Switching envelope based trajectory tracking and stability coordinated control method

Abstract

The present application relates to the field of intelligent driving control of vehicles, and provides a trajectory tracking and stability coordination control method based on switching envelope; including a vehicle stability domain switching envelope method based on front and rear wheel saturation characteristics, a stability evaluation and weight self-adaptive adjustment driven by the switching envelope, and an MPC trajectory tracking controller design based on switching envelope constraint and weight self-adaptive adjustment. The present application proposes dynamic safety constraints and adaptive weight distribution considering front and rear wheel saturation limits, improves the vehicle trajectory tracking accuracy and stability control ability; a trajectory tracking switching envelope considering front and rear wheel saturation is designed, which can dynamically update the vehicle stability boundary according to the tracking trajectory, vehicle state and actuator actuation amount; through adaptive adjustment of the weight factor of multiple control objectives based on the vehicle stability evaluation index of the switching envelope, the steering loss and spin instability problems of the unmanned vehicle under intense steering operation are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent driving control of vehicles, and particularly relates to a trajectory tracking and stability coordination control method for unmanned vehicles based on switching envelope. BACKGROUND

[0002] Under extreme conditions, trajectory tracking and stability control are two important and conflicting problems for unmanned vehicles, which involves calculating the required steering angle to guide the vehicle to accurately track the preset trajectory under the premise of ensuring vehicle stability. The vehicle stability domain is an important basis for the design of unmanned systems, providing rich reference information in vehicle stability analysis and dynamic control target design. Currently, the stability domain estimation research generally targets traditional vehicles with drivers operating the steering wheel, only considering limiting the rear wheel saturation to prevent vehicle instability, while ignoring the active control of the front wheel steering angle in the trajectory tracking task of autonomous vehicles. Front wheel saturation may cause the vehicle to lose steering ability, and there is a risk of trajectory deviation or even collision. SUMMARY

[0003] To solve the above technical problems, the present application proposes a trajectory tracking and stability coordination control method based on switching envelope, comprising the following steps:

[0004] Step one, vehicle stability domain switching envelope method based on front and rear wheel saturation characteristics:

[0005] In The phase plane is constructed by the front and rear wheel saturation side slip angle to determine the center of mass side slip angle stability boundary as the vehicle state switching envelope, while avoiding the steering loss caused by front wheel saturation and the spinout instability caused by rear wheel saturation; based on the center of mass side slip angle stability boundary and the yaw rate stability boundary determined by the front and rear wheel saturation side slip angle, the critical steering angle is derived as the switching criterion of the center of mass side slip angle stability boundary, and the envelope is dynamically switched with vehicle speed, road adhesion coefficient and steering angle; the stability domain is mapped from The phase plane to the front and rear wheel side slip angle The phase plane, so that the stability domain is evenly distributed in the front and rear wheel side slip angle space;

[0006] Step two, stability evaluation and weight adaptive adjustment driven by switching envelope;

[0007] After the switching envelope is mapped to The phase plane, the utilization rate of the current state of the vehicle relative to the dynamic stability domain is calculated in real time based on the dynamic stability domain defined by the switching envelope, and a vehicle stability evaluation index is constructed; the is used as the basis for weight adjustment, and the control weights of longitudinal speed, lateral position, yaw rate and center of mass side slip angle tracking are adaptively adjusted when When far away from the stability boundary, the controller increases the tracking weights of the ideal longitudinal velocity, ideal lateral position and ideal yaw rate, and decreases the tracking weight of the ideal center of mass side slip angle, to improve the trajectory tracking accuracy; when When close to the stability boundary, the tracking weights of the ideal longitudinal velocity, ideal lateral position and ideal yaw rate are decreased, and the tracking weight of the ideal center of mass side slip angle is increased, to reduce the trajectory tracking accuracy and improve the stability control performance.

[0008] Step three, design of the MPC trajectory tracking controller based on switching envelope constraint and weight adaptive adjustment;

[0009] Relying on the control architecture of model predictive control algorithm, a model predictive control (MPC) trajectory tracking controller containing switching envelope constraint and weight adaptive adjustment is designed, the dynamic stability domain defined by the switching envelope of step one is introduced to the yaw rate and the center of mass side slip angle Vehicle state constraints are applied, a multi-objective quadratic cost function containing longitudinal velocity, lateral position, yaw rate, center of mass side slip angle tracking error and actuator actuation amount is defined, and the dynamic control requirements are realized by introducing the weight adaptive adjustment of step two; the front wheel steering angle and longitudinal acceleration control amount are obtained through iterative optimization, to realize the comprehensive optimization of trajectory tracking accuracy, vehicle stability and actuator smoothness.

[0010] Further, the step one includes:

[0011] The center of mass side slip angle stability boundary determined by the rear wheel saturated side slip angle and the yaw rate stability boundary are used as the preliminary range of the vehicle state stability envelope, and the envelope lines about the vehicle state yaw rate and the center of mass side slip angle are expressed as:

[0012]

[0013] wherein, max and min yaw rate stability boundaries respectively, max and min center of mass side slip angle stability boundaries determined by the rear wheel saturated side slip angle respectively, μ represents the road adhesion coefficient, g represents the gravity acceleration, L represents the distance from the vehicle center of mass to the rear wheel, v represents the longitudinal velocity of the vehicle, δr represents the rear wheel saturated side slip angle corresponding to the maximum lateral tire force;

[0014] With the increase of the steering angle, Stable equilibrium motions in the phase plane should be confined within the stability envelope; two boundaries are added on the basis of the preliminary range of the stability envelope, which are determined by the side slip angle of the front tire at the peak tire force, and the equation of the new boundaries is as follows:

[0015]

[0016] where, and represent the maximum and minimum center of mass side slip angle stability boundaries determined by the front tire saturation side slip angle, represents the distance from the vehicle center of mass to the front tire, is the steering angle of the front tire, represents the front tire saturation side slip angle corresponding to the maximum lateral tire force.

[0017] Further, the step of step one further comprises:

[0018] In the phase plane vehicle state stability boundary diagram, the critical steering angle is determined by the intersection of the envelope line related to , and the critical steering angle related to the stability envelope line is obtained using the following formula:

[0019]

[0020] where, and represent the minimum and maximum values of the critical steering angle, , represents the wheelbase of the vehicle;

[0021] A dynamic stability boundary based on front tire saturation determination and its switching mechanism with the rear tire boundary are introduced:

[0022] The switching envelope expression of the maximum steady-state center of mass side slip angle and the minimum steady-state center of mass side slip angle is:

[0023] .

[0024] Further, the step of step one further comprises:

[0025] According to the driving environment and control input, respectively design the saddle point position adjustment function of the phase plane vehicle state stability boundary, and the expression of the yaw rate stability boundary is:

[0026]

[0027] where, the expression of the saddle point position adjustment function is:

[0028]

[0029] The expression of the centroid side-slip angle stability boundary is:

[0030]

[0031] The expression of the saddle point position adjustment function is:

[0032]

[0033] wherein, respectively represent the saddle point position adjustment function parameters;

[0034] The expression equation of the saddle point position in the phase plane is:

[0035] .

[0036] Further, in step two, the is taken as the weight adjustment basis, and the control weight of trajectory tracking and stability maintenance is adaptively adjusted according to the size: when the is low (far away from the stability boundary), the controller increases the tracking weight of the longitudinal velocity, lateral position and yaw angle velocity, and improves the trajectory tracking accuracy; when the increases close to the stability boundary, the tracking weight of the longitudinal velocity, lateral position and yaw angle velocity is gradually reduced, and the tracking weight of the centroid side-slip angle is increased, so as to inhibit the vehicle from further approaching the instability region and guarantee the vehicle stability.

[0037] Further, the step two includes the following steps:

[0038] Firstly, the vehicle stability evaluation index is designed according to the position of the vehicle state in the phase plane, which represents the vehicle stability degree:

[0039]

[0040] wherein, represents the distance from the real-time vehicle state point to the origin of the phase plane, are respectively the radii of the safe zone, the transition zone and the dangerous zone; are respectively the values of the stability evaluation index when the position is in the safe zone , the transition zone and the dangerous zone ;

[0041] The safe zone ​​A green area representing the safe zone is drawn with the origin as the center and the rear wheel saturation sideslip angle as the radius; as the vehicle's state gradually moves away from the origin, the stability evaluation index... The value gradually increases if the location is within the safe zone. If the boundary is defined, then the stability evaluation index is taken as: ;when When this condition is met, the vehicle's dynamic capabilities are under low utilization under the current operating conditions, and the vehicle is stable; transition zone The blue area representing the transition zone is obtained by drawing a circle with the front wheel saturation sideslip angle as the radius. Boundary to Boundary, where the vehicle's power utilization rate continuously increases under current operating conditions; danger zone. The red area is represented by a circle with a radius equal to half the distance between the two saddle points. The index starts from... Corresponding to the danger zone from Boundary to The vehicle's dynamic capabilities are highly utilized at the boundary, and even slight disturbances can lead to vehicle instability.

[0042] As a preferred option, when the vehicle is located in a danger zone In addition, the stability index Restricted to To avoid due to Excessive changes in weighting factors can cause oscillations and limit the performance of the controller.

[0043] Furthermore, step two also includes:

[0044] Stability partitioning characterizes different vehicle stability states and is applied to the control system as a condition for switching dynamic safety requirements; this is combined with stability evaluation indices based on the vehicle switching envelope method. The vehicle's position and stability are quantitatively identified. By dynamically adjusting the weighting factors of the objective function, the relationship between the vehicle's stable state and dynamic control requirements is described as follows: When the vehicle is in the stable region R1, The primary goal is to improve vehicle handling; therefore, tracking the ideal values ​​of longitudinal velocity, lateral position, and yaw rate during vehicle operation is the priority control objective, leading to increased tracking weights for these parameters. When the vehicle is far from the stable region, and in a state of... Boundary to At the boundary, The priority of stability control based on the sideslip angle increases with the increase of the stability exponent, while the priority of longitudinal velocity, lateral position, and yaw rate tracking decreases with the increase of the stability exponent; when the stability exponent exceeds the transition zone, , stability control is dominant, while in trajectory tracking task, lateral position tracking accuracy is prioritized;

[0045] By adjusting the weight factors of multiple control objectives: longitudinal velocity tracking weight , lateral position tracking weight and yaw rate tracking weight Dynamic adjustment of maneuverability control requirements is realized; the weight factors of the weight adaptive adjustment function are as follows:

[0046]

[0047] wherein, denote longitudinal velocity, lateral position and yaw rate respectively, is an adjustment parameter;

[0048] By adjusting the weight factors of multiple control objectives: center of mass side slip angle tracking weight Dynamic adjustment of stability control requirements is realized; the weight factors of the weight adaptive adjustment function are as follows:

[0049]

[0050] wherein, denotes center of mass side slip angle tracking, and is an adjustment parameter;

[0051] Further, the steps of step two further comprise:

[0052] According to the relationship between the weight factors of the weight adaptive adjustment function and the adjustment parameters, the adjustment parameters are determined by key points and . In order to determine the optimal values of the key points and , weight factor sensitivity analysis is carried out through control performance indicators, including root mean square error and maximum error, and the control performance indicators include:

[0053] Longitudinal velocity tracking:

[0054]

[0055] Path tracking 1-lateral position tracking:

[0056]

[0057] Path tracking 2-yaw angle tracking:

[0058]

[0059] yaw rate tracking:

[0060]

[0061] side slip angle tracking:

[0062]

[0063] where, and denote the root mean square value and the maximum error of longitudinal velocity tracking, respectively, denotes the reference longitudinal velocity; and denote the root mean square value and the maximum error of lateral position tracking, respectively, denotes the reference lateral position, determined by the tracking path; and denote the root mean square value and the maximum error of attitude angle tracking, respectively, and denote the yaw angle and the reference yaw angle, respectively, determined by the tracking path; and denote the root mean square value and the maximum error of yaw rate tracking, respectively, denotes the reference yaw rate, calculated by the steady-state gain of the vehicle dynamics model; and denote the root mean square value and the maximum error of side slip angle tracking, respectively; , and denote the total number of sampling points, a single sampling point, and the test duration of the sensitivity analysis test, respectively.

[0064] Further, the step three comprises:

[0065] First, a 3-DOF monorail vehicle dynamics model for phase plane vehicle stability analysis is built, and then a vehicle prediction model for trajectory tracking MPC controller is built on this basis;

[0066] The monorail vehicle dynamics model consists of longitudinal, lateral and yaw motion degrees of freedom in the body coordinate system, and the model is as follows:

[0067]

[0068] where, is the vehicle mass; are the longitudinal and lateral velocities of the vehicle, respectively; is the moment of inertia around the z-axis; is the tire force, subscript respectively denote longitudinal, lateral and vertical tire forces, the subscript respectively denote front and rear tire forces;

[0069] The front and rear lateral tire forces are obtained using an improved Magic Formula (MF) tire model which is able to capture the lateral force drop due to the applied longitudinal force:

[0070]

[0071] where, is the shape factor, is the stiffness factor, is the peak, is the curvature value; is the tire slip angle, the front tire slip angle , the rear tire slip angle ; is the reduction factor of the lateral force capability of the longitudinal tire force, ;

[0072] The lateral force is modeled by repeatedly linearizing the tire force model around the current slip angle at each time step, resulting in an affine function of the slip angle:

[0073]

[0074] where, considering the nonlinear characteristics of the tire, is the equivalent cornering stiffness of the front and rear tires; at each sampling time, the equivalent cornering stiffness should be updated according to the real-time tire slip angle.

[0075] According to the geometric relationship, the vehicle position in the fixed ground coordinate system and the yaw angle between the reference ground axis and the vehicle longitudinal axis are added to the 3-DOF monorail vehicle dynamics model, and the expression is:

[0076]

[0077] where, are the longitudinal and lateral positions of the mass center, respectively, denote the derivatives of the longitudinal, lateral positions and yaw angle of the mass center with respect to time;

[0078] The comprehensive vehicle prediction model for the trajectory tracking MPC controller is:

[0079]

[0080] where, denote the derivatives of the lateral velocity, longitudinal velocity, yaw angle and yaw rate with respect to time, respectively, represents the longitudinal acceleration.

[0081] Further, the step of step three further comprises:

[0082] For the vehicle prediction model of the built MPC controller, by defining a state vector, an input vector, an output vector of the system, the state space expression is obtained:

[0083]

[0084] wherein, represents the derivative of the state vector with respect to time, respectively, the state matrix, the input matrix and the output matrix; by performing a first-order Taylor expansion around the current time reference point of the prediction model, linearization processing is realized to accelerate the model calculation speed:

[0085]

[0086] Error feedback is introduced in the linear prediction model: according to the model prediction value obtained by the linear prediction model, the prediction model error is calculated with the current state quantity measured value :

[0087]

[0088] wherein, the prediction model error ;

[0089] After substituting the current time reference point , the prediction model is updated as:

[0090]

[0091] wherein, , , , ;

[0092] ;

[0093] ;

[0094] , ;

[0095] By adopting the forward Euler method, discretization is performed around the sampling time to obtain the discrete-time state space equation:

[0096]

[0097] where, denotes the state vector after discretization with one sampling step difference, denote the discretized input vector and prediction model error, respectively, is an identity matrix, denotes the current time.

[0098] Further, the step of step three further comprises:

[0099] minimizing the difference between the prediction output and the reference value, so that the vehicle is stably driven along the centerline within the given feasible region, i.e.,

[0100]

[0101] where, denotes the sum of the difference between the prediction output and the reference value in the prediction horizon; denote the prediction output and the reference output of a single sampling point, respectively, is the prediction length, denotes the rolling step;

[0102] minimizing the actuator control increment to avoid the influence of sharp steering and acceleration / braking operations on the comfort and safety of the driving process, i.e.,

[0103]

[0104] where, denotes the sum of the control increment in the control horizon, denotes the control increment of a single sampling step, is the control horizon;

[0105] Considering the limitations of the actuator hardware and the road conditions on the steering angle and longitudinal acceleration limit values and their rates of change, the input vector and the control increment are limited, i.e.,

[0106]

[0107]

[0108] where, denote the front wheel steering angle and the longitudinal acceleration control increment, respectively, denote the minimum and maximum values of the front wheel steering angle determined by the actuator hardware execution capability, denote the minimum and maximum values of the front wheel steering angle control increment, respectively; denote the minimum and maximum values of the longitudinal acceleration control increment, respectively;

[0109] The relaxation term is introduced to solve the case that the optimization problem has no solution, and the multi-objective cost function is expressed as follows:

[0110]

[0111] Wherein, The multi-objective cost function is represented by, The control target weight matrix is represented by, The control increment weight matrix is represented by; The relaxation factor weight coefficient and the relaxation factor are represented by and respectively.

[0112] The divergence of the lateral angle velocity and the mass center side deflection angle is limited by the vehicle state stability envelope built, so as to ensure the vehicle stability of the full-automatic vehicle in the trajectory tracking process:

[0113]

[0114] Wherein, The minimum and maximum lateral angle velocity stability boundaries and the minimum and maximum steady-state mass center side deflection angles are represented by and respectively.

[0115] The optimization problem is expressed as a quadratic programming for solving, and the first element of the optimal control sequence is applied to the vehicle system; then the prediction range is pushed forward by one time interval, and the optimization problem is solved again by using the new process measurement value.

[0116] The beneficial effects of the present application are:

[0117] (1) The present application proposes a trajectory tracking and stability coordination control method for unmanned vehicles based on switching envelope, which takes into account the dynamic safety constraints of front and rear wheel saturation limitation and adaptive weight distribution, improves the vehicle trajectory tracking ability under the premise of ensuring the vehicle stability.

[0118] (2) The present application designs a trajectory tracking switching envelope considering the front and rear wheel saturation, adjusts the priority of preventing steering loss and vehicle instability through the critical steering angle switching criterion, can dynamically update the vehicle stability boundary according to the tracking trajectory, vehicle state and actuator actuation amount, and improve the accuracy of the vehicle stability boundary description.

[0119] (3) The present application constructs a vehicle stability evaluation index based on switching envelope, dynamically adjusts the control demand through the weight adaptive adjustment scheme based on the vehicle stability evaluation index, and avoids the steering loss and instability of the unmanned vehicle in the extreme working condition. DETAILED DESCRIPTION

[0120] Figure 1 It is the overall structure flow schematic diagram of the method of the present application;

[0121] Figure 2This is a schematic diagram of the vehicle switching envelope design based on the saturation characteristics of the front and rear wheels according to the present invention;

[0122] Figure 3 This is a schematic diagram illustrating the stability evaluation of the envelope switching drive in this invention;

[0123] Figure 4 This is a schematic diagram of the adaptive adjustment of weights of multiple control targets driven by switching envelopes according to the present invention;

[0124] Figure 5 This is a schematic diagram of the MPC trajectory tracking controller design based on switching envelope constraints and adaptive weight adjustment according to the present invention. Detailed Implementation

[0125] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0126] like Figure 1 As shown, the trajectory tracking and stability coordination control method based on switching envelopes provided by this invention includes the following steps:

[0127] Step 1 proposes a vehicle stability domain switching envelope method based on the saturation characteristics of the front and rear wheels:

[0128] based on Phase plane ( and Let the sideslip angle and yaw rate be represented respectively. A stable boundary for the sideslip angle of the center of gravity, determined by the saturation sideslip angles of the front and rear wheels, is constructed. The critical steering angle is derived as a switching criterion to address the loss of steering capability in autonomous vehicles caused by considering only rear wheel saturation. This envelope can dynamically switch with vehicle speed, road adhesion coefficient, and steering angle, and is converted to... Phase plane ( and (representing the front and rear wheel slip angles respectively), ensuring a uniform distribution of the stability domain in the slip angle space, which facilitates the design of subsequent vehicle stability evaluation indicators to accurately reflect the vehicle's stability margin.

[0129] Furthermore, such as Figure 2 As shown, the vehicle stability domain switching envelope method based on front and rear wheel saturation characteristics described in this invention is as follows:

[0130] First of all, The phase plane is used to construct a preliminary range of the stability domain, including a yaw rate stability boundary and a center-of-gravity sideslip angle stability boundary determined by the rear wheel saturation sideslip angle. A center-of-gravity sideslip angle stability boundary determined by the front wheel saturation sideslip angle is introduced to avoid loss of steering capability due to large steering angle operations, serving as the basis for dynamic constraints on the vehicle state. By analyzing the variation characteristics of the three stability boundaries, the expression for the critical steering angle is derived, enabling dynamic switching of the stability envelope under different steering angles. Subsequently, the stability domain is expanded from... Phase plane mapping to The phase plane ensures a uniform distribution of the stability domain along the front and rear wheel sideslip angles, facilitating more effective capture of the vehicle's overall stability and serving as the basis for designing vehicle stability evaluation indicators. The dynamic stability domain, based on a switching envelope, can be updated in real-time with vehicle speed, adhesion coefficient, and steering input, providing dynamic safety constraints for subsequent stability evaluation and controller design, thereby improving the controllability and safety of autonomous vehicles during trajectory tracking.

[0131] Specifically, step one of this invention can be carried out in the following ways:

[0132] The yaw rate stability boundary and the center-of-gravity slip angle stability boundary, determined by the rear wheel saturation slip angle, serve as the initial range of the vehicle's stable envelope. Based on the quasi-steady-state cornering assumption and a given tire model, each boundary reflects the tire's maximum capacity. Therefore, regarding the vehicle's yaw rate... and centroid side slip angle The envelope is represented as:

[0133]

[0134]

[0135]

[0136]

[0137] in, These represent the maximum and minimum yaw rate stability boundaries, respectively. These represent the maximum and minimum centroidal sideslip angle stability boundaries determined by the rear wheel saturation sideslip angle, respectively. Indicates the road surface adhesion coefficient. Represents gravitational acceleration. This indicates the distance from the vehicle's center of gravity to the rear wheel. Indicates yaw rate. Indicates the longitudinal speed of the vehicle. This represents the rear wheel saturation slip angle corresponding to the maximum lateral tire force.

[0138] To prevent vehicle instability under given conditions, the stable equilibrium motion in the yaw rate-slip angle phase plane should be confined within the stability envelope as the steering angle increases. In reality, front axle saturation will cause the vehicle to tend towards extreme understeer, or even lose steering ability, causing panic among occupants. Therefore, as... Figure 2 As shown, two more are added based on the initial range of the stable envelope. These boundaries are determined by the slip angle of the front tires at peak tire force, and the equations for these newly added boundaries are as follows:

[0139]

[0140]

[0141] in, and These represent the maximum and minimum centroidal sideslip angle stability boundaries determined by the front wheel saturation sideslip angle, respectively. This indicates the distance from the vehicle's center of gravity to the front wheels. It's the steering angle of the front wheels. This represents the front wheel saturation slip angle corresponding to the maximum lateral tire force.

[0142] This study investigates the influence of steering angle on the vehicle's stability boundary, analyzing the switching criteria for the vehicle's stability boundary to prevent loss of steering ability and instability under different steering angle ranges. To derive the critical steering angle for front wheel saturation, the following boundary formulas are used to show the values ​​at different steering angles. Phase-plane vehicle state stability boundary diagram. In the phase plane, as the steering angle increases, the overall shape and intersection of the stability envelope, determined by the steady-state yaw rate and the rear wheel saturation sideslip angle, remain unchanged; however, the stability boundary line and intersection of the front wheel saturation sideslip angle change with the steering angle. Figure 2 The stability boundary of the maximum yaw rate becomes more pronounced with increasing steering angle. For the critical steering angle, the stability boundary of the maximum yaw rate is... The minimum centroid sideslip angle stability boundary determined by the front wheel saturation sideslip angle The minimum center-of-gravity sideslip angle stability boundary determined by the rear wheel saturation sideslip angle The intersection of their envelopes indicates that in The stable equilibrium point in the phase plane moves from (0,0) to the drift equilibrium point, where the vehicle trajectory bifurcates. A symmetric characteristic exists for the critical steering angle in opposite directions. Therefore, the critical steering angle is determined by... The intersection of the relevant envelopes determines the critical turning angle associated with the stability envelope, which can be obtained using the following formula:

[0143]

[0144]

[0145] in, These represent the minimum and maximum critical steering angles, respectively. , indicates the vehicle's wheelbase.

[0146] While the aforementioned phase plane analysis reveals the divergent relationship between the critical steering angle and the system, it is based on the open-loop assumption and cannot reflect the stability characteristics of the closed-loop control system in actual driving. Under extreme conditions such as large-angle trajectory tracking or emergency obstacle avoidance, the front wheel steering angle often instantaneously exceeds the critical value. Closed-loop control can improve vehicle handling performance while ensuring stability. After the steering angle exceeds the critical value, the range of the front wheel saturation sideslip angle stability boundary constraint is included within the range of the rear wheel saturation sideslip angle stability boundary constraint. With the rear wheel saturation sideslip angle as the envelope, the vehicle may experience front wheel saturation and loss of steering ability before the rear wheels saturate and become unstable, leading to panic among passengers. Therefore, it is necessary to introduce a dynamic stability boundary determined based on front wheel saturation and its switching mechanism with the rear axle boundary.

[0147] Further, the steady-state boundary of the vehicle's center of gravity sideslip angle under different front wheel steering angles was determined. The determination of both the maximum and minimum center of gravity sideslip angle stability boundaries is influenced by the front wheel steering angle: when the front wheel steering angle is positive and less than the critical steering angle, The centroid sideslip angle value corresponding to the intersection point is less than The centroid sideslip angle value corresponding to the intersection point; the minimum centroid sideslip angle stability boundary at this stage is determined by... Determined jointly; the current wheel angle is equal to the critical steering angle. The three intersect at the same point; when the front wheel steering angle is greater than the critical steering angle, then The centroid sideslip angle value corresponding to the intersection point is actually greater than The centroid sideslip angle value corresponding to the intersection point, at which point the minimum centroid sideslip angle stability boundary is determined by... and Determined. Based on the symmetry of the vehicle response under opposite steering angle inputs, the method for determining the stability boundary of the maximum centroid sideslip angle is the same as that for determining the stability boundary of the minimum centroid sideslip angle, and will not be repeated here.

[0148] From this, the maximum steady-state center of gravity sideslip angle of the vehicle can be derived. Side slip angle with minimum steady-state centroid The switching envelope expression is:

[0149]

[0150]

[0151] Designed according to driving environment and control input respectively The expression of the yaw rate stability boundary is:

[0152]

[0153]

[0154] The expression of the saddle position adjustment function and is:

[0155]

[0156]

[0157] The expression of the center of mass side slip angle stability boundary is:

[0158]

[0159]

[0160] The expression of the saddle position adjustment function and is:

[0161]

[0162]

[0163] wherein, respectively represent the saddle position adjustment function parameters;

[0164] According to the analysis results of the switching envelope stability boundary of the yaw rate and the center of mass side slip angle, combined with the front and rear wheel side slip angle calculation formula, the saddle position in the phase plane is constructed as follows:

[0165]

[0166]

[0167] The vehicle dynamic stability domain is dynamically changed by the driving environment and control input, including the road adhesion coefficient, vehicle speed and front wheel steering angle factors. The influence of various factors on the stability domain is shown in the vehicle state stability boundary and the saddle position adjustment function. The vehicle speed and the road adhesion coefficient are respectively inversely related and positively related to the size of the phase plane stability domain, while the front wheel steering angle only changes the stability domain position before the critical turning angle without changing the size.

[0168] Step two, stability evaluation and weight adaptive adjustment of switching envelope driving:

[0169] like Figure 3 and Figure 4 As shown, first, switch the envelope mapping to After the phase plane is switched, based on the dynamically stable domain defined by the envelope, the utilization rate of the vehicle's current state relative to the dynamically stable domain is calculated in real time to construct a vehicle stability evaluation index. This method quantifies the control margin of the current vehicle state in terms of steering ability and stability maintenance. Unlike traditional evaluation methods that only use the rear wheel saturation boundary, the switching envelope considers both front and rear wheel saturation and the critical steering angle, making the stability domain dynamically change with road adhesion, vehicle state, and steering angle input. The evaluation method based on the switching envelope can more accurately reflect the risk of steering loss and instability in the current state, realizing stability domain partitioning and vehicle stability evaluation; then, As a basis for weight adjustment, according to Size adaptively adjusts the control weights for longitudinal velocity, lateral position, yaw rate, and center of mass sideslip angle tracking: when At lower values ​​(far from the stability boundary), it means the vehicle has sufficient steering ability and stability margin. The controller increases the tracking weights of longitudinal velocity, lateral position, and yaw rate to improve trajectory tracking accuracy. Approaching the stability boundary means the vehicle has a greater risk of loss of steering and instability. Therefore, the tracking weights for ideal longitudinal velocity, ideal lateral position, and ideal yaw rate are reduced, while the tracking weight for the ideal center-of-gravity sideslip angle is increased, thus reducing trajectory tracking accuracy and improving stability control performance. Because... Based on the switching envelope calculation, its value is more sensitive to front / rear wheel saturation and steering angle changes, which can avoid the systematic overestimation of stability margin by the traditional single boundary of rear wheel saturation. This makes the weight adjustment more targeted and improves the effectiveness and robustness of trajectory tracking and stability control under intense steering operations. At the same time, it introduces consideration of vehicle steering ability into the traditional trajectory tracking control requirements to avoid vehicle instability, taking into account both handling and stability.

[0170] Specifically, step two of this invention can be carried out in the following ways:

[0171] First, to characterize the degree of vehicle stability, the vehicle state is used in... Position in the phase plane Design vehicle stability evaluation indicators :

[0172]

[0173] in, This represents the distance from the real-time vehicle status point to the origin of the phase plane. , , These are the radii of the safe zone, transition zone, and danger zone, respectively. The locations are in the safe zone. Transition Zone and danger zone The value of the stability evaluation index at the boundary time;

[0174] Based on the vehicle model's dynamic characteristics, the saturation sideslip angle of the front wheels is generally greater than that of the rear wheels. For example... Figure 3 As shown, a green area representing the safety zone is obtained by drawing a circle with the origin as the center and the rear wheel saturation sideslip angle as the radius. As the vehicle's state gradually deviates from its origin, the stability evaluation indicators... The value gradually increases if the location is within the safe zone. If the boundary is defined, then the stability evaluation index is taken as: It can be seen that when When this condition is met, the vehicle's dynamic capabilities are utilized at a low rate under the current operating conditions, and the vehicle is stable. The blue area representing the transition zone is obtained by drawing a circle with the front wheel saturation sideslip angle as the radius. The index range of 0.3 to 0.7 corresponds to the transition zone from... Boundary to The boundary is where the vehicle's power utilization rate continuously increases under the current operating conditions. A red area representing the danger zone is drawn with a radius equal to half the distance between the two saddle points. The indicator is from Corresponding to the danger zone from Boundary to The boundary and vehicle dynamics capabilities are used very frequently, and even slight disturbances can cause vehicle instability. It is worth noting that, in order to avoid... Excessive changes in weighting factors cause oscillations and limit controller performance, especially when the vehicle is in a danger zone. In addition, the stability index Restricted to .

[0175] Then, the dynamic safety requirements are adjusted according to the changes in the vehicle's stability zone. The stability zone characterizes different vehicle stability states and can be used as a condition for switching dynamic safety requirements in the control system. This is combined with stability evaluation indices based on the vehicle switching envelope method. It can quantitatively identify the position and stability of the vehicle state, and by dynamically adjusting the weight factors of the objective function, which reflect the priority of the control objective and the value of the constraints in the design control framework, it can clearly achieve the switching of power safety requirements shown in Table I.

[0176] Table I

[0177]

[0178] Referring to Table I, the relationship between the vehicle stable state and the dynamic control requirement is described as follows: when the vehicle state is in the stable region R1, it is expected to mainly improve the maneuverability of the vehicle, so the longitudinal speed tracking, lateral position tracking and yaw angular velocity tracking are the priority control targets, and the tracking weights of the longitudinal speed, lateral position and yaw angular velocity are increased. When the vehicle state is far away from the safety region, the safety requirement of lateral stability needs to be considered, so the priority of stability control increases with the increase of the stability index, and the priority of trajectory tracking decreases with the increase of the stability index. However, when the stability index is large, the lateral position tracking accuracy is given priority in the trajectory tracking task compared with the longitudinal speed tracking accuracy.

[0179] As can be seen from the above, the weight factors of longitudinal speed tracking and lateral position tracking are related to the value of the stability evaluation index. At the same time, by adjusting the weight factors of multiple control targets: longitudinal speed tracking weight , lateral position tracking weight and yaw angular velocity tracking weight , the dynamic adjustment of the maneuverability control requirement is realized; the adjustment of the weight values reflects the priority of the control targets in realizing the safety dynamic requirement in the whole control process; the weight factors of the weight self-adaptive adjustment function are as follows:

[0180]

[0181] wherein, represents the longitudinal speed, lateral position and yaw angular velocity, is an adjustment parameter, and in this embodiment, the value is 0.5.

[0182] By adjusting the weight factors of multiple control targets: the center of mass side slip angle tracking weight , the dynamic adjustment of the stability control requirement is realized; the weight factors of the weight self-adaptive adjustment function are as follows:

[0183]

[0184] wherein, represents the center of mass side slip angle tracking, is an adjustment parameter, and in this embodiment, the value is 0.5.

[0185] In order to explore the optimal value of the weight of the balanced vehicle speed tracking, position tracking and stability dynamic requirement under different working conditions, the joint simulation of the vehicle dynamics simulation software CarSim and MATLAB / Simulink is carried out, and the optimal value is determined through the sensitivity analysis of the control parameters. According to the relationship between the weight factors of the weight self-adaptive adjustment function and the adjustment parameters, the adjustment parameters are determined by the key point values. and Jointly determined. Key points for determining weighting factors. and The optimal values ​​for the weighting factors are determined through sensitivity analysis of the control performance indicators, including the root mean square error and maximum error, as shown in Table II. Furthermore, mathematically, smaller values ​​indicate better performance. It is worth noting that to enable vehicle operation under extreme conditions, such as low-traction surfaces, relatively high speeds, and emergency steering, some typical scenarios need to be included in the operation. Therefore, the performance indicators evaluate the control performance of different adjustment parameters under different road adhesion coefficients and vehicle speeds for double lane change and serpentine maneuvers. Only one parameter is changed in each evaluation, while the remaining parameters remain unchanged as a baseline. Adjustments to the weighting coefficients directly affect the overall control performance; the smaller the area enclosed by the five control performance indicators, the better the overall control performance.

[0186] Table II

[0187]

[0188] in, and These represent the root mean square error and the maximum error of longitudinal velocity tracking, respectively. Indicates the reference longitudinal velocity; and These represent the root mean square error and the maximum error of lateral position tracking, respectively. The reference horizontal position is determined by the tracking path; and Let represent the root mean square error and the maximum error of attitude angle tracking, respectively. and These represent the yaw angle and the reference yaw angle, respectively, which are determined by the tracking path; and These represent the root mean square error and the maximum error of yaw rate tracking, respectively. The reference yaw rate is calculated using the steady-state gain of the vehicle dynamics model. and These represent the root mean square error and the maximum error of the centroid sideslip angle tracking, respectively. These represent the total number of sampling points, a single sampling point, and the test duration, respectively.

[0189] Step 3: Design of MPC trajectory tracking controller based on switching envelope constraints and adaptive weight adjustment:

[0190] According to the control architecture of the model predictive control algorithm, a model predictive control (MPC) trajectory tracking controller containing switching envelope constraints and weight self-adaptive adjustment is designed, the dynamic stability domain defined by the switching envelope in step one is introduced to the yaw rate and the sideslip angle of the center of mass Vehicle state constraints are applied to define a multi-objective quadratic cost function containing the longitudinal speed, lateral position, yaw rate, sideslip angle tracking error of the center of mass and actuator actuation amount, and the dynamic control requirements are realized by introducing the weight self-adaptive adjustment in step two; the front wheel steering angle and longitudinal acceleration control amount are obtained through iterative optimization, and the trajectory tracking accuracy, vehicle stability and actuator smoothness are comprehensively optimized.

[0191] The design enables the controller to dynamically adjust the optimization target according to the remaining steering capability and stability state of the vehicle, while ensuring the maintenance of the steering capability and stability of the vehicle, and realizes the collaborative control of trajectory tracking and vehicle stability.

[0192] Specifically, as shown in Figure 5 Step three can be performed in the following aspects:

[0193] Firstly, a 3-DOF single-track vehicle dynamics model for phase plane vehicle stability analysis is built, and then a vehicle prediction model for the trajectory tracking MPC controller is built on this basis;

[0194] Further, the single-track vehicle dynamics model is composed of longitudinal, lateral and yaw motion degrees of freedom in the body coordinate system, and the model is as follows:

[0195]

[0196] Among them, is the mass of the vehicle; are the longitudinal and lateral speeds of the vehicle, respectively; is the moment of inertia around the z-axis; is the yaw rate; and are the distances from the center of mass of the vehicle to the front and rear wheels, respectively; is the tire force, and the subscripts indicate the longitudinal, lateral and vertical tire forces, respectively, and the subscripts indicate the front and rear tire forces, respectively, is the steering angle of the front wheel.

[0197] In the present application, the front and rear lateral tire forces and are obtained using the improved Magic Formula (MF) tire modelThe model is able to capture the lateral force drop due to the applied longitudinal force:

[0198]

[0199] wherein, is the lateral tire force, is the shape factor, is the stiffness factor, is the peak, is the curvature value; is the tire slip angle, front tire slip angle , rear tire slip angle ; is the derating factor providing capability of longitudinal tire force to lateral force, , is the road friction coefficient, is the vertical, longitudinal tire force;

[0200] The lateral force is modeled by repeatedly linearizing the tire force model around the current slip angle at each time step, resulting in an affine function of the slip angle:

[0201]

[0202]

[0203] wherein, is the steering angle of the front wheel, is the vehicle center of mass slip angle; considering the nonlinear characteristics of the tire, and are the equivalent cornering stiffness of the front and rear wheels; at each sampling time, the equivalent cornering stiffness should be updated according to the real-time tire slip angle.

[0204] According to the geometric relationship, the vehicle position in the fixed ground coordinate system and the yaw angle between the reference ground axis and the vehicle longitudinal axis are added to the 3-DOF monorail vehicle dynamics model, and the expression is:

[0205]

[0206]

[0207]

[0208] wherein, are the longitudinal and lateral positions of the center of mass, is the yaw angle, denotes the derivative of the longitudinal, lateral position and yaw angle of the center of mass with respect to time.

[0209] According to the small angle assumption, the vehicle prediction model for the trajectory tracking MPC controller is obtained as follows:

[0210]

[0211] where, denote the derivatives of the lateral velocity, longitudinal velocity, yaw angle and yaw rate with respect to time, denotes the longitudinal acceleration.

[0212] Then, for the vehicle prediction model of the built MPC controller, by defining as the state vector, as the input vector, as the output vector of the system, the state space expression is obtained as follows:

[0213]

[0214]

[0215] where, denotes the derivative of the state vector with respect to time, are the state matrix, input matrix and output matrix respectively; by performing the first-order Taylor expansion around the current time reference point of the prediction model, the linearization processing is realized to accelerate the model calculation speed:

[0216]

[0217] In order to compensate for the influence of the high-order terms ignored in the first-order linear expansion of the nonlinear model, the error feedback is introduced in the linear prediction model: the model prediction value obtained according to the linear prediction model is compared with the measured value of the current state quantity to calculate the prediction model error :

[0218]

[0219] where, the prediction model error ;

[0220] After substituting the current time reference point , the prediction model is updated as follows:

[0221]

[0222] where, , , , ;

[0223] ;

[0224] ;

[0225] , ;

[0226] Further, by employing forward Euler method, the above equation is discretized around the sampling time to obtain the discrete-time state-space equation:

[0227]

[0228] where, denotes the state vector one sampling step ahead of the current state vector, denote the discretized input vector and the prediction model error, respectively, is the identity matrix, denotes the current time;

[0229] In the designed MPC-based integrated strategy, multiple control objectives and constraints are considered to improve the overall handling stability of the vehicle. To meet the trajectory tracking requirement of the controller, the trajectory tracking problem is formulated as an optimization problem aiming to minimize the error of the vehicle longitudinal speed, lateral position and the desired driving trajectory. In addition, it is also a major task to make the vehicle travel along the predetermined trajectory stably, and the vehicle stability envelope is applied to the lateral velocity and the side slip angle constraints in the MPC controller. To travel along the centerline within the given feasible region, it is required to minimize the difference between the predicted output and the reference value, i.e.:

[0230]

[0231] where, denotes the total sum of the difference between the predicted output and the reference value within the prediction horizon; denote the predicted output and the reference output at a single sampling point, respectively, is the prediction length, denotes the rolling step;

[0232] The actuator control increment is minimized to avoid the impact of sharp steering and acceleration / braking operations on the driving process comfort and safety, i.e.:

[0233]

[0234] where, denotes the total sum of the control increment within the control horizon, denotes the control increment at a single sampling step, is the control horizon;

[0235] Considering the actuator hardware and road condition constraints on the steering angle and longitudinal acceleration limits and rates, the input vector and control increments are limited, i.e.,

[0236]

[0237]

[0238] where, and denote the front wheel steering angle and longitudinal acceleration control increments, respectively, and denote the minimum and maximum values of the front wheel steering angle determined by the actuator hardware execution capability, respectively, and denote the minimum and maximum values of the front wheel steering angle control increments, respectively; and denote the minimum and maximum values of the longitudinal acceleration control increments, respectively;

[0239] A relaxation term is introduced to solve the case of no solution to the optimization problem, and the multi-objective cost function is expressed as follows:

[0240]

[0241] where, denotes the multi-objective cost function, denotes the control target weight matrix, denotes the control increment weight matrix; and denote the relaxation factor weight coefficient and relaxation factor, respectively;

[0242] By building a vehicle state stability envelope to limit the divergence of the yaw rate and the center of mass side slip angle, the vehicle stability in the trajectory tracking process of the full-automatic vehicle is ensured:

[0243]

[0244]

[0245] where, and denote the minimum and maximum yaw rate stability boundaries, and the minimum and maximum steady-state center of mass side slip angles, respectively;

[0246] According to the above analysis, the optimization problem can be re-expressed as a quadratic programming (QP) for solving, and the first element of the optimal control sequence is applied to the vehicle system; then the prediction horizon is pushed forward by one time interval, and the optimization problem is solved again using the new process measurement values.

Claims

1. A trajectory tracking and stability coordinated control method based on switching envelope, characterized in that: Comprising the following steps: Step one, in The phase plane is respectively constructed by the front and rear wheel saturation side slip angle to determine the center of mass side slip angle stability boundary as the vehicle state switching envelope, while avoiding the steering loss caused by the front wheel saturation and the spinout instability caused by the rear wheel saturation; Based on the center of mass side slip angle stability boundary and the yaw rate stability boundary respectively determined by the front and rear wheel saturation side slip angle, the critical steering angle is derived as the switching criterion of the center of mass side slip angle stability boundary, and the envelope is dynamically switched with the vehicle speed, road adhesion coefficient and steering angle; The stability domain is switched from The phase plane is respectively constructed by the front and rear wheel saturation side slip angle to determine the center of mass side slip angle stability boundary as the vehicle state switching envelope, while avoiding the steering loss caused by the front wheel saturation and the spinout instability caused by the rear wheel saturation; Based on the center of mass side slip angle stability boundary and the yaw rate stability boundary respectively determined by the front and rear wheel saturation side slip angle, the critical steering angle is derived as the switching criterion of the center of mass side slip angle stability boundary, and the envelope is dynamically switched with the vehicle speed, road adhesion coefficient and steering angle; The stability domain is switched from The phase plane is respectively constructed by the front and rear wheel saturation side slip angle to determine the center of mass side slip angle stability boundary as the vehicle state switching envelope, while avoiding the steering loss caused by the front wheel saturation and the spinout instability caused by the rear wheel saturation; Based on the center of mass side slip angle stability boundary and the yaw rate stability boundary respectively determined by the front and rear wheel saturation side slip angle, the critical steering angle is derived as the switching criterion of the center of mass side slip angle stability boundary, and the envelope is dynamically switched with the vehicle speed, road The stability boundary of the center of mass side slip angle determined by the yaw rate stability boundary and the rear wheel saturation side slip angle as a preliminary range of the vehicle state stability envelope, with respect to the vehicle state yaw rate and the center of mass side slip angle is expressed as: ； wherein, and respectively denote the maximum and minimum yaw rate stability boundary, and respectively denote the maximum and minimum center of mass side slip angle stability boundary determined by the rear wheel saturation side slip angle, denotes the road surface adhesion coefficient, denotes the gravitational acceleration, denotes the distance of the vehicle center of mass to the rear wheels, denotes the longitudinal speed of the vehicle, denotes the rear wheel saturation side slip angle corresponding to the maximum lateral tire force; With increasing steering angle, Stable equilibrium motion in the phase plane should be limited to the stability envelope; two boundaries, determined by the side slip angle of the front tires at peak tire force, are added, the equations of which are as follows: ； wherein, and respectively denote the maximum and minimum center of mass cornering angle stability boundaries determined by the front wheel saturation cornering angle, denotes the distance from the vehicle center of mass to the front wheels, is the steering angle of the front wheels, denotes the front wheel saturation cornering angle corresponding to the maximum lateral tire force; In The critical steering angle in the phase plane vehicle state stability boundary diagram is determined by the intersection of the envelope lines related to The critical steering angle related to the stability envelope is obtained using the following formula: ； wherein and respectively denote the minimum and maximum values of the critical cornering angle, denotes the wheelbase of the vehicle; Introducing dynamic stability boundaries based on front-wheel saturation determination and switching mechanism between them and rear-wheel boundaries: The determination of the maximum and minimum center-of-gravity sideslip angle stability boundaries is affected by the front wheel steering angle: when the front wheel steering angle is positive and less than the critical steering angle, The centroid sideslip angle value corresponding to the intersection point is less than The centroid sideslip angle value corresponding to the intersection point; the minimum centroid sideslip angle stability boundary at this stage is determined by... Determined jointly; the current wheel angle is equal to the critical steering angle. The three intersect at the same point; when the front wheel steering angle is greater than the critical steering angle, then The centroid sideslip angle value corresponding to the intersection point is actually greater than The centroid sideslip angle value corresponding to the intersection point, at which point the minimum centroid sideslip angle stability boundary is determined by... and Determined; Based on the symmetry of the vehicle response under opposite steering angle inputs, the method for determining the maximum centroid sideslip angle stability boundary is the same as that for determining the minimum centroid sideslip angle stability boundary. Vehicle maximum steady-state center of mass side slip angle with a minimum steady-state center of mass side slip angle is given by: ； According to the driving environment and the control input respectively design The expression of the saddle point position adjustment function of the phase plane vehicle state stability boundary and the yaw rate stability boundary is: ； wherein the saddle point position adjustment function and is expressed as: ； The expression of the center-of-mass side-slip angle stability boundary is: ； wherein the saddle point position adjustment function and is expressed as: ； wherein, respectively represent the saddle position adjustment function parameters; Construction Saddle point position in phase plane And The expression equations are respectively: ； Step 2, switch envelope mapping to After the phase plane is switched, based on the dynamically stable domain defined by the envelope, the utilization rate of the vehicle's current state relative to the dynamically stable domain is calculated in real time to construct a vehicle stability evaluation index. ;Will As a basis for weight adjustment, the control weights for longitudinal velocity, lateral position, yaw rate, and center of gravity sideslip angle tracking are adaptively adjusted. When moving away from the stability boundary, the controller increases the tracking weight of the ideal longitudinal velocity, ideal lateral position, and ideal yaw rate, while decreasing the tracking weight of the ideal centroid sideslip angle; when As the system approaches the stability boundary, the tracking weights for the ideal longitudinal velocity, ideal lateral position, and ideal yaw rate are reduced, while the tracking weight for the ideal centroid sideslip angle is increased. The stable region represents different vehicle stability states, which are applied in the control system as the condition of switching dynamic safety requirements; the stability evaluation index based on the vehicle switching envelope method is combined , the position and stability of the vehicle state are quantitatively identified, and the relationship between the vehicle stability state and the dynamic control demand is described by dynamically adjusting the weight factor of the objective function: when the vehicle state is in the stable region R1, , the vehicle's maneuverability is expected to be mainly improved, so the tracking of the longitudinal speed, lateral position and yaw rate to the ideal value is the priority control target, and the tracking weight of the longitudinal speed, lateral position and yaw rate is increased; when the vehicle state is far away from the stable region and is in the boundary to boundary, , the stability control priority based on the centroid side slip angle increases with the increase of the stability index, and the priority of the tracking of the longitudinal speed, lateral position and yaw rate decreases with the increase of the stability index; when the stability index exceeds the transition zone, , the stability control is dominant, and the lateral position tracking accuracy is given priority in the trajectory tracking task; By adjusting the weight factors of multiple control objectives: longitudinal velocity tracking weight , lateral position tracking weight and yaw angular velocity tracking weight Dynamic adjustment of maneuverability control requirements is achieved; weight adaptive adjustment function of weight factor As follows: ； wherein, respectively denote longitudinal velocity, lateral position and yaw angular velocity, is an adjustment parameter; By adjusting the weight factor of multiple control objectives: the weight of the centroid side slip angle tracking Achieving dynamic adjustment of stability control requirements; weight factor of weight adaptive adjustment function The following is announced: ； wherein, denotes a centroid side-slip angle tracking, is an adjustment parameter; Based on the relationship between the weight factors and adjustment parameters of the weight adaptive adjustment function, the adjustment parameters are determined by taking values ​​at key points. and Jointly determined; key points for determining weighting factors and The optimal value is determined through sensitivity analysis of the weighting factors using control performance indicators, including the root mean square error and the maximum error. These control performance indicators include: Longitudinal velocity tracking: ； Path tracking 1 - lateral position tracking: ； Path tracking 2 - yaw angle tracking: ； Yaw rate tracking: ； Center-of-mass side-slip angle tracking: ； wherein, and respectively represent the error root mean square value and the maximum error of the longitudinal velocity tracking, represents the reference longitudinal velocity; and respectively represent the error root mean square value and the maximum error of the lateral position tracking, represents the reference lateral position, determined by the tracking path; and respectively represent the error root mean square value and the maximum error of the attitude angle tracking, and respectively represent the yaw angle and the reference yaw angle, determined by the tracking path; and respectively represent the error root mean square value and the maximum error of the yaw rate tracking, represents the reference yaw rate, calculated by the steady-state gain of the vehicle dynamics model; and respectively represent the error root mean square value and the maximum error of the mass center side slip angle tracking; respectively represent the total sampling points, the single sampling point and the test duration of the sensitivity analysis test; Step three, based on the control architecture of the model predictive control algorithm, a model predictive control trajectory tracking controller is designed, which contains switching envelope constraints and weight adaptive adjustment. The dynamic stability domain defined by the switching envelope in step one is introduced to the yaw rate and the sideslip angle of the center of mass The vehicle state constraints are applied to define a multi-objective quadratic cost function containing longitudinal speed, lateral position, yaw rate, sideslip angle tracking error of the center of mass, and actuator actuation amount, and the dynamic control requirements are achieved by introducing the weight adaptive adjustment in step two; the front wheel steering angle and longitudinal acceleration control amount are obtained by iterative optimization.

2. The trajectory tracking and stability coordination control method based on switching envelope according to claim 1, characterized in that: The steps of step two include: First, by the position of the vehicle state in the phase plane designing a vehicle stability evaluation index , representing the degree of vehicle stability: ； wherein, represents the distance from the real-time vehicle state point to the origin of the phase plane, , , are the radii of the safe zone, the transition zone and the danger zone, respectively; are the values of the stability evaluation index when the position is at the boundary of the safe zone , the transition zone and the danger zone , respectively. safe zone A green area representing the safe zone is drawn with the origin as the center and the rear wheel saturation sideslip angle as the radius; as the vehicle's state gradually moves away from the origin, the stability evaluation index... The value gradually increases if the location is within the safe zone. If the boundary is defined, then the stability evaluation index is taken as: ;when When this condition is met, the vehicle's dynamic capabilities are under low utilization under the current operating conditions, and the vehicle is stable; transition zone The blue area representing the transition zone is obtained by drawing a circle with the front wheel saturation sideslip angle as the radius. Boundary to Boundary, where the vehicle's power utilization rate continuously increases under current operating conditions; danger zone. The red area is represented by a circle with a radius equal to half the distance between the two saddle points. The index starts from... Corresponding to the danger zone from Boundary to The vehicle's dynamic capabilities are highly utilized at the boundary, and even slight disturbances can lead to vehicle instability.

3. The trajectory tracking and stability coordination control method based on switching envelope according to claim 1, characterized in that: The steps of step three include: First, a 3-DOF monorail vehicle dynamics model for phase plane vehicle stability analysis is built, and then a vehicle prediction model for trajectory tracking MPC controller is built on this basis; The 3-DOF monorail vehicle dynamics model consists of longitudinal, lateral and yaw motion degrees of freedom in the body coordinate system, and the model is as follows: ； wherein is the vehicle mass; and are the longitudinal and lateral velocities of the vehicle, respectively; is the moment of inertia about the z-axis; is the yaw rate; and are the distances from the vehicle center of mass to the front and rear wheels, respectively; is the tire force, the subscripts denote the longitudinal, lateral, and vertical tire forces, respectively, the subscripts denote the front and rear tire forces, respectively, is the steering angle of the front wheels; The front and rear wheel lateral tire forces are obtained using the modified magic formula MF tire model and which is able to capture the lateral force drop due to the applied longitudinal force: ； wherein, is the lateral tire force, is the shape factor, is the stiffness factor, is the peak, is the curvature value; is the tire slip angle, front tire slip angle , rear tire slip angle ; is the derating factor for the longitudinal tire force to lateral force capability, , is the road surface friction coefficient, is the vertical, longitudinal tire force; The lateral force is modeled by repeatedly linearizing the tire force model around the current side-slip angle at each time step to obtain an affine function of the side-slip angle: ； wherein, is the steering angle of the front wheels, is the vehicle mass center side slip angle; the non-linear characteristics of the tires are taken into account, is the equivalent cornering stiffness of the front and rear wheels; at each sampling time, the equivalent cornering stiffness should be updated according to the real-time tire side slip angle; According to the geometric relationship, the vehicle position in the fixed ground coordinate system and the yaw angle between the reference ground axis and the vehicle longitudinal axis are added to the 3-DOF monorail vehicle dynamics model, and the expression is: ； wherein, respectively the longitudinal and lateral position of the center of mass, denote the derivatives of the longitudinal, lateral position and yaw angle of the center of mass with respect to time; The vehicle prediction model for the trajectory tracking MPC controller is obtained by integration as follows: ； wherein respectively denote the derivative of the lateral velocity, longitudinal velocity, yaw angle and yaw rate with respect to time, denotes the longitudinal acceleration.

4. The trajectory tracking and stability coordination control method based on switching envelope according to claim 3, characterized in that: The steps of step three further include: For the vehicle prediction model of the built MPC controller, by defining x as the state vector, u as the input vector, y as the output vector of the system, the state space representation is obtained: ； wherein, denotes the derivative of the state vector with respect to time, are the state matrix, the input matrix and the output matrix, respectively; by performing a first order Taylor expansion around a reference point of the prediction model at the current time instant linearization is achieved, accelerating the model computation speed: ； Introducing error feedback in linear prediction model: model predicted value according to linear prediction model with current state quantity measured value Calculate prediction model error : ； wherein the prediction model error ; Substitute the current time reference point After that, the prediction model is updated as: ； wherein , , , ; ； ； , ； By using the forward Euler method, the state-space equations are discretized around the sampling time t k, yielding the discrete-time state-space equations: ； wherein, denotes the state vector after discretization and phase difference one sampling step, denote the discretized input vector and the prediction model error, respectively, is the identity matrix, denotes the current time.

5. The trajectory tracking and stability coordination control method based on switching envelope according to claim 4, characterized in that: The steps of step three further include: Minimize the difference between the predicted output and the reference value to make the vehicle travel stably along the centerline within the given feasible region, i.e. ； wherein, denotes the sum of the differences between the predicted output and the reference values in the prediction horizon; denote the predicted output and the reference output of a single sample point, respectively, is the prediction length, denotes the rolling step. Minimize the actuator control increment to avoid the influence of sharp steering and acceleration / braking operations on the comfort and safety of the driving process, i.e. ； wherein denotes the sum of control increments within the control horizon, denotes a control increment of a single sampling step, is the control horizon; Considering the limitations of actuator hardware and road conditions on the limit values and rates of change of steering angle and longitudinal acceleration, the input vector and control increment are limited, i.e. ； wherein, and respectively represent a front wheel steering angle and a longitudinal acceleration control increment, and respectively represent a front wheel steering angle minimum value and a maximum value determined by an actuator hardware execution capability, and respectively represent a front wheel steering angle control increment minimum value and a maximum value; respectively represent a longitudinal acceleration control increment minimum value and a maximum value; A relaxation term is introduced to solve the case where the optimization problem has no solution, and the multi-objective cost function is expressed as follows: ； wherein, represents a multi-objective cost function, represents a control target weight matrix, represents a control increment weight matrix; respectively represent a relaxation factor weight coefficient and a relaxation factor. By building the vehicle state stability envelope to limit the divergence of yaw rate and center-of-mass side-slip angle, the stability of the vehicle during trajectory tracking is ensured: ； wherein, respectively denote the minimum, maximum yaw rate stability boundary, and the minimum, maximum steady state side slip angle. The optimization problem is formulated as a quadratic program for solution, and the optimal control sequence The first element of the sequence is applied to the vehicle system; the prediction horizon is then advanced by one time interval, and the optimization problem is solved again using the new process measurements.

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