Four-wheel steering bus trajectory tracking control method based on dynamic game

Abstract

The application discloses a four-wheel steering passenger car trajectory tracking control method based on dynamic game, and the method comprises the following steps: determining an output adjustment model based on a feedforward compensation mechanism, and compensating disturbance error of a coordinated control model based on the output adjustment model; constructing a non-zero-sum dynamic game controller based on three-system game players and the coordinated control model after compensation; deriving Nash equilibrium based on the non-zero-sum dynamic game controller; learning Nash equilibrium by using measured data to drive the controller, and solving corresponding feedback control gain; solving feedforward control gain, and integrating feedback- feedforward compound control strategy based on the feedback control gain and the feedforward control gain; the application establishes a feedforward compensation mechanism based on an output adjustment theory in view of the problem that road curvature disturbance influences trajectory tracking, constructs a non-zero-sum dynamic game framework in view of the problem that trajectory tracking and stability are difficult to balance due to system coupling conflicts, and realizes collaborative control of vehicle trajectory tracking precision and driving stability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle subsystem joint control, in particular to a four-wheel-steering passenger car trajectory tracking control method based on dynamic game. BACKGROUND

[0002] In the field of motion control of four-wheel-steering and distributed driving autonomous vehicles, trajectory tracking and stability control are core design goals, and the coordinated optimization of the two directly determines the vehicle driving performance; among them, the realization of the trajectory tracking function depends on the line control chassis steering system, that is, by adjusting the tire lateral force to change the vehicle lateral acceleration, and then correcting the lateral displacement, the position deviation and heading deviation of the vehicle relative to the reference path are reduced in real time, and finally the vehicle accurately follows the expected path.

[0003] However, under extreme conditions such as emergency obstacle avoidance, high-speed large-curvature driving, or sudden change of road friction coefficient, the nonlinearity of the tire is significantly enhanced, which easily leads to the tire lateral force exceeding the stability margin, not only seriously threatening the safety of motion control, but also greatly reducing the trajectory tracking accuracy under steering control; four-wheel drive electric vehicles based on hub motors provide a technical basis for solving the above problems - by fully utilizing the longitudinal force of front and rear tires, and by using the difference between left and right wheel driving and braking force to generate active yaw moment, an additional control dimension is provided for vehicle lateral motion, which can significantly improve the handling and stability under extreme conditions, and effectively expand the application range of trajectory tracking control.

[0004] However, excessive yaw moment or rear wheel steering angle may improve stability, but it will reduce the trajectory tracking accuracy to some extent, so the coordinated control of trajectory tracking and stability becomes the core of multi-objective optimization; the dynamic interaction between such subsystems is highly consistent with the idea of game theory, which has been preliminarily applied in the field of automobile chassis control. The core requirement is that the controller design needs to explore the optimal control strategy of multiple agents (subsystems) under independent goals, as well as the conflict decision problem under the interaction between different actuators, and finally realize the simultaneous improvement of trajectory tracking ability and driving stability under complex dynamic conditions, thereby optimizing the overall motion control performance of the four-wheel-steering distributed driving system.

[0005] In existing commercial passenger car chassis control research programs: on the one hand, there is a lack of research on modeling multiple subsystems of the chassis as intelligent agents for coordinated control; on the other hand, most research does not consider the problem of variable mass caused by the change of passenger capacity of the passenger car, resulting in significant parameter uncertainty in the established dynamic model; traditional control methods based on the model are difficult to accurately reflect the real-time dynamics of the vehicle, and may even cause a decline or failure in control performance; Specifically, existing related patent technologies also have many limitations, which are difficult to meet the control requirements under complex conditions, such as:

[0006] Chinese patent CN113978450B discloses a roll-resistant path tracking game-theoretic control method for commercial vehicles. This method proposes a path tracking control method for commercial vehicles based on Stackelberg equilibrium game theory. It establishes a yaw-roll coupled dynamic model, designs an active front wheel steering and active roll-resistant system, and uses a distributed model predictive control to coordinate subsystem conflicts. However, this method does not clearly analyze the impact of model uncertainties on the game coordination effect, such as uncertainties in vehicle mass distribution, road friction coefficient fluctuations, and sensor noise, which leads to insufficient robustness of distributed model predictive control under actual complex working conditions.

[0007] Chinese patent CN117141577A discloses a four-wheel steering coordination control method and system. This method proposes a four-wheel steering coordination control method based on path deviation structure identification, which achieves independent steering control of the four wheels by dividing the steering mode and matching the wheel angle allocation strategy. However, it has significant drawbacks: First, it simplifies four-wheel coordination to rule mapping, without systematically modeling the dynamic coupling relationship between the front and rear axles, ignoring the differences in force and response between the front and rear wheels caused by changes in suspension stiffness, vehicle mass, and tire lateral stiffness, and thus cannot handle the complex coordination problem caused by the combined effect of multiple factors. Second, the control objective is singular, focusing only on minimizing trajectory tracking error and rapid wheel angle response, without incorporating global performance indicators such as lateral stability, making it difficult to meet the requirements of multi-objective coordinated control.

[0008] Chinese patent CN116424353B discloses a coordinated control strategy for a drive-by-wire chassis system based on distributed vehicles. This scheme proposes a cooperative control method based on bifurcation theory and Nash equilibrium game theory, which optimizes the torque distribution of four-wheel drive by switching control modes. However, this method has three shortcomings: First, it relies on a precise mathematical model, which is highly sensitive to parameter estimation. Sensor delays or noise can easily lead to a decrease in control accuracy and instability risk under extreme conditions. Second, it only optimizes two subsystems, ignoring the coupling effects of other subsystems, which limits the improvement of overall performance. Third, the computational complexity of combining game theory and bifurcation theory is high, which may cause response delays and affect the control effect under emergency conditions.

[0009] In summary, existing research and technologies generally suffer from three core problems:

[0010] First, traditional methods rely on accurate vehicle dynamics models, which are difficult to adapt to parameter uncertainties caused by vehicle characteristics or environmental factors.

[0011] Secondly, insufficient coordinated control of multiple subsystems of the drive-by-wire chassis often leads to conflicts between trajectory tracking and stability objectives.

[0012] Third, due to limitations of offline modeling or high computational complexity, its real-time performance, efficiency, and robustness to complex working conditions and external disturbances are poor.

[0013] Therefore, there is an urgent need for a model-free data-driven control method to learn the vehicle dynamic characteristics and environmental uncertainties by online acquisition of system data, combine multi-objective coordination optimization strategy, realize the coordinated improvement of trajectory tracking accuracy and driving stability, and further enhance the overall control performance and robustness of the automatic driving bus. SUMMARY

[0014] The application aims to provide a four-wheel steering bus trajectory tracking control method based on dynamic game, thereby solving all or one of the above problems in the prior art.

[0015] To solve the above technical problems, the specific technical solutions of the application are as follows:

[0016] The application provides a four-wheel steering bus trajectory tracking control method based on dynamic game, comprising the following steps:

[0017] Model initialization step:

[0018] A dynamics and path tracking coordination control model of the four-wheel steering distributed drive vehicle is constructed, an output adjustment model is determined based on a feedforward compensation mechanism, and the path curvature disturbance error of the dynamics and path tracking coordination control model is compensated based on the output adjustment model;

[0019] Non-zero-sum dynamic game controller construction step:

[0020] The three-system game participants are determined, a non-zero-sum dynamic game controller is constructed based on the three-system game participants and the compensated dynamics and path tracking coordination control model, and Nash equilibrium derivation is performed based on the non-zero-sum dynamic game controller;

[0021] Nash equilibrium learning step:

[0022] Nash equilibrium learning of the non-zero-sum dynamic game controller is driven by measured data, and the feedback control gain under data-driven Nash equilibrium is calculated;

[0023] Feedforward gain calculation step:

[0024] The feedforward control gain is solved, the feedback-feedforward compound control strategy is integrated based on the feedback control gain and the feedforward control gain, and the trajectory tracking control of the four-wheel steering distributed drive vehicle is performed based on the feedback-feedforward compound control strategy.

[0025] As an improved scheme, the dynamics and path tracking coordination control model of the four-wheel steering distributed drive vehicle is further constructed, comprising:

[0026] A four-wheel-steering distributed drive vehicle dynamics model is constructed, which includes two degrees of freedom of lateral and yaw motion;

[0027] A correlation between path tracking error and vehicle motion state is established, a stability index is introduced, and a path tracking error equation and a stability error equation of the four-wheel-steering distributed drive vehicle are determined;

[0028] The four-wheel-steering distributed drive vehicle dynamics model, the path tracking error equation and the stability error equation are integrated into a state space model as the dynamics and path tracking coordinated control model.

[0029] As an improved scheme, the output adjustment model determined based on the feedforward compensation mechanism further includes:

[0030] The control law of the vehicle front wheel system, the rear wheel system and the distributed drive system of the four-wheel-steering distributed drive vehicle are all set to a feedback-feedforward structure;

[0031] The output adjustment model is derived based on the dynamics and path tracking coordinated control model and the feedback-feedforward structure.

[0032] As an improved scheme, the output adjustment model is:

[0033] ;

[0034] wherein, is a state transition matrix; , , are input matrices; is a disturbance matrix; C is an output matrix; is a compensation term; is a column vector representing the steady-state influence of external disturbance on the system state.

[0035] As an improved scheme, the output adjustment model compensates for the road curvature disturbance error of the dynamics and path tracking coordinated control model, further including:

[0036] A variable transformation formula about path curvature is determined based on the path curvature change rate;

[0037] The variable transformation formula is substituted into the dynamics and path tracking coordinated control model to obtain an error system model;

[0038] Under the condition of satisfying the output adjustment model, the error system model is converted into a disturbance-free form.

[0039] As an improved scheme, the three-system game participants are determined, and a non-zero-sum dynamic game controller is constructed based on the three-system game participants and the kinetic and path tracking coordination control model after compensation, and the non-zero-sum dynamic game controller further includes:

[0040] The objects participating in the game in the trajectory tracking and stability coordination control task of the four-wheel steering distributed drive vehicle are set as the front-wheel steering system, the rear-wheel steering system and the distributed drive system of the four-wheel steering distributed drive vehicle, and the front-wheel steering system, the rear-wheel steering system and the distributed drive system are taken as the three-system game participants; and the constituent elements of the game strategy set are determined as the front-wheel steering angle, the rear-wheel steering angle and the additional yaw moment.

[0041] A cost function is constructed for the three-system game participants, the optimization target of the front-wheel steering system is set as trajectory accurate tracking, the optimization target of the rear-wheel steering system is set as lateral stability improvement, and the optimization target of the distributed drive system is set as optimizing the tire longitudinal force to provide additional stability control; and the three-system game participants all take minimizing their respective quadratic cost functions as the optimization target.

[0042] According to the control targets of the three-system game participants, corresponding state weighting matrices and control weighting matrices are set.

[0043] As an improved scheme, the Nash equilibrium derivation is performed based on the non-zero-sum dynamic game controller, and the Nash equilibrium derivation further includes:

[0044] A Nash equilibrium condition is determined.

[0045] A Hamilton function is constructed through the Pontryagin maximum principle, and a co-state equation is derived.

[0046] Based on the co-state equation and the Hamilton function extreme condition, an optimal control strategy of the three-system game participants under the Nash equilibrium is determined.

[0047] Iterative control gains are used to make a positive definite matrix in the optimal control strategy converge to a stable solution, so as to achieve the Nash equilibrium.

[0048] As an improved scheme, the non-zero-sum dynamic game controller is driven by measured data to learn the Nash equilibrium, and feedback control gains under the data-driven Nash equilibrium are calculated, and the method includes:

[0049] The general solution of the column vector is solved based on the output regulation model.

[0050] define a new state variable, transform the parameter uncertainty term in the dynamic and path tracking coordinated control model into a form that can be represented by the measured data based on the new state variable; construct a Lyapunov function for the three-system game participants, replace the parameter uncertainty term with measurable states, inputs and disturbances to obtain a variation equation of the Lyapunov function;

[0051] set a long-term excitation signal, and perform real-time data sampling based on the long-term excitation signal; construct an output difference matrix, a state integral matrix, a control input matrix and a disturbance matrix based on the sampled real-time data;

[0052] transform the variation equation of the Lyapunov function into a linear equation group; when the matrix corresponding to the linear equation group satisfies the column full rank condition, solve the feedback control gain based on the least square method.

[0053] As an improved scheme, the solving of the feedforward control gain comprises:

[0054] construct a linear constraint equation based on the output adjustment model and the general solution of the column vector;

[0055] determine the optimal solution of the column vector and the compensation term under the constraint condition, with the goal of minimizing the quadratic cost of the column vector and the compensation term;

[0056] represent the feedforward control gain based on the optimal solution.

[0057] As an improved scheme, the feedback-feedforward compound control strategy comprises:

[0058]

[0059] wherein, is a compound control strategy; is a feedforward control gain; is a feedback control gain; is a system overall state variable; is a reference path curvature.

[0060] The beneficial effects of the technical scheme of the present application are:

[0061] The four-wheel steering passenger car trajectory tracking control method based on dynamic game of the application aims at the problem of road curvature disturbance affecting trajectory tracking, establishes a feedforward compensation mechanism based on output regulation theory, realizes robust compensation of road curvature disturbance through online acquisition of system data combined with least square parameter calculation, and breaks through the dependence of traditional methods on model accuracy, significantly improves the generalization ability and anti-external disturbance performance of automatic driving passenger car trajectory tracking, and adapts to tracking requirements in complex road conditions. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to more clearly illustrate the specific embodiments of the application or the technical solutions in the prior art, the drawings needed in the specific embodiments or the prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0063] Fig. 1 Fig. 1 is a flowchart of the four-wheel steering passenger car trajectory tracking control method based on dynamic game according to Embodiment 1 of the application.

[0064] Fig. 2 Fig. 2 is an architecture diagram of the coordination control model in the four-wheel steering passenger car trajectory tracking control method based on dynamic game according to Embodiment 1 of the application. DETAILED DESCRIPTION

[0065] The preferred embodiments of the application will be described in detail below with reference to the accompanying drawings, so that the advantages and features of the application can be more easily understood by those skilled in the art, and the protection scope of the application can be more clearly defined.

[0066] In the description of the application, it should be noted that the embodiments described in the application are part of the embodiments of the application, not all the embodiments; based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor belong to the protection scope of the application.

[0067] The terms "first", "second", and the like, as used in the description and the claims herein, and in the above DETAILED DESCRIPTION of the Invention, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the use of such terms as "first" and "second" are arbitrary labels and are used for purposes of distinguishing between the elements being referred to, and therefore, it is to be understood that the "first" element could be termed the "second" element, and, similarly, the "second" element can be termed the "first" element, without changing the meaning of the description, and that "first" and "second" are only used to distinguish one element from another. It is to be understood that the use of the singular herein, like "a" or "an", means "one or more" unless explicitly indicated to the contrary. It is to be understood that the singular includes the plural unless indicated to the contrary by the usage of the term "only one" or by textual intent indicating that the plural is excluded.

[0068] Embodiment 1 provides a four-wheel-steering bus trajectory tracking control method based on dynamic game, as shown in the following steps: Figs. 1-2

[0069] S100, model initialization step:

[0070] In this step, the vehicle dynamics model, the vehicle path tracking error model and the stability error model are constructed; then the dynamics and path tracking coordination control model is integrated based on the constructed vehicle dynamics model, the vehicle path tracking error model and the stability error model, the steady-state error elimination is carried out based on the coordination control model, and the corresponding output adjustment model and disturbance-free error system are obtained, which specifically includes:

[0071] S101, by focusing on the two key motion degrees of freedom of vehicle lateral and yaw, a dynamics model accurately reflecting the dynamic characteristics of the vehicle is constructed, which provides the bottom dynamics basis for subsequent path tracking, coordination control and game strategy design, as follows:

[0072] Specifically, a four-wheel-steering distributed drive vehicle dynamics model containing two degrees of freedom of lateral and yaw motion is constructed, and its dynamics equation is:

[0073]

[0074] It should be noted that in the above dynamics equation: m is the mass of the vehicle; are the lateral stiffness of the front and rear wheels, respectively; is the longitudinal vehicle speed; is the moment of inertia around the z-axis; is the additional yaw moment; is the yaw angular velocity; is the mass center side slip angle; a and b are the distances from the front and rear wheels to the mass center, respectively; are the front and rear wheel angles, respectively.

[0075] ​​S102. Through coordinate system transformation, error definition and simplification, the relationship between path tracking error and vehicle motion state is established. Simultaneously, stability indicators are incorporated to ultimately determine the vehicle's path tracking error equation and stability error equation, as follows:

[0076] S1021. The equation of motion of the vehicle's center of mass in the inertial coordinate system is:

[0077] ;

[0078] It should be noted that in the above equations of motion: X represents the vehicle's yaw angle; X and Y are the coordinates in an inertial coordinate system fixed to the ground, respectively. , These are the velocities of the vehicle's center of mass in the inertial coordinate system; , These are the vehicle's longitudinal speed and lateral speed, respectively.

[0079] S1022. Based on the transformation relationship between the vehicle coordinate system and the inertial coordinate system in equation (2), the rate of change of the vehicle's lateral displacement is expressed as:

[0080] ;

[0081] S1023. Equation simplification, including: based on the small angle assumption, it is simplified to:

[0082] ;

[0083] S1024, Definition of heading error, including: expressing the error between the vehicle's actual heading and the heading of the reference trajectory as:

[0084] ;

[0085] It should be noted that in equation (5): This is the vehicle's actual heading angle. The heading angle is for reference path.

[0086] S1025. Based on equations (4) and (5), derive the rate of change of the vehicle's lateral error and the rate of change of its heading error, including: expressing the rate of change of the vehicle's lateral error and heading error as:

[0087] ;

[0088] It should be noted that in equation (6): This represents the rate of change of heading error. This represents the rate of change of the vehicle's lateral error. For reference path curvature; The rate of change of the heading angle of the reference trajectory.

[0089] S1026, determining the corresponding stability index, including: in order to embody the tracking performance of the vehicle stability index in the subsequent control model, the side slip angle of the mass center is selected and the yaw rate As a stability-related state quantity, the deviation between the ideal value given by the reference model , is taken as the tracking target state quantity, expressed as:

[0090] .

[0091] S103, the four-wheel steering distributed drive vehicle dynamics model, path tracking error equation and stability error equation constructed in the previous two steps are integrated into a unified state space model, that is, a dynamics and path tracking coordinated control model, as follows:

[0092] Specifically, the spatial state model is constructed, including: based on formula (1), formula (6) and formula (7), the vehicle lateral dynamics state, path tracking error and stability error are uniformly modeled, and then the coordinated control model integrating vehicle dynamics model evolution and path tracking information update is constructed, expressed in the form of state space, specifically:

[0093] ;

[0094] It should be noted that in formula (8):

[0095] is the system overall state variable, specifically:

[0096] ;

[0097] wherein, is the lateral error; is the error between the actual side slip angle of the mass center and the ideal side slip angle of the mass center; is the error between the actual yaw rate and the ideal yaw rate.

[0098] is the state transition matrix, specifically:

[0099] ;

[0100] , , are input matrices, respectively:

[0101] ;

[0102] ;

[0103] ;

[0104] is the disturbance matrix, specifically:

[0105] ;

[0106] C is the output matrix, specifically:

[0107] ;

[0108] 、 、 are the system control variables, representing the front wheel steering angle, rear wheel steering angle and additional yaw moment, respectively.

[0109] It should be noted that the above model has corresponding parameter uncertainty challenges, including: the load state of the commercial passenger vehicle dynamically affects the mass distribution and inertia characteristics of the vehicle, and the tire cornering stiffness is also affected by temperature, wear degree and tire pressure; therefore, the accurate acquisition of matrices 、 and is usually difficult, and the mutual coupling of these factors complicates the accurate modeling and control of passenger vehicle dynamics; under this technical problem, the subsequent step S300 of the present application is driven by model-free data.

[0110] S104, considering that the path curvature disturbance term in equation (8) will always exist in the feedback control of the vehicle in the dynamic driving process, and the steady-state error cannot be eliminated, therefore, for the steady-state error problem caused by the path curvature disturbance, a feedback- feedforward composite control law is introduced, and the adjustment equation is derived through the dynamic output adjustment principle, the system with disturbance is converted into a disturbance error-free system, and the vehicle can asymptotically track the reference trajectory as follows:

[0111] S1041, define the control law form of the three subsystems (front wheel / rear wheel / drive), including: the control law of the vehicle front wheel system, rear wheel system and distributed drive system is set to feedback- feedforward, the structure is as follows:

[0112] ;

[0113] It should be noted that in equation (9): describes the control law of different subsystems, subscript , 2, 3 represent the front wheel system, the rear wheel system, and the distributed drive system, respectively; and are feedback control gains and feedforward control gains, respectively; is used to compensate for the disturbance term Role in state dynamics; As a column vector to characterize the steady-state influence of external disturbance on system state;

[0114] S1042, derive the regulation equation, including: And Satisfy the following output regulation equation:

[0115] ;

[0116] S1043, through variable transformation, the original system containing disturbance is transformed into a disturbance-free error system, and then the subsequent control law solving is simplified, including:

[0117] (i) In general, determine the road curvature The rate of change in a short period of time is very small, which can be approximated to zero, so define the following transformation:

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] It should be noted that the above variable transformation represents the "error" state of the system after compensating for the road disturbance, 、 、 Respectively, the front wheel steering angle, rear wheel steering angle, and additional yaw moment control input after disturbance compensation; The system state vector after disturbance compensation.

[0123] (ii) Substitute the above transformation into equation (8) to convert it into an error system model as follows:

[0124] ;

[0125] (iii) Under the condition of satisfying equation (10), the error system Is converted into a disturbance-free form as follows:

[0126] .

[0127] S200, non-zero and dynamic game controller construction steps:

[0128] In this step, the three subsystems (front wheel steering system, rear wheel steering system, distributed drive system) are innovatively regarded as "game participants", a non-zero-sum dynamic game framework is constructed, and by designing the cost function, deriving the Nash equilibrium condition and optimal control law, the balance between local optimization and global coordination of each subsystem is realized, as follows:

[0129] S201, determining a game framework, comprising:

[0130] (i) The objects participating in the game in the trajectory tracking and stability coordination control task of the electric passenger car are set as the three subsystems in the line control chassis, namely: front wheel steering system, rear wheel steering system and distributed drive system.

[0131] (ii) The corresponding strategy set is composed of the control amount corresponding to each game participant, that is: front wheel steering angle, rear wheel steering angle and additional yaw moment.

[0132] (iii) A cost function is constructed for each controlled participant. Since the cumulative cost of the three game participants is non-zero, a non-zero-sum game problem is set as follows: the front wheel target is accurate tracking of the trajectory, the rear wheel target is improvement of lateral stability, and the drive system target is optimization of tire longitudinal force to provide additional stability control; let the three game participants respectively minimize their respective quadratic cost functions, and finally express the optimization problems of the three main bodies in the game system as:

[0133] 、

[0134] 、

[0135] ;

[0136] It should be noted that in formula (13): , , are the cost functions of the front wheel steering control system, the rear wheel steering control system and the distributed drive control system, respectively; is the start time of the game; 、 、 are the states of each game participant, respectively; , , are the control input weight matrices of each game participant, respectively; wherein each participant makes a decision independently, but is also affected by the behavior of other participants, so is recorded as the control weight under the game interaction between the three intelligent agents.

[0137] ​(iv) Based on the different control objectives of each participant, the state weighting matrix and control weighting matrix are set as follows:

[0138] ;

[0139] ;

[0140] ;

[0141] ;

[0142] It should be noted that, in order to minimize the dependence of the j-th participant's cost function on the control policies of other participants, interaction weight coefficients are defined. .

[0143] S202. Derivation of Nash equilibrium and optimal control law, including:

[0144] (i) Determine the Nash equilibrium condition: When the dynamic game reaches Nash equilibrium, no participant can reduce its own cost function value by unilaterally changing its control strategy; at the same time, all three subsystems achieve their local optimal control strategies, and the global system achieves a coordinated balance between trajectory tracking and vehicle stability; to ensure the realization of Nash equilibrium, the following conditions must be met:

[0145] ,

[0146] ,

[0147] ;

[0148] It should be noted that in equation (14): the left side of the inequality sign represents the... The cost of achieving Nash equilibrium; the right side of the inequality sign indicates the corresponding change in control strategy. , , The cost of the lower limit.

[0149] (ii) Construct Hamiltonian functions using the Pontryagin maximum principle and derive costate equations, including: When calculating the closed-loop Nash equilibrium solution of the above equations, Hamiltonian functions of the three participants need to be constructed using the Pontryagin maximum principle, as shown below:

[0150] ;

[0151] It should be noted that, Different values ​​of the subscript j represent the front wheels, rear wheels, or the drive system, respectively. Let be the costate variables; the corresponding costate equation is:

[0152] ;

[0153] S203, in combination with the Hamilton function extreme condition and the coordination equation, the optimal control strategy of all participants at the Nash equilibrium is determined, including:

[0154] (i) To derive the optimal control law of the object participating in the game, the minimum value of the Hamilton function needs to satisfy the following formula:

[0155] ;

[0156] (ii) Based on the constructed linear differential game problem, when solving the closed-loop Nash equilibrium, the coordination variable and the state variable are assumed to be linearly related as follows:

[0157] ;

[0158] (iii) Based on formula (16), formula (17) and formula (18), the relationship between the control law of the three participants and the state variable is established. Since is positive definite, exists, so the optimal control strategy of all participants at the Nash equilibrium is expressed as:

[0159] ;

[0160] It should be noted that in formula (19), is a positive definite matrix, which is obtained by solving the coupling Riccati equation specific to the game framework, and the corresponding coupling Riccati equation is as follows:

[0161]

[0162] It should be noted that formula (20) models the dynamic interaction between the three subsystems through the coupling relationship between matrices , and , and can reflect the mutual influence of the control strategies of all participants.

[0163] S204, by iteratively updating the control gain, the positive definite matrix converges to a stable solution, and finally realizes the Nash equilibrium, including:

[0164] The iterative method is used to solve formula (20), and it is determined that it remains unchanged after k games, and the equation for solving is obtained as follows:

[0165]

[0166] It should be noted that through the above iterative solution, the optimization of the state feedback control law is realized, and finally converges to the Nash equilibrium. The iterative update expression of the feedback control gain of the three participants in formula (21) is:

[0167] .

[0168] S300, Nash equilibrium learning step:

[0169] In this step, in view of the parameter uncertainty problem mentioned in S103, the dependence on the accurate model is abandoned, and the control gain under the Nash equilibrium is learned from the measured data through data acquisition, incentive design and least squares method and positive definite matrix , to ensure the effectiveness of the controller in the scene of parameter dynamic change, as follows:

[0170] S301, solve the general solution of X based on the output adjustment equation (0=CX), including:

[0171] Since the matrix C is known, based on the output adjustment condition equation of formula (10), the general solution of can be solved, which is expressed as:

[0172] ;

[0173] It should be noted that in formula (23): ; According to the kernel space theorem, is the basis vector of the null space of the C matrix in the adjustment equation, which satisfies , and the dimension is 2, takes the value of {2,3}, is the linear combination coefficient.

[0174] S302, define new state variables and convert the parameter uncertainty term into a form that can be represented by measured data, including:

[0175] Define the variable: , into the coordination control model of formula (8), to obtain:

[0176] ;

[0177] It should be noted that in order to facilitate description, the above formula is recorded as:

[0178] , + . ​​

[0179] S303, construct Lyapunov function for each of the three participants, by analyzing its change in the time interval, replace the parameter uncertainty term with measurable state, input and disturbance, including:

[0180] (i) in order to calculate the formula (21) by data-driven policy iteration method , and then get the optimal control control gain , so as to construct the Lyapunov function of the front wheel system, the rear wheel system and the drive system, respectively recorded as:

[0181] ;

[0182] (ii) based on the above Lyapunov function, further represent its dynamic change in the time interval [t, t+ ], as follows:

[0183] ;

[0184] (iii) from the above formula, there is a parameter uncertainty term discussed in S103 (i.e. matrix A and B term), so replace it with the variable that can be measured by online state and input information through formula (21) and formula (22), as follows:

[0185] ;

[0186] (iii) similarly, the value function and describing the rear wheel system and the drive system are represented as:

[0187] ;

[0188] ;

[0189] (iv) it should be noted that in order to simplify the description, the relevant terms in the above formula are defined as follows:

[0190] ;

[0191] (v) based on the above simplified definition, rewrite the terms in formula (27), formula (28) and formula (29) into the form of Kronecker product, as follows:

[0192] ,

[0193] ,

[0194] ,

[0195] ;

[0196] (vi) It should be noted that in formula (31): .

[0197] S304, set long-term incentive signal, avoid input signal lack of diversity caused by learning into local optimum, including:

[0198] In the data learning phase, avoid input lack of enough "persistent incentive" signal caused by learning process into local optimum or unable to converge; at the same time, in order to meet the full rank condition (i.e. the full rank condition required for solving the data matrix established in the following by using least square method), select appropriate incentive noise As follows:

[0199] ;

[0200] S305, parameter sampling, including:

[0201] In dynamic system, the initial control strategy must ensure the closed loop stability, especially the dynamic system in the application also has uncertainty; as the starting point of learning process, the stable control gain of three participants is recorded as ; the initial control strategy is applied to the system, set each data sampling time period[ , ] for 2 seconds, through high frequency 100HZ to collect system real-time data (such as: lateral error, heading error, mass side slip angle, yaw rate, mass side slip angle deviation, yaw rate deviation, control input and environmental disturbance data).

[0202] S306, construct output difference matrix, state integral matrix, control input matrix and disturbance matrix, quantify system dynamic behavior, including:

[0203] Construct the following data matrix to represent the dynamic behavior of the system:

[0204]

[0205] 、

[0206] 、

[0207] 、

[0208] ;

[0209] It should be noted that in formula (33), the output difference matrix For capturing the dynamic difference evolution of the state within the sampling interval; state integral matrix For describing the long-term cumulative effect of the state; control input matrix For capturing the correlation between the state and the control input in the time interval, quantifying the influence of the control input on the state trajectory; environmental disturbance matrix For depicting the influence of external interference on the system state.

[0210] S307, convert the Lyapunov function change equation into a linear equation set, including:

[0211] Transforming equations (27), (28) and (29) into equations as follows:

[0212] ;

[0213] ;

[0214] ;

[0215] It should be noted that based on the above equations, equation (36) can be obtained:

[0216] 、

[0217] 、

[0218] 、

[0219] 、

[0220] 、

[0221] ;

[0222] S308, when the matrix 、 and satisfy the column full rank condition, the least square method is used to obtain the unique solution of the above equation, as follows:

[0223] ;

[0224] ;

[0225] ;

[0226] S309, by solving the above three equations respectively, the 、 、 and the specific value of X, and then the control variable under the data-driven Nash equilibrium is obtained.

[0227] S400, feedforward gain calculation step:

[0228] In this step, the feedforward control gain is solved and the feedback control gain obtained in S300 and the feedforward gain of this step form the final feedback-feedforward composite control strategy, which is as follows:

[0229] S401, combining the output adjustment equation with the general solution of X, a linear constraint equation is constructed, including:

[0230] (i) Based on the output adjustment equation of formula (10), formula (23) is expressed as:

[0231]

[0232]

[0233] ;

[0234] (ii) Formulas (41) and (23) are combined to form a linear equation, which is used as a constraint equation, as follows:

[0235] ,

[0236] ,

[0237] ;

[0238] It should be noted that in formula (42): for the feedforward control strategy, the calculation of parameters U and X is necessary; in the constraint , is the coefficient matrix, and the vector b provides known solutions and disturbance information, which are obtained by online data calculation, is the solution vector, which includes the linear combination coefficient and the to-be-solved parameters X and U; the data-driven equation established above, i.e., formulas (38), (39) and (40), is used to calculate G; since , by , the expression of G is brought in, and then the disturbance W is calculated from the data matrix; after that, the information of known W is used to determine when is calculated, and is calculated from formula (22).

[0239] S402, to minimize the quadratic cost of X and U, the optimal X and are solved under the constraint Aχ=b, including:

[0240] After obtaining the constraint equation information in a data-driven manner, since the solution of the output adjustment equation of formula (10) is not unique, it is recorded as ; and X and U can be determined by solving the following optimization problem as follows:

[0241] ;

[0242] The solution of the optimization problem of formula (43) is limited by the constraint condition of formula (42);

[0243] Therefore, the feedforward control gain is expressed as:

[0244] ;

[0245] S403、Finally, in combination with the Nash equilibrium control quantity solved by the above data-driven manner, the feedback-feedforward control strategy applied to the system at the next sampling time is:

[0246] .

[0247] It should be noted that the above examples are only for the purpose of explaining the present application and cannot limit the protection scope of the present application.

[0248] Embodiment 2, based on the same inventive concept as the four-wheel steering bus trajectory tracking control method based on dynamic game in embodiment 1, provides a four-wheel steering bus trajectory tracking control system based on dynamic game, at least comprising:

[0249] A model initialization module is configured to: construct a dynamics and path tracking coordinated control model of a four-wheel steering distributed drive vehicle, determine an output adjustment model based on a feedforward compensation mechanism, and compensate for path curvature disturbance error of the dynamics and path tracking coordinated control model based on the output adjustment model;

[0250] A non-zero-sum dynamic game controller construction module is configured to: determine three-system game participants, construct a non-zero-sum dynamic game controller based on the three-system game participants and the compensated dynamics and path tracking coordinated control model, and perform Nash equilibrium derivation based on the non-zero-sum dynamic game controller;

[0251] A Nash equilibrium learning module is configured to: perform Nash equilibrium learning of the non-zero-sum dynamic game controller by using measured data, and calculate feedback control gain under data-driven Nash equilibrium;

[0252] The feedforward gain calculation module is configured to: solve a feedforward control gain, integrate a feedback-feedforward compound control strategy based on the feedback control gain and the feedforward control gain, and perform trajectory tracking control of the four-wheel steering distributed drive vehicle based on the feedback-feedforward compound control strategy.

[0253] It should be noted that, for the convenience and brevity of description, the specific working processes of the above-described system, device and unit can refer to the corresponding processes in the foregoing method embodiments, which will not be described here.

[0254] Embodiment 3 provides a computer readable storage medium, comprising:

[0255] The storage medium is used to store computer software instructions for implementing the four-wheel steering bus trajectory tracking control method based on dynamic game in Embodiment 1, which contains an executable program for performing the four-wheel steering bus trajectory tracking control method based on dynamic game; specifically, the executable program can be built in the four-wheel steering bus trajectory tracking control system based on dynamic game in Embodiment 2, so that the four-wheel steering bus trajectory tracking control system based on dynamic game can implement the four-wheel steering bus trajectory tracking control method based on dynamic game in Embodiment 1 by executing the built-in executable program.

[0256] In addition, the computer readable storage medium in the embodiment can adopt any combination of one or more readable storage media, wherein the readable storage medium includes an electrical, optical, electromagnetic, infrared or semiconductor system, device or component, or any combination thereof.

[0257] It should be understood that, in various embodiments herein, the size of the sequence number of each process does not mean the order of execution, and the execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments herein.

[0258] It should also be understood that, in the embodiments herein, the term "and / or" only describes the association relationship of the associated objects, which means that there can be three relationships. For example, A and / or B can represent three cases: A exists alone, A and B exist together, and B exists alone. In addition, the character " / " in this paper generally represents that the front and rear associated objects are in an "or" relationship.

[0259] Those skilled in the art can understand that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized in electronic hardware, computer software or a combination of both. In order to clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been described in the above description in a general manner. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. A person skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present disclosure.

[0260] In several embodiments provided herein, it should be understood that the disclosed system, device and method can be implemented in other ways. For example, the above-described device embodiments are merely illustrative, for example, the division of the units is only a logical function division, and actual implementation can have another division manner, for example, multiple units or components can be combined or integrated into another system, or some features can be omitted or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interfaces, devices or units, and can also be electrical, mechanical or other forms of connection.

[0261] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, that is, they can be located in one place, or they can be distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiments of the present disclosure.

[0262] In addition, each functional unit in each embodiment herein can be integrated in one processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or in the form of a software functional unit.

[0263] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable storage medium. Based on such understanding, the technical solutions herein or the entire or part of the technical solutions that essentially contribute to the prior art can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments herein. The aforementioned storage medium includes various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0264] The above description is only an embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation, or direct or indirect application in other related technical fields, which is made by using the content of the specification and drawings of the present application, is also included in the patent protection scope of the present application.

Claims

1. A trajectory tracking control method for a four-wheel steering bus based on dynamic game theory, characterized in that, Includes the following steps: Model initialization steps: A dynamics and path tracking coordinated control model for a four-wheel steering distributed drive vehicle is constructed. An output adjustment model is determined based on a feedforward compensation mechanism. The path curvature disturbance error of the dynamics and path tracking coordinated control model is compensated based on the output adjustment model. Steps for building a non-zero-sum dynamic game controller: The participants in the three-system game are identified, and a non-zero-sum dynamic game controller is constructed based on the participants in the three-system game and the compensated dynamics and path tracking coordination control model. Nash equilibrium derivation is based on the aforementioned non-zero-sum dynamic game controller; The determination of the three-system game participants further includes: setting the game participants in the trajectory tracking and stability coordination control task of the four-wheel steering distributed drive vehicle as the front wheel steering system, rear wheel steering system and distributed drive system of the four-wheel steering distributed drive vehicle, and taking the front wheel steering system, the rear wheel steering system and the distributed drive system as the three-system game participants; Nash equilibrium learning steps: The non-zero-sum dynamic game controller is driven to learn Nash equilibrium using measured data, and the feedback control gain under data-driven Nash equilibrium is calculated. Feedforward gain calculation steps: Solve for the feedforward control gain, integrate the feedback control gain and the feedforward control gain into a feedback-feedforward composite control strategy, and perform trajectory tracking control of the four-wheel steering distributed drive vehicle based on the feedback-feedforward composite control strategy; The feedback-feedforward composite control strategy includes: ; in, For feedback-feedforward composite control strategy; For feedforward control gain; For feedback control gain; For the overall state variables of the system; The reference path curvature.

2. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 1, characterized in that: The construction of the dynamics and path tracking coordinated control model for a four-wheel steering distributed drive vehicle further includes: Construct a dynamics model for a four-wheel steering distributed drive vehicle that includes two degrees of freedom: lateral and yaw motion. The correlation between path tracking error and vehicle motion state is established, a stability index is introduced, and the path tracking error equation and stability error equation of the four-wheel steering distributed drive vehicle are determined. The four-wheel steering distributed drive vehicle dynamics model, the path tracking error equation, and the stability error equation are integrated into a state-space model as the dynamics and path tracking coordinated control model.

3. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 1, characterized in that: The output adjustment model determined based on the feedforward compensation mechanism further includes: The control laws of the front wheel system, rear wheel system and distributed drive system of the four-wheel steering distributed drive vehicle are all set as feedback-feedforward structures. The output regulation model is derived based on the dynamics and path tracking coordinated control model and the feedback-feedforward structure.

4. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 3, characterized in that: The output adjustment model is as follows: ； in, This is the state transition matrix; , , Both are input matrices; C is the interference matrix; C is the output matrix; These are the compensation items; This is a column vector characterizing the steady-state effect of external disturbances on the system state.

5. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 1, characterized in that: The compensation for path curvature disturbance error of the dynamics and path tracking coordinated control model based on the output adjustment model further includes: Determine the variable transformation formula for path curvature based on the rate of change of path curvature; Substituting the variable transformation formula into the dynamics and path tracking coordinated control model, the error system model is obtained; Under the condition that the output adjustment model is satisfied, the error system model is transformed into a disturbance-free form.

6. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 1, characterized in that: The construction of a non-zero-sum dynamic game controller based on the three-system game participants and the compensated dynamics and path-tracking coordination control model further includes: The components of the game strategy set are determined to be the front wheel angle, the rear wheel angle, and the additional yaw moment; A cost function is constructed for the participants in the three-system game. The optimization objective of the front-wheel steering system is set as accurate trajectory tracking, the optimization objective of the rear-wheel steering system is set as improving lateral stability, and the optimization objective of the distributed drive system is set as optimizing tire longitudinal force to provide additional stability control. Each participant in the three-system game aims to minimize its own quadratic cost function. Based on the control objectives of the participants in the three-system game, set the corresponding state weighting matrix and control weighting matrix.

7. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 1, characterized in that: The derivation of Nash equilibrium based on the non-zero-sum dynamic game controller further includes: Determine the Nash equilibrium condition: The Hamiltonian function is constructed using the Pontryagin maximum principle, and the costate equation is derived. Based on the costate equation and the Hamiltonian function extremum condition, the optimal control strategy of the three-system game participants under Nash equilibrium is determined. The gain is iteratively controlled so that the positive definite matrix in the optimal control strategy converges to a stable solution, achieving Nash equilibrium.

8. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 4, characterized in that: The step of using measured data to drive the non-zero-sum dynamic game controller to learn Nash equilibrium and calculating the feedback control gain under data-driven Nash equilibrium includes: The general solution of the column vector is solved based on the output adjustment model. Define new state variables, and based on the new state variables, transform the parameter uncertainties in the dynamics and path tracking coordinated control model into a form that can be characterized by the measured data; construct Lyapunov functions for the participants in the three-system game, and replace the parameter uncertainties with measurable states, inputs and disturbances to obtain the change equations of the Lyapunov functions; Set a long-term excitation signal, and perform real-time data sampling based on the long-term excitation signal; construct an output difference matrix, a state integral matrix, a control input matrix, and a disturbance matrix based on the sampled real-time data; The transformation equation of the Lyapunov function is transformed into a system of linear equations; when the matrix corresponding to the system of linear equations satisfies the full column rank condition, the feedback control gain is solved based on the least squares method.

9. The four-wheel steering bus trajectory tracking control method based on dynamic game theory according to claim 8, characterized in that: The solution for the feedforward control gain includes: Based on the output adjustment model and the general solution of the column vector, a linear constraint equation is constructed; With the objective of minimizing the quadratic cost of the column vector and the compensation term, the optimal solution for the column vector and the compensation term is determined under constraints. The feedforward control gain is represented based on the optimal solution.

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