

[0215] Step 5.2) Combining the safety set of the centroid sideslip angle and yaw rate, and the adaptive multi-objective coordination strategy, the control problem is expressed as a quadratic programming optimization problem with inequality constraints, namely:

[0216] (31)

[0217]

[0218]

[0219] In the formula, , , , and These are the lower and upper limits of the control quantity in the control time domain, respectively. and These are the lower and upper limits for controlling the increment, respectively;

[0220] Step 5.3) Solve the quadratic programming optimization problem to obtain the optimal control increment sequence; set the first element of the optimal control increment sequence... As the actual control increment, it is added to the control quantity at the previous moment. ,get Optimal control input at time 1 ,Right now:

[0221] (32)

[0222] In the formula, This is the optimal control input.

[0223] Example 10:

[0224] A method for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles based on safety set constraints, with technical content identical to any one of embodiments 1-9, further comprising, in step 6), the additional torque of each tire... As shown below:

[0225] (33)

[0226] In the formula, The effective radius of the tire; It is half the wheel track; This is the total vertical load;

[0227] Vertical loads of left front, right front, left rear, and right rear tires , , , As shown below:

[0228] (34)

[0229] In the formula, It is the acceleration due to gravity; and These are longitudinal and lateral accelerations, respectively. The height of the vehicle's center of gravity.

[0230] Example 11:

[0231] An adaptive cooperative control method for path tracking and yaw stability in intelligent vehicles based on safety set constraints is proposed. The overall architecture of the cooperative model predictive controller is as follows: Figure 1 As shown, a predictive model for coordinated control of path tracking and yaw stability is established based on vehicle state information and reference path curvature. The adhesion coefficient estimator uses the estimation method proposed in Chapter 2 to estimate the road adhesion coefficient at the current moment in real time. This information is then passed to the safety set constraint module and the adaptive multi-objective coordination strategy module. The safety set constraint based on the control barrier function is used to dynamically limit the stability index in the prediction model within a safe range and outputs the coefficient matrix in the inequality constraints. and constraint vector The adaptive multi-objective coordination strategy dynamically adjusts the weights of each term in the cost function based on the saturation level of the tire side slip characteristics, generating an adaptive weight matrix for the output variables, control increments, and control inputs. , and Finally, by combining the results from each module, a quadratic programming optimization problem is constructed, and the optimal front wheel steering angle is obtained by solving it. and additional yaw moment After torque distribution, the additional torque of each tire can be obtained. and the front wheel cornering The commands are transmitted together to the corresponding actuators in the vehicle to complete the actual execution of the control commands.

[0232] The specific steps include:

[0233] 1. Establish vehicle dynamics and path tracking model

[0234] To describe the lateral and yaw motion of a four-wheel independently driven vehicle while ensuring computational efficiency, a two-degree-of-freedom vehicle dynamics model considering active yaw moment is established as shown. The vehicle dynamics equations can be expressed as:

[0235]

[0236] In the formula, For vehicle quality; and These are the vehicle's longitudinal and lateral speeds, respectively. This refers to the yaw rate; This is the moment of inertia of yaw rotation; and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. For active yaw moment; and The lateral forces are for the front and rear wheels, respectively, and can be calculated using a linear tire model:

[0237]

[0238] In the formula, and These are the lateral stiffness of the front and rear wheels, respectively. and The slip angles are for the front and rear wheels, respectively, and can be calculated using the following formula:

[0239]

[0240] In the formula, This refers to the steering angle of the front wheels.

[0241] The deviation between the vehicle's actual trajectory and the reference path is shown below. Based on this, the path tracking model can be described as follows:

[0242]

[0243] In the formula, This is the lateral distance error between the current position of the vehicle's center of gravity and its orthogonal projection point on the reference path; The actual heading angle of the vehicle Tangent angle at the orthogonal projection point of the vehicle's center of gravity on the reference path The heading angle error between them.

[0244] Assuming heading angle error If it is small enough, then equation (8) can be rewritten as:

[0245]

[0246] In the formula, Let be the path curvature at the orthogonal projection point of the vehicle's center of mass on the reference path.

[0247] 2. State Prediction

[0248] Based on the constructed vehicle dynamics model and path tracking model, the state-space equations are established as follows:

[0249]

[0250] In the formula, the state variable Control input Additional variables Output variables ,

[0251] , , , .

[0252] Discretizing equation (5) yields:

[0253]

[0254] In the formula, , , , , It is the identity matrix. is the discrete time step.

[0255] To ensure stable control, the state variables are augmented as follows:

[0256]

[0257] The augmented state space can be represented as:

[0258]

[0259] In the formula, , , , , .

[0260] Select the prediction time domain as Control time domain is Then the system output can be predicted as:

[0261]

[0262] In the formula, , , ,

[0263] , ,

[0264] .

[0265] 3. Safety set constraints based on control barrier functions

[0266] In the coordinated control of path tracking and yaw stability, the sideslip angle and yaw rate should be limited within safety boundaries to ensure the vehicle's stability and handling performance under extreme conditions. The safety boundaries for the sideslip angle and yaw rate are related to the road adhesion conditions and can be defined as follows:

[0267]

[0268] In the formula, , , , , This is the road surface adhesion coefficient.

[0269] Define constraint variables Define security set :

[0270]

[0271]

[0272]

[0273] In the formula, For the control barrier function; Represents the boundary of the safe set; This represents the interior of the safe set.

[0274] To ensure safe collection Forward invariance, control barrier function The following conditions must be met:

[0275]

[0276] generally, Selected to include constant coefficients If the function is a linear function, then the safety set constraint can be written as:

[0277]

[0278] In the formula, and Represent Time and Time-control barrier function The value of . Discrete-time safety set constraints can be written as:

[0279]

[0280] In the formula, For inclusion and The smaller the value of scalar, the smaller the forward reachable set, the more stringent the constraints, and the greater the safety margin between the constraint state and the boundary. In this paper, the value is taken as 0.2.

[0281] Regarding the issue of vehicle yaw stability control, The upper boundary control barrier function of the time-stability index can be designed as follows:

[0282]

[0283] Then the safe set satisfying the upper boundary can be represented as: That is, constraint variables It should be smaller than the upper boundary.

[0284] According to equation (14), the upper boundary control barrier function must satisfy the following during the prediction process:

[0285]

[0286] Therefore, the safety set constraint in the prediction time domain can be expressed as:

[0287]

[0288] Substituting equation (15) into the equation, we get:

[0289] (18)

[0290] In the formula, .

[0291] To write equation (18) in a compact form:

[0292]

[0293] In the formula, , ,

[0294] .

[0295] Similar to the derivation process of equation (9), and It can be represented as:

[0296]

[0297]

[0298] Then equation (19) can be further written as:

[0299]

[0300] Similarly, The lower boundary control barrier function at time step 1 can be designed as follows:

[0301]

[0302] Therefore, the safe set satisfying the lower boundary can be represented as That is, constraint variables It should be greater than the lower boundary.

[0303] Following a similar derivation, the complete safety set constraint including upper and lower limits can be expressed as:

[0304]

[0305] In the formula, ,

[0306] .

[0307] Figure 4 The diagram compares safety set constraints and direct constraints, where ellipses with gradually increasing areas from left to right represent the evolution of the system state in the prediction time domain. In the figure, safety set constraints constrain the range of system state evolution by partitioning the reachable set at each prediction step into a safety set. This can be achieved by adjusting parameters. This method can modify the range of the safe set within the reachable set, thereby adjusting the strictness of the safe set constraint. It proactively limits the trend of change before the predicted state approaches the boundary, thus achieving a more forward-looking safety assurance mechanism. Direct constraints are only passively triggered when there is an intersection between the system's reachable set and the safe boundary, lacking the ability to intervene in advance. Overall, safe set constraints are more predictable and proactive, and have a certain safety margin, effectively improving system security and control smoothness.

[0308] 4. Adaptive Multi-Objective Strategy

[0309] Vehicle operating conditions are complex and varied, making it difficult to simultaneously achieve both path tracking accuracy and vehicle yaw stability. To dynamically adapt to the vehicle control requirements under different operating conditions, the control objective priority of the cooperative controller should be adaptively adjusted based on the vehicle's stability status under the current operating condition.

[0310] The saturation level of the tire slip angle can effectively reflect the stability of a vehicle. Figure 4 The tire sidewall characteristic curve and region division are shown, among which The maximum sideslip angle in the linear region. This is the saturation slip angle. The linear region of most tire characteristics is concentrated within the first 25% of the saturation slip angle; therefore, in this paper... When the tire operates in the linear region (0~ When the tire lateral force is linearly related to the slip angle, it has good lateral force output capability and good vehicle stability; however, in the nonlinear region (…), the lateral force is linearly related to the slip angle, resulting in good lateral force output capability and good vehicle stability. ~ When the sideslip angle increases, the increase in lateral force gradually decreases until it saturates, resulting in a significant decrease in the vehicle's lateral stability and making it prone to skidding or instability. The switching of control priorities can be achieved by flexibly adjusting the weights of each control objective in the cost function.

[0311] Based on this, an adaptive multi-objective coordination strategy based on the tire slip angle saturation degree is proposed as follows:

[0312] (1) In the linear region, yaw stability has a large safety margin, so its weight can be appropriately reduced to ensure path tracking accuracy. However, in the nonlinear region, especially when it is close to the saturation region, the vehicle is prone to instability. Therefore, the weight of yaw stability should be increased rapidly to ensure driving stability.

[0313] (2) In the linear region, path tracking is less difficult, so the control increment weight can be increased appropriately to take into account the smoothness of control; in the nonlinear region, the control increment weight can be reduced appropriately, sacrificing some smoothness to obtain a faster control response and ensure driving safety.

[0314] (3) In the linear region, the active steering of the front wheels is sufficient to complete the path tracking task, and there is no need for frequent intervention of the active yaw moment. Therefore, the total weight of the direct yaw moment control is increased, and the weight of the front wheel steering angle is introduced to avoid control oscillation. In the nonlinear region, in order to quickly stabilize the vehicle, the active intervention of the direct yaw moment control is required. Therefore, the total weight of the direct yaw moment control is reduced, and the weight of the front wheel steering angle is reduced to prioritize the coordinated control effect of path tracking and stability.

[0315] Therefore, the cost function is designed as follows:

[0316]

[0317] In the formula, the reference value of the output variable is... , , and These are adaptive weight matrices for the output variable, control increment, and control input, respectively. The reference centroid sideslip angle is also considered. and reference yaw rate It can be calculated using the following formula:

[0318]

[0319] In the formula, , .

[0320] To achieve adaptive changes in the weight matrices as the tire slip angle changes, the adaptive weights are designed as follows:

[0321]

[0322]

[0323]

[0324] In the formula, ~ , , , , As the initial weights, , These are adaptive coefficients that are directly proportional to and inversely proportional to the tire slip angle, respectively, and are designed as follows:

[0325]

[0326] In the formula, This represents the tire's saturated slip angle. Compared to the rear wheels, the front wheels play a dominant role in path tracking control. Their slip angle changes are more sensitive, and they are more likely to enter nonlinear or even saturated regions, thus reflecting potential vehicle instability trends earlier. To more accurately reflect the overall stability of the vehicle, the adaptive coefficient is calculated for the tire with the larger ratio of its current slip angle to its saturated slip angle between the left and right front tires. Saturated slip angle The expression is:

[0327]

[0328] In the formula, and These are the saturated sideslip angles for the left and right front wheels, respectively. Since front wheel steering and active yaw moment act simultaneously, the saturated sideslip angle is affected by longitudinal tire slippage. Therefore, based on the coupled brush tire model, the saturated sideslip angle of the left or right front wheel considering longitudinal slippage can be derived. for:

[0329]

[0330] In the formula, For the vertical load of the left or right front wheel. The slip ratio of the left front wheel or the right front wheel. This refers to the longitudinal slip stiffness of the front wheel.

[0331] The curve of the adaptive coefficient as a function of tire slip angle is shown below. Figure 5 As shown. In the linear region, The increase is small and slow, the stability weight is small, and the path tracking accuracy dominates the control objective. A larger and slowly decreasing yaw rate results in a greater penalty for control increments and direct yaw moment control, which helps maintain smooth control and avoids premature intervention of active yaw moment. Simultaneously, a certain front wheel steering angle penalty helps prevent control oscillations. In the nonlinear region, It increases rapidly and reaches its maximum value near the saturation region, where the stability weight increases significantly and yaw stability becomes dominant. The penalty is reduced rapidly and reaches its minimum value when approaching the saturation region, thus enhancing the control response and prioritizing vehicle stability.

[0332] 5. Optimize the solution

[0333] The cooperative control problem needs to be further transformed into a solvable optimization problem to obtain the optimal control increment sequence. In addition to the safety constraints mentioned above, physical constraints related to the actuator response capability need to be imposed on the control quantity and its increment to ensure the feasibility of the control signal in practical applications.

[0334] The control sequence within the time domain can be predicted as follows:

[0335]

[0336] In the formula, , ,

[0337] .

[0338] Combining equations (23), (24), and (30), the control problem can be expressed as a quadratic programming optimization problem with inequality constraints:

[0339]

[0340]

[0341]

[0342] In the formula, , , , and These are the lower and upper limits of the control quantity in the control time domain, respectively. and These are the lower and upper limits for controlling the increment, respectively.

[0343] After solving, the optimal control increment sequence can be obtained. The first element of this sequence... As the actual control increment, it is added to the control quantity at the previous moment. You can get Optimal control input at time 1 :

[0344]

[0345] 6. Torque Distribution

[0346] The optimal front wheel steering angle obtained from the solution can be directly executed by the steering mechanism, while the vehicle's active yaw moment needs to be achieved by distributing the additional torque to each wheel. To balance real-time performance, dynamic adaptability, and stability, this paper dynamically distributes the torque based on the tire's vertical load. The additional torque distribution to each tire is as follows:

[0347] In the formula, The effective radius of the tire; It is half the wheel track; This is the total vertical load; , , , The vertical loads of the left front, right front, left rear, and right rear tires are respectively, and can be calculated by the following formula:

[0348]

[0349]

[0350] In the formula, It is the acceleration due to gravity; and These are longitudinal and lateral accelerations, respectively. The height of the vehicle's center of gravity.

[0351] The proposed collaborative model predictive controller overall architecture is as follows: Figure 1As shown, a predictive model for coordinated control of path tracking and yaw stability is established based on vehicle state information and reference path curvature. The adhesion coefficient estimator uses the estimation method proposed in Chapter 2 to estimate the road adhesion coefficient at the current moment in real time. This information is then passed to the safety set constraint module and the adaptive multi-objective coordination strategy module. The safety set constraint based on the control barrier function is used to dynamically limit the stability index in the prediction model within a safe range and outputs the coefficient matrix in the inequality constraints. and constraint vector The adaptive multi-objective coordination strategy dynamically adjusts the weights of each term in the cost function based on the saturation level of the tire side slip characteristics, generating an adaptive weight matrix for the output variables, control increments, and control inputs. , and Finally, by combining the results from each module, a quadratic programming optimization problem is constructed, and the optimal front wheel steering angle is obtained by solving it. and additional yaw moment After torque distribution, the additional torque of each tire can be obtained. and the front wheel cornering The commands are transmitted together to the corresponding actuators in the vehicle to complete the actual execution of the control commands.

[0352] Table 1 CarSim Vehicle Configuration Parameters

[0353]

[0354] To verify the effectiveness of the proposed cooperative control method, simulation tests were conducted under typical operating conditions using the CarSim / Simulink co-simulation platform. To evaluate the algorithm's performance under different control difficulties, scenario A was designed as a single lane change condition on a dry road surface at high speed, while scenario B was designed as a double lane change condition on a wet road surface at high speed. The parameters of the vehicles used for simulation verification are shown in Table 1.

[0355] The sampling time of the collaborative controller is set to 20 ms, and the prediction time domain is... 30, Control Time Domain 5. Initial weights (4000, 2000, 1000, 6000), (1000, 0.001), (500, 0.0004). The comparison algorithm in this section is explained as follows:

[0356] DC-AMPC: MPC based on direct constraints and adaptive multi-objective coordination strategy, using the most basic form of direct constraints to limit the centroid sideslip angle and yaw rate.

[0357] SSC-MPC: An MPC based on safety set constraints and fixed weights. To ensure relatively balanced control performance, a fixed weight matrix is ​​set. (4000, 2000, 1000, 6000), (550, 0.00055) (275, 0.00022).

[0358] SSC-AMPC: This paper proposes an MPC cooperative controller based on safety set constraints and an adaptive multi-objective coordination strategy.

[0359] Experiment 1: Scenario A

[0360] In this scenario, the vehicle speed is 90 km / h, the road surface adhesion coefficient is 0.7, and the reference path is a single lane change. Figure 6 and Figure 7 The results are for path tracking and yaw stability control, respectively. Figure 8 The changes in front wheel sideslip angle and adaptive coefficients in the SSC-AMPC adaptive multi-objective coordination strategy are shown. Table 2 compares the quantization results of each cooperative controller, including path lateral deviation. , centroid side slip angle deviation yaw rate deviation The maximum value (MAX) and root mean square value (RMS).

[0361] like Figure 6 As shown in Table 2, under high-speed, high-adhesion conditions, both SSC-AMPC and SSC-MPC can track the reference path well, while DC-AMPC exhibits a significant deviation after lane changes. According to Table 2, compared to DC-AMPC and SSC-MPC, SSC-AMPC... The maximum values ​​decreased by 37.50% and 23.34% respectively, and the root mean square values ​​decreased by 22.72% and 16.60% respectively. This is because the direct constraints in DC-AMPC only take effect when the yaw rate reaches the constraint boundary, which can easily trigger a control mutation at the moment of constraint activation. In contrast, the safety set constraint mechanism of SSC-AMPC can actively apply control adjustment before the system state approaches the safety boundary. Figure 7 This proactively mitigates potential instability trends, significantly improving vehicle stability and controllability under extreme conditions. SSC-AMPC in... Figure 6 The DC-AMPC exhibits a smoother front wheel steering angle, while the DC-AMPC shows a larger front wheel steering angle and abrupt changes when the yaw rate reaches the constraint boundary, demonstrating the advantage of safety set constraints in control smoothness. Because the DC-AMPC can track the reference yaw rate better at the constraint boundary, and the tire force is close to saturation, Figure 6Its active yaw moment before the longitudinal displacement X=58 m is significantly smaller than other controllers. However, in the short period after X=58 m, Figure 7 When the yaw rate briefly exceeds the boundary, the active yaw moment increases sharply to quickly correct the vehicle's yaw state. In contrast, the SSC-AMPC, with its predictive safety set constraint mechanism, achieves smoother control of both front wheel steering angle and active yaw moment. The fixed weights in the SSC-MPC result in a slight delay in its front wheel steering angle response compared to the SSC-AMPC, which is more noticeable at X=51 m and 77 m.

[0362] Table 2 Quantitative Results for Scenario A

[0363]

[0364] like Figure 7 As shown, the DC-AMPC exhibits a larger range of sideslip angle variation and a larger phase trajectory region, reflecting the instability of the vehicle's yaw motion, while the SSC-MPC and SSC-AMPC show better overall stability. Figure 7 In the DC-AMPC model, to better track the reference value, constraints are only triggered when the actual yaw rate reaches the boundary, causing the yaw rate to briefly exceed the boundary at X=59 m. While this passive constraint method improves the tracking accuracy of the reference value to some extent, the lack of advance adjustment leads to an overly abrupt yaw response, resulting in decreased vehicle stability. In contrast, SSC-MPC and SSC-AMPC, through forward-looking safety set constraints, can proactively apply restrictions before the critical state, weakening instability trends in advance and preventing the yaw rate from excessively approaching the boundary, thus achieving a smoother yaw dynamic response and significantly improving the vehicle's dynamic stability and controllability. Due to the relatively delayed front wheel steering response caused by the fixed weights of SSC-MPC, Table 2 shows that SSC-AMPC has better vehicle stability than SSC-MPC. Compared to DC-AMPC and SSC-MPC, SSC-AMPC... The root mean square values ​​decreased by 46.73% and 13.09%, respectively.

[0365] Figure 8 During the process, under the influence of active yaw moment and lateral load transfer, the saturation sideslip angle exhibits a certain range of variation around ±8 degrees. At a longitudinal displacement of 58 m, the nonlinearity of the right front wheel's sideslip characteristic exceeds that of the left front wheel, causing the saturation sideslip angle to switch to be determined by the right front wheel, thus leading to... Figure 8 The sudden change in the direction of the mid-saturation slip angle. The closer the front wheel slip angle is to the saturation slip angle, the more pronounced the nonlinearity of the tire characteristics. Figure 8 The adaptive coefficient in the equation also increases accordingly.

[0366] Experiment 2: Scenario B

[0367] In this scenario, the vehicle speed is 72 km / h, the road surface adhesion coefficient is 0.4, and the reference path is a double lane change. Figure 9 and Figure 10 The results are for path tracking and yaw stability control, respectively. Figure 11 The variations in front wheel slip angle and adaptive coefficient in SSC-AMPC are shown. Table 3 compares the quantization results of each cooperative controller.

[0368] Compared to scenario A, scenario B involves a greater range of maneuvers, has worse adhesion conditions, and makes it easier for the tires to enter the nonlinear region, significantly increasing the difficulty of control. Figure 9 It can be seen that the SSC-AMPC has a more significant advantage in path tracking performance in this scenario. On the one hand, the DC-AMPC's yaw rate remains near the safety boundary for a long time in scenario B. Figure 10 (b) The vehicle remains in a critical stable state for a longer period compared to scenario A. Under the constraint of the safety set, SSC-AMPC can actively suppress yaw response before approaching the boundary, keeping the yaw rate within a safe range and effectively avoiding instability risks. Furthermore, Figure 9 The DC-AMPC exhibits a significantly increased number of front wheel steering angle jumps (X=17, 38, 88, 127 m), resulting in a more abrupt control response and impacting both vehicle yaw stability and ride comfort. In contrast, the SSC-AMPC achieves smoother steering control through forward-looking constraints, helping to maintain the vehicle's continued stability and controllability under extreme conditions. On the other hand, Figure 11 (b) shows that the adaptive coefficients of SSC-AMPC change more significantly in this scenario, thus exhibiting a more pronounced control performance advantage compared to the fixed-weight SSC-MPC. Table 3 shows that, compared to DC-AMPC and SSC-MPC, SSC-AMPC... The maximum values ​​decreased by 34.08% and 378% respectively, and the root mean square values ​​decreased by 325% and 29.90% respectively.

[0369] Table 3 Quantitative Results of Scenario B

[0370]

[0371] In terms of yaw stability control, SSC-MPC and SSC-AMPC with safety set constraints are used at the centroid sideslip angle ( Figure 10 (a) and phase plane trajectory ( Figure 10 (c) It exhibits superior control performance in all aspects. Compared to DC-AMPC and SSC-MPC, SSC-AMPC... The maximum values ​​decreased by 59.19% and 9.49% respectively, and the root mean square values ​​decreased by 22.40% and 21.25%, significantly improving the vehicle's yaw stability. Figure 10 (b) In this model, SSC-MPC and SSC-AMPC, relying on the safety set constraint mechanism, consistently and actively limit the vehicle's yaw rate within a safe range. The control process is smooth and without significant oscillations, demonstrating excellent stability maintenance. Conversely, DC-AMPC experiences multiple abrupt changes in yaw rate near the constraint boundaries, even exceeding them, leading to drastic fluctuations in vehicle motion and insufficient stability. This demonstrates that safety set constraints, through forward-looking restrictions and gradual adjustments to state variables, can effectively prevent instability and maintain control smoothness under critical conditions. Compared to DC-AMPC and SSC-MPC, SSC-AMPC... The maximum values ​​decreased by 43.35% and 17.40%, respectively. Because the DC-AMPC tracks the reference value with a wider range of yaw rate variations, the DC-AMPC's... The maximum value is larger than that of SSC-AMPC, but The root mean square value is smaller. However, this control strategy, which sacrifices stability for short-term accuracy, carries significant risks in practice.

[0372] Figure 11 In (a), the saturated sideslip angle fluctuates around ±4.5 deg. Due to the lower road adhesion coefficient in this scenario, the saturated sideslip angle is significantly smaller than in scenario A. Simultaneously, the lower road adhesion coefficient also increases the tire's nonlinearity in this scenario, making it easier for the front wheel sideslip angle to enter the nonlinear region. Figure 11 In (b), the frequency and magnitude of the adaptive coefficient changes are more pronounced compared to scenario A. Thanks to the more significant adaptive multi-objective coordination effect, the advantages of SSC-AMPC over SSC-MPC are also more prominent in this scenario.

Claims

1. An adaptive cooperative control method for path tracking and yaw stability of intelligent vehicles based on safety set constraints, characterized in that, Includes the following steps: Step 1) Establish a vehicle dynamics model and a vehicle path tracking model that consider active yaw moment; Step 2) Based on the vehicle dynamics model and path tracking model, construct an adaptive cooperative control predictive output equation that considers the path tracking and yaw stability of the intelligent vehicle; Step 3) Construct a safety set for the sideslip angle and yaw rate of the center of mass; Step 4) Construct an adaptive multi-objective coordination strategy based on the tire slip angle saturation level, and use the adaptive multi-objective coordination strategy to output the adaptive weight matrix of output variables, control increments, and control inputs. , and ; Step 5) Based on the adaptive cooperative control, predict the output equation, the safety set of the center of mass sideslip angle and yaw rate, and the adaptive weight matrix. , and The quadratic programming optimization problem is constructed and solved to obtain the optimal control input parameters, including the optimal front wheel steering angle and the vehicle's active yaw moment. Step 6) Distribute the active yaw moment of the entire vehicle to obtain the additional torque of each tire. ; Optimal front wheel steering angle and additional torque of each tire The data is transmitted to the vehicle's control mechanism to complete the execution of control commands.

2. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, In step 1), the vehicle dynamics model considering the active yaw moment is shown below: （1） In the formula, For vehicle quality; and These are the vehicle's longitudinal and lateral speeds, respectively. This refers to the yaw rate; This is the moment of inertia of yaw rotation; and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. For active yaw moment; and These are the lateral forces on the front and rear wheels, respectively. The lateral forces on the front and rear wheels are shown below: （2） In the formula, and These are the lateral stiffness of the front and rear wheels, respectively. Front wheel slip angle and rear wheel slip angle As shown below: （3） In the formula, This refers to the steering angle of the front wheels.

3. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, In step 1), the vehicle path tracking model is as follows: （4） In the formula, Let be the path curvature at the orthogonal projection point of the vehicle's center of mass onto the reference path; This is the lateral distance error between the current position of the vehicle's center of gravity and its orthogonal projection point on the reference path; The actual heading angle of the vehicle Tangent angle at the orthogonal projection point of the vehicle's center of gravity on the reference path The heading angle error between them.

4. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, In step 2), the predicted output equation for the intelligent vehicle's path tracking and yaw stability adaptive cooperative control is shown below: （5） In the formula, the predicted output The mapping matrix from state to output Control input increment sequence , Additional variable matrix Dynamic influence matrix , Interference effect matrix C is the output matrix; A is the state transition matrix; B is the input matrix; E is the disturbance distribution matrix.

5. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 4, characterized in that, Step 2) involves constructing the predictive output equation for the adaptive cooperative control of intelligent vehicle path tracking and yaw stability, including the following steps: Step 2.1) Construct the state-space equations, i.e.: （6） In the formula, the state variable Control input Additional variables Output variables ; ， ， ， ； Step 2.2) Discretize the state-space equations to obtain: （7） In the formula, , , , , It is the identity matrix. The discrete time step; Step 2.3) Augment the state variables to obtain: （8） Step 2.4) Based on the augmented state variables, construct the augmented state space, i.e.: （9） In the formula, , , , , ; Step 2.5) Based on the augmented state space, in the prediction time domain... Control Time Domain The predictive output equations for adaptive cooperative control of path tracking and yaw stability of intelligent vehicles are constructed below.

6. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, In step 3), the safety sets for the sideslip angle and yaw rate are as follows: （10） In the formula, , 。 7. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, In step 3), the safety sets for the sideslip angle and yaw rate include the upper boundary safety set and the lower boundary safety set; The steps for constructing the upper boundary safety set include: Step 3.1) Determine the safety boundaries for the sideslip angle and yaw rate, i.e.: （11） In the formula, , , , , The road surface adhesion coefficient; Step 3.2) Based on constraint variables Build a secure set ,Right now: （12） In the formula, For the control barrier function; Represents the boundary of the safe set; Indicates the interior of the safe set; Among them, the control barrier function The constraints are as follows: （13） Step 3.3) Let For including constant coefficients A linear function, constructing a safety set constraint, namely: （14） In the formula, and Represent Time and Time-of-flight control barrier function The value; Step 3.4) Construct discrete-time safety set constraints, namely: （15） In the formula, For inclusion and scalar; Step 3.5) Construction The upper boundary control barrier function of the time-stability index is: （16） Step 3.6) Construct an expression for the safe set that satisfies the upper boundary. ; Step 3.7) Construct the constraints of the upper boundary control barrier function during the prediction process, namely: （17） Step 3.8) Construct the upper boundary safety set constraints in the prediction time domain, i.e.: （18） Step 3.9) Based on the upper boundary control barrier function, update the upper boundary safety set constraints to obtain: （19） In the formula, ; Step 3.10) Rewrite the updated upper boundary safety set constraints in compact form, resulting in: （20） In the formula, , , ； Step 3.12) Construct control output and ,Right now: （21） Step 3.11) Based on control output and The compact form of the upper bound safety set constraint is updated to the final upper bound safety set, i.e.: （22） Lower boundary safe set passes The lower boundary control barrier function at time t is determined; The lower boundary control barrier function is shown below: （23） In the formula, , This is the lower bound for the sideslip angle and yaw rate of the center of mass.

8. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, In step 4), the adaptive multi-objective coordination strategy based on the tire slip angle saturation level is as follows: （24） In the formula, the reference value of the output variable is... , , and These are the adaptive weight matrices for the output variable, control increment, and control input, respectively. Among them, the reference centroid sideslip angle and reference yaw rate As shown below: （25） In the formula, , ; The adaptive weights are shown below: （26） In the formula, ~ , , , , These are the initial weights; Adaptive coefficients that are directly and inversely proportional to the tire slip angle , As shown below: （27） Among them, tire saturation slip angle As shown below: （28） In the formula, and These are the saturation sideslip angles of the left and right front wheels, respectively. Among them, the saturation sideslip angle of the left or right front wheel during longitudinal slip is considered. As shown below: （29） In the formula, For the vertical load of the left or right front wheel. The slip ratio of the left front wheel or the right front wheel. Let j be the longitudinal slip stiffness of the front wheel; j = l, r.

9. The intelligent vehicle path tracking and yaw stability adaptive cooperative control method based on safety set constraints according to claim 1, characterized in that, Step 5) involves constructing and solving the quadratic programming optimization problem, including: Step 5.1) Construction The control sequence expression in the time domain is: （30） In the formula, , , ； Step 5.2) Combining the safety set of the centroid sideslip angle and yaw rate, and the adaptive multi-objective coordination strategy, the control problem is expressed as a quadratic programming optimization problem with inequality constraints, namely: （31） In the formula, , , , and These are the lower and upper limits of the control quantity in the control time domain, respectively. and These are the lower and upper limits for controlling the increment, respectively; Step 5.3) Solve the quadratic programming optimization problem to obtain the optimal control increment sequence; set the first element of the optimal control increment sequence... As the actual control increment, it is added to the control quantity at the previous moment. ,get Optimal control input at time 1 ,Right now: （32） In the formula, This is the optimal control input.

10. The adaptive cooperative control method for intelligent vehicle path tracking and yaw stability based on safety set constraints according to claim 1, characterized in that, In step 6), the additional torque of each tire As shown below: （33） In the formula, The effective radius of the tire; It is half the wheel track; This represents the total vertical load. Vertical loads of left front, right front, left rear, and right rear tires , , , As shown below: （34） In the formula, It is the acceleration due to gravity; and These are longitudinal and lateral accelerations, respectively. The height of the vehicle's center of gravity.

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