4wid-4ws vehicle trajectory tracking control method and system based on dynamic feasible stable constraint and vehicle

Abstract

The present application relates to the technical field of vehicle chassis control, in particular to a 4WID-4WS vehicle trajectory tracking control method and system based on dynamic feasible stability constraints and a vehicle. The method first acquires vehicle state, road adhesion, reference trajectory and front and rear axle longitudinal force, updates equivalent side slip stiffness online, and constructs a joint coordination controller. Then, combined with road adhesion, dynamic vertical load, longitudinal force and equivalent side slip stiffness, the remaining lateral force after the longitudinal force occupies the adhesion resources and the saturated side slip angle of the tire are calculated, the dynamic steering boundary is generated with the center of the reference steering angle, the intersection with the steering mechanism physical boundary is obtained, the dynamic feasible stability constraints are obtained and are included in the rolling optimization feasible region. Finally, the front and rear wheel equivalent steering angles and the front and rear axle longitudinal forces are solved, and are distributed as four-wheel steering angles and driving and braking torque to be executed. The present application can make the steering constraint boundary expand and retract in real time with the remaining lateral ability, effectively improve the trajectory tracking accuracy, adhesion utilization rate and vehicle driving stability under strong coupling conditions.

Description

Technical Field

[0001] This invention relates to the field of vehicle chassis control technology, specifically a 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints, a 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints, and a 4WID-4WS intelligent vehicle. Background Technology

[0002] With the development of drive-by-wire chassis and distributed drive technology, four-wheel independent drive-four-wheel steering (4WID-4WS) vehicles, with their multi-degree-of-freedom execution advantages, have become an important technological direction for intelligent electric vehicle chassis. Currently, the trajectory tracking control of 4WID-4WS vehicles generally adopts a lateral and longitudinal layered decoupled architecture: the steering degree of freedom is responsible for lateral trajectory tracking, and the longitudinal drive and braking degree of freedom is responsible for vehicle speed tracking and stability control. The two controllers solve independently and output commands separately; some integrated solutions are also based on linear vehicle models with fixed parameters, coupled with stability constraint boundaries with fixed thresholds.

[0003] However, under strong steering-braking coupling conditions, this type of technical solution has a fundamental physical defect: the total adhesion between the tire and the road surface is constrained by the friction circle. After the longitudinal braking force occupies part of the adhesion resources, the maximum lateral force that the tire can provide will decrease accordingly. The independently operating steering controller is unable to perceive the degree of longitudinal force occupying the adhesion resources in real time and still outputs steering angle commands according to the trajectory tracking requirements. This can easily cause the tire slip angle to exceed the saturation threshold, and the lateral force to enter the nonlinear saturation region. Ultimately, this manifests as a decrease in yaw gain, an increase in trajectory tracking deviation, and even sideslip instability.

[0004] Meanwhile, existing control schemes mostly use offline calibrated fixed lateral stiffness to build predictive models. However, longitudinal load transfer and tire slippage under forced driving conditions will significantly change the actual equivalent lateral stiffness of the tire. The mismatch between model parameters and the tire's real-time operating point will further reduce the accuracy of predictive control and exacerbate overshoot and oscillation of control variables. In addition, existing stability constraints mostly use fixed steering angle limits, yaw rate thresholds, or static lateral stiffness thresholds. Even if some schemes consider the adhesion limit, they usually do not continuously convert the current longitudinal force on the front and rear axles to the amount of adhesion resources, dynamic vertical load, and online equivalent lateral stiffness into the dynamic boundary of the front and rear axle steering angles. Furthermore, they do not write the intersection of this dynamic boundary and the physical boundary of the steering mechanism into the rolling optimization feasible region. Therefore, it is difficult to tighten the boundary in real time under low-adhesion forced driving conditions and release steering ability under high-adhesion low-braking conditions.

[0005] In summary, existing 4WID-4WS vehicle trajectory control technology still suffers from shortcomings in the context of strong coupling between steering and braking, including poor coordination of adhesion resources, insufficient model parameter adaptability, and a disconnect between stability constraints and tire remaining lateral capacity. There is a need to propose an integrated control scheme that can generate feasible steering boundaries in real time based on road surface adhesion, dynamic vertical loads, current longitudinal forces, and equivalent lateral stiffness. In particular, current technologies lack a solution to link the current longitudinal forces of the front and rear axles, the dynamic vertical loads of the four wheels, and the online-updated equivalent lateral stiffness of the front and rear axles, continuously converting them into dynamic steering angle boundaries for the front and rear axles that are written into the model's predictive control feasible domain. Summary of the Invention

[0006] To address the technical problems of insufficient trajectory tracking accuracy, easy tire lateral force saturation, and poor vehicle driving stability in existing 4WID-4WS vehicle trajectory tracking control under strong steering-braking coupling conditions, due to its lateral and longitudinal decoupling architecture, fixed lateral stiffness model, and the failure of stability constraints to change in real time with the remaining lateral capacity after the longitudinal force occupies the attachment resources, this invention provides a 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints. Based on this vehicle trajectory tracking control method, this invention also provides a 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints and a 4WID-4WS intelligent vehicle.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints includes the following steps: Acquire vehicle status information A, road surface adhesion information B, and reference trajectory information C. The vehicle status information A includes at least the vehicle motion state, wheel angle, wheel speed, and current longitudinal force information of the front and rear axles. Establish vehicle dynamics model F and path tracking error model S. Based on vehicle status information A, calculate tire working status D and four-wheel dynamic vertical load E, and update the front and rear axle equivalent lateral stiffness K online by combining road surface adhesion information B and four-wheel dynamic vertical load E. Based on F, S, and the updated K, a joint coordination controller G is constructed. G uses the vehicle's longitudinal speed, lateral position, and heading angle as tracking outputs, and the equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles as unified control quantities to generate a predictive output equation H. At the same time, the control quantity amplitude constraint I and the control increment change constraint J are preset. Based on road surface adhesion information B, four-wheel dynamic vertical load E, current front and rear axle longitudinal forces, and updated front and rear axle equivalent lateral stiffness K, the remaining available lateral force after the longitudinal force occupies the adhesion resources is calculated; the tire saturation lateral force is calculated according to the remaining available lateral force; the front and rear wheel dynamic steering boundaries M are generated with the front and rear axle reference steering angle corresponding to the current vehicle motion state as the center; and the intersection of the front and rear wheel dynamic steering boundaries M and the steering mechanism physical boundary N is taken to obtain the dynamic feasible stability constraint P; Construct an objective function Q, using the predicted output equation H as the prediction basis, and jointly define the dynamic feasible stability constraint P, the control quantity amplitude constraint I, and the control increment change constraint J as the optimization feasible region R. Then, perform rolling optimization solution on the equivalent steering angle of the front and rear wheels and the longitudinal force of the front and rear axles within the optimization feasible region R. The equivalent steering angles and longitudinal forces of the front and rear axles obtained from the rolling optimization solution are converted into four-wheel independent steering angles T and four-wheel drive braking torques U, and then sent to the four-wheel steering mechanism and the four-wheel drive brake actuator.

[0008] As a further improvement to the above scheme: the vehicle dynamics model F is a three-degree-of-freedom vehicle dynamics model, and its expression is: ; Where m is the total vehicle mass; I z V represents the moment of inertia of the entire vehicle about the Z-axis of the vehicle coordinate system. x The velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system; For V x The first derivative of V, i.e., longitudinal acceleration; y The velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system; For V y The first derivative of , i.e., lateral acceleration; r is the vehicle's yaw rate; l f The distance from the vehicle's center of gravity to the front axle; r d is the distance from the vehicle's center of gravity to the rear axle; d is the vehicle's half track width; F x,fl F x,fr F x,rl F x,rr These are the forces acting along the positive X-axis of the vehicle coordinate system on the left front, right front, left rear, and right rear wheels, respectively, i.e., longitudinal forces; F y,fl F y,fr F y,rl F y,rr These are the forces acting along the positive Y-axis of the vehicle coordinate system for the left front, right front, left rear, and right rear wheels, respectively, i.e., the lateral forces.

[0009] As a further improvement to the above scheme, the expression for the path tracking error model S is: ; In the formula, y e This refers to the tracking error along the positive Y-axis of the vehicle coordinate system, i.e., the lateral tracking error. For y e The first derivative; V x The velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system; β is the heading tracking error; L is the vehicle's center of gravity sideslip angle; p is the preview distance of the vehicle's reference trajectory; r is the vehicle's yaw rate; ρ is the first derivative of r, i.e., the vehicle's yaw acceleration; ρ is the road curvature of the vehicle's reference trajectory.

[0010] As a further improvement to the above scheme: the tire working state D is jointly characterized by the tire slip ratio, tire side slip angle, four-wheel dynamic vertical load E, and road adhesion coefficient; the tire longitudinal force and lateral force are calculated based on a joint slip correction tire model, which includes the Pacejka tire model, and its correction form is as follows: ; ; Among them, F x,i F is the corrected force exerted by the i-th wheel along the positive X-axis of the vehicle coordinate system, i.e., the longitudinal force; y,i This is the corrected force exerted by the i-th wheel along the positive Y-axis of the vehicle coordinate system, i.e., the lateral force; μ i G represents the road adhesion coefficient corresponding to the i-th wheel; xα G is the correction factor for the longitudinal force by the wheel slip angle α. yκ F is the correction factor for the slip ratio κ with respect to the lateral force. x0,i F is the longitudinal force of the i-th wheel under pure longitudinal slip; y0,i Let be the lateral force of the i-th wheel under pure lateral slip; The four-wheel dynamic vertical load E is calculated in real time based on the vehicle's longitudinal acceleration, lateral acceleration, center of gravity height, wheelbase, and half-track.

[0011] As a further improvement to the above scheme: the joint coordination controller G is a multi-input multi-output linear time-varying model predictive controller, and its state vector and control vector are defined as follows: ; ; Among them, V x V is the velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system. y X represents the velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system; X and Y represent the longitudinal and lateral positions of the vehicle's center of mass in the geodetic coordinate system, respectively. δ is the vehicle's heading angle. fδ is the equivalent steering angle of the front wheels. r F is the equivalent steering angle of the rear wheels. x,f F is the total longitudinal force on the front axle. x,r This represents the total longitudinal force on the rear axle. The controller uses the control increment as the optimization variable and combines it with the real-time updated front and rear axle equivalent lateral stiffness K to correct the model parameters, thus constructing the predicted output equation H: ; Where Y is the output vector in the prediction time domain; Let ΔU be the extended state vector at the current moment, and let ΔU be the control increment sequence in the prediction time domain. , All are prediction coefficient matrices that are updated in real time with the equivalent lateral stiffness K of the front and rear axles.

[0012] As a further improvement to the above scheme: the dynamic feasible stability constraint P is obtained through a continuous calculation chain of longitudinal forces on the front and rear axles, remaining available lateral forces, tire saturation slip angle, and the physical boundary of the steering mechanism; for the j-th axle, the maximum available lateral force corresponding to that axle is first calculated based on the adhesion margin after the longitudinal forces are occupied: ; Then, the tire saturation slip angle L is calculated based on the maximum available lateral force and the equivalent lateral stiffness, so that the tire slip angle boundary changes in real time with the remaining lateral capacity after the longitudinal force is occupied: ; In the formula, Corresponding to the front axle and rear axle respectively; The maximum available lateral force on the j-th axis after the current longitudinal force has occupied the attachment resources; Let J be the road surface adhesion coefficient corresponding to the j-th axis; For the dynamic vertical load of the j-th axis; The longitudinal force is along the j-th axis; Let be the equivalent lateral stiffness of the j-th axis; The tire saturation sideslip angle for the j-th axis; With the j-th axis as the reference steering angle δ j,c Centered on the tire saturation sideslip angle, a dynamic steering boundary is generated, and the intersection of the dynamic steering boundary and the physical boundary of the steering mechanism is taken to obtain the final steering angle constraint range corresponding to the dynamic feasible stability constraint P written into the optimization feasible domain R: ; ; In the formula, , These are the final lower and final upper bounds of the steering angle of the j-th axis, respectively; The reference steering angle for the j-th axis; Let be the physical limit angle of the j-th axis steering mechanism.

[0013] As a further improvement to the above scheme: the objective function Q is a quadratic cost function, which includes a tracking error penalty term, a control increment penalty term, a slack variable penalty term, and a longitudinal force consistency penalty term between the front and rear axles, and its specific expression is as follows: ; In the formula, J is the cost; Y is the output vector in the prediction time domain; Y ref The reference output vector is denoted by Q; the tracking error weight matrix is ​​denoted by ΔU; the control increment sequence in the prediction time domain is denoted by R; the control increment weight matrix is ​​denoted by ζ; the slack variable weights are denoted by ε; and the slack variable weights are denoted by λ. F For the consistency weight of longitudinal forces between the front and rear axles; F x,f F is the total longitudinal force on the front axle. x,r The total longitudinal force is at the rear axle; T represents matrix transpose. The optimal feasible region R is composed of dynamic feasible stability constraints P, control magnitude constraints I, and control increment change constraints J, specifically in the following form: ; in, , These are the lower and upper bounds of the control variable U, respectively. , These are the lower and upper bounds of the control increment ΔU, respectively. The equivalent steering angle of the j-th axis; , These are the final lower and final upper bounds of the steering angle of the j-th axis, respectively.

[0014] The rolling optimization solution process involves minimizing the objective function Q within the feasible region R, and outputting the optimal equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles.

[0015] As a further improvement to the above scheme: the four-wheel independent steering angle T is generated by Ackermann steering geometry mapping, which converts the equivalent steering angles of the front and rear axles into the independent steering angles of the left and right wheels of the corresponding axles; The four-wheel drive braking torque U is generated based on the proportional distribution of the dynamic vertical load E of the four wheels. According to the proportion of the vertical load of a single wheel to the total vertical load of the corresponding axle, the total longitudinal force of the front and rear axles is decomposed into the longitudinal force of the four wheels, and then converted into wheel end torque through the wheel rolling radius. The conversion relationship is as follows: ; In the formula, U i R is the driving and braking torque of the i-th wheel; w F is the rolling radius of the wheel; x,i Let be the longitudinal force of the i-th wheel.

[0016] A 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints is characterized in that it executes a 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints, including an information acquisition unit, a vehicle modeling unit, an equivalent lateral stiffness update unit, a controller construction unit, a residual lateral force and dynamic constraint generation unit, a rolling optimization unit, and an execution allocation unit connected in sequence. The information acquisition unit is used to acquire vehicle status information A, road surface adhesion information B, and reference trajectory information C; The vehicle modeling unit is used to establish the vehicle dynamics model F and the path tracking error model S; The equivalent lateral stiffness update unit is used to calculate the tire working state D and the dynamic vertical load E of the four wheels based on the vehicle state information A, and update the equivalent lateral stiffness K of the front and rear axles online in combination with the road surface adhesion information B. The controller construction unit is used to construct a joint coordination controller G based on the vehicle dynamics model F, the path tracking error model S, and the updated equivalent lateral stiffness K of the front and rear axles, generate the predictive output equation H, and preset the control quantity amplitude constraint I and the control increment change constraint J. The residual lateral force and dynamic constraint generation unit is used to calculate the remaining available lateral force after the longitudinal force occupies the adhesion resources, the tire saturation slip angle L, and the dynamic steering boundary M of the front and rear wheels by combining the dynamic vertical load E of the four wheels, the updated equivalent lateral stiffness K of the front and rear axles with the road adhesion information B and the current longitudinal force of the front and rear axles. The dynamic feasible stability constraint P is obtained by taking the intersection of the dynamic steering boundary M of the front and rear wheels and the physical boundary N of the steering mechanism. The rolling optimization unit is used to construct the objective function Q. Based on the prediction output equation H, it integrates the dynamic feasible stability constraint P, the control quantity amplitude constraint I, and the control increment change constraint J to limit the optimization feasible region R, and solves the optimal front and rear wheel equivalent steering angle and front and rear axle longitudinal force. The execution distribution unit is used to convert the solved equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles into independent steering angles T of the four wheels and braking torques U of the four wheels, and then send them to the four-wheel steering mechanism V and the four-wheel drive brake actuator W.

[0017] A 4WID-4WS intelligent vehicle includes a vehicle body, a four-wheel steering mechanism V, a four-wheel drive brake actuator W, and a 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints. The output of the trajectory tracking control system is connected to the four-wheel steering mechanism V and the four-wheel drive brake actuator W respectively. It is used to send four-wheel independent steering angle T control commands to the four-wheel steering mechanism V and four-wheel drive braking torque U control commands to the four-wheel drive brake actuator W.

[0018] Compared with the prior art, the beneficial effects of the present invention are: Compared with the prior art, the beneficial effects of the present invention include at least the following three points: First, the equivalent steering angle of the front and rear wheels and the longitudinal force of the front and rear axles are incorporated into the same joint coordination controller for rolling optimization solution, avoiding control conflicts and internal friction of drive and brake caused by the separate occupation of adhesion resources by the lateral and longitudinal decoupled control under the forced dynamic steering condition; Second, based on the road adhesion coefficient, the dynamic vertical load of the four wheels, the current longitudinal force of the front and rear axles and the online equivalent lateral stiffness, the remaining available lateral force, the tire saturation lateral angle and the dynamic steering boundary of the front and rear axles are calculated in sequence, and the intersection of this boundary and the physical boundary of the steering mechanism is used to form a dynamic feasible stability constraint, so that the lateral capacity of the constraint boundary expands and contracts in real time after the longitudinal force occupies the adhesion resources; Third, the prediction model is corrected by updating the equivalent lateral stiffness of the front and rear axles online, and a consistency penalty term for the longitudinal force of the front and rear axles is introduced into the objective function, so that the model parameters, stability constraints and execution output are all matched with the real-time working state of the tires, thereby improving the trajectory tracking accuracy, adhesion utilization efficiency and vehicle driving stability under the strong coupling condition of steering-braking. Attached Figure Description

[0019] Figure 1 The flowchart shows the 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints. The dynamic constraint generation step includes the current longitudinal force input of the front and rear axles, the calculation of the remaining available lateral force, the calculation of the tire saturation slip angle, and the generation path of the dynamic steering boundary.

[0020] Figure 2 This is a schematic diagram of the path tracking error model.

[0021] Figure 3 This is a force diagram of the three-degree-of-freedom dynamic model of the 4WID-4WS vehicle.

[0022] Figure 4 A flowchart for generating dynamic feasible stability constraints is provided, illustrating the calculated relationships between the road adhesion coefficient, dynamic vertical load, current longitudinal forces on the front and rear axles, equivalent lateral stiffness, remaining available lateral force, tire saturation lateral angle, and the physical boundaries of the steering mechanism. Among these, Figure 4 The final stability constraint in the equation is the dynamic feasible stability constraint P.

[0023] Figure 5 This is a schematic diagram of the vehicle trajectory tracking control system.

[0024] Figure 6 Comparison curves of vehicle trajectories under variable attachment double lane change conditions.

[0025] Figure 7 A comparison curve of lateral tracking error under variable attachment dual-line shifting conditions. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] like Figure 1 As shown, this specific implementation focuses on the 4WID-4WS vehicle trajectory control scheme based on dynamic feasible stability constraints. Based on a unified benchmark of the vehicle coordinate system and the geodetic coordinate system, it refines the following in sequence: the construction of the vehicle dynamics model and path tracking error model; the calculation of tire working states and four-wheel dynamic vertical loads; the online update mechanism of the equivalent lateral stiffness of the front and rear axles; the derivation process of the joint coordination controller; the calculation logic for calculating the remaining available lateral forces from the current longitudinal forces of the front and rear axles and generating dynamic feasible stability constraints; the objective function and optimization feasible region construction method; and the execution layer conversion rules for Ackerman steering mapping and vertical load proportional allocation. The specific content is as follows: I. A 4WID-4WS Vehicle Trajectory Tracking Control Method Based on Dynamically Feasible Stability Constraints This section presents a 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints. This method is executed by the vehicle chassis domain controller, and the overall process is as follows: Figure 1 As shown, its core lies in converting the remaining available lateral force after the longitudinal force occupies the attachment resources into dynamic steering boundaries for the front and rear axles, and using it as a real-time feasible constraint for rolling optimization. Specifically, it includes the following steps: (I) Information Acquisition and Basic Model Establishment Obtain vehicle status information A, road surface adhesion information B, and reference trajectory information C, and establish vehicle dynamics model F and path tracking error model S.

[0028] Among them, vehicle status information A is collected in real time through the on-board sensor network, including parameters such as the longitudinal velocity of the vehicle's center of gravity, the lateral velocity of the center of gravity, the yaw rate, the longitudinal acceleration, the lateral acceleration, the wheel speeds of the four wheels, the steering angles of the four wheels, the braking pressure, and the current longitudinal forces of the front and rear axles estimated from the wheel-end driving braking torque or braking pressure; road surface adhesion information B can be provided by the vehicle electronic stability control system, the tire force estimation module, or the road condition recognition module, outputting the road surface adhesion coefficient corresponding to each wheel; reference trajectory information C is output by the upper-level planning system, including the discrete path point sequence, road curvature, and desired longitudinal velocity. The controller extracts the reference sequence in the prediction time domain according to the current vehicle position and the preview distance.

[0029] 1. Vehicle dynamics model F

[0030] The vehicle dynamics model F is a three-degree-of-freedom vehicle dynamics model used to describe the dynamic response of the vehicle in the longitudinal, lateral, and yaw degrees of freedom. A schematic diagram of the model is shown below. Figure 3 As shown. Figure 3 Based on a vehicle coordinate system XY with its origin at the vehicle's center of mass, the following parameters are defined: longitudinal velocity Vx, lateral velocity Vy, sideslip angle β, yaw rate r, distances from the center of mass to the front and rear axles lf and lr, semi-track d, and the independent steering angles, longitudinal forces, lateral forces, and sideslip angles of the four wheels. These parameters are used to characterize the force relationships of the 4WID-4WS vehicle under steering-braking coupling conditions. The expression for this is: ; Where m is the total vehicle mass; I z V represents the moment of inertia of the entire vehicle about the Z-axis of the vehicle coordinate system. x The velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system; For V x The first derivative of V, i.e., longitudinal acceleration; y The velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system; For V y The first derivative of , i.e., lateral acceleration; r is the vehicle's yaw rate; l f The distance from the vehicle's center of gravity to the front axle; r d is the distance from the vehicle's center of gravity to the rear axle; d is the vehicle's half track width; F x,fl F x,fr F x,rl F x,rr These are the forces acting along the positive X-axis of the vehicle coordinate system on the left front, right front, left rear, and right rear wheels, respectively, i.e., longitudinal forces; F y,fl F y,fr F y,rl F y,rr These are the forces acting along the positive Y-axis of the vehicle coordinate system for the left front, right front, left rear, and right rear wheels, respectively, i.e., the lateral forces.

[0031] The vehicle dynamics model F can accurately reflect the coupling relationship between longitudinal, lateral and yaw motions under steering-braking coupling conditions, while controlling the model complexity to meet the real-time calculation requirements of the on-board controller.

[0032] 2. Path tracking error model S

[0033] The path tracking error model S is used to quantify the degree of deviation of the vehicle from the reference trajectory. A schematic diagram of the model is shown below. Figure 2 As shown. Figure 2 Constructed based on the XY geodetic coordinate system, it displays the reference trajectory, vehicle's current position, preview point, preview distance L, and heading angle. and reference heading angle Ref is used to define lateral tracking error and heading tracking error, and its expression is: ; In the formula, y e This refers to the tracking error along the positive Y-axis of the vehicle coordinate system, i.e., the lateral tracking error. For y e The first derivative; V x The velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system; β is the heading tracking error; L is the vehicle's center of gravity sideslip angle; p is the preview distance of the vehicle's reference trajectory; r is the vehicle's yaw rate; ρ is the first derivative of r, i.e., the vehicle's yaw acceleration; ρ is the road curvature of the vehicle's reference trajectory.

[0034] The path tracking error model S directly correlates the vehicle's motion state with the trajectory tracking deviation, providing a quantitative basis for the subsequent controller's tracking output definition and objective function error calculation.

[0035] (II) Tire condition calculation and equivalent lateral stiffness update

[0036] Based on vehicle status information A, calculate tire working state D and four-wheel dynamic vertical load E, and update the front and rear axle equivalent lateral stiffness K by combining road surface adhesion information B.

[0037] 1. Obtain tire operating status D

[0038] The tire operating state D is characterized by tire slip ratio, tire slip angle, four-wheel dynamic vertical load E, and road adhesion coefficient. First, based on vehicle state information A, the longitudinal slip ratio and slip angle of each wheel are calculated: ; ; Among them, κ i Let α be the slip ratio of the i-th wheel; i R is the sideslip angle of the i-th wheel; w ω is the rolling radius of the wheel; i v is the angular velocity of the i-th wheel; x,i v is the velocity of the i-th wheel along the X-axis of the vehicle coordinate system; n,i The nominal reference speed of the i-th wheel is usually the larger of the longitudinal velocity at the wheel center and the linear velocity of the wheel; v y,i Let δ be the velocity of the i-th wheel along the Y-axis of the vehicle coordinate system; i Let be the steering angle of the i-th wheel.

[0039] The longitudinal and lateral forces of the tire are calculated based on a combined slip correction tire model, which includes the Pacejka tire model, and its correction form is as follows: ; ; Among them, F x,i F is the corrected force exerted by the i-th wheel along the positive X-axis of the vehicle coordinate system, i.e., the longitudinal force; y,i This is the corrected force exerted by the i-th wheel along the positive Y-axis of the vehicle coordinate system, i.e., the lateral force; μ i G represents the road adhesion coefficient corresponding to the i-th wheel; xα G is the correction factor for the longitudinal force by the wheel slip angle α. yκ F is the correction factor for the slip ratio κ with respect to the lateral force. x0,i F is the longitudinal force of the i-th wheel under pure longitudinal slip; y0,i Let be the lateral force of the i-th wheel under pure lateral slip; The combined slip correction tire model can accurately reflect the weakening effect of longitudinal slip on lateral force under the coupled steering and braking conditions, thus improving the accuracy of tire force calculation.

[0040] 2. Calculate the dynamic vertical load E of the four wheels.

[0041] The four-wheel dynamic vertical load E is calculated in real time based on the vehicle's longitudinal acceleration, lateral acceleration, center of gravity height, wheelbase, and semi-track width, reflecting the load transfer effect during braking and steering. The calculation formula is as follows: ; ; ; ; In the formula, m is the total vehicle mass. This refers to the vehicle's wheelbase. This is the distance from the vehicle's center of gravity to the front axle. This is the distance from the vehicle's center of gravity to the rear axle. The height of the vehicle's center of gravity. This refers to the vehicle's longitudinal acceleration. ρ is the lateral acceleration of the vehicle. g is the acceleration due to gravity. d is the semi-track width of the vehicle. , , , The dynamic vertical loads are for the left front, right front, left rear, and right rear wheels, respectively.

[0042] The calculated four-wheel dynamic vertical load E will be used simultaneously for the correction of the equivalent lateral stiffness K of the front and rear axles, the calculation of the tire saturation lateral slip angle L, and the distribution of the four-wheel drive braking torque U.

[0043] 3. Update the equivalent lateral stiffness K of the front and rear axles.

[0044] Based on the four-wheel dynamic vertical load E and the inherent lateral stiffness parameters of the tires, the equivalent lateral stiffness K of the front and rear axles is updated online. The equivalent lateral stiffness of a single axle is synthesized from the lateral stiffness of the left and right wheels of that axle, and the calculation formula is: ; Where j∈{f,r} correspond to the front axis and the back axis, respectively; F z,j This represents the total dynamic vertical load corresponding to the axle; F z0 P is the tire's rated vertical load. KY1 P KY2 P KY3 P KY4 P KY5 γ represents the fitting parameters for tire lateral stiffness; γ is the wheel camber angle.

[0045] When driving at low speeds or when the reliability of sensor signals is insufficient, the joint coordination controller G temporarily stores the effective lateral stiffness value of the previous cycle to avoid abnormal updates that could cause control jitter.

[0046] (III) Constructing a joint coordination controller

[0047] Based on the vehicle dynamics model F, the path tracking error model S, and the updated equivalent lateral stiffness K of the front and rear axles, a joint coordination controller G is constructed. The joint coordination controller G uses the vehicle's longitudinal velocity, lateral position, and heading angle as tracking outputs, and the equivalent steering angle of the front and rear wheels and the longitudinal force of the front and rear axles as unified control quantities to generate the predictive output equation H. At the same time, the control quantity amplitude constraint I and the control increment change constraint J are preset.

[0048] In this section, the joint coordination controller G is a multi-input multi-output linear time-varying model predictive controller that synchronously coordinates the steering control quantity and the longitudinal force control quantity within the same optimization framework, thereby eliminating the attached resource friction of lateral and longitudinal decoupled control from the architecture.

[0049] 1. State vector and control vector

[0050] The state vector and control vector of the joint coordination controller G are defined as follows: ; ; Among them, V x V is the velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system. yX represents the velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system; X and Y represent the longitudinal and lateral positions of the vehicle's center of mass in the geodetic coordinate system, respectively. δ is the vehicle's heading angle. f δ is the equivalent steering angle of the front wheels. r F is the equivalent steering angle of the rear wheels. x,f F is the total longitudinal force on the front axle. x,r This represents the total longitudinal force on the rear axle.

[0051] 2. Construct the prediction output equation H

[0052] The continuous-time state equation is linearized and discretized near the current operating point to obtain the discrete state equation: ; Where, x k x k+1 These are the state vectors at the current time (time k) and the next time (time k+1), respectively; A k B k The state matrix and control matrix are at the current time (time k), and their parameters are dynamically adjusted according to the real-time updated equivalent lateral stiffness K of the front and rear axles and the longitudinal vehicle speed.

[0053] To construct an extended state vector and control increment using the control increment as the optimization variable: ; ; Where, ξ k U is the extended state vector at the current time (time k); k U k-1 These are the control variables at the current time (time k) and the previous time (time k-1), respectively; ΔU k This is the control increment at the current time (time k).

[0054] The extended system equations are: ; Where, ξ k+1 This is the extended state vector at the next time step (time k+1); A e B e These are the extended state matrix and extended control matrix at the current time (time k), respectively; In the prediction time domain N p Internal recursion yields the predicted output equation H: ; Where Y is the output vector in the prediction time domain; Let ΔU be the extended state vector at the current moment, and let ΔU be the control increment sequence in the prediction time domain. , All are prediction coefficient matrices that are updated in real time with the equivalent lateral stiffness K of the front and rear axles.

[0055] 3. Preset constraints

[0056] The preset control amplitude constraint I and control increment change constraint J are determined by the physical limits of the actuator and the ride comfort requirements. Control amplitude constraint I: limits the physical limit range of the equivalent steering angle of the front and rear wheels and the maximum output capacity of the longitudinal force of the front and rear axles; Control Incremental Change Constraint J: Limits the rate of change of steering angle and longitudinal force within a single control cycle, suppresses abrupt changes in control commands, and improves ride comfort.

[0057] (iv) Generate dynamic feasible stability constraints

[0058] Using the four-wheel dynamic vertical load E, the updated equivalent lateral stiffness K of the front and rear axles, combined with road adhesion information B and the current longitudinal forces of the front and rear axles, the remaining available lateral force after the longitudinal force occupies the adhesion resources is calculated, and the tire saturation lateral slip angle L is calculated based on the remaining available lateral force; then, the dynamic steering boundary M of the front and rear wheels is generated with the reference steering angle of the front and rear axles corresponding to the current vehicle motion state as the center, and the intersection of this boundary M with the physical boundary N of the steering mechanism is taken to obtain the dynamic feasible stability constraint P. The constraint generation process is as follows: Figure 4 As shown.

[0059] 1. Calculate the tire saturation slip angle L

[0060] Based on the tire friction circle constraint, the maximum available lateral force of the tire is determined by both the total adhesion force and the occupied longitudinal force. For the j-th axis, the larger the current longitudinal force, the smaller the remaining adhesion capacity available for lateral control. The maximum available lateral force is: ; In the formula, The maximum available lateral force on the j-th axis after the current longitudinal force has occupied the attachment resources; Let J be the road surface adhesion coefficient corresponding to the j-th axis; For the dynamic vertical load of the j-th axis; Let be the longitudinal force along the j-th axis.

[0061] Based on the equivalent sideslip stiffness, the critical sideslip angle for the tire to enter the nonlinear saturation region is calculated, i.e., the tire saturation sideslip angle L: ; In the formula, Corresponding to the front axle and rear axle respectively; This is the tire saturation slip angle corresponding to the axle; This is the equivalent lateral stiffness of the corresponding axle.

[0062] 2. Calculate the reference value of the steering angle.

[0063] Using the geometric steering angle corresponding to a tire slip angle of 0 under the current vehicle motion state as a reference, calculate the reference steering angles for the front and rear wheels respectively: ; ; Where, δ f,c This is the front axle reference steering angle, which is the equivalent steering angle when the front wheel slip angle is 0 under the current vehicle motion state. δ r,c V is the rear axle reference steering angle, which is the equivalent steering angle when the rear wheel slip angle is 0 under the current vehicle motion state. x V represents the velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system. y ω is the velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system. r is the vehicle's yaw rate.

[0064] The reference steering angles of the front and rear wheels reflect the geometric steering requirements corresponding to the current motion state of the vehicle. By superimposing the saturation slip angle on this as the center, it can be ensured that the actual working slip angle of the tire does not exceed the saturation threshold.

[0065] 3. Generate dynamic steering boundaries and final constraints

[0066] Based on the tire saturation slip angle after considering the longitudinal force occupying the adhesion resources, a dynamic steering boundary is generated with the reference steering angle corresponding to the current vehicle motion state as the center, and its intersection with the physical limit of the steering mechanism is taken: ; ; in, , These are the final lower and upper bounds of the steering angle of the j-th axis, respectively, which are the boundaries of the dynamic feasible stability constraint P. This indicates the operation of retrieving the maximum value; This indicates the operation of finding the minimum value; The reference steering angle for the j-th axis; Let be the physical limit angle of the j-th axis steering mechanism. Together they constitute the physical boundary N of the steering mechanism.

[0067] The aforementioned constraints form a closed-loop calculation chain from the current longitudinal forces on the front and rear axles to the remaining available lateral forces, then to the tire saturation slip angle and the final steering angle range. On low-adhesion surfaces or under forced braking conditions, the available lateral forces of the tire decrease, and the dynamic steering boundary automatically tightens to prevent the tire from entering the deep saturation region; on high-adhesion surfaces or under light braking conditions, the dynamic steering boundary automatically widens to fully utilize the tire's lateral force capacity, balancing stability and control flexibility.

[0068] In this embodiment, the dynamic feasible stability constraint P is updated synchronously with the control cycle of the chassis domain controller. Each control cycle recalculates the remaining available lateral force, tire saturation slip angle, and front and rear wheel dynamic steering boundaries based on the currently acquired longitudinal forces of the front and rear axles, road surface adhesion information, dynamic vertical loads of the four wheels, and online updated equivalent lateral stiffness of the front and rear axles, and writes the updated constraints into the optimized feasible domain R of the current cycle.

[0069] (v) Rolling optimization solution

[0070] The objective function Q is constructed, and the predicted output equation H is used as the basis for prediction. The dynamic feasible stability constraint P, the control magnitude constraint I, and the control increment change constraint J are integrated to limit the optimization feasible region R. The equivalent steering angle of the front and rear wheels and the longitudinal force of the front and rear axles are solved by rolling optimization.

[0071] 1. Construct the objective function Q

[0072] The objective function Q is a quadratic cost function, which includes a tracking error penalty term, a control increment penalty term, a slack variable penalty term, and a longitudinal force consistency penalty term between the front and rear axles. Its specific expression is as follows: ; In the formula, J is the cost; Y is the output vector in the prediction time domain; Y ref The reference output vector is denoted by Q; the tracking error weight matrix is ​​denoted by ΔU; the control increment sequence in the prediction time domain is denoted by R; the control increment weight matrix is ​​denoted by ζ; the slack variable weights are denoted by ε; and the slack variable weights are denoted by λ. F For the consistency weight of longitudinal forces between the front and rear axles; F x,f F is the total longitudinal force on the front axle. x,r The total longitudinal force is at the rear axle; T represents matrix transpose.

[0073] The effects of each penalty are as follows: Tracking error penalty The penalty is applied to the deviation between the predicted output and the reference trajectory to ensure the tracking accuracy of longitudinal velocity, lateral position, and heading angle. Controlling incremental penalty items : Punishing drastic changes in the amount of control, improving execution smoothness, and extending the service life of the execution mechanism; Slack Variable Penalty Terms : Introducing slack variables temporarily relaxes constraints, ensuring that the optimization problem has a feasible solution under extreme conditions; the weights of the slack variables are set to relatively large values, so that the controller only breaks the stability boundary when absolutely necessary; Front and rear axle longitudinal force consistency penalty It punishes the difference in longitudinal force between the front and rear axles, suppresses the uncoordinated internal friction of one axle driving and one axle braking, and improves the utilization rate of road surface adhesion resources.

[0074] 2. Optimize the solution to find the feasible region R.

[0075] The optimal feasible region R is composed of dynamic feasible stability constraints P, control magnitude constraints I, and control increment change constraints J, specifically in the following form: ; in, , These are the lower and upper bounds of the control variable U, respectively. , These are the lower and upper bounds of the control increment ΔU, respectively. The equivalent steering angle of the j-th axis; , These are the final lower and final upper bounds of the steering angle of the j-th axis, respectively.

[0076] The rolling optimization solution process involves minimizing the objective function Q within the feasible region R, transforming the optimization problem into a standard quadratic programming form, and solving it using the effective set method or interior point method to obtain the optimal control increment sequence in the prediction time domain. The first set of control increments in the sequence is then applied to the current control cycle, and the prediction-optimization process is repeated in the next control cycle to achieve rolling optimization control.

[0077] (vi) Execution layer allocation and instruction issuance

[0078] The equivalent steering angles and longitudinal forces of the front and rear axles obtained from the rolling optimization solution are converted into four-wheel independent steering angles T and four-wheel drive braking torques U, and then sent to the four-wheel steering mechanism and the four-wheel drive brake actuator.

[0079] 1. Generate independent steering angle T for four wheels

[0080] The four-wheel independent steering angle T is generated through Ackermann steering geometry mapping, which converts the equivalent steering angles of the front and rear axles into independent steering angles of the left and right wheels of the corresponding axles, ensuring pure wheel rolling during steering, reducing tire wear, and improving control accuracy.

[0081] 2. Generate four-wheel drive braking torque U

[0082] The four-wheel drive braking torque U is generated based on the proportional distribution of the dynamic vertical load E of the four wheels. According to the proportion of the vertical load of a single wheel to the total vertical load of the corresponding axle, the total longitudinal force of the front and rear axles is decomposed into the longitudinal force of the four wheels, and then converted into wheel end torque through the wheel rolling radius. The conversion relationship is as follows: ; In the formula, U i R is the driving and braking torque of the i-th wheel; w F is the rolling radius of the wheel; x,i Let be the longitudinal force of the i-th wheel.

[0083] After completing the control quantity allocation, the chassis domain controller sends the four-wheel independent steering angle T and the four-wheel drive braking torque U to the corresponding actuators via the vehicle CAN-FD bus to achieve physical output. The specific process is as follows: Steering physical control link: The steer-by-wire control unit of each wheel receives the target steering angle command of the corresponding wheel, and uses the actual wheel steering angle collected in real time by the steering angle sensor as the feedback quantity to construct a dual closed-loop control algorithm of "position outer loop - current inner loop", and outputs PWM drive signal to control the operation of the steering motor; the rotational torque output by the steering motor is amplified by the planetary reduction mechanism, and then pushes the steering knuckle to deflect around the kingpin through the steering tie rod, causing the wheel to generate a physical steering angle deflection; after the wheel deflects, the tire contacts the road surface to form a corresponding slip angle, and generates lateral adhesion force based on the tire slip characteristics, which acts on the vehicle body to change its lateral motion and yaw motion state, and realizes the lateral adjustment of trajectory tracking.

[0084] Drive and Braking Physical Control Link: The drive control unit and brake control unit of each wheel receive the target torque command for the corresponding wheel. During drive torque control, the motor control unit converts the target torque into a three-phase stator current command based on the field-oriented control strategy. This command is then used by the power inverter to drive the hub motor to output the corresponding mechanical torque, which is transmitted to the wheel via the hub bearing. The adhesion between the tire and the road surface is then converted into longitudinal driving force. During braking torque control, the brake control unit adjusts the brake wheel cylinder pressure (hydraulic braking) or drives the brake motor to output clamping force (electromechanical braking) according to the target torque. This generates wheel-end braking torque through the friction pair between the brake caliper and the brake disc, which is then converted into longitudinal braking force through the tire. The physical application of longitudinal force directly changes the longitudinal motion state of the vehicle. At the same time, it changes the dynamic vertical load of each wheel through longitudinal and lateral load transfer effects, indirectly affecting the tire lateral adhesion limit.

[0085] During execution, wheel angle sensors, wheel speed sensors, motor torque sensors, and brake pressure sensors collect the actual output state of each actuator and the wheel motion state in real time, and feed them back to the chassis domain controller and the corresponding actuator control unit. On the one hand, local millisecond-level closed-loop correction is achieved at the actuator level to ensure that the deviation between the physical output and the target command is within the allowable range. On the other hand, the actual execution result is used as the input for the vehicle state information A in the next control cycle, and the information acquisition and optimization solution process is re-entered, forming a complete cycle closed loop of "state perception - online optimization - physical execution - state feedback", realizing continuous rolling trajectory tracking control under dynamic feasible stability constraints.

[0086] Ultimately, the independent steering angle T of the four wheels is sent to the four-wheel steering mechanism, and the braking torque U of the four-wheel drive is sent to the four-wheel drive brake actuator, completing the entire control closed loop.

[0087] II. 4WID-4WS Vehicle Trajectory Tracking Control System Based on Dynamically Feasible Stability Constraints

[0088] This section presents a 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints. It implements the 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints. The system structure block diagram is shown below. Figure 5 As shown.

[0089] The system comprises an information acquisition unit, a vehicle modeling unit, an equivalent lateral stiffness update unit, a controller construction unit, a residual lateral force and dynamic constraint generation unit, a rolling optimization unit, and an execution allocation unit, connected sequentially by signals. The specific functions of each unit are as follows: Information acquisition unit: used to acquire vehicle status information A, road surface adhesion information B, reference trajectory information C and current longitudinal force information of front and rear axles, and output the acquired information to vehicle modeling unit, equivalent lateral stiffness update unit and residual lateral force and dynamic constraint generation unit.

[0090] Vehicle modeling unit: used to establish the vehicle dynamics model F and the path tracking error model S, and output them to the controller construction unit to provide the dynamic basis and error calculation benchmark for controller construction.

[0091] Equivalent lateral stiffness update unit: It is used to calculate the tire working state D and the dynamic vertical load E of the four wheels based on the vehicle state information A, and update the equivalent lateral stiffness K of the front and rear axles online in combination with the road surface adhesion information B, and output the update results to the controller construction unit and the residual lateral force and dynamic constraint generation unit.

[0092] The controller construction unit is used to construct a joint coordinated controller G based on the vehicle dynamics model F, the path tracking error model S, and the updated equivalent lateral stiffness K of the front and rear axles, generate the predictive output equation H, and preset the control magnitude constraint I and the control increment change constraint J, and output to the rolling optimization unit.

[0093] The residual lateral force and dynamic constraint generation unit is used to calculate the remaining available lateral force after the longitudinal force occupies the adhesion resources, the tire saturation slip angle L, and the dynamic steering boundary M of the front and rear wheels by combining the dynamic vertical load E of the four wheels, the updated equivalent lateral stiffness K of the front and rear axles with the road adhesion information B and the current longitudinal force of the front and rear axles. The dynamic feasible stability constraint P is obtained by taking the intersection of the dynamic steering boundary M of the front and rear wheels and the physical boundary N of the steering mechanism, and then output to the rolling optimization unit.

[0094] Rolling optimization unit: used to construct objective function Q, based on the predicted output equation H, and integrates dynamic feasible stability constraint P, control quantity amplitude constraint I and control increment change constraint J to limit the optimization feasible domain R, solve for the optimal front and rear wheel equivalent steering angle and front and rear axle longitudinal force, and output to the execution allocation unit.

[0095] The execution distribution unit is used to convert the obtained equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles into independent steering angles T of the four wheels and braking torques U of the four-wheel drive, and then send them to the four-wheel steering mechanism V and the four-wheel drive brake actuator W.

[0096] The aforementioned units can be integrated into the same chassis domain controller, or they can be deployed in a distributed architecture with a central computing unit and a chassis execution controller.

[0097] III. 4WID-4WS Intelligent Vehicles

[0098] This section provides a 4WID-4WS intelligent vehicle, including a vehicle body, a four-wheel steering mechanism V, a four-wheel drive brake actuator W, and a 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints.

[0099] The output of the trajectory tracking control system is connected to the four-wheel steering mechanism V and the four-wheel drive brake actuator W respectively. It is used to send four-wheel independent steering angle T control commands to the four-wheel steering mechanism V to drive the steer-by-wire actuator to complete the steering angle action; and to send four-wheel drive braking torque U control commands to the four-wheel drive brake actuator W to drive the hub motor and brake actuator to complete the torque output.

[0100] The vehicle body is a four-wheel independent drive and four-wheel steering configuration. Each of the four wheels is equipped with an independent steer-by-wire actuator and an independent drive / brake actuator, which can realize independent steering of the front and rear wheels and independent drive and braking of the four wheels, providing a hardware foundation for integrated control.

[0101] IV. Implementation Results and Simulation Verification

[0102] To verify the technical effect of the present invention, a simulation was conducted using the variable adhesion double lane change condition as a strong coupling scenario of steering and braking, and the solution of the present invention was compared with the lateral and longitudinal decoupling solution and the fixed stiffness ablation solution. Figure 6 The results of the vehicle trajectory comparison are shown. Figure 7 The results of the lateral tracking error comparison are shown.

[0103] In terms of simulation settings, this implementation method establishes a closed-loop model of the vehicle and chassis domain controller based on the CarSim and Simulink joint simulation platform. Each comparison scheme uses the same vehicle parameters, tire parameters, road adhesion conditions, reference trajectory and braking requirements. The difference lies in whether or not integrated rolling optimization of front and rear wheel steering and front and rear axle longitudinal forces, online equivalent lateral stiffness update and dynamic feasible stability constraints are adopted.

[0104] Depend on Figure 6 and Figure 7 It is known that, under the condition of changes in road surface adhesion and accompanying braking demand, the present invention can make the actual trajectory of the vehicle closer to the reference trajectory and reduce the lateral tracking error. The reason is that the dynamic feasible stability constraint transforms the remaining available lateral force after the current longitudinal force occupies the adhesion resources into the front and rear axle steering angle constraint boundary in real time, thereby suppressing the tire slip angle from entering the deep saturation region.

[0105] Table 1 Comparison of root mean square tracking errors under variable adhesion dual-track shifting conditions

[0106] As shown in Table 1, compared with the lateral and longitudinal decoupling comparison scheme, the present invention reduces the lateral tracking error, heading tracking error and longitudinal vehicle speed tracking error by 42.7%, 49.6% and 28.5% respectively. This indicates that the integrated rolling optimization of front and rear wheel steering and front and rear axle longitudinal forces, online equivalent lateral stiffness update and dynamic feasible stability constraints have a synergistic effect on improving trajectory tracking accuracy.

[0107] Furthermore, under low-adhesion serpentine conditions, compared with the lateral and longitudinal decoupling comparison scheme, the present invention reduces the lateral error, heading angle error, and longitudinal velocity error RMSE by 42.3%, 64.7%, and 46.4%, respectively. Under the equivalent lateral stiffness ±20% parameter perturbation scenario, the closed-loop response remains bounded, indicating that online equivalent lateral stiffness update and dynamic feasible stability constraints can improve the control robustness under low-adhesion continuous steering and parameter mismatch scenarios.

[0108] In one implementation, the controller control cycle is 20ms. The 99.9th percentile of the quadratic programming solution time is 7.022ms under the variable adhesion double-line-shifting condition and 2.338ms under the low adhesion serpentine condition, both of which are less than the control cycle, indicating that the rolling optimization solution process meets the requirements for online implementation of the vehicle controller.

[0109] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints, characterized in that, Includes the following steps: Acquire vehicle status information A, road surface adhesion information B, and reference trajectory information C, and establish vehicle dynamics model F and path tracking error model S; Based on A, calculate the tire working state D and the four-wheel dynamic vertical load E, and then update the front and rear axle equivalent lateral stiffness K online in combination with B and the four-wheel dynamic vertical load E. Based on F, S, and the updated K, a joint coordination controller G is constructed. G uses the vehicle's longitudinal speed, lateral position, and heading angle as tracking outputs, and the equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles as unified control quantities to generate a predictive output equation H. At the same time, the control quantity amplitude constraint I and the control increment change constraint J are preset. Based on B, E, current front and rear axle longitudinal force, and updated K, calculate the remaining available lateral force F after the longitudinal force occupies the adhesion resource y ; According to F y Calculate the tire saturation side slip angle L, generate the front and rear wheel dynamic steering boundary M with the front and rear axle reference steering angle corresponding to the current vehicle motion state as the center, and take the intersection of M and the steering mechanism physical boundary N to obtain the dynamic feasible stability constraint P; Construct an objective function Q, with H as the prediction basis, and define P, I and J together as the optimization feasible region R. Then, perform rolling optimization within R to solve for the equivalent steering angle of the front and rear wheels and the longitudinal force of the front and rear axles. The solution results are converted into four-wheel independent steering angle T and four-wheel drive braking torque U, and sent to the four-wheel steering mechanism and four-wheel drive brake actuator.

2. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, The vehicle dynamics model F is a three-degree-of-freedom vehicle dynamics model, and its expression is: ； Where m is the total vehicle mass; I z V is the moment of inertia of the entire vehicle about the Z-axis of the vehicle coordinate system; x The velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system; For V x The first derivative of V, i.e., longitudinal acceleration; y The velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system; For V y The first derivative of , i.e., lateral acceleration; r is the vehicle's yaw rate; l f The distance from the vehicle's center of gravity to the front axle; r d is the distance from the vehicle's center of gravity to the rear axle; d is the vehicle's half track width; F x,fl F x,fr F x,rl F x,rr These are the forces acting along the positive X-axis of the vehicle coordinate system on the left front, right front, left rear, and right rear wheels, respectively, i.e., longitudinal forces; F y,fl F y,fr F y,rl F y,rr These are the forces acting along the positive Y-axis of the vehicle coordinate system on the left front, right front, left rear, and right rear wheels, respectively, i.e., the lateral forces.

3. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, The expression for the path tracking error model S is: ； In the formula, y e This refers to the tracking error along the positive Y-axis of the vehicle coordinate system, i.e., the lateral tracking error. For y e The first derivative; V x The velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system; β is the heading tracking error; L is the vehicle's center of gravity sideslip angle; p is the preview distance of the vehicle's reference trajectory; r is the vehicle's yaw rate; Let r be the first derivative, i.e., the yaw acceleration of the vehicle; ρ represents the road curvature of the vehicle's reference trajectory.

4. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, The tire operating state D is characterized by the tire slip ratio, tire side slip angle, four-wheel dynamic vertical load E, and road adhesion coefficient. The tire longitudinal force and lateral force are calculated based on a combined slip correction tire model, which includes the Pacejka tire model, and its correction form is as follows: ； ； Among them, F x,i F is the corrected force exerted by the i-th wheel along the positive X-axis of the vehicle coordinate system, i.e., the longitudinal force; y,i This is the corrected force exerted by the i-th wheel along the positive Y-axis of the vehicle coordinate system, i.e., the lateral force; μ i G represents the road adhesion coefficient corresponding to the i-th wheel; xα G is the correction factor for the longitudinal force by the wheel slip angle α. yκ F is the correction factor for the slip ratio κ with respect to the lateral force. x0,i F is the longitudinal force of the i-th wheel under pure longitudinal slip; y0,i Let be the lateral force of the i-th wheel under pure lateral slip; The four-wheel dynamic vertical load E is calculated in real time based on the vehicle's longitudinal acceleration, lateral acceleration, center of gravity height, wheelbase, and half-track width.

5. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, The joint coordination controller G is a multi-input multi-output linear time-varying model predictive controller, and its state vector and control vector are defined as follows: ； ； Among them, V x V is the velocity of the vehicle's center of mass along the positive X-axis of the vehicle coordinate system. y X represents the velocity of the vehicle's center of mass along the positive Y-axis of the vehicle coordinate system; X and Y represent the longitudinal and lateral positions of the vehicle's center of mass in the geodetic coordinate system, respectively. δ is the vehicle's heading angle. f δ is the equivalent steering angle of the front wheels. r F is the equivalent steering angle of the rear wheels. x,f F is the total longitudinal force on the front axle. x,r This represents the total longitudinal force on the rear axle. The controller uses the control increment as the optimization variable and combines it with the real-time updated front and rear axle equivalent lateral stiffness K to correct the model parameters, thus constructing the predicted output equation H: ； Where Y is the output vector in the prediction time domain; Let ΔU be the extended state vector at the current moment, and let ΔU be the control increment sequence in the prediction time domain. , All are prediction coefficient matrices that are updated in real time with the equivalent lateral stiffness K of the front and rear axles.

6. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, In step S4, the dynamic feasible stability constraint P is obtained through a continuous calculation chain of longitudinal forces on the front and rear axles, remaining available lateral forces, tire saturation sideslip angle, and the physical boundary of the steering mechanism; for the j-th axle, the maximum available lateral force corresponding to that axle is first calculated based on the adhesion margin after the longitudinal forces are occupied: ； Then, the tire saturation slip angle L is calculated based on the maximum available lateral force and the equivalent lateral stiffness, so that the tire slip angle boundary changes in real time with the remaining lateral capacity after the longitudinal force is occupied: ； In the formula, Corresponding to the front axle and rear axle respectively; The maximum available lateral force on the j-th axis after the current longitudinal force has occupied the attachment resources; Let J be the road surface adhesion coefficient corresponding to the j-th axis; For the dynamic vertical load of the j-th axis; The longitudinal force is along the j-th axis; Let be the equivalent lateral stiffness of the j-th axis; The tire saturation sideslip angle for the j-th axis; With the j-th axis as the reference steering angle δ j,c Centered on the tire saturation sideslip angle, a dynamic steering boundary is generated, and the intersection of the dynamic steering boundary and the physical boundary of the steering mechanism is taken to obtain the final steering angle constraint range corresponding to the dynamic feasible stability constraint P written into the optimization feasible domain R: ； ； In the formula, , These are the final lower and final upper bounds of the steering angle of the j-th axis, respectively; The reference steering angle for the j-th axis; Let be the physical limit angle of the j-th axis steering mechanism.

7. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, The objective function Q is a quadratic cost function, which includes a tracking error penalty term, a control increment penalty term, a slack variable penalty term, and a longitudinal force consistency penalty term between the front and rear axles. Its specific expression is as follows: ； In the formula, J is the cost; Y is the output vector in the prediction time domain; Y ref The reference output vector is denoted by Q; the tracking error weight matrix is ​​denoted by ΔU; the control increment sequence in the prediction time domain is denoted by R; the control increment weight matrix is ​​denoted by ζ; the slack variable weights are denoted by ε; and the slack variable weights are denoted by λ. F For the consistency weight of longitudinal forces between the front and rear axles; F x,f F is the total longitudinal force on the front axle. x,r The total longitudinal force is at the rear axle; T represents matrix transpose. The optimal feasible region R is composed of dynamic feasible stability constraints P, control magnitude constraints I, and control increment change constraints J, specifically in the following form: ； in, , These are the lower and upper bounds of the control variable U, respectively. , These are the lower and upper bounds of the control increment ΔU, respectively. The equivalent steering angle of the j-th axis; , These are the final lower and final upper bounds of the steering angle of the j-th axis, respectively; The rolling optimization solution process involves minimizing the objective function Q within the feasible region R, and outputting the optimal equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles.

8. The 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints according to claim 1, characterized in that, The four-wheel independent steering angle T is generated through Ackermann steering geometry mapping, which converts the equivalent steering angles of the front and rear axles into the independent steering angles of the left and right wheels of the corresponding axles. The four-wheel drive braking torque U is generated based on the proportional distribution of the dynamic vertical load E of the four wheels. According to the proportion of the vertical load of a single wheel to the total vertical load of the corresponding axle, the total longitudinal force of the front and rear axles is decomposed into the longitudinal force of the four wheels, and then converted into wheel end torque through the wheel rolling radius. The conversion relationship is as follows: ； In the formula, U i R is the driving and braking torque of the i-th wheel; w F is the rolling radius of the wheel; x,i Let be the longitudinal force of the i-th wheel; The dynamic feasible stability constraint P is updated synchronously according to the control cycle of the vehicle chassis domain controller. In each control cycle, the remaining available lateral force, tire saturation slip angle and dynamic steering boundary of the front and rear wheels are recalculated based on the currently acquired longitudinal forces of the front and rear axles, road surface adhesion information, dynamic vertical loads of the four wheels and equivalent lateral stiffness of the front and rear axles, and the updated dynamic feasible stability constraint P is written into the optimized feasible domain R of the current control cycle.

9. A 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints, characterized in that, The method for implementing a 4WID-4WS vehicle trajectory tracking control method based on dynamic feasible stability constraints as described in any one of claims 1-8 includes an information acquisition unit, a vehicle modeling unit, an equivalent lateral stiffness update unit, a controller construction unit, a residual lateral force and dynamic constraint generation unit, a rolling optimization unit, and an execution allocation unit connected in sequence. The information acquisition unit is used to acquire vehicle status information A, road surface adhesion information B, and reference trajectory information C; The vehicle modeling unit is used to establish the vehicle dynamics model F and the path tracking error model S; The equivalent lateral stiffness update unit is used to calculate the tire working state D and the dynamic vertical load E of the four wheels based on the vehicle state information A, and update the equivalent lateral stiffness K of the front and rear axles online in combination with the road surface adhesion information B. The controller construction unit is used to construct a joint coordination controller G based on the vehicle dynamics model F, the path tracking error model S, and the updated equivalent lateral stiffness K of the front and rear axles, generate the predictive output equation H, and preset the control quantity amplitude constraint I and the control increment change constraint J. The residual lateral force and dynamic constraint generation unit is used to calculate the remaining available lateral force after the longitudinal force occupies the adhesion resources, the tire saturation slip angle L, and the dynamic steering boundary M of the front and rear wheels by combining the dynamic vertical load E of the four wheels, the updated equivalent lateral stiffness K of the front and rear axles with the road adhesion information B and the current longitudinal force of the front and rear axles. The dynamic feasible stability constraint P is obtained by taking the intersection of the dynamic steering boundary M of the front and rear wheels and the physical boundary N of the steering mechanism. The rolling optimization unit is used to construct the objective function Q. Based on the prediction output equation H, it integrates the dynamic feasible stability constraint P, the control quantity amplitude constraint I, and the control increment change constraint J to limit the optimization feasible region R, and solves the optimal front and rear wheel equivalent steering angle and front and rear axle longitudinal force. The execution distribution unit is used to convert the solved equivalent steering angles of the front and rear wheels and the longitudinal forces of the front and rear axles into independent steering angles T of the four wheels and braking torques U of the four wheels, and then send them to the four-wheel steering mechanism V and the four-wheel drive brake actuator W.

10. A 4WID-4WS intelligent vehicle, characterized in that, It includes a vehicle body, a four-wheel steering mechanism V, a four-wheel drive brake actuator W, and a 4WID-4WS vehicle trajectory tracking control system based on dynamic feasible stability constraints as described in claim 9. The output of the trajectory tracking control system is connected to the four-wheel steering mechanism V and the four-wheel drive brake actuator W respectively. It is used to send four-wheel independent steering angle T control commands to the four-wheel steering mechanism V and four-wheel drive braking torque U control commands to the four-wheel drive brake actuator W.

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