Distributed electric vehicle optimal tracking control method based on dynamic stability domain

Abstract

The invention discloses a distributed electric vehicle optimal tracking control method based on a dynamic stability domain, and relates to the technical field of distributed electric drive vehicle motion control. The method comprises the following steps: analyzing strong nonlinear characteristics of tire ground contact dynamics under time varying, analyzing a tire sequence saturation mechanism after direct yawing moment intervention, constructing a dynamic stability domain with a mathematical analysis form, and reconstructing a stability boundary of the distributed driving electric vehicle; based on the reconstructed stability boundary, a control Lyapunov function, a control obstacle function and quadratic programming, a distributed driving electric vehicle motion controller is designed in an integrated mode, and the optimal balance between vehicle tracking accuracy and stability is achieved. According to the motion control method, the advantage that four wheels of the distributed driving electric vehicle are independent and controllable is fully utilized, the vehicle dynamic stability domain reconstruction technology is integrated into a motion control algorithm, and the motion control capacity of the electric vehicle in a high-dynamic scene is remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of motion control technology of distributed drive intelligent electric vehicles, in particular to a distributed electric vehicle optimal tracking control method based on dynamic stability domain. BACKGROUND

[0002] Distributed drive electric vehicles, compared with centralized drive electric vehicles, are a new chassis drive configuration, which directly installs driving motors in each driving wheel or wheel edge, and cancels the mechanical transmission link of the vehicle. This new power configuration has four-wheel independent control capability, which can realize more accurate torque distribution and motion control, and therefore is evaluated by automobile experts as the best chassis for intelligent electric vehicles and the best carrier for realizing high dynamic safety driving, and has become the mainstream trend of the development of future intelligent electric vehicles.

[0003] Distributed electric drive vehicles provide a wider control space for achieving the above goals due to higher driving freedom, but at the same time significantly increase the design complexity of the motion control system. Vehicle motion control technology is one of the important links for the realization of automatic driving technology. Since vehicles generally travel in complex traffic environments or at high speeds, the requirements for vehicle motion control algorithms are generally higher than those of traditional control methods, and more stability and safety factors need to be considered. Commonly used motion control algorithm classifications include model predictive control-based algorithms, sliding mode control-based algorithms, adaptive control-based algorithms, robust control-based algorithms, optimal control-based algorithms, and intelligent control-based algorithms.

[0004] Vehicle high dynamic motion control is one of the common driving scenarios. When the vehicle is driving on the road and encounters emergency obstacle avoidance, extreme cornering, etc., a motion control strategy that can guarantee the stability of the vehicle needs to be designed, and a control method that meets the vehicle dynamics constraints, stability domain constraints, and actuator constraints is needed. The optimal control strategy has high tracking accuracy, strong stability, and multi-objective optimization of control performance. At present, traditional intelligent electric vehicle motion control algorithms are generally conservative, and stability factors are considered relatively more while ignoring tracking performance factors. The mechanism of dynamic stability domain of distributed electric drive vehicles greatly affects the final effect of motion control. How to closely combine tracking performance and stability for vehicle control has become one of the key problems of distributed electric drive intelligent electric vehicle motion control. Therefore, the present application proposes a distributed electric vehicle optimal tracking control method based on dynamic stability domain. SUMMARY

[0005] The purpose of this invention is to provide an optimal tracking control method for distributed electric vehicles based on dynamic stability domain. The motion control algorithm fully utilizes the advantage of the independent controllability of four wheels in distributed electric drive vehicles, and its dynamic performance is significantly improved compared with centralized methods. The dynamic stability domain reconstruction technology of the vehicle is integrated into the motion control algorithm, which provides a theoretically rigorous guarantee for the stability and safety of distributed electric drive vehicles. The motion control capability, safety and robustness of electric vehicles in high dynamic scenarios are significantly improved.

[0006] According to a first aspect of the present invention, in order to achieve the above objective, the present invention provides the following technical solution: a distributed electric vehicle optimal tracking control method based on a dynamic stability domain, comprising the following steps: The system receives vehicle handling control parameters and vehicle structural parameters. The vehicle handling control parameters include longitudinal forces, direct yaw moments, and front wheel steering angles for the left front wheel, right front wheel, left rear wheel, and right rear wheel. The vehicle structural parameters include vehicle mass, chassis parameters, and tire parameters. Based on vehicle handling control parameters and vehicle structural parameters, a nonlinear dynamic model of a distributed electric drive vehicle is established. The output of the nonlinear dynamic model is the time-varying parameters of vehicle motion, which include road adhesion coefficient, front wheel steering angle, direct yaw moment, and vehicle lateral and longitudinal velocities. Based on the analysis of the time-varying parameters of vehicle motion, the sequential saturation mechanism of tires after direct yaw moment intervention is analyzed, and transient and steady-state critical instability dynamic models are constructed based on the saturation mechanism to establish the correlation between time-varying parameters and dynamic stability domain. By inputting time-varying parameters into transient and steady-state critical instability dynamic models, the boundary points of the dynamic stability domain are calculated, and the dynamic stability domain with analytical form is reconstructed. A vehicle motion tracking error model is established, in which the output of the tracking error model is the heading angle error and the lateral error. Based on the vehicle motion tracking error model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. The reconstructed dynamic stability domain is used as the safety boundary to construct a control obstacle function to ensure that the vehicle state is always within the safety boundary.

[0007] Using the control Lyapunov function and the control barrier function as constraints, a quadratic programming optimization problem is established. The quadratic programming optimization problem is solved by a quadratic programming solver, and the optimal control strategy is output.

[0008] Furthermore, the chassis parameters include the vehicle's moment of inertia about its vertical axis, the distance from the center of gravity to the front axle, the distance from the center of gravity to the rear axle, the direct yaw moment, the front wheel track, and the rear wheel track. Tire parameters include wheel lateral stiffness, wheel vertical load, wheel saturation tire force lateral slip angle, front axle lateral slip angle, and rear axle lateral slip angle.

[0009] Furthermore, a nonlinear dynamics model for a distributed electric drive vehicle is established, as follows: (31) Characterize the distributed electric drive vehicle as having a total mass of Inertial torque is A nominal vehicle model is established based on the following assumptions for a single rigid body: Assumption 1: The vehicle's geometry is symmetrical about the longitudinal central plane, and the origin of the coordinate system coincides with the position of the centroid of the four-wheeled vehicle model in the Cartesian coordinate system XOY. Assumption 2: Ignore the pitch and roll motion of the vehicle system, and do not consider the mechanical-mechanical coupling modeling of the suspension and steering system, where there is no dynamic transfer of longitudinal and lateral loads; Assumption 3: Assume the ideal steering system satisfies: and ,when ,exist and ; (32) Based on the assumptions, a three-degree-of-freedom vehicle dynamics model is established for distributed electric drive vehicles: In the formula, For the total mass of the vehicle. For the longitudinal speed of the vehicle, For the vehicle's lateral speed, Let yaw rate be the vehicle's angular velocity. , , , These are the longitudinal forces on the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. , , , The lateral forces are respectively applied to the left front wheel, right front wheel, left rear wheel, and right rear wheel. For the front wheel steering angle, Let be the moment of inertia of the vehicle about its vertical axis. This is the distance from the center of gravity to the front axle. This is the distance from the center of mass to the rear axle. For direct yaw moment, The front wheel track. This refers to the rear wheel track. Based on the aforementioned three-degree-of-freedom vehicle nonlinear dynamics equations, the vehicle's center of gravity sideslip angle is defined as... The sideslip angle of the center of mass is obtained through dynamic transformation. and yaw rate The equivalent dynamic equation for the state variables is: In the formula, The sideslip angle is the angle at the vehicle's center of gravity. The rate of change of the centroid sideslip angle. This is the yaw acceleration; (33) Construct a Fiala nonlinear brush tire model. The tire model is used to describe the nonlinear characteristics of the tire and provide a method for calculating the tire's lateral force. The tire model expression is: when hour: when hour: in, In the formula, superscript Indicates wheel position markings, where These represent the front axle and the rear axle, respectively. These represent the left wheel and the right wheel, respectively. The lateral forces of each wheel, Let be the lateral stiffness of each wheel. The vertical load on each wheel. The tire-road adhesion coefficient, The sideslip angles are the saturated tire force sideslip angles for each wheel, and the sideslip angle for the rear axle is... The sideslip angle corresponding to the front axle is .

[0010] Furthermore, based on the output time-varying parameters of vehicle motion, the sequential saturation mechanism of the tires after direct yaw moment intervention is analyzed. Transient and steady-state critical instability dynamic models are constructed based on the saturation mechanism, and the correlation between time-varying parameters and the dynamic stability domain is established, as follows: (41) When analyzing the tire sequential saturation mechanism after the intervention of direct yaw moment, the Stanford stability region is introduced as the basic theory for stability region reconstruction. The Stanford stability region belongs to the convergence range of the attraction region and satisfies ; The upper and lower limits of the ideal yaw rate are determined based on the ideal tire-ground contact conditions as follows: According to the tire saturation slip angle Determine the range of the maximum stable center-of-mass sideslip angle within the Stanford stability region, and establish kinematic constraints between the center-of-mass sideslip angle, tire sideslip angle, and front wheel steering angle under different initial vehicle conditions: In the formula, To determine the undetermined coefficients of the Stanford stability region; (42) However, the direct yaw moment intervention of the distributed electric vehicle changes the inherent phase plane manifold, and the previously defined Stanford stability region is no longer applicable to the design of the distributed electric vehicle tracking controller. The mechanism by which direct yaw moment intervention affects the equilibrium point, saddle point, and track topology in the phase plane is analyzed. Its manifestation is an implicit influence. The Stanford stability region contains an implicit precondition: the front and rear wheel slip angles simultaneously reach their saturation limits. Steady-state conditions are then defined. and The steady-state tire forces at the front and rear are expressed as: In the formula, the steady-state tire forces of the front and rear wheels are constrained by the maximum lateral adhesion force, and the proportional relationship between the lateral forces of the front and rear wheels is... and the ratio between their respective maximum lateral forces Determined as ,in, , This represents the maximum lateral force on the front wheel. This represents the maximum lateral force on the rear wheel. After the direct yaw moment intervenes, the steady-state tire force is re-expressed as: In the formula, Under certain conditions, the slip angles of the front and rear tires exhibit sequential saturation characteristics, rather than reaching their respective saturation limits simultaneously; the range of direct yaw moment and yaw rate determines the order in which the front and rear tires reach saturation. (43) Based on the lateral force of the tire satisfying and Under the given conditions, reconstruct the upper and lower boundaries of the yaw rate: Derivation of yaw rate The feasible region is: in, , and ; Maximum yaw rate and minimum yaw rate They are represented as follows: The prerequisite for its validity is the direct yaw moment. and yaw rate The relationships can be combined in four different ways: , , , .

[0011] Furthermore, by inputting time-varying parameters into the transient and steady-state critical instability dynamic models, the boundary points of the dynamic stability domain are calculated, and the dynamic stability domain with analytical form is reconstructed, as follows: (51) Regarding Under these operating conditions, the front wheels of a distributed electric drive vehicle will first enter a saturation state: Assumption , , Then the yaw moment is directly lateral. The maximum rear wheel slip angle achievable with intervention is expressed as: Based on the established maximum rear wheel slip angle It incorporates the direct yaw moment effect and transient boundary point The explicit mathematical expression is: Determine the transient stability boundary under left-turn maneuver conditions. The key points The explicit derivation of the determination is as follows: In the formula, , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. The maximum front wheel steering angle, The maximum rear wheel slip angle, The maximum front wheel slip angle, The nominal rear wheel saturation sideslip angle, The lateral force on the rear wheel under direct yaw moment. This represents the nominal maximum lateral force on the rear wheel. (52) Regarding In this situation, the rear wheels of a distributed electric drive vehicle will saturate first when operating under these conditions: Assumption , , Then the yaw moment is directly lateral. The maximum front wheel slip angle achievable with intervention is expressed as: Based on the established maximum front wheel slip angle It incorporates the direct yaw moment effect, and the explicit mathematical expression of the transient boundary point A is as follows: Determine the transient stability boundary under right turn maneuver conditions. The key points The explicit derivation of the determination is as follows: In the formula, , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. Minimum front wheel steering angle, The maximum front wheel slip angle, The maximum rear wheel slip angle, The nominal front wheel saturation sideslip angle, The lateral force on the front wheel under the direct action of yaw moment. This represents the nominal maximum lateral force on the front wheel; (53) Establish transient boundaries and Define a closed convex region, defined as follows: This convex region configuration reconstructs the safety boundary of distributed electric drive vehicles, targeting The operating conditions are further characterized, and the resulting closed region is defined as follows: The expression for the transient boundary is: In the formula, This is the convex hull region of the reconstructed stability domain when the direct yaw moment is positive. This is the convex hull region of the reconstructed stability domain when the direct yaw moment is negative. Indicates the origin of the point , , , The convex hull formed , , , These represent the Shuntai boundary line segments connecting the corresponding vertices. , , , This represents the transient boundary vertex corresponding to a negative direct yaw moment. (54) Targeting and Under the operating conditions, when the distributed electric drive vehicle satisfies the negative direct yaw moment Non-zero yaw rate values or Establish a deterministic saturation order between the front and rear wheels, and calculate and determine the transient boundary points. , , , ,in, , , , The transient boundary vertex under the condition of negative direct yaw moment. This indicates a negative direct yaw moment constraint condition. Indicates the positive yaw rate. This indicates a negative yaw rate.

[0012] Furthermore, a vehicle motion tracking error model is established. Based on this model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. Using the reconstructed dynamic stability domain as the safety boundary, a control barrier function is constructed to ensure that the vehicle state always remains within the safety boundary, as detailed below: (61) Establish a distributed electric vehicle tracking error model: In the formula, The sideslip angle is the angle at the vehicle's center of gravity. Let yaw rate be the vehicle's angular velocity. For the front wheel steering angle, For the longitudinal force of each tire, The lateral forces of each tire. The slip angles of each tire are given, where the superscript indicates the slip angle. The system systematically corresponds to the left front wheel, right front wheel, left rear wheel, and right rear wheel. This represents the total longitudinal force of the tire. and These are the longitudinal and lateral components of the vehicle speed, respectively. This represents the error between the vehicle's heading angle and the ideal path direction angle. For lateral error, For the path in displacement Curvature at that point; (62) For a class of nonlinear controlled radiation systems: In the formula, For state variables, To control the input, the function and It is locally Lipschitz continuous; Given a closed-loop feedback control law, the closed-loop dynamic system is expressed as: In the formula, This is a feedback control law, which ensures that the autonomous system's state always remains within the safe region, i.e. ; (63) For any initial conditions There exists a unique continuously differentiable solution. ,satisfy And this solution is defined on the maximum existence interval. ;in, For system drift terms, To control the input matrix, In the state The set of safety control input constraints below, It is a space of continuously differentiable functions. To start from the initial state The maximum possible space of origin; (64) Let open set ,in Suppose there exists a function It is It is continuously differentiable, positive definite, and radially unbounded, and there exists a... Class function , such that for any There is a control input This makes the following inequality hold: In the formula, the function The system is opening a set. Control the Lyapunov function on it. Let be an open set in the state space. Let be the set of nonnegative real numbers. Class function For strictly increasing and satisfying Continuous functions, For function Along the system drift term Li Daoshu, For function Along the control input matrix The Lie derivative, radially unbounded, refers to when hour, ; (65) Let the system state space be ,gather Defined by the following conditions: In the formula, It is a continuously differentiable function; If an extension exists Class function , so that for any The following inequalities hold: Then it is called For set Control barrier function on. Let be an open set in the system's state space. The safe set is defined by the non-negative level set of the control barrier function. Candidate functions for the control barrier function, The class function is strictly increasing, continuous and satisfies as well as The function, To control the set of input constraints, For function Along the system drift term Li Daoshu, For function Along the control input matrix Li Daoshu, In the constraint set The supremum operation.

[0013] Furthermore, using the control Lyapunov function and the control barrier function as constraints, a quadratic programming optimization problem is established. This problem is then solved using a quadratic programming solver, and the optimal control strategy is output, as follows: (71) Constructing a nonlinear controlled radiation system: In the formula, For state variables, i.e. Including vehicle center of gravity sideslip angle yaw rate Longitudinal velocity Heading angle error and lateral position error ; To control input Including total longitudinal force Front wheel steering angle and direct yaw moment ; For system drift terms, To control the input matrix; (72) To achieve the design goal of a controller that combines the control Lyapunov function and the control barrier function, the nonlinear control radiation system is decomposed into: In the formula, This refers to vehicle stability-related conditions. To track performance-related status; (73) To design a tracking controller that controls a Lyapunov function to track a predetermined path, given the desired state: In the formula, For the desired longitudinal velocity, For the desired heading angle error, The desired lateral position error; (74) Construct the Lyapunov function as follows: In the formula, For reference only. It is a positive definite weight matrix; Therefore, the derivative of the Lyapunov function is: In the formula, This is the error vector; According to the theory of controlling Lyapunov functions, the following must be satisfied: In the formula, The attenuation rate, Used as slack variables to handle constraint feasibility; The structure for controlling Lyapunov inequalities is as follows: While tracking the desired state, the vehicle's stability state must remain within the boundary of the stability domain: In the formula, Indicates the origin of the vertex , , , The convex hull formed; The stability region constraint is expressed as: In the formula, , , For the stable boundary Undetermined coefficients of linear constraints; (75) Safety boundary , , , Described as: According to the safety boundary , , , Construct the corresponding control barrier functions respectively Using digital labeling express: In the formula, , , For the stable boundary Undetermined coefficients of linear constraints; coefficient vector , , They are constructed as follows: In the formula, , , , Vertices , , , The yaw rate coordinates , , , These are the centroidal lateral tilt angle coordinates of the corresponding vertices; (76) Based on the control Lyapunov function and control barrier function theory, the quadratic programming optimization problem is constructed as follows: In the formula, For reference control input, To control the weight matrix, To relax the penalty weights; The constraints include: Controlling Lyapunov function constraints: Control barrier function constraints: In the formula, To control the convergence parameters of the barrier function; Control input constraints: In the formula, This is the input for front wheel steering angle control. For direct yaw moment control input, and These are the minimum and maximum values ​​of the front wheel steering angle, respectively. and These are the minimum and maximum values ​​of the direct yaw moment, respectively. Variable constraints. , To control the input dimension, relax the penalty weights. Ensure slack variables minimize.

[0014] According to a second aspect of the present invention, a distributed electric vehicle optimal tracking control system based on a dynamic stability domain is provided for implementing the distributed electric vehicle optimal tracking control method based on a dynamic stability domain described in the first aspect, comprising: The receiving module is used to receive vehicle handling control parameters and vehicle structural parameters. The vehicle handling control parameters include longitudinal forces, direct yaw moments, and front wheel steering angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel. The vehicle structural parameters include vehicle mass, chassis parameters, and tire parameters. The first building module is used to establish a nonlinear dynamic model of a distributed electric drive vehicle based on vehicle handling control parameters and vehicle structural parameters. The output of the nonlinear dynamic model is the time-varying parameters of vehicle motion, which include road adhesion coefficient, front wheel steering angle, direct yaw moment, and vehicle lateral and longitudinal velocities. The second construction module is used to analyze the sequential saturation mechanism of the tire after the direct yaw moment intervention based on the output time-varying parameters of vehicle motion, and to construct transient and steady-state critical instability dynamic models based on the saturation mechanism, and establish the correlation between time-varying parameters and dynamic stability domain. The reconstruction module is used to input time-varying parameters into transient and steady-state critical instability dynamic models, calculate the boundary points of the dynamic stability domain, and reconstruct the dynamic stability domain with analytical form. The third module is used to establish a vehicle motion tracking error model, in which the output of the tracking error model is the heading angle error and the lateral error. Based on the vehicle motion tracking error model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. The reconstructed dynamic stability domain is used as the safety boundary to construct a control obstacle function to ensure that the vehicle state is always within the safety boundary.

[0015] The optimization output module is used to establish a quadratic programming optimization problem with control Lyapunov function and control barrier function as constraints, solve the quadratic programming optimization problem through a quadratic programming solver, and output the optimal control strategy.

[0016] According to a third aspect of the present invention, the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein when the processor loads and executes the computer program, it employs the distributed electric vehicle optimal tracking control method based on dynamic stability domain described in the first aspect.

[0017] According to a fourth aspect of the present invention, the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the distributed electric vehicle optimal tracking control method based on a dynamic stability domain as described in the first aspect.

[0018] This invention has at least the following beneficial effects: 1. This invention constructs a safe and feasible domain for vehicles by reconstructing the dynamic stability domain, controlling the Lyapunov function, and controlling the obstacle function. Based on a quadratic programming optimization algorithm, it balances tracking accuracy, stability, and safety indices in vehicle motion control. This overcomes the conservatism of traditional control methods in the process of balancing tracking performance and stability, and avoids the problem of ignoring tracking accuracy when using stability control algorithms alone. It achieves the optimal trade-off between vehicle tracking accuracy and stability, improves the motion control accuracy and performance of vehicles in complex traffic scenarios, and enables vehicles to track target trajectories more accurately.

[0019] 2. This invention establishes a vehicle motion tracking error model, designs a control Lyapunov function to ensure asymptotic stability of the system, and constructs a control obstacle function to ensure that the vehicle state remains within the safe and stable domain. By combining the constraints of the control Lyapunov function and the control obstacle function, a quadratic programming optimization problem is established and solved in real time to obtain the optimal control output. This safety assurance mechanism based on the CLF-CBF-QP theoretical architecture can monitor and adjust the vehicle state in real time during vehicle operation, ensuring that the vehicle remains stable under various complex conditions, including emergency obstacle avoidance and extreme conditions, effectively preventing vehicle loss of control and greatly improving driving safety. 3. The motion control algorithm proposed in this invention is applicable to high-speed or low-speed driving conditions, as well as complex traffic scenarios such as emergency obstacle avoidance and extreme condition stability control. Whether in high-speed cornering, emergency collision avoidance, or high-dynamic driving scenarios such as slippery roads and complex road conditions, the vehicle maintains good stability and tracking performance, significantly improving the vehicle's environmental adaptability and versatility, and meeting the usage needs of modern intelligent electric vehicles under different conditions.

[0020] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the tracking control method described in this invention; Figure 2 This is a system block diagram of the tracking control method described in this invention; Figure 3 This is a schematic diagram of the nonlinear dynamics model of the present invention; Figure 4 This is a schematic diagram of the tracking error model of the present invention; Figure 5 This is a graph showing the stability domain analysis results for vehicle speed in this invention; Figure 6 This is a graph showing the stability domain analysis results of the adhesion coefficient in this invention; Figure 7 This is a diagram showing the stability domain analysis results of the direct yaw moment according to the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0023] Example 1: Please see Figures 1-7 This invention provides a technical solution: a distributed electric vehicle optimal tracking control method based on dynamic stability domain, comprising: Step 1: Establish a nonlinear dynamic model of a distributed electric drive vehicle and analyze the influence mechanism of tire saturation order after the intervention of direct yaw moment; based on the tire saturation order influence mechanism, construct transient and steady-state critical instability dynamic models; establish the correlation between time-varying parameters and dynamic stability domain, where time-varying parameters include vehicle speed, road adhesion coefficient, steering wheel angle and direct yaw moment; Step one involves designing the transient and steady-state critical instability dynamic models, which includes the following parts: (I) For distributed electric drive vehicles, the distributed electric drive vehicle is characterized as having a total mass of Inertial torque is Construct a nominal vehicle dynamics model from a single rigid body: a) Construct a dynamic model with three degrees of freedom: longitudinal, lateral, and yaw. In the formula, For the total mass of the vehicle. For the longitudinal speed of the vehicle, For the vehicle's lateral speed, Let yaw rate be the vehicle's angular velocity. , , , These are the longitudinal forces on the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. , , , The lateral forces are respectively applied to the left front wheel, right front wheel, left rear wheel, and right rear wheel. For the front wheel steering angle, Let be the moment of inertia of the vehicle about its vertical axis. This is the distance from the center of gravity to the front axle. This is the distance from the center of mass to the rear axle. For direct yaw moment, The front wheel track. This refers to the rear wheel track. b). Based on the aforementioned three-degree-of-freedom vehicle nonlinear dynamics equations, the vehicle's center-of-gravity sideslip angle is defined as... The sideslip angle of the center of mass is obtained through dynamic transformation. and yaw rate The equivalent dynamic equation for the state variables is: In the formula, The sideslip angle is the angle at the vehicle's center of gravity. The rate of change of the centroid sideslip angle. This is the yaw acceleration; c) Construct a Fiala nonlinear brush tire model, which describes the tire's nonlinear characteristics and provides a method for calculating the tire's lateral force. The tire model expression is as follows: when hour: when hour: in, In the formula, superscript Indicates wheel position markings, where These represent the front axle and the rear axle, respectively. These represent the left wheel and the right wheel, respectively. The lateral forces of each wheel, Let be the lateral stiffness of each wheel. The vertical load on each wheel. The tire-road adhesion coefficient, The saturated tire force sideslip angle for each wheel is [value], and the sideslip angle corresponding to the rear pull is [value]. The sideslip angle corresponding to the front axle is ; (II) When analyzing the mechanism of direct yaw moment intervention on the tires and the order of events, the Stanford stability region is introduced as the basic theory for stability region reconstruction. The Stanford stability region belongs to the convergence range of the attraction region and satisfies the following conditions: ; a) The upper and lower limits of the ideal yaw rate are determined based on the ideal tire-ground contact conditions: b) Based on the tire saturation slip angle Determine the range of the maximum stable center-of-mass sideslip angle within the Stanford stability region, and establish kinematic constraints between the center-of-mass sideslip angle, tire sideslip angle, and front wheel steering angle under different initial vehicle conditions: In the formula, To determine the undetermined coefficients of the Stanford stability region, however, the direct yaw moment intervention of the distributed electric vehicle alters the inherent phase plane manifold, and the previously defined Stanford stability region is no longer applicable to the design of the distributed electric vehicle tracking controller. c) Analyze the mechanism by which the direct yaw moment affects the equilibrium point, saddle point, and track topology in the phase plane. Its manifestation is an implicit influence. The Stanford stability region contains an implicit precondition: the front and rear wheel slip angles simultaneously reach their saturation limits. Set the steady-state conditions. and The steady-state tire forces at the front and rear can be expressed as: In the formula, the steady-state tire forces of the front and rear wheels are constrained by the maximum lateral adhesion force; the proportional relationship between the lateral forces of the front and rear wheels... and the ratio between their respective maximum lateral forces Determined as ,in, , This represents the maximum lateral force on the front wheel. This represents the maximum lateral force on the rear wheel. d) The introduction of direct yaw moment disrupts established mathematical relationships, where steady-state tire forces can be re-expressed as: In the formula, Under certain conditions, the slip angles of the front and rear tires exhibit sequential saturation characteristics, rather than reaching their respective saturation limits simultaneously. The range of direct yaw moment and yaw rate determines the order in which the front and rear tires reach saturation, based on the lateral force of the tires satisfying... and Under the given conditions, reconstruct the upper and lower boundaries of the yaw rate: e). By combining the above formulas, the yaw rate is derived. The feasible region is: in, , and ; Correspondingly, the maximum yaw rate and minimum yaw rate They are represented as follows: The prerequisite for its validity is the direct yaw moment. and yaw rate Relationship combinations can be strictly classified into four different cases: , , , ; Step 2: Based on the transient and steady-state critical instability dynamic models, reconstruct the dynamic stability domain with analytical form to form a mathematical expression of the stability boundary of the distributed electric drive vehicle; Step two involves reconstructing the dynamically stable domain in analytical form, which includes the following parts: (I) Based on the aforementioned transient and steady-state critical instability dynamics models, a dynamic stability domain with analytical form is reconstructed: a) Targeting Under these operating conditions, the front wheels of a distributed electric drive vehicle will first enter saturation; assuming , , Then the yaw moment is directly lateral. The maximum rear wheel slip angle achievable with intervention is expressed as: Based on the established maximum rear wheel slip angle It incorporates the direct yaw moment effect and transient boundary point The explicit mathematical expression is: Determine the transient stability boundary under left-turn maneuver conditions. The key points The explicit derivation of the determination is as follows: In the formula, , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. The maximum front wheel steering angle, The maximum rear wheel slip angle, The maximum front wheel slip angle, The nominal rear wheel saturation sideslip angle, The lateral force on the rear wheel under direct yaw moment. This represents the nominal maximum lateral force on the rear wheel. b) Targeting In this scenario, the rear wheels of a distributed electric drive vehicle will saturate first when operating under these conditions; assuming , , Then the yaw moment is directly lateral. The maximum front wheel slip angle achievable with intervention is expressed as: Based on the established maximum front wheel slip angle It incorporates the direct yaw moment effect, and the explicit mathematical expression of the transient boundary point A is as follows: Determine the transient stability boundary under right turn maneuver conditions. The key points The explicit derivation of the determination is as follows: In the formula, , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. Minimum front wheel steering angle, The maximum front wheel slip angle, The maximum rear wheel slip angle, The nominal front wheel saturation sideslip angle, The lateral force on the front wheel under the direct action of yaw moment. This represents the nominal maximum lateral force on the front wheel; c) Through the above formula derivation, strictly establish the transient boundary. and A closed convex region is defined as follows: This convex region configuration critically reconstructs the safety envelope boundary of distributed electric drive vehicles; for The operating conditions are further characterized, and the resulting closed region is defined as follows: The expression for the transient boundary is: In the formula, This is the convex hull region of the reconstructed stability domain when the direct yaw moment is positive. This is the convex hull region of the reconstructed stability domain when the direct yaw moment is negative. Indicates the origin of the point , , , The convex hull formed , , , These represent the Shuntai boundary line segments connecting the corresponding vertices. , , , This represents the transient boundary vertex corresponding to a negative direct yaw moment. d) Targeting and Under the operating conditions, when the distributed electric drive vehicle satisfies the negative direct yaw moment Non-zero yaw rate values or This allows for the establishment of a deterministic saturation order between the front and rear wheels; correspondingly, the transient boundary points can be determined. , , , The process of calculating these boundary points follows the same methodology as the aforementioned theory; among which, , , , The transient boundary vertex under the condition of negative direct yaw moment. This indicates a negative direct yaw moment constraint condition. Indicates the positive yaw rate. Indicates negative yaw rate; e) Based on the defined range of the stability region, different vehicle absolute speeds, road adhesion coefficients, front wheel steering angles, and direct yaw moments are selected to analyze different stability regions. The specific steps are as follows: When the road surface adhesion coefficient, front wheel steering angle, and direct yaw moment remain constant, different absolute vehicle speeds of 5, 10, 15, 20, 25, 30, 35, 40, 50, 60, 70, 80, 90, 100, 110, and 120 km / h are selected respectively. Perform stability domain analysis separately; When the absolute vehicle speed, front wheel steering angle, and direct yaw moment remain constant, stability domain analysis is performed with different road surface adhesion coefficients of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 respectively. When the absolute vehicle speed, road surface adhesion coefficient, and direct yaw moment remain constant, different front wheel steering angles are selected: -35°, -30°, -25°, -20°, -15°, -10°, -5°, 0°, 5°, 10°, 15°, 20°, 25°, 30°, and 35°. Perform stability domain analysis separately; When the absolute vehicle speed, road surface adhesion coefficient, and front wheel steering angle remain constant, stability domain analysis is performed for different direct yaw moments, and the following relationship is satisfied: ; Step 3: Establish a vehicle motion tracking error model; based on the vehicle motion tracking error model, design a control Lyapunov function to ensure the asymptotic stability of the tracking error system; based on the reconstructed dynamic stability domain, construct a control barrier function to ensure that the vehicle state is always within the safe stability domain; Step three, designing the control Lyapunov function and the control barrier function, includes the following steps: (I) Establish a distributed electric vehicle tracking error model: In the formula, The sideslip angle is the angle at the vehicle's center of gravity. Let yaw rate be the vehicle's angular velocity. For the front wheel steering angle, For the longitudinal force of each tire, The lateral forces of each tire. The slip angles of each tire are given, where the superscript indicates the slip angle. The system systematically corresponds to the left front wheel, right front wheel, left rear wheel, and right rear wheel. This represents the total longitudinal force of the tire. and These are the longitudinal and lateral components of the vehicle speed, respectively. This represents the error between the vehicle's heading angle and the ideal path direction angle. For lateral error, For the path in displacement Curvature at that point; (II) For distributed electric drive vehicles, design a control obstacle function to ensure system safety, design a control Lyapunov function to ensure system stability, and use quadratic programming to solve for the optimal control input that satisfies the constraints of the control obstacle function and the control Lyapunov function in real time; a) For a class of nonlinear controlled radiation systems: In the formula, For state variables, To control the input, the function and It is locally Lipschitz continuous; Given a closed-loop feedback control law, the closed-loop dynamic system is expressed as: In the formula, This is a feedback control law, which ensures that the autonomous system's state always remains within the safe region, i.e. ; For any initial conditions There exists a unique continuously differentiable solution. ,satisfy And the solution is defined in the maximum existence interval. ;in, For system drift terms, To control the input matrix, In the state The set of safety control input constraints below, It is a space of continuously differentiable functions. To start from the initial state The maximum possible space of origin; b) Let open set ,in If there exists a function It is It is continuously differentiable, positive definite, and radially unbounded, and there exists a... Class function Yes, for any There is a control input This makes the following inequality hold: In the formula, the function The system is opening a set. Control of Lyapunov functions on; Let be an open set in the state space. Let be the set of nonnegative real numbers. Class function For strictly increasing and satisfying Continuous functions, For function Along the system drift term Li Daoshu, For function Along the control input matrix The Lie derivative, radially unbounded, refers to when hour, ; c) Let the system state space be... ,gather Defined by the following conditions: In the formula, It is a continuously differentiable function; If an extension exists Class function , so that for any The following inequalities hold: Then it is called For set Control barrier function on; Let be an open set in the system's state space. The safe set is defined by the non-negative level set of the control barrier function. Candidate functions for the control barrier function, The class function is strictly increasing, continuous and satisfies as well as The function, To control the set of input constraints, For function Along the system drift term Li Daoshu, For function Along the control input matrix Li Daoshu, In the constraint set Supremum operation on; Step 4: Combine the constraints of the control Lyapunov function and the control obstacle function to establish a quadratic programming optimization problem; solve the quadratic programming optimization problem using a quadratic programming solver to obtain the optimal control output that satisfies the stability and safety constraints, thus achieving the optimal trade-off between vehicle tracking accuracy and stability. Step four involves establishing a quadratic programming problem based on the control function constraints and solving for the optimal control output. This step includes the following parts: (I) Constructing a nonlinear controlled radiation system: In the formula, For state variables, i.e. Including vehicle center of gravity sideslip angle yaw rate Longitudinal velocity Heading angle error and lateral position error ; To control input Including total longitudinal force Front wheel steering angle and direct yaw moment ; For system drift terms, To control the input matrix; (II) Establishing a quadratic programming problem: a) To achieve the design goal of combining a control Lyapunov function and a control barrier function controller, the nonlinear control radiation system is decomposed into: In the formula, This refers to vehicle stability-related conditions. To track performance-related status; b) To design a tracking controller that controls Lyapunov functions to track a predetermined path, given a desired state: In the formula, For the desired longitudinal velocity, For the desired heading angle error, The desired lateral position error; c). Furthermore, the Lyapunov function is constructed as follows: In the formula, For reference only. It is a positive definite weight matrix; d). Therefore, the derivative of the Lyapunov function is: In the formula, This is the error vector; e). According to the theory of controlling Lyapunov functions, the following must be satisfied: In the formula, The attenuation rate, Used as slack variables to handle constraint feasibility; f). Construct the controlling Lyapunov inequality structure as follows: g) While tracking the desired state, the vehicle stability state must remain within the boundary of the stability domain: In the formula, Indicates the origin of the vertex , , , The convex hull formed; h). The stability region constraint is expressed as: In the formula, , , For the stable boundary Undetermined coefficients of linear constraints; i) Based on security boundaries , , , Construct the corresponding control barrier functions respectively. Using digital labeling express: In the formula, , , For the stable boundary Undetermined coefficients of linear constraints; The coefficient vector , , They are constructed as follows: In the formula, , , , Vertices , , , The yaw rate coordinates , , , These are the centroidal lateral tilt angle coordinates of the corresponding vertices; (III) Solve the nominal quadratic programming problem: a) Based on the theories of control Lyapunov functions and control barrier functions, the quadratic programming optimization problem is constructed as follows: In the formula, For reference control input, To control the weight matrix, To relax the penalty weights; The constraints include: b). Controlling Lyapunov function constraints: c) Control barrier function constraints: In the formula, To control the convergence parameters of the barrier function; d) Control input constraints: In the formula, This is the input for front wheel steering angle control. For direct yaw moment control input, and These are the minimum and maximum values ​​of the front wheel steering angle, respectively. and These are the minimum and maximum values ​​of the direct yaw moment, respectively; variable constraints. , To control the input dimension, relax the penalty weights. Ensure slack variables As small as possible.

[0024] like Figure 5 The figure shown is a stability domain analysis result of a distributed electric drive vehicle with respect to vehicle speed. This three-dimensional surface plot depicts the nonlinear mapping relationship between the vehicle's longitudinal velocity and the sideslip angle and yaw rate. The horizontal axis represents the sideslip angle and yaw rate, and the vertical axis represents the vehicle's longitudinal velocity. The color intensity represents the numerical magnitude, demonstrating the coupling characteristics between the system's state variables.

[0025] like Figure 6 The figure shown is a stability domain analysis result of a distributed electric drive vehicle with respect to the adhesion coefficient. This three-dimensional surface plot depicts the relationship between the road adhesion coefficient and the sideslip angle and yaw rate. The horizontal axis represents the sideslip angle and yaw rate, the vertical axis represents the road adhesion coefficient, and the color gradient reflects the numerical changes, revealing the boundary characteristics of vehicle stability under different road conditions.

[0026] like Figure 7 The figure shows the stability domain analysis results of a distributed electric drive vehicle regarding the direct yaw moment. This three-dimensional surface plot depicts the relationship between the direct yaw moment and the sideslip angle and yaw rate. The horizontal axis represents the sideslip angle and yaw rate, and the vertical axis represents the magnitude of the direct yaw moment. The color intensity represents the change in the moment value, reflecting the impact of the direct yaw moment on vehicle stability.

[0027] In summary, the motion control algorithm proposed in this invention can handle complex traffic scenarios such as emergency obstacle avoidance and extreme condition stability control in highly dynamic driving environments, and is equally applicable in high-speed or low-speed driving conditions. The motion control algorithm fully leverages the advantage of independently controllable four wheels in distributed electric drive vehicles, significantly improving their dynamic performance compared to centralized systems. It integrates vehicle dynamic stability domain reconstruction technology and the control Lyapunov function-control obstacle function-quadratic programming theoretical framework into the motion control algorithm, providing a rigorous theoretical guarantee for the stability and safety of distributed electric drive vehicles. This significantly improves the motion control capability, safety, and robustness of electric vehicles in highly dynamic scenarios.

[0028] Example 2: This embodiment provides a distributed electric vehicle optimal tracking control system based on a dynamic stability domain, used to implement the distributed electric vehicle optimal tracking control method based on a dynamic stability domain described in the first aspect, including: The receiving module is used to receive vehicle handling control parameters and vehicle structural parameters. The vehicle handling control parameters include longitudinal forces, direct yaw moments, and front wheel steering angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel. The vehicle structural parameters include vehicle mass, chassis parameters, and tire parameters. The first building module is used to establish a nonlinear dynamic model of a distributed electric drive vehicle based on vehicle handling control parameters and vehicle structural parameters. The output of the nonlinear dynamic model is the time-varying parameters of vehicle motion, which include road adhesion coefficient, front wheel steering angle, direct yaw moment, and vehicle lateral and longitudinal velocities. The second construction module is used to analyze the sequential saturation mechanism of the tire after the direct yaw moment intervention based on the output time-varying parameters of vehicle motion, and to construct transient and steady-state critical instability dynamic models based on the saturation mechanism, and establish the correlation between time-varying parameters and dynamic stability domain. The reconstruction module is used to input time-varying parameters into transient and steady-state critical instability dynamic models, calculate the boundary points of the dynamic stability domain, and reconstruct the dynamic stability domain with analytical form. The third module is used to establish a vehicle motion tracking error model, in which the output of the tracking error model is the heading angle error and the lateral error. Based on the vehicle motion tracking error model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. The reconstructed dynamic stability domain is used as the safety boundary to construct a control obstacle function to ensure that the vehicle state is always within the safety boundary.

[0029] The optimization output module is used to establish a quadratic programming optimization problem with control Lyapunov function and control barrier function as constraints, solve the quadratic programming optimization problem through a quadratic programming solver, and output the optimal control strategy.

[0030] Example 3: The present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it adopts the distributed electric vehicle optimal tracking control method based on dynamic stability domain described in Embodiment 1.

[0031] It should be noted that the terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server, and the terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0032] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0033] Example 4: The present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the distributed electric vehicle optimal tracking control method based on dynamic stability domain described in Embodiment 1.

[0034] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0035] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0036] For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances. When an element is referred to as being "assembled on," "mounted on," "fixed to," or "set on" another element, it may be directly on the other element or there may be an intermediate element present. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be an intermediate element present. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible embodiments.

[0037] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

[0038] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

Claims

1. A distributed electric vehicle optimal tracking control method based on dynamic stability domain, characterized in that, Includes the following steps: The system receives vehicle handling control parameters and vehicle structural parameters. The vehicle handling control parameters include longitudinal forces, direct yaw moments, and front wheel steering angles for the left front wheel, right front wheel, left rear wheel, and right rear wheel. The vehicle structural parameters include vehicle mass, chassis parameters, and tire parameters. Based on vehicle handling control parameters and vehicle structural parameters, a nonlinear dynamic model of a distributed electric drive vehicle is established. The output of the nonlinear dynamic model is the time-varying parameters of vehicle motion, which include road adhesion coefficient, front wheel steering angle, direct yaw moment, and vehicle lateral and longitudinal velocities. Based on the analysis of the time-varying parameters of vehicle motion, the sequential saturation mechanism of tires after direct yaw moment intervention is analyzed, and transient and steady-state critical instability dynamic models are constructed based on the saturation mechanism to establish the correlation between time-varying parameters and dynamic stability domain. By inputting time-varying parameters into transient and steady-state critical instability dynamic models, the boundary points of the dynamic stability domain are calculated, and the dynamic stability domain with analytical form is reconstructed. A vehicle motion tracking error model is established, in which the output of the tracking error model is the heading angle error and the lateral error. Based on the vehicle motion tracking error model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. The reconstructed dynamic stability domain is used as the safety boundary to construct a control obstacle function to ensure that the vehicle state is always within the safety boundary. Using the control Lyapunov function and the control barrier function as constraints, a quadratic programming optimization problem is established. The quadratic programming optimization problem is solved by a quadratic programming solver, and the optimal control strategy is output.

2. The distributed electric vehicle optimal tracking control method based on dynamic stability domain according to claim 1, characterized in that: The chassis parameters include the vehicle's moment of inertia about its vertical axis, the distance from the center of gravity to the front axle, the distance from the center of gravity to the rear axle, the direct yaw moment, the front track width, and the rear track width. Tire parameters include wheel lateral stiffness, wheel vertical load, wheel saturation tire force lateral slip angle, front axle lateral slip angle, and rear axle lateral slip angle.

3. The distributed electric vehicle optimal tracking control method based on dynamic stability domain according to claim 2, characterized in that: A nonlinear dynamics model for a distributed electric drive vehicle is established, as follows: (31) Characterize the distributed electric drive vehicle as having a total mass of Inertial torque is A nominal vehicle model is established based on the following assumptions for a single rigid body: Assumption 1: The vehicle's geometry is symmetrical about the longitudinal central plane, and the origin of the coordinate system coincides with the position of the centroid of the four-wheeled vehicle model in the Cartesian coordinate system XOY. Assumption 2: Ignore the pitch and roll motion of the vehicle system, and do not consider the mechanical-mechanical coupling modeling of the suspension and steering system, where there is no dynamic transfer of longitudinal and lateral loads; Assumption 3: Assume the ideal steering system satisfies: and ,when ,exist and ; (32) Based on the assumptions, a three-degree-of-freedom vehicle dynamics model is established for distributed electric drive vehicles: In the formula, For the total mass of the vehicle. For the longitudinal speed of the vehicle, For the vehicle's lateral speed, Let yaw rate be the vehicle's angular velocity. , , , These are the longitudinal forces on the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. , , , The lateral forces are respectively applied to the left front wheel, right front wheel, left rear wheel, and right rear wheel. For the front wheel steering angle, Let be the moment of inertia of the vehicle about its vertical axis. This is the distance from the center of gravity to the front axle. This is the distance from the center of mass to the rear axle. For direct yaw moment, The front wheel track. This refers to the rear wheel track. Based on the aforementioned three-degree-of-freedom vehicle nonlinear dynamics equations, the vehicle's center of gravity sideslip angle is defined as... The sideslip angle of the center of mass is obtained through dynamic transformation. and yaw rate The equivalent dynamic equation for the state variables is: In the formula, The sideslip angle is the angle at the vehicle's center of gravity. The rate of change of the centroid sideslip angle. This is the yaw acceleration; (33) Construct a Fiala nonlinear brush tire model. The tire model is used to describe the nonlinear characteristics of the tire and provide a method for calculating the tire's lateral force. The tire model expression is: when hour: when hour: in, In the formula, superscript Indicates wheel position markings, where These represent the front axle and the rear axle, respectively. These represent the left wheel and the right wheel, respectively. The lateral forces of each wheel, Let be the lateral stiffness of each wheel. The vertical load on each wheel. The tire-road adhesion coefficient, The sideslip angles are the saturated tire force sideslip angles for each wheel, and the sideslip angle for the rear axle is... The sideslip angle corresponding to the front axle is .

4. The distributed electric vehicle optimal tracking control method based on dynamic stability domain according to claim 3, characterized in that: Based on the analysis of the time-varying parameters of vehicle motion, the sequential saturation mechanism of the tires after direct yaw moment intervention is analyzed. Transient and steady-state critical instability dynamic models are constructed based on the saturation mechanism, and the correlation between time-varying parameters and the dynamic stability domain is established, as follows: (41) When analyzing the tire sequential saturation mechanism after the intervention of direct yaw moment, the Stanford stability region is introduced as the basic theory for stability region reconstruction. The Stanford stability region belongs to the convergence range of the attraction region and satisfies ; The upper and lower limits of the ideal yaw rate are determined based on the ideal tire-ground contact conditions as follows: According to the tire saturation slip angle Determine the range of the maximum stable center-of-mass sideslip angle within the Stanford stability region, and establish kinematic constraints between the center-of-mass sideslip angle, tire sideslip angle, and front wheel steering angle under different initial vehicle conditions: In the formula, To determine the undetermined coefficients of the Stanford stability region; (42) However, the direct yaw moment intervention of the distributed electric vehicle changes the inherent phase plane manifold, and the previously defined Stanford stability region is no longer applicable to the design of the distributed electric vehicle tracking controller. The mechanism by which direct yaw moment intervention affects the equilibrium point, saddle point, and track topology in the phase plane is analyzed. Its manifestation is an implicit influence. The Stanford stability region contains an implicit precondition: the front and rear wheel slip angles simultaneously reach their saturation limits. Steady-state conditions are then defined. and The steady-state tire forces at the front and rear are expressed as: In the formula, the steady-state tire forces of the front and rear wheels are constrained by the maximum lateral adhesion force, and the proportional relationship between the lateral forces of the front and rear wheels is... and the ratio between their respective maximum lateral forces Determined as ,in, , This represents the maximum lateral force on the front wheel. This represents the maximum lateral force on the rear wheel. After the direct yaw moment intervenes, the steady-state tire force is re-expressed as: In the formula, Under certain conditions, the slip angles of the front and rear tires exhibit sequential saturation characteristics, rather than reaching their respective saturation limits simultaneously; the range of direct yaw moment and yaw rate determines the order in which the front and rear tires reach saturation. (43) Based on the lateral force of the tire satisfying and Under the given conditions, reconstruct the upper and lower boundaries of the yaw rate: Derivation of yaw rate The feasible region is: in, , and ; Maximum yaw rate and minimum yaw rate They are represented as follows: The prerequisite for its validity is the direct yaw moment. and yaw rate The relationships can be combined in four different ways: , , , .

5. The distributed electric vehicle optimal tracking control method based on dynamic stability domain according to claim 4, characterized in that: By inputting time-varying parameters into transient and steady-state critical instability dynamic models, the boundary points of the dynamic stability domain are calculated, and the dynamic stability domain with analytical form is reconstructed, as follows: (51) Regarding Under these operating conditions, the front wheels of a distributed electric drive vehicle will first enter a saturation state: Assumption , , Then the yaw moment is directly lateral. The maximum rear wheel slip angle achievable with intervention is expressed as: Based on the established maximum rear wheel slip angle It incorporates the direct yaw moment effect and transient boundary point The explicit mathematical expression is: Determine the transient stability boundary under left-turn maneuver conditions. The key points The explicit derivation of the determination is as follows: In the formula, , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. The maximum front wheel steering angle, The maximum rear wheel slip angle, The maximum front wheel slip angle, The nominal rear wheel saturation sideslip angle, The lateral force on the rear wheel under the direct action of yaw moment. This represents the nominal maximum lateral force on the rear wheel. (52) Regarding In this situation, the rear wheels of a distributed electric drive vehicle will saturate first when operating under these conditions: Assumption , , Then the yaw moment is directly lateral. The maximum front wheel slip angle achievable with intervention is expressed as: Based on the established maximum front wheel slip angle It incorporates the direct yaw moment effect, and the explicit mathematical expression of the transient boundary point A is as follows: Determine the transient stability boundary under right turn maneuver conditions. The key points The explicit derivation of the determination is as follows: In the formula, , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. , These are transient boundary points. The yaw rate and the sideslip angle coordinates of the center of mass. Minimum front wheel steering angle, The maximum front wheel slip angle, The maximum rear wheel slip angle, The nominal front wheel saturation sideslip angle, The lateral force on the front wheel under the direct action of yaw moment. This represents the nominal maximum lateral force on the front wheel; (53) Establish transient boundaries and Define a closed convex region, defined as follows: This convex region configuration reconstructs the safety boundary of distributed electric drive vehicles, targeting The operating conditions are further characterized, and the resulting closed region is defined as follows: The expression for the transient boundary is: In the formula, This is the convex hull region of the reconstructed stability domain when the direct yaw moment is positive. This is the convex hull region of the reconstructed stability domain when the direct yaw moment is negative. Indicates the origin of the point , , , The convex hull formed , , , These represent the Shuntai boundary line segments connecting the corresponding vertices. , , , This represents the transient boundary vertex corresponding to a negative direct yaw moment. (54) Targeting and Under the operating conditions, when the distributed electric drive vehicle satisfies the negative direct yaw moment Non-zero yaw rate values or Establish a deterministic saturation order between the front and rear wheels, and calculate and determine the transient boundary points. , , , ,in, , , , The transient boundary vertex under the condition of negative direct yaw moment. This indicates a negative direct yaw moment constraint condition. Indicates the positive yaw rate. This indicates a negative yaw rate.

6. The distributed electric vehicle optimal tracking control method based on dynamic stability domain according to claim 5, characterized in that: A vehicle motion tracking error model is established. Based on this model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. Using the reconstructed dynamic stability domain as a safety boundary, a control barrier function is constructed to ensure that the vehicle state always remains within the safety boundary, as detailed below: (61) Establish a distributed electric vehicle tracking error model: In the formula, The sideslip angle is the angle at the vehicle's center of gravity. Let yaw rate be the vehicle's angular velocity. For the front wheel steering angle, For the longitudinal force of each tire, The lateral forces of each tire. The slip angles of each tire are given, where the superscript indicates the slip angle. The system systematically corresponds to the left front wheel, right front wheel, left rear wheel, and right rear wheel. This represents the total longitudinal force of the tire. and These are the longitudinal and lateral components of the vehicle speed, respectively. This represents the error between the vehicle's heading angle and the ideal path direction angle. For lateral error, For the path in displacement Curvature at that point; (62) For a class of nonlinear controlled radiation systems: In the formula, For state variables, To control the input, the function and It is locally Lipschitz continuous; Given a closed-loop feedback control law, the closed-loop dynamic system is expressed as: In the formula, This is a feedback control law, which ensures that the autonomous system's state always remains within the safe region, i.e. ; (63) For any initial conditions There exists a unique continuously differentiable solution. ,satisfy And this solution is defined on the maximum existence interval. ;in, For system drift term, To control the input matrix, In the state The set of safety control input constraints below, It is a space of continuously differentiable functions. To start from the initial state The maximum possible space at which it originates; (64) Let open set ,in Suppose there exists a function It is It is continuously differentiable, positive definite, and radially unbounded, and there exists a... Class function , such that for any There is a control input This makes the following inequality hold: In the formula, the function The system is opening a set. Control the Lyapunov function on it. Let be an open set in the state space. Let be the set of nonnegative real numbers. Class function For strictly increasing and satisfying Continuous functions, For function Along the system drift term Li Daoshu, For function Along the control input matrix The Lie derivative, radially unbounded, refers to when hour, ; (65) Let the system state space be ,gather Defined by the following conditions: In the formula, It is a continuously differentiable function; If an extension exists Class function , so that for any The following inequalities hold: Then it is called For set Control barrier function on. Let be an open set in the system's state space. The safe set is defined by the non-negative level set of the control barrier function. Candidate functions for the control barrier function, The class function is strictly increasing, continuous and satisfies as well as The function, To control the set of input constraints, For function Along the system drift term Li Daoshu, For function Along the control input matrix Li Daoshu, In the constraint set The supremum operation.

7. The distributed electric vehicle optimal tracking control method based on dynamic stability domain according to claim 6, characterized in that: Using the control Lyapunov function and the control barrier function as constraints, a quadratic programming optimization problem is established. This problem is then solved using a quadratic programming solver, and the optimal control strategy is output, as follows: (71) Constructing a nonlinear controlled radiation system: In the formula, For state variables, i.e. Including vehicle center of gravity sideslip angle yaw rate Longitudinal velocity Heading angle error and lateral position error ; To control input Including total longitudinal force Front wheel steering angle and direct yaw moment ; For system drift term, To control the input matrix; (72) To achieve the design goal of a controller that combines the control Lyapunov function and the control barrier function, the nonlinear control radiation system is decomposed into: In the formula, This refers to vehicle stability-related conditions. To track performance-related status; (73) To design a tracking controller that controls a Lyapunov function to track a predetermined path, given the desired state: In the formula, For the desired longitudinal velocity, For the desired heading angle error, The desired lateral position error; (74) Construct the Lyapunov function as follows: In the formula, For reference only. It is a positive definite weight matrix; Therefore, the derivative of the Lyapunov function is: In the formula, This is the error vector; According to the theory of controlling Lyapunov functions, the following must be satisfied: In the formula, The attenuation rate, Used as slack variables to handle constraint feasibility; The structure for controlling Lyapunov inequalities is as follows: While tracking the desired state, the vehicle's stability state must remain within the boundary of the stability domain: In the formula, Indicates the origin of the vertex , , , The convex hull formed; The stability region constraint is expressed as: In the formula, , , For the stable boundary Undetermined coefficients of linear constraints; (75) Safety boundary , , , Described as: According to the safety boundary , , , Construct the corresponding control barrier functions respectively Using digital labeling express: In the formula, , , For the stable boundary Undetermined coefficients of linear constraints; coefficient vector , , They are constructed as follows: In the formula, , , , Vertices , , , The yaw rate coordinates , , , These are the centroidal lateral tilt angle coordinates of the corresponding vertices; (76) Based on the control Lyapunov function and control barrier function theory, the quadratic programming optimization problem is constructed as follows: In the formula, For reference control input, To control the weight matrix, To relax the penalty weights; The constraints include: Controlling Lyapunov function constraints: Control barrier function constraints: In the formula, To control the convergence parameters of the barrier function; Control input constraints: In the formula, This is the input for front wheel steering angle control. For direct yaw moment control input, and These are the minimum and maximum values ​​of the front wheel steering angle, respectively. and These are the minimum and maximum values ​​of the direct yaw moment, respectively. Variable constraints. , To control the input dimension, relax the penalty weights. Ensure slack variables minimize.

8. A distributed electric vehicle optimal tracking control system based on a dynamic stability domain, used to implement the distributed electric vehicle optimal tracking control method based on a dynamic stability domain as described in any one of claims 1 to 7, characterized in that, include: The receiving module is used to receive vehicle handling control parameters and vehicle structural parameters. The vehicle handling control parameters include longitudinal forces, direct yaw moments, and front wheel steering angles of the left front wheel, right front wheel, left rear wheel, and right rear wheel. The vehicle structural parameters include vehicle mass, chassis parameters, and tire parameters. The first building module is used to establish a nonlinear dynamic model of a distributed electric drive vehicle based on vehicle handling control parameters and vehicle structural parameters. The output of the nonlinear dynamic model is the time-varying parameters of vehicle motion, which include road adhesion coefficient, front wheel steering angle, direct yaw moment, and vehicle lateral and longitudinal velocities. The second construction module is used to analyze the sequential saturation mechanism of the tire after the direct yaw moment intervention based on the output time-varying parameters of vehicle motion, and to construct transient and steady-state critical instability dynamic models based on the saturation mechanism, and establish the correlation between time-varying parameters and dynamic stability domain. The reconstruction module is used to input time-varying parameters into transient and steady-state critical instability dynamic models, calculate the boundary points of the dynamic stability domain, and reconstruct the dynamic stability domain with analytical form. The third module is used to establish a vehicle motion tracking error model, in which the output of the tracking error model is the heading angle error and the lateral error. Based on the vehicle motion tracking error model, a control Lyapunov function is designed to ensure the asymptotic stability of the tracking error model. The reconstructed dynamic stability domain is used as the safety boundary to construct a control obstacle function to ensure that the vehicle state is always within the safety boundary. The optimization output module is used to establish a quadratic programming optimization problem with control Lyapunov function and control barrier function as constraints, solve the quadratic programming optimization problem through a quadratic programming solver, and output the optimal control strategy.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor loads and executes the computer program, it employs the distributed electric vehicle optimal tracking control method based on dynamic stability domain as described in any one of claims 1 to 7.

10. A storage medium containing computer-executable instructions, characterized in that, The computer-executable instructions, when executed by a computer processor, are used to perform the distributed electric vehicle optimal tracking control method based on a dynamic stability domain as described in any one of claims 1 to 7.

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