Vehicle trajectory tracking control method and system considering lateral and vertical coupling and vehicle

Abstract

The present application relates to the technical field of vehicle control, in particular to a vehicle trajectory tracking control method and system considering lateral and vertical coupling and a vehicle. The control method realizes dynamic cooperative control of trajectory and attitude through four-step closed loop: first, a nine-degree-of-freedom whole vehicle dynamics model is constructed based on the vehicle state vector; second, the core error is screened and dynamically updated through the difference between the expected value and the real-time state; third, a first-order and second-order constraint is designed and converted into a second-order state constraint; finally, the nominal and uncertain parts of the model are decomposed, and the core, compensation and anti-disturbance control forces are calculated to synthesize the total control quantity (including four-wheel steering angle and suspension control force). Thus, the lateral and vertical coupling characteristics are accurately captured, the trajectory tracking accuracy and attitude stability are considered, the anti-disturbance ability is strong, the problems of traditional technology conflict and cooperative lag are effectively solved, the complex working conditions such as high-speed driving and rough road are adapted, and the driving safety and riding comfort are guaranteed.

Description

Technical Field

[0001] This invention relates to the field of vehicle control technology, specifically to a vehicle trajectory tracking control method, system, and vehicle with lateral and vertical coupling. Background Technology

[0002] With the rapid development of intelligent transportation and automotive engineering technologies, the trajectory tracking accuracy, driving stability, and ride comfort of intelligent vehicles have become core indicators for evaluating vehicle performance. Especially under dynamic conditions such as high-speed driving and complex road conditions, the vehicle's dynamic characteristics and control strategies face severe challenges. During acceleration, braking, and turning, vehicles are prone to significant yaw, pitch, and roll movements, which not only seriously affect the comfort of passengers but may also lead to a decrease in vehicle handling, and in extreme cases, even cause safety accidents such as loss of control and rollovers. Therefore, the coordinated optimization of vehicle trajectory tracking and attitude control has become a key research direction in the industry.

[0003] Currently, there are three main technical approaches in the field of vehicle control, but all have significant limitations: First, traditional independent front-wheel steering trajectory control technology aims to accurately track a predetermined trajectory, relying on fixed vehicle dynamic parameters. However, in actual driving, factors such as changes in vehicle load (e.g., changes in the number of occupants or cargo weight) and road condition fluctuations (e.g., rough roads or changes in gradient) frequently occur, causing the preset steering angle-trajectory mapping relationship to fail and the trajectory tracking deviation to increase. Furthermore, this technology does not incorporate a vehicle attitude feedback mechanism, making it prone to attitude instability, resulting in poor overall robustness, weak anti-interference ability, and difficulty in adapting to complex driving scenarios. Second, traditional independent vehicle attitude control technology focuses on suppressing roll, pitch, and vertical vibrations, but is disconnected from steering control. During attitude adjustment, it easily leads to vehicle trajectory deviation, creating a contradiction between "attitude stability and trajectory accuracy." Third, distributed steering-attitude coordinated control technology often employs a "steering first, attitude later" time-sequential coordination or hard threshold-triggered coordination mode, which suffers from coordination lag and slow dynamic response. More importantly, this type of technology has not established a dynamic coupling model between steering angle and attitude parameters, lacks a unified control framework, has insufficient coupling optimization, and has narrow scenario adaptability. It can only play a limited role under ideal road conditions and cannot cope with multiple complex disturbances in actual driving.

[0004] Furthermore, the uncertainties encountered during vehicle operation further exacerbate the control difficulty. External and internal disturbances such as crosswinds, load variations, and uneven road surfaces can cause deviations in vehicle dynamics, significantly reducing the control accuracy of traditional control methods and even leading to system instability. Existing technologies fail to fully consider the strong coupling characteristics between the lateral and vertical systems. Changes in the vertical load of each wheel affect tire lateral stiffness, thereby interfering with steering control. Steering operations also have a reaction effect on vehicle attitude. This coupling effect is not effectively coordinated, making it difficult to overcome control performance bottlenecks. Therefore, there is an urgent need for an integrated control technology that can balance trajectory tracking accuracy and attitude stability, adapt to complex operating conditions, and resist multiple uncertainties, in order to solve the problems of separate control conflicts, coordination lags, and insufficient robustness in existing technologies. Summary of the Invention

[0005] To address the technical problem of limited vehicle control accuracy caused by insufficient consideration of lateral and vertical coupling effects and uncertainties under complex operating conditions, this invention provides a vehicle trajectory tracking control method that considers lateral and vertical coupling. Based on this control method, this invention also provides a vehicle trajectory tracking control system that considers lateral and vertical coupling, and a vehicle.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A vehicle trajectory tracking control method considering lateral and vertical coupling includes the following control steps:

[0008] Based on the state vector Q during vehicle operation, a vehicle dynamics model is constructed. M is the mass matrix. Let Q be the second derivative, B be the input matrix, and N be the resultant external force vector; The control parameter input vector includes the front wheel steering angle δ. f Rear wheel steering angle δ r and four-wheel suspension control force f d1 ~f d4 ;

[0009] From the desired state vector Q d and real-time state vector Q t Calculate the error vector E=Q t -Q d The core error vector E is composed of errors in lateral displacement, vertical displacement, yaw angle, roll angle, and pitch angle. c ;

[0010] Design first-order constraints Second-order constraints And transform it into a second-order state constraint. Λ1 and Λ2 are both positive definite diagonal matrices, Ec (t) represents E at time t. c , , E respectively c The first and second derivatives of (t), For Q t The second derivative of , where A is the constraint matrix and b is the second-order constraint vector;

[0011] Decompose M and N into nominal parts , Let the uncertain parts ΔM and ΔN be... Combined with the real-time status calculation of the vehicle And control the vehicle:

[0012] ;

[0013] As the core control force, To compensate for the lack of control, For disturbance rejection control; κ1 and κ2 are both control coefficients; Let be the constraint deviation vector; Γ be the control matrix; Π be the overall uncertainty boundary function; η and γ are both weighting coefficients; (·) + It is the Moore-Penrose generalized inverse.

[0014] As a further aspect of the present invention: The derivation process is as follows:

[0015] Extract the kinetic equations from the nominal portion:

[0016] ;

[0017] Combining constraints ,right Find the inverse:

[0018] ;

[0019] Substitution constraints Establish the "constraint-control quantity" relationship:

[0020] ;

[0021] right The whole is taken from the Moore–Penrose generalized inverse. Organized .

[0022] As a further aspect of the present invention: The derivation process is as follows:

[0023] Introducing constraint deviation vector Quantization of first-order bias:

[0024] ;

[0025] In the formula, c is the first derivative of the desired state vector. The target value after processing by A;

[0026] right Take the Moore–Penrose generalized inverse, denoted as ;

[0027] Introducing the control coefficient κ1 and the inverse Γ of the control matrix Γ -1 The constraint deviation is transformed into a compensating control force, and the final derivation is as follows: .

[0028] As a further aspect of the present invention: The derivation process is as follows:

[0029] Extracting the uncertainties from the dynamic equations:

[0030] ;

[0031] The upper bound of the uncertain part is described by Π, and both ΔM and ΔN are bounded. ), A constant greater than -1 For adaptive parameters, the disturbance and constraint deviation are correlated simultaneously through the robust disturbance resistance weighting coefficient η: ;

[0032] Introducing the uncertainty parameter of adaptive rate estimation Its first derivative It is expressed as follows:

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] in, , Π is the basis function, and the superscript T indicates the matrix transpose. Φ is introduced as a nonlinear control coefficient, and the mode is switched according to the size of Π to achieve smooth suppression of excessive adaptation under small uncertainties and maintain fast tracking capability under large uncertainties. L1, L2, and L3 are all gain parameters that control the estimated speed and stability. exp is the natural logarithm. n is the order of the vehicle dynamics system. Ω is an intermediate variable. κ3 is the control coefficient.

[0038] right Take the Moore–Penrose generalized inverse, denoted as ;

[0039] Introducing the control coefficient κ2 and the inverse Γ of the control matrix Γ -1 The constraint deviation is transformed into disturbance rejection control force, and the final derivation is as follows: .

[0040] As a further aspect of the present invention, the transformation process of the second-order state constraint is as follows:

[0041] Based on first-order and second-order constraints, we can obtain:

[0042] ;

[0043] In the formula, The real-time state core term vector Q t,c The second derivative; Expected state core term vector Q d,c The second derivative;

[0044] Substituting into the second-order constraint formula, we get:

[0045] ;

[0046] Combining this with the first-order constraint formula, we can obtain:

[0047] ;

[0048] Construct the following constraint matrix A, where only the column elements corresponding to the core state acceleration are 1, and the rest are 0:

[0049] ;

[0050] Construct the second-order constraint vector b, as follows:

[0051] ;

[0052] Based on the above analysis, we can conclude that .

[0053] As a further aspect of the present invention: a vehicle dynamics model The specific details of each part are as follows:

[0054] ;

[0055] In the formula, m s m is the sprung mass. ui Let i be the unsprung mass of the i-th wheel, i = 1, 2, 3, 4, and the corresponding wheels are the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. I ρ and I θ These are the vehicle's yaw moment of inertia, roll moment of inertia, and pitch moment of inertia, respectively.

[0056] ;

[0057] In the formula, , and These are the vehicle yaw acceleration, vehicle pitch acceleration, and vehicle roll acceleration, respectively. , and These are the vehicle's lateral acceleration, vehicle's vertical acceleration, and the vertical acceleration of the i-th unsprung mass, respectively, i=1,2,3,4;

[0058] ;

[0059] In the formula, f xf =f x1 +f x2 f xf For the longitudinal tire force on the front axle, f x1 f is the longitudinal tire force of the left front wheel. x2 f is the longitudinal tire force of the right front wheel. xr =f x3 +f x4 f xr For the longitudinal tire force on the rear axle, f x3 f is the longitudinal tire force of the left rear wheel. x4 C is the longitudinal tire force of the right rear wheel; f C represents the lateral stiffness of the front axle tires. r Rear axle tire lateral stiffness; t f t r These are the front and rear track widths, respectively; l f l r These are the distances from the front and rear wheel axles to the vehicle's center of gravity, respectively.

[0060] ;

[0061] In the formula, δ f δ is the steering angle of the front wheels. rf is the steering angle of the rear wheels. d1 f d2 f d3 f d4 To input the control forces of the left front, right front, left rear, and right rear wheel suspensions;

[0062]

[0063] In the formula, ρ and θ are the vehicle yaw angle, vehicle pitch angle and vehicle roll angle, respectively; , and These are the vehicle yaw rate, vehicle pitch rate, and vehicle roll rate, respectively. , and These are the vehicle's longitudinal velocity, lateral velocity, and vertical velocity, respectively; h r h p These are the distances from the center of mass to the roll center and pitch center, respectively; f si f ci and f di These represent the spring force, damping force, and input control force of the i-th suspension, respectively, f. ti Let be the dynamic load of the i-th tire, i = 1, 2, 3, 4.

[0064] As a further aspect of the present invention: the vehicle dynamics model has nine degrees of freedom, and its equation set is as follows:

[0065] ;

[0066] In the formula, F x1 F x2 F x3 and F x4 These represent the road-tire interaction forces acting on the 1st, 2nd, 3rd, and 4th wheels along the longitudinal direction of the vehicle coordinate system; F y1 F y2 F y3 and F y4 These represent the road-tire interaction forces acting on the 1st, 2nd, 3rd, and 4th wheels in the lateral direction of the vehicle coordinate system; F z1 F z2 F z3 and F z4 These are the 1st, 2nd, 3rd, and 4th suspension forces in the vehicle's coordinate system.

[0067] As a further aspect of the present invention, the specific calculation formulas for each force in the vehicle coordinate system are as follows:

[0068] ;

[0069] ;

[0070] ;

[0071] In the formula, F xi Let F be the road-tire interaction force acting on the i-th wheel in the longitudinal direction of the vehicle coordinate system. yi Let F be the road-tire interaction force acting on the i-th wheel in the lateral direction of the vehicle coordinate system. zi f is the i-th suspension force in the vehicle coordinate system. xi Let f be the longitudinal tire force of the wheel in the i-th tire coordinate system. yi Let δ be the lateral tire force of the wheel in the i-th tire coordinate system, i=1,2,3,4; cos is the cosine function, sin is the sine function, and δ i Let be the angle between the positive u-axis of the i-th tire coordinate system and the positive x-axis of the vehicle coordinate system.

[0072] A vehicle trajectory tracking control system considering lateral and vertical coupling includes a state acquisition module, a control processing module, and an execution module;

[0073] The status acquisition module is used to acquire real-time status data of the vehicle's operation and generate a real-time state vector Q. t ;

[0074] The control processing module is used to execute the control method and calculate the control parameter input vector. ;

[0075] The execution module includes four-wheel steering actuators and four-wheel active suspension actuators for receiving... Front wheel steering angle δ f Rear wheel steering angle δ r and four-wheel suspension control force f d1 ~f d4 This enables the vehicle to achieve coordinated control of trajectory tracking and attitude stabilization.

[0076] A vehicle that employs a vehicle trajectory tracking control system.

[0077] Compared with the prior art, the beneficial effects of the present invention are:

[0078] First, this invention constructs a nine-degree-of-freedom vehicle dynamics model that includes core states such as lateral, vertical, yaw, roll, and pitch, integrating the front wheel steering angle, rear wheel steering angle, and four-wheel suspension control forces into a unified control parameter input vector. This system dynamically links steering operations with suspension adjustments, avoiding trajectory deviation caused by attitude stabilization and resolving attitude instability caused by trajectory tracking, achieving synergistic optimization of "precise trajectory tracking" and "stable attitude control." Secondly, an error vector is constructed by the difference between the desired state and the real-time state. Core errors that play a crucial role in the control effect are then selected and dynamically updated, avoiding redundant error interference. Simultaneously, first-order and second-order constraints are designed to achieve rapid error convergence and oscillation-free convergence, respectively. Finally, these are transformed into second-order state constraints embedded in the dynamic model, making error correction more targeted and significantly improving the accuracy of trajectory tracking and the smoothness of attitude adjustment. Furthermore, the control quantity is decomposed into core control forces. Compensation and control With disturbance rejection control , Achieve basic control objectives based on the nominal model. Targeted offsetting of first-order biases to accelerate system convergence By employing an adaptive robust mechanism to suppress internal and external disturbances such as load variations, crosswind interference, and road surface irregularities, these three elements work together to form a triple guarantee of "precise control + deviation compensation + disturbance rejection," significantly improving the system's stability and adaptability under dynamic conditions and overcoming the shortcomings of traditional control methods, such as poor robustness and weak anti-interference capabilities. Furthermore, the Moore-Penrose generalized inverse is used to handle the constraint correlation problem of underactuated systems, flexibly adapting to the multi-input, multi-output characteristics of vehicle dynamics models. The mass matrix and resultant external force vector are decomposed into nominal and uncertain parts, ensuring model accuracy while allowing the control scheme to adapt to the dynamic characteristics of different vehicle models and driving scenarios through uncertainty boundary functions and adaptive rate estimation, thus broadening its applicability. Finally, a complete closed-loop control process is formed from state acquisition, error calculation, constraint transformation to control force solution. The dynamic update mechanism of the core error and the real-time nature of constraint transformation ensure that the control parameters can respond quickly to changes in vehicle state, avoiding the timing lag problem in traditional cooperative control. This enables the vehicle to maintain excellent trajectory tracking performance and attitude stability under dynamic conditions such as high-speed driving and complex road conditions. Attached Figure Description

[0079] Figure 1 This is a flowchart of the control method in this invention.

[0080] Figure 2 This is a schematic diagram of the 1 / 4 equivalent suspension model in this invention.

[0081] Figure 3 This is a schematic diagram of the trajectory tracking and the forces acting on the nine-degree-of-freedom model of the whole vehicle in the xy plane of the vehicle coordinate system in this invention.

[0082] Figure 4This is a schematic diagram of the forces acting on the nine-degree-of-freedom model of the vehicle in the yz plane of the vehicle coordinate system in this invention.

[0083] Figure 5 This is a schematic diagram of the forces acting on the nine-degree-of-freedom vehicle model in the vehicle coordinate system xz plane of this invention.

[0084] Figure 6 These are the left and right road surface excitation images output by Carsim in the simulation experiment.

[0085] Figure 7 This is a schematic diagram of the pulse changes in the wind speed matrix during the simulation experiment.

[0086] Figure 8 This is a schematic diagram of wind direction changes during a simulation experiment.

[0087] Figure 9 This is a graph comparing the expected trajectory of the vehicle with the actual tracking trajectory in the simulation experiment.

[0088] Figure 10 This is an error curve between the vehicle's expected trajectory and the actual tracking trajectory in the simulation experiment.

[0089] Figure 11 This is a graph showing the change of the vehicle's vertical displacement over time during the simulation experiment.

[0090] Figure 12 This is a graph showing the change of the vehicle's vertical acceleration over time in a simulation experiment.

[0091] Figure 13 This is a graph showing the change of the vehicle's yaw angle over time during a simulation experiment.

[0092] Figure 14 This is a graph showing the change of vehicle roll angle over time in a simulation experiment.

[0093] Figure 15 This is a graph showing the change of the vehicle's pitch angle over time during a simulation experiment.

[0094] Figure 16 This is a graph showing the change of the front and rear wheel steering angle inputs of the controller designed for the simulation experiment over time.

[0095] Figure 17 The graph shows the change of the input of the controller designed for the four-wheel active suspension in the simulation experiment over time. Detailed Implementation

[0096] 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.

[0097] I. Vehicle Dynamics Model

[0098] To accurately capture the strongly coupled lateral and vertical dynamics of a vehicle during driving and to provide solid theoretical support for the coordinated control of trajectory tracking and attitude stability, this section constructs a nine-degree-of-freedom vehicle dynamics model that covers the core motion state and multi-dimensional control inputs. It comprehensively integrates the dynamic characteristics of lateral, vertical, yaw, roll, pitch, and unsprung mass of the four wheels, and systematically describes the force and motion relationship of each component.

[0099] 1. Construct a nine-degree-of-freedom vehicle dynamics model

[0100] like Figure 2 The diagram shown is a simplified mechanical model of a vehicle's single-wheel suspension, focusing on the core components and force relationships of the suspension system for any one of the front left, front right, rear left, or rear right wheels.

[0101] like Figure 3 As shown, using the Earth coordinate system O-XYZ as a reference, a vehicle coordinate system o-xyz is established for the moving vehicle: the longitudinal direction of the vehicle body is the x-axis, with the direction of vehicle movement being positive; the transverse direction of the vehicle body is the y-axis, with the direction perpendicular to the positive x-axis pointing to the left being positive; the z-axis is perpendicular to the xoy plane, with the direction vertically upwards being positive. Each wheel has its own independent wheel coordinate system o-uvw, with the length direction of the corresponding wheel as the u-axis, the width direction as the v-axis, and the height direction as the w-axis. Combining the above coordinate systems, Figure 3 It visually demonstrates the force distribution in the horizontal direction in a nine-degree-of-freedom model. Figure 3 The text clearly indicates the longitudinal road-tire interaction force (F) acting on the four wheels. x1 ~F x4 ), lateral road-tire interaction force (F y1 ~F y4 The angles δ1~δ4 between the positive u-axis of each wheel coordinate system and the positive x-axis of the vehicle coordinate system, as well as the sideslip angles α1~α4, clearly show the direction and point of application of each force in the xy plane of the vehicle coordinate system, and also relate them to the force causes of the vehicle's yaw angle. Figure 3 This allows for an intuitive understanding of the dynamic relationship between wheel forces and vehicle lateral displacement and yaw motion, providing visual support for constructing the vehicle's horizontal dynamic equations and analyzing the yaw angle variation.

[0102] Figure 4Focusing on the yz plane of the vehicle coordinate system, the suspension forces (F) of each wheel are clearly marked. z1 ~F z4 Data such as these provide an intuitive basis for analyzing the dynamic mechanism of vehicle roll angle and vertical displacement, and are key visualization tools for accurately capturing lateral and vertical coupling effects and deriving equations related to roll stability.

[0103] like Figure 5 As shown, the distance (h) from the center of mass to the pitch center is marked in the xz plane of the vehicle coordinate system. p Data such as these provide a clear force analysis framework for constructing pitch angle dynamic equations and analyzing longitudinal-vertical coupling characteristics, which is an important foundation for ensuring vehicle pitch stability control design.

[0104] Based on the above analysis, the following nine-degree-of-freedom vehicle dynamics model is established in the vehicle coordinate system:

[0105] ;

[0106] In the formula:

[0107] m s m is the sprung mass. ui Let be the unsprung mass of the i-th wheel, i = 1, 2, 3, 4, and the corresponding wheels are the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; g is the acceleration due to gravity.

[0108] I ρ and I θ These are the vehicle's yaw moment of inertia, roll moment of inertia, and pitch moment of inertia, respectively.

[0109] h r h p These are the distances from the center of mass to the roll center and pitch center, respectively; t f t r These are the track widths of the front and rear axles, respectively; l f l r These are the distances from the front and rear wheel axles to the vehicle's center of gravity, respectively.

[0110] ρ and θ are the vehicle yaw angle, vehicle pitch angle and vehicle roll angle, respectively; , and These are the vehicle yaw rate, vehicle pitch rate, and vehicle roll rate, respectively. , and These are the vehicle yaw acceleration, vehicle pitch acceleration, and vehicle roll acceleration, respectively.

[0111] x, y, z and z in a nine-degree-of-freedom vehicle dynamics model ui These are the vehicle's longitudinal displacement, lateral displacement, vertical displacement, and vertical displacement of the i-th unsprung mass, respectively. , and These are the vehicle's longitudinal velocity, lateral velocity, and vertical velocity, respectively. , , and These are the vehicle's longitudinal acceleration, lateral acceleration, vertical acceleration, and the vertical acceleration of the i-th unsprung mass, respectively.

[0112] In the vehicle coordinate system, F x1 F x2 F x3 and F x4 These are the road-tire interaction forces acting longitudinally on the 1st, 2nd, 3rd, and 4th wheels of the vehicle; F y1 F y2 F y3 and F y4 These are the road-tire interaction forces acting laterally on the 1st, 2nd, 3rd, and 4th wheels of the vehicle, respectively; F z1 F z2 F z3 and F z4 These are the 1st, 2nd, 3rd, and 4th suspension forces, respectively. F ti Let be the dynamic load of the i-th tire.

[0113] ;

[0114] In the formula, F zi f is the i-th suspension force; si f ci and f di These represent the spring force, damping force, and input control force of the i-th suspension, respectively.

[0115] 2. Vehicle control parameters

[0116] Vehicle control parameters include the front wheel steering angle δ f The steering angle δ of the rear wheels r Input the control force f of the left front wheel suspension. d1 Input the control force f of the right front wheel suspension. d2 Input the control force f of the left rear wheel suspension. d3 and input the control force f of the right rear wheel suspension d4 These control parameters are integrated into a vector representation:

[0117] ;

[0118] In the formula, represents the input vector of control parameters; T represents the vector transpose.

[0119] 3. Matrix form

[0120] Based on the nine-degree-of-freedom vehicle dynamics model, the vehicle's state vector is constructed:

[0121] ;

[0122] In the formula, Q is the state vector. The first derivative of the state vector; The second derivative of the state vector is z. u1 z u2 z u3 and z u4 These are the vertical displacements of the 1st, 2nd, 3rd, and 4th unsprung masses, respectively. , , and These are the vertical velocities of the 1st, 2nd, 3rd, and 4th unsprung masses, respectively. , , and These are the vertical accelerations of the 1st, 2nd, 3rd, and 4th unsprung masses, respectively.

[0123] Based on the nine-degree-of-freedom vehicle dynamics model, the vehicle's state vector, and the control parameter input vector, a dynamic matrix representation is constructed:

[0124] ;

[0125] In the formula, M is a 9×9 mass matrix; B is the input matrix; and N is the resultant external force vector.

[0126] The corresponding matrix is ​​represented as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] Among them, f xf =f x1 +f x2 ,based on Figure 2 The tire coordinate system of the left front wheel and the tire coordinate system of the right front wheel, and the longitudinal tire force f of the front axle. xf Including the longitudinal tire force f of the left front wheel x1 And the longitudinal tire force f of the right front wheel x2 ;f xr=f x3 +f x4 ,based on Figure 2 The tire coordinate system of the left rear wheel and the tire coordinate system of the right rear wheel, and the longitudinal tire force f of the rear axle. xr Including the longitudinal tire force f of the left rear wheel x3 and the longitudinal tire force f of the right rear wheel x4 C f C represents the lateral stiffness of the front axle tires. r This refers to the lateral stiffness of the rear axle tires.

[0131] ;

[0132] ;

[0133] In the formula, F xi f is the longitudinal tire force of the i-th wheel in the vehicle coordinate system. xi F represents the longitudinal tire force of the wheel in the i-th tire coordinate system. yi f is the lateral tire force of the i-th wheel in the vehicle coordinate system; yi δ represents the lateral tire force of the wheel in the i-th tire coordinate system. i Let be the angle between the positive u-axis of the i-th tire coordinate system and the positive x-axis of the vehicle coordinate system.

[0134] II. Error Calculation

[0135] This section is based on a nine-degree-of-freedom vehicle dynamics model. First, the desired state vector containing the preset desired trajectory and ideal attitude is defined. Then, the real-time state vector of the vehicle operation is obtained. The difference between the two is used to quantify the deviation between the actual and the desired trajectory and attitude in core dimensions, providing key dynamic error basis for subsequent constraint design and generation of coupled control quantities.

[0136] 1. Expected state vector

[0137] Based on the preset desired trajectory and ideal posture, establish the desired state vector Q. d :

[0138] ;

[0139] Trajectory-class expected parameter: y d , d These are the vehicle's expected lateral displacement and the vehicle's expected yaw angle, respectively.

[0140] Pose-related expected parameters: z d ρ d and θ d These are the vehicle's desired vertical displacement, vehicle's desired pitch angle, and vehicle's desired roll angle, respectively.

[0141] Unsprung mass desired parameter: z u1,d z u2,d z u3,d and z u4,d These represent the expected vertical displacements of the 1st, 2nd, 3rd, and 4th unsprung masses, respectively.

[0142] 2. Real-time state vector

[0143] Based on the state definition of the nine-degree-of-freedom vehicle dynamics model, real-time data during vehicle operation is acquired, and the actual state is input into the state vector Q to form the real-time state vector Q. t Real-time state vector Q t With the desired state vector Q d The dimensions are completely consistent, ensuring a one-to-one correspondence in error calculation.

[0144] 3. Error Vector

[0145] An error vector is constructed by subtracting the expected state vector from the real-time state vector. The core formula is directly related to the state dimension of the model, ensuring the comprehensiveness and accuracy of deviation quantification.

[0146] Error vector E:

[0147] ;

[0148] Expanded into a component-wise error formula (9-dimensional error corresponds to 9-dimensional state):

[0149] ;

[0150] Each component of the error vector directly reflects the "degree of deviation" of the corresponding state. A positive value indicates that the actual state is ahead of the expected state, while a negative value indicates that the actual state is behind the expected state, providing a clear direction and magnitude of the deviation for subsequent control decisions.

[0151] 4. Screening core error items

[0152] Based on the Udwadia-Kalaba method and the core control objective of "trajectory tracking + attitude stabilization," key error terms are selected from the 9-dimensional error vector, and secondary errors (non-sprung mass vertical errors) are eliminated to ensure that subsequent constraint design and controller decisions focus on the core requirements. The selected core error vector E c for:

[0153] ;

[0154] Unsprung mass vertical error e u1 -e u4It has been indirectly optimized through suspension force control, so it does not need to be used as a separate core constraint target. After screening, it can simplify the calculation complexity of subsequent constraint design, while ensuring that core requirements are not overlooked.

[0155] 5. Dynamic error updates

[0156] Since the vehicle is in continuous operation, the real-time state vector Q t The data will be updated in real time according to changes in dynamic response and external operating conditions. Therefore, it is necessary to repeatedly acquire real-time data according to the dynamic calculation cycle of the nine-degree-of-freedom model to realize the core error vector E. c Real-time dynamic updates ensure that subsequent constraint design and controller output are always based on the latest deviation, avoiding control failure due to error lag.

[0157] 6. Output error data

[0158] The dynamically updated real-time core error vector E c (t) is passed directly to the constraint design stage as the output, and is a first-order constraint. Second-order constraints It provides key inputs to ensure that the constraint target and the error state are accurately matched, laying the foundation for the subsequent generation of coupled control variables.

[0159] III. Constraint Design

[0160] The core objective of this section is to transform the error into a mathematical constraint, clarifying that the error must meet the requirements of "rapid convergence and no oscillation", and finally transforming it into a "second-order state constraint" that can be identified by the dynamic model, providing a clear objective for the subsequent controller to solve the coupled control quantities (steering angle + suspension force).

[0161] 1. First-order constraints

[0162] The core function of first-order constraints is to force the error to approach 0 rapidly over time, thus avoiding error accumulation.

[0163] The general formula for first-order constraints is expressed as follows:

[0164] ;

[0165] In the formula, Λ1 is a 5×5 positive definite diagonal matrix used for first-order constraints, with each diagonal element being greater than 0, used to independently adjust the convergence speed of each core error. Real-time core error vector E c The first derivative of (t).

[0166] 2. Second-order constraints

[0167] First-order constraints only guarantee "fast convergence", which may lead to error oscillations (such as trajectory back and forth correction, attitude swaying). Therefore, second-order constraints need to be designed to supplement "damping characteristics".

[0168] The general formula for second-order constraints is expressed as follows:

[0169] ;

[0170] In the formula, Λ2 is a 5×5 positive definite diagonal matrix used for second-order constraints, with each diagonal element being greater than 0, used to adjust the damping effect of error convergence. Real-time core error vector E c The second derivative of (t).

[0171] 3. Constraint Transformation

[0172] Second-order constraints are "error-level constraints" and need to be transformed into "state-acceleration-level constraints" before they can be embedded into the dynamic model and provide a basis for the controller to solve for the control force.

[0173] The above analysis shows that:

[0174] ;

[0175] In the formula, The real-time state core term vector Q t,c The second derivative; Expected state core term vector Q d,c The second derivative of .

[0176] Substituting into the general formula for second-order constraints, we get:

[0177] ;

[0178] Combining this with the general formula for first-order constraints, we can obtain:

[0179] ;

[0180] Construct constraint matrix A: The purpose of A is to "select the state accelerations that need to be constrained" (only constrain the state accelerations corresponding to the 5 core errors, and have no constraints on non-core states), with a dimension of 5×9 (5 core constraints, 9-dimensional state vector):

[0181] ;

[0182] In constraint matrix A, only the column element corresponding to the core state acceleration is 1, and the rest are 0, ensuring... To extract a 9-dimensional real-time state vector The five core items.

[0183] Constructing second-order constraint vectors

[0184] The second-order constraint vector b defines the target value of the core state acceleration. It has a dimension of 5×1 and is represented as follows:

[0185] ;

[0186] Based on the above analysis, we can conclude that:

[0187] ;

[0188] Its physical meaning is: real-time acceleration. After A is selected, it must be equal to the target value defined by b. This forces the acceleration of the core state (trajectory + attitude) to meet the requirement of "rapid and stable convergence of error".

[0189] IV. Adaptive Robust Control

[0190] The core objective of this section is to generate executable coupled control variables (four-wheel steering angle + four-wheel active suspension force). Through the triple logic of "precise control + deviation compensation + disturbance rejection", the corresponding constraint requirements are met, while dealing with uncertainties such as load changes and crosswinds, and finally achieving coordinated control of "trajectory tracking + attitude stabilization".

[0191] 1. System Decomposition

[0192] Dynamic matrix representation based on a nine-degree-of-freedom vehicle dynamics model Decompose M and N as follows: they only change with state q and time t, with no unknown disturbances.

[0193] ;

[0194] ;

[0195] make:

[0196] ;

[0197] ;

[0198] ;

[0199] Combining the above formula, we can obtain:

[0200] ;

[0201] ;

[0202] In the formula, The nominal mass matrix represents the deterministic portion of the mass matrix M, which consists of known calibration parameters, such as the sprung mass m. s and the corresponding moment of inertia I ρ I θIt changes only with state and time, without any unknown perturbations. V and G are transition parameters used for brief description, and I is the identity matrix.

[0203] ΔM is the perturbation mass matrix, representing the uncertain part of the mass matrix M, which is the fluctuation of inertial parameters caused by external factors, such as the increase in the mass of the vehicle after passengers are loaded. It is an unknown dynamic term. ΔV is the parameter perturbation term of the inverse of the mass matrix M.

[0204] The nominal perturbation vector represents the deterministic part of the perturbation vector N, which are known calibration parameters.

[0205] Let N be the disturbance vector, representing the uncertain part of the disturbance vector N. The damping / stiffness fluctuations caused by external factors (such as changes in the damping coefficient due to suspension aging) are unknown dynamic terms.

[0206] m s For the total vehicle weight; m ui Let be the unsprung mass of the i-th wheel, i = 1, 2, 3, 4, and the corresponding wheels are the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively; g is the acceleration due to gravity.

[0207] Substituting into the dynamic matrix representation From this, we can obtain:

[0208] ;

[0209] 2. Design control force

[0210] Design core control force When the vehicle system has no uncertainties, that is, the model is completely accurate, there are no external disturbances, and the initial conditions are unbiased, Based on the Udwadia-Klaba method, it is the core control force for achieving trajectory tracking and stability control.

[0211] Design compensation control force To address first-order deviations, such as discrepancies between the vehicle's lateral velocity and attitude and the desired state during startup, a constraint deviation vector is designed to suppress them. It is a compensatory control force that eliminates first-order bias and allows the system to converge quickly to the desired state.

[0212] Design disturbance rejection control force It is used to resist uncertainties in the system, such as crosswind interference that can cause vehicle body swaying, resulting in changes in lateral velocity and roll angle, which can lead to trajectory tracking deviation. This is designed to generate a tire swerve angle to counteract this disturbance, such as changes in occupant position leading to increased sprung mass, pitch and roll angles, and moment of inertia. The method addresses this uncertainty by coordinating and controlling the suspension spring force to ensure vehicle stability. At the same time, due to the high coupling between the vehicle's lateral and vertical systems, the vertical load on each wheel will also affect the tire's lateral stiffness and thus the steering angle control output. This is the advantage of this control method in handling uncertainties in highly coupled vehicle systems.

[0213] Therefore, the adaptive robust controller designed for a nine-DOF underactuated vehicle system takes the following form:

[0214] ;

[0215] ;

[0216] ;

[0217] ;

[0218] In the formula, It is overall control; It is a control matrix with values ​​greater than 0; κ1 and κ2 are both control constants with values ​​greater than 0; (·) + Represents the Moore–Penrose generalized inverse; For the constraint deviation vector, Where c is the first derivative of the desired state vector. The target value after processing by constraint matrix A; Π is the overall uncertainty boundary function; η is the weight coefficient of robust disturbance resistance; γ is the weight of uncertainty suppression term.

[0219] 3. Calculate core control force

[0220] It is the core control variable when "no disturbance and accurate model", combined with the constraints in Part 3. (The 'b' in the constraint part is the target acceleration vector for error convergence, which is an independent constraint term and a non-dynamic model redundancy term.) The following calculations are performed:

[0221] Extract the dynamic equations from the nominal portion (ΔM=ΔN=0):

[0222] ;

[0223] Combining constraints Invert the nominal mass matrix:

[0224] ;

[0225] Substitution constraints Establish the "constraint-control quantity" relationship:

[0226]

[0227] right The whole is taken from the Moore–Penrose generalized inverse. After sorting, we get:

[0228] ;

[0229] 4. Calculate the compensation control force

[0230] This is for the "initial error of the nominal part during startup / operating condition switching", and is derived based on the first-order deviation of the core error. The specific derivation process is as follows:

[0231] Introducing constraint deviation vector Quantization of first-order bias:

[0232] ;

[0233] In order to constrain the deviation vector Converted into control quantity It is necessary to construct a joint mapping of "constraint matrix A, nominal mass matrix M, and input matrix B" for... Take the Moore–Penrose generalized inverse, denoted as .

[0234] Introducing the control coefficient κ1 (amplification deviation weight) and the inverse Γ of the control matrix Γ -1 (Scaling control magnitude) converts constraint deviation into compensating control force, ultimately leading to:

[0235] ;

[0236] 5. Calculate disturbance rejection control force

[0237] The form of the nine-DOF vehicle dynamics model containing uncertainties is as follows:

[0238] ;

[0239] The upper bound of the uncertain part is described by Π. Bounded, having ), A constant greater than -1 For adaptive parameters, the disturbance and constraint deviation are correlated simultaneously through the robust disturbance resistance weighting coefficient η: .

[0240] Introducing the uncertainty parameter of adaptive rate estimation Its first derivative It is expressed as follows:

[0241] ;

[0242] ;

[0243] ;

[0244] ;

[0245] in, , Let Π be the basis function, Π be the global uncertainty boundary function, and the superscript T be the matrix transpose. Φ is introduced as a nonlinear control coefficient, and the mode is switched according to the magnitude of Π to achieve smooth suppression of over-adaptation under small uncertainties and maintain fast tracking capability under large uncertainties. L1, L2, and L3 are all gain parameters that control the estimated speed and stability. exp is the natural logarithm; n is the order of the vehicle dynamics system; Ω is an intermediate variable used to simplify the formula. κ3 is the control coefficient.

[0246] To transform the "uncertain disturbance" into a control variable, the constraint-input joint generalized inverse from the compensation control force is used: .

[0247] Based on the above analysis, we can conclude that:

[0248] ;

[0249] This is the control coefficient. Thus, the solution is obtained. The analytical expression.

[0250] 6. Summary

[0251] The abstract control objective of "trajectory tracking + attitude stabilization" is transformed into specific, executable coupled control variables. It integrates "precise control of nominal dynamics" Rapid compensation for initial deviation Robust suppression of uncertain disturbances ", the final output It includes two core parameters: four-wheel steering angle and four-wheel active suspension force. The reason it can be directly used for control is precisely because its components completely correspond to the functions of the vehicle's actuators: the steering angle component precisely matches the steering angle adjustment requirements of the four-wheel steering actuators, while the suspension force component corresponds to the output control requirements of the active suspension actuators. This is equivalent to translating the mathematical objectives of "error convergence and constraint satisfaction" into physical action commands that the actuators can recognize. And it is precisely for this reason that when... Once determined, the subsequent "actuator coordination and linkage" stage can be entered, which transforms these parameters into actual hardware actions, allowing the control strategy to be implemented from the theoretical level into the actual operation of the vehicle.

[0252] V. Simulation Experiment Verification

[0253] To verify the practical application effect of the control method of the present invention, the simulation experiment adopted the form of Simulink-CarSim co-simulation, and the parameters of the experimental vehicle are shown in Table 1 below:

[0254] Table 1 Vehicle Parameters

[0255]

[0256] The initial simulation state vector is selected as follows:

[0257] ;

[0258] ;

[0259] ;

[0260] The controller parameters are: κ1=20, κ2=0.005.

[0261] like Figure 6 The diagram shows the left and right road surface excitations output by Carsim in the simulation experiment. The two graphs respectively present the road surface irregularities along the driving paths of the left and right wheels of the vehicle. The graphs accurately simulate complex road conditions such as continuous bumps and small undulations that may be encountered in actual driving, using the displacement amplitude on the vertical axis (range approximately 0.02~0.03m) and the time on the horizontal axis (0~12s). This provides a realistic external excitation scenario for subsequent verification of the controller's resistance to road disturbances. This road surface excitation serves as a key experimental input, directly used to test the dynamic response and coordinated adjustment effect of the four-wheel active suspension control force, and is a core prerequisite for verifying the stability and comfort of the entire control scheme under complex road conditions.

[0262] like Figure 7 and Figure 8 The diagrams shown illustrate the pulse and direction changes of the wind speed matrix during simulation experiments, used to simulate crosswind interference scenarios encountered by vehicles during driving. Through an intuitive display of the reflected distribution, the diagrams present the pulse characteristics of wind speed changes over time (such as instantaneous wind speed abrupt changes, duration, and amplitude fluctuations) and the dynamic switching of wind direction, accurately reproducing the randomness and uncertainty of crosswinds during actual driving. As a key experimental input, this diagram provides controllable crosswind interference conditions to verify the adaptive robust controller's resistance to crosswind disturbances.

[0263] like Figure 9 and Figure 10 As shown, the desired trajectory and the actual tracking trajectory, as well as the error between them, indicate that the vehicle turning angle output by the controller applied to the Carsim vehicle model has a good trajectory tracking control effect, with high accuracy and good robustness. There is no obvious deviation or lag. The lateral tracking error is always stable within the range of ±0.1m, and it can converge quickly after fluctuations. This shows that the controller responds to the disturbance adjustment in a timely manner and the control accuracy meets the standard.

[0264] like Figure 11 As shown, the magnitude of the vertical displacement of the vehicle body is reflected. The control method of the present invention can effectively suppress the magnitude of the vertical displacement of the vehicle body center of gravity and effectively absorb the excitation transmitted from the road surface. The calculation shows that the root mean square value of the relative vertical displacement is 0.0116 when using passive suspension and the root mean square value of the acceleration after applying the four-wheel suspension control force is 0.0098, which is reduced by 15.5% compared with passive suspension, effectively improving ride comfort.

[0265] like Figure 12 As shown, the change in the magnitude of the vehicle's vertical acceleration is reflected. As an evaluation index of passenger comfort, the control method of this invention can effectively suppress the magnitude of the vehicle's acceleration and significantly reduce high-frequency, large-amplitude vertical vibrations. The calculated root mean square value of acceleration when using passive suspension is 0.0153, and the root mean square value of acceleration after applying four-wheel suspension control force is 0.0079, which is 48.3% less than that of passive suspension, thus greatly improving ride comfort.

[0266] like Figure 13 As shown, the change in the vehicle's yaw angle demonstrates that, in a four-wheel steering vehicle, the vehicle can change its position diagonally during trajectory tracking, effectively improving the situation of excessive yaw angle when changing lanes in a front-wheel steering vehicle. The overall fluctuation range of the yaw angle is controlled within ±0.015 rad throughout the process, and it can quickly converge back to a stable range near 0 after fluctuations caused by road surface / crosswind disturbances, without continuous oscillation or divergence, demonstrating the robustness of the controller, i.e., its ability to quickly adjust to disturbances.

[0267] like Figure 14 As shown, the change in vehicle roll angle is evident. The curve of the passive suspension exhibits disordered and violent oscillations. After applying active suspension control, the roll angle fluctuates slightly around the target value, the curve is smoother, and the convergence is better. Compared with the roll angle of a vehicle with ordinary passive suspension, the peak value is reduced by 40%. The root mean square values ​​of the roll angle before and after control are 0.0101 and 0.0062, respectively, a reduction of 38.6%. This indicates that the control can effectively suppress vehicle roll oscillations and improve roll stability during driving.

[0268] like Figure 15As shown, the pitch angle of the vehicle changes. After the control is applied, the pitch angle fluctuates smoothly around the target value. The "sharpness" of the curve is greatly reduced, and the stability under long-term steady state is significantly improved. Compared with the pitch angle of the vehicle with passive suspension, the peak value is reduced by 66%. The root mean square values ​​of the roll angle before and after control are 0.0018 and 0.0009, respectively, which is reduced by 50%. This shows that the control can effectively counteract the interference of excitations such as road unevenness on pitch motion.

[0269] like Figure 16 As shown, the curves of the angle input changes applied to the four wheels of the vehicle calculated by the control method are illustrated, reflecting the control strategy of "coordinated steering between the front and rear wheels". By synchronously adjusting the steering angle between the wheels, the influence of external disturbances (such as uneven road surface and crosswinds) on the vehicle's attitude / trajectory can be quickly offset. The convergence is fast, without continuous oscillation or large fluctuations, and the robustness is good. The steering angle of the front and rear wheels is within ±7 degrees, which is within the executable range of the automotive actuator, indicating the feasibility of the invention.

[0270] like Figure 17 As shown, the curves of the input changes of the active suspension control force applied to the four wheels of the vehicle calculated by the control method are shown. The coordination, responsiveness and anti-disturbance ability are all good. The control force can quickly and synchronously follow the fluctuations. The response delay to the perception of road excitation and the force output is small. The magnitude of the control force does not exceed 5000N when there are large road undulations, which is within the executable range of the vehicle actuator, indicating the feasibility of the present invention.

[0271] 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 vehicle trajectory tracking control method considering lateral and vertical coupling, characterized in that, Includes the following control steps: Based on the state vector Q during vehicle operation, a vehicle dynamics model is constructed. M is the mass matrix. Let Q be the second derivative, B be the input matrix, and N be the resultant external force vector; The control parameter input vector includes the front wheel steering angle δ. f Rear wheel steering angle δ r and four-wheel suspension control force f d1 ~f d4 ; From the desired state vector Q d and real-time state vector Q t Calculate the error vector E=Q t -Q d The core error vector E is composed of errors in lateral displacement, vertical displacement, yaw angle, roll angle, and pitch angle. c ; Design first-order constraints Second-order constraints And transform it into a second-order state constraint. Λ1 and Λ2 are both positive definite diagonal matrices, E c (t) represents E at time t. c , , E respectively c The first and second derivatives of (t), For Q t The second derivative of , where A is the constraint matrix and b is the second-order constraint vector; Decompose M and N into nominal parts , Let the uncertain parts ΔM and ΔN be... Combined with the real-time status calculation of the vehicle And control the vehicle: ； As the core control force, To compensate for the lack of control, For disturbance rejection control; κ1 and κ2 are both control coefficients; Let be the constraint deviation vector; Γ be the control matrix; Π be the overall uncertainty boundary function; η and γ are both weighting coefficients; (·) + It is the Moore-Penrose generalized inverse.

2. The vehicle trajectory tracking control method considering lateral and vertical coupling according to claim 1, characterized in that, The derivation process is as follows: Extract the kinetic equations from the nominal portion: ； Combining constraints ,right Find the inverse: ； Substitution constraints Establish the "constraint-control quantity" relationship: ； right The whole is taken from the Moore–Penrose generalized inverse. Organized .

3. The vehicle trajectory tracking control method considering lateral and vertical coupling according to claim 1, characterized in that, The derivation process is as follows: Introducing constraint deviation vector Quantization of first-order bias: ； In the formula, c is the first derivative of the desired state vector. The target value after processing by A; right Take the Moore–Penrose generalized inverse, denoted as ; Introducing the control coefficient κ1 and the inverse Γ of the control matrix Γ -1 The constraint deviation is transformed into a compensating control force, and the final derivation is as follows: .

4. The vehicle trajectory tracking control method considering lateral and vertical coupling according to claim 1, characterized in that, The derivation process is as follows: Extracting the uncertainties from the dynamic equations: ； The upper bound of the uncertain part is described by Π, and both ΔM and ΔN are bounded. , A constant greater than -1 For adaptive parameters, the disturbance and constraint deviation are correlated simultaneously through the robust disturbance resistance weighting coefficient η: ; Introducing the uncertainty parameter of adaptive rate estimation Its first derivative It is expressed as follows: ； ； ； ； in, , Π is the basis function, and the superscript T indicates the matrix transpose. Φ is introduced as a nonlinear control coefficient, and the mode is switched according to the size of Π to achieve smooth suppression of excessive adaptation under small uncertainties and maintain fast tracking capability under large uncertainties. L1, L2, and L3 are all gain parameters that control the estimated speed and stability. exp is the natural logarithm. n is the order of the vehicle dynamics system. Ω is an intermediate variable. κ3 is the control coefficient. right Take the Moore–Penrose generalized inverse, denoted as ; Introducing the control coefficient κ2 and the inverse Γ of the control matrix Γ -1 The constraint deviation is transformed into disturbance rejection control force, and the final derivation is as follows: .

5. A vehicle trajectory tracking control method considering lateral and vertical coupling according to claim 4, characterized in that, The transformation process of the second-order state constraint is as follows: Based on first-order and second-order constraints, we can obtain: ； In the formula, The real-time state core term vector Q t,c The second derivative; Expected state core term vector Q d,c The second derivative; Substituting into the second-order constraint formula, we get: ； Combining this with the first-order constraint formula, we can obtain: ； Construct the following constraint matrix A, where only the column elements corresponding to the core state acceleration are 1, and the rest are 0: ； Construct the second-order constraint vector b, as follows: ； Based on the above analysis, we can conclude that .

6. A vehicle trajectory tracking control method considering lateral and vertical coupling according to any one of claims 1-5, characterized in that, Vehicle dynamics model The specific details of each part are as follows: ； In the formula, m s m is the sprung mass. ui Let i be the unsprung mass of the i-th wheel, i = 1, 2, 3, 4, and the corresponding wheels are the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. I ρ and I θ These are the vehicle's yaw moment of inertia, roll moment of inertia, and pitch moment of inertia, respectively. ； In the formula, , and These are the vehicle yaw acceleration, vehicle pitch acceleration, and vehicle roll acceleration, respectively. , and These are the vehicle's lateral acceleration, vehicle's vertical acceleration, and the vertical acceleration of the i-th unsprung mass, respectively, i=1,2,3,4; ； In the formula, f xf =f x1 +f x2 f xf f is the longitudinal tire force on the front axle. x1 f is the longitudinal tire force of the left front wheel. x2 f is the longitudinal tire force of the right front wheel. xr =f x3 +f x4 f xr For the longitudinal tire force on the rear axle, f x3 f is the longitudinal tire force of the left rear wheel. x4 C is the longitudinal tire force of the right rear wheel; f C represents the lateral stiffness of the front axle tires. r Rear axle tire lateral stiffness; t f t r These are the front and rear track widths, respectively; l f l r These are the distances from the front and rear wheel axles to the vehicle's center of gravity, respectively. ； In the formula, δ f δ is the steering angle of the front wheels. r f is the steering angle of the rear wheels. d1 f d2 f d3 f d4 To input the control forces of the left front, right front, left rear, and right rear wheel suspensions; ； In the formula, ρ and θ are the vehicle yaw angle, vehicle pitch angle and vehicle roll angle, respectively; , and These are the vehicle yaw rate, vehicle pitch rate, and vehicle roll rate, respectively. , and These are the vehicle's longitudinal velocity, lateral velocity, and vertical velocity, respectively; h r h p These are the distances from the center of mass to the roll center and pitch center, respectively; f si f ci and f di These represent the spring force, damping force, and input control force of the i-th suspension, respectively, f. ti Let be the dynamic load of the i-th tire, i = 1, 2, 3, 4.

7. A vehicle trajectory tracking control method considering lateral and vertical coupling according to claim 6, characterized in that, The vehicle dynamics model has nine degrees of freedom, and its equations are as follows: ； In the formula, F x1 F x2 F x3 and F x4 These represent the road-tire interaction forces acting on the 1st, 2nd, 3rd, and 4th wheels along the longitudinal direction of the vehicle coordinate system; F y1 F y2 F y3 and F y4 These represent the road-tire interaction forces acting on the 1st, 2nd, 3rd, and 4th wheels in the lateral direction of the vehicle coordinate system; F z1 F z2 F z3 and F z4 These are the 1st, 2nd, 3rd, and 4th suspension forces in the vehicle's coordinate system.

8. A vehicle trajectory tracking control method considering lateral and vertical coupling according to claim 7, characterized in that, The specific calculation formulas for each force in the vehicle coordinate system are as follows: ； ； ； In the formula, F xi Let F be the road-tire interaction force acting on the i-th wheel in the longitudinal direction of the vehicle coordinate system. yi Let F be the road-tire interaction force acting on the i-th wheel in the lateral direction of the vehicle coordinate system. zi f is the i-th suspension force in the vehicle coordinate system. xi Let f be the longitudinal tire force of the wheel in the i-th tire coordinate system. yi Let δ be the lateral tire force of the wheel in the i-th tire coordinate system, i=1,2,3,4; cos is the cosine function, sin is the sine function, and δ i Let be the angle between the positive u-axis of the i-th tire coordinate system and the positive x-axis of the vehicle coordinate system.

9. A vehicle trajectory tracking control system considering lateral and vertical coupling, characterized in that, It includes a status acquisition module, a control processing module, and an execution module; The status acquisition module is used to acquire real-time status data of the vehicle's operation and generate a real-time state vector Q. t ; The control processing module is used to execute the control method according to any one of claims 1-8 and calculate the control parameter input vector. ; The execution module includes four-wheel steering actuators and four-wheel active suspension actuators for receiving... Front wheel steering angle δ f Rear wheel steering angle δ r and four-wheel suspension control force f d1 ~f d4 This enables the vehicle to achieve coordinated control of trajectory tracking and attitude stabilization.

10. A vehicle, characterized in that, It employs the vehicle trajectory tracking control system as described in claim 9.

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