Automatic driving vehicle trajectory tracking control method and system based on recursive sliding mode

Abstract

The application discloses a kind of based on recursive sliding mode's automatic driving vehicle trajectory tracking control method and system, method includes the following steps: using vehicle kinematics model and vehicle dynamics model determines the state quantity of vehicle;Lateral error and heading error are combined to form mapping error, and the second derivative of mapping error is solved to obtain the state quantity required by intelligent controller;Power integral sliding mode function and recursive function are combined to obtain recursive sliding surface;Error control parameters on recursive sliding surface are adjusted online using adaptive control algorithm;Exponential approach law is used to design recursive sliding mode controller.Compared with existing sliding mode control method, the application not only can effectively suppress the interference of external unknown environment on automatic driving vehicle, but also can combine adaptive control algorithm to realize online adjustment of error control parameters on sliding surface, so as to ensure that automatic driving vehicle can realize accurate trajectory tracking and lateral stability when subjected to external unknown interference.

Description

TECHNICAL FIELD

[0001] The application relates to a recursive sliding mode-based automatic driving vehicle trajectory tracking control method and system, and belongs to the technical field of automatic driving vehicle trajectory tracking. BACKGROUND

[0002] In the intelligent era, advanced technologies such as big data analysis, sensors and artificial intelligence provide new opportunities for the development of automatic driving vehicles. Therefore, automated driving technology, which contains multidisciplinary theories and methods, has become a hot research topic. Automatic driving vehicles have precise trajectory tracking functions, which greatly alleviate road congestion. In addition, automatic driving vehicles also have good lateral stability, further improving the safety and comfort of passengers. This makes automatic driving vehicles have a broader development prospect in the automobile industry.

[0003] Trajectory tracking is a crucial aspect of automatic driving vehicle technology, and its purpose is to make the vehicle follow the reference path with minimal deviation. Currently, many related researches have emerged in the field of automatic driving, such as PID control, improved RRT algorithm and reinforcement learning algorithm. However, automatic driving vehicles are easily affected by unknown environments during driving, resulting in uncontrollable trajectory tracking accuracy and lateral stability. The PID algorithm controller can only calculate the output control quantity by measuring the difference between the current state and the target state, and cannot effectively predict and suppress disturbances, so the use of PID algorithm to control the stability of automatic driving vehicles usually has poor effect. The main advantage of the improved RRT algorithm is that it can quickly find a feasible path, but it does not consider the dynamics of the environment, so it cannot effectively handle disturbances. Reinforcement learning algorithms are usually used to solve complex control problems, but in the control of automatic driving vehicles, there are some unpredictable disturbances and changes, which are difficult to model and train, so the reinforcement learning algorithm cannot reliably guarantee the trajectory tracking accuracy and lateral stability of automatic driving vehicles.

[0004] Sliding mode control, as a classic nonlinear control strategy, can produce non-continuous control to force the driving system to follow the reference trajectory. At the same time, the sliding mode controller has the advantages of fast response, high precision and strong reliability. The common sliding mode control at present includes traditional sliding mode control, non-singular sliding mode control, integral sliding mode control and terminal sliding mode control. Since automatic vehicles will be affected by external disturbances such as roads and environments during driving, it brings uncontrollable influence to the longitudinal and lateral control of automatic driving vehicles. Since the above sliding mode control cannot handle the influence of unknown disturbances, and itself has problems such as chattering, slow convergence speed, etc. SUMMARY

[0005] To solve the above problems, the application provides a trajectory tracking control method and system for an autonomous vehicle based on recursive sliding mode, which can ensure accurate trajectory tracking and lateral stability of the autonomous vehicle under external unknown disturbance.

[0006] The application solves the technical problems by adopting the technical solutions of:

[0007] In a first aspect, the application provides a trajectory tracking control method for an autonomous vehicle based on recursive sliding mode, which comprises the following steps:

[0008] The state quantity of the vehicle is determined by using a vehicle kinematics model and a vehicle dynamics model;

[0009] The lateral error and the heading error are combined to form a mapping error, and the second derivative of the mapping error is solved to obtain the state quantity required by the intelligent controller;

[0010] The power integral sliding mode function and the recursive function are combined to obtain a recursive sliding mode surface;

[0011] An adaptive control algorithm is used to adjust the error control parameters on the recursive sliding mode surface online;

[0012] An exponential reaching law is used to design a recursive sliding mode controller.

[0013] As a possible implementation manner of the embodiment, the vehicle dynamics model is:

[0014]

[0015] Wherein, β is the slip angle of the vehicle; γ is the yaw rate of the vehicle; m is the total mass of the vehicle; v x is the longitudinal speed of the vehicle; I z is the yaw inertia moment of the vehicle; a and b are the distances from the center of gravity of the vehicle to the front axle and the rear axle; F fl ,F fr are the lateral forces of the left and right tires of the front axle of the vehicle; F rl ,F rr are the lateral forces of the left and right tires of the rear axle of the vehicle. As the vehicle passes through different road sections at different speeds, the slip angle and the yaw rate of the vehicle will be too large or too small, thereby causing the vehicle to lose stability.

[0016] In the process of path tracking, the tire force of the vehicle is also a key factor. In order to fully represent the turning characteristics of the tire, the following estimation method of nonlinear tire lateral force is adopted:

[0017]

[0018] Wherein, C fl , C frThese are the cornering stiffnesses of the left and right tires on the front axle of the vehicle, respectively; C rl C rr These are the cornering stiffnesses of the left and right rear tires of the vehicle, respectively; α f α r These are the front axle slip angle and the rear axle slip angle, respectively. Using the small angle approximation method, the tire slip angle can be expressed as follows:

[0019]

[0020] Where, δ f β is the front wheel steering angle; β is the vehicle's slip angle; γ is the vehicle's yaw rate; a and b are the distances from the vehicle's center of gravity to the front and rear axles, respectively; v x It is the longitudinal speed of the vehicle.

[0021] From the above, the total cornering stiffness of the front axle k1 and the total cornering stiffness of the rear axle k2 are obtained as follows:

[0022]

[0023] Among them, C fl C fr These are the cornering stiffnesses of the left and right tires on the front axle of the vehicle, respectively; C rl C rr These are the cornering stiffness of the left and right tires on the rear axle of the vehicle, respectively.

[0024] As one possible implementation of this embodiment, the vehicle kinematics model specifically includes:

[0025]

[0026] Among them, e m The mapping error is used to integrate the lateral error e and the heading error ψ,x m It is a constant projection distance; φ, φ r These are the vehicle heading angle and the reference path heading angle, v x It is the longitudinal speed of the vehicle, v y d is the lateral velocity of the vehicle, and d is the distance the vehicle travels along the reference path.

[0027] According to the small angle approximation method, for e m Differentiating with respect to ψ, we obtain the following equation:

[0028]

[0029] Among them, e m The mapping error is used to integrate the lateral error e and the heading error ψ,x m It is a constant projection distance; φ, φ rrespectively the vehicle heading angle and the reference path heading angle, v x is the vehicle longitudinal speed, v y is the vehicle lateral speed, d is the distance traveled by the vehicle along the reference path.

[0030] The second derivative of the heading error ψ and the second derivative of the lateral error e are obtained from the above formulae:

[0031]

[0032] where γ is the vehicle yaw rate; ρ is the path curvature; is the vehicle lateral acceleration; is the vehicle longitudinal acceleration; v x is the vehicle longitudinal speed; d is the distance traveled by the vehicle along the reference path.

[0033] As a possible implementation manner of the embodiment, the function expression of the mapping error e m is:

[0034]

[0035] where d e represents the disturbance uncertainty; δ f is the front wheel steering angle of the vehicle; k1, k2 are respectively the total front axle cornering stiffness and the total rear axle cornering stiffness of the vehicle; ρ is the path curvature; a, b are respectively the distance from the center of gravity of the vehicle to the front axle and the rear axle; I z is the yaw inertia moment of the vehicle; e is the lateral error; ψ is the heading error; is the vehicle lateral acceleration; is the vehicle longitudinal acceleration; α r is the rear axle cornering angle of the vehicle; γ is the vehicle yaw rate; d is the distance traveled by the vehicle along the reference path.

[0036] As a possible implementation manner of the embodiment, the recursive sliding mode surface obtained by combining the power integral sliding mode function and the recursive function includes:

[0037] The recursive integral terminal sliding mode function is defined as:

[0038]

[0039] where σ is the integral terminal sliding mode function:

[0040]

[0041] where ζ>1; q, p are two positive odd numbers; the initial value The adaptive law is used to update the control parameters on line in real time; The expression is:

[0042]

[0043] Wherein, η1, η2, η3 are positive adaptive gains.

[0044] As a possible implementation manner of the embodiment, the recursive sliding mode controller is:

[0045]

[0046] Wherein, ε1, ε2>0 are two normal numbers to be designed; The terminal sliding mode controller parameter is estimated on line. In order to ensure the convergence of the system, the value of ε1 must be greater than the upper limit value of the disturbance uncertainty d e , that is,

[0047] ε1>D≥|d e |

[0048] Wherein, ε1, D are constants greater than 0; d e is external disturbance.

[0049] As a possible implementation manner of the embodiment, the correction condition of the recursive sliding mode controller is:

[0050]

[0051]

[0052]

[0053] Wherein, α e >0, α σ >0 are positive parameters.

[0054] As a possible implementation manner of the embodiment, the boundary layer condition of the recursive sliding mode controller is:

[0055]

[0056] Wherein, δ>0 is the thickness of the boundary layer. When the value of δ is selected, the tracking accuracy and the control stability should be considered.

[0057] In the second aspect, the embodiment of the application provides an automatic driving vehicle trajectory tracking control system based on a recursive sliding mode, which comprises:

[0058] A state quantity determination module is configured to determine the state quantity of the vehicle by using a vehicle kinematics model and a vehicle dynamics model. ​

[0059] a mapping error solving module, configured to combine the lateral error and the heading error to form a mapping error, and to solve a second derivative of the mapping error to obtain a state quantity required by the intelligent controller;

[0060] a function combining module, configured to combine the power integral sliding mode function and the recursive function to obtain a recursive sliding mode surface;

[0061] an online adjustment module, configured to adjust an error control parameter on the recursive sliding mode surface online by using an adaptive control algorithm;

[0062] a controller design module, configured to design the recursive sliding mode controller by using an exponential reaching law.

[0063] In a third aspect, an embodiment of the present application provides a computer device, including a processor, a memory and a bus, the memory stores machine readable instructions executable by the processor, when the computer device is running, the processor and the memory communicate through the bus, and the processor executes the machine readable instructions to perform steps of any of the above trajectory tracking control methods based on the recursive sliding mode for the autonomous vehicle.

[0064] In a fourth aspect, an embodiment of the present application provides a storage medium, the storage medium stores a computer program, when the computer program is run by a processor, steps of any of the above trajectory tracking control methods based on the recursive sliding mode for the autonomous vehicle are performed.

[0065] The technical scheme of the embodiment of the present application can have the following beneficial effects:

[0066] The embodiment of the application provides a kind of trajectory tracking control method of automatic driving vehicle based on recursive sliding mode, comprising the following steps: the state quantity of vehicle is determined using vehicle kinematics model and vehicle dynamics model;The mapping error is formed by combining lateral error and heading error, and the second derivative of mapping error is solved to obtain the state quantity required by intelligent controller;Power integral sliding mode function and recursive function are combined to obtain recursive sliding surface;Adaptive control algorithm is used to adjust error control parameter on recursive sliding surface online;Exponential approach law is used to design recursive sliding mode controller.The application designs a kind of recursive integral terminal sliding mode controller (RITSMC, Recursive integral terminal sliding mode controller), compared with existing sliding mode control method, the application not only can effectively inhibit the disturbance of external unknown environment to automatic driving vehicle, and also can be combined adaptive control algorithm, realize online adjustment error control parameter on sliding surface, to ensure that automatic driving vehicle can realize accurate trajectory tracking and lateral stability when being subjected to external unknown disturbance.Compared with traditional sliding mode controller (SMC) and integral terminal sliding mode controller (ITSMC), the difference of the method is that the advantages of multiple sliding surfaces are combined, so that the controller has higher robustness and better tracking performance.In addition, the adaptive control algorithm in the application can adjust the control parameter on the sliding surface online, further improve the performance and stability of the controller.Compared with existing method, the controller of the application has faster response speed, higher precision and stronger robustness, while better inhibiting external unknown disturbance in practical application, effectively improving the trajectory tracking and lateral stability performance of automatic driving vehicle.

[0067] 1. The application designs an improved integral terminal sliding surface, which can effectively suppress the disturbance of external environment, improve system accuracy and reduce oscillation, thereby improving system response speed and robustness. By designing an exponential function, the control system can be quickly stabilized in a limited time, and higher trajectory tracking accuracy and more stable control effect can be achieved. Compared with the traditional integral terminal sliding mode controller, the improved sliding surface of the application enhances the robustness and performance of the system, providing an efficient and reliable solution for the practical application of the control system.

[0068] 2. The intelligent controller of the present application adopts a control strategy based on an exponential approach law algorithm, which has the advantages of simple structure and high calculation efficiency. Compared with traditional control strategies, this algorithm can more effectively solve the problem of external disturbance and avoid system jitter caused by adjustment parameters. By utilizing the characteristics of the exponential function, the controller can quickly respond, achieve precise control and optimize the control effect. In addition, this algorithm can maintain good performance when facing complex nonlinear systems, providing a more reliable and effective solution for control field applications.

[0069] 6. The present application aims to solve the problems of trajectory tracking and control parameter adjustment of autonomous vehicles in complex external environments. By designing an adaptive algorithm, the error control parameters on the integral terminal sliding mode surface, the error power integral control parameters and the recursive control parameters are adjusted online, further improving the adaptability and stability of the intelligent control system to the external environment, while reducing the complexity of the control system and the requirements on the system. The algorithm has high real-time performance and can adapt to various external disturbances in actual scenarios, thereby ensuring high-precision trajectory tracking and stable control of autonomous vehicles in complex environments. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1 is a flowchart of a recursive sliding mode-based autonomous vehicle trajectory tracking control method according to an exemplary embodiment;

[0071] Figure 2 is a schematic diagram of a recursive sliding mode-based autonomous vehicle trajectory tracking control system according to an exemplary embodiment;

[0072] Figure 3 is a schematic diagram of a vehicle kinematic model and a vehicle dynamic model according to an exemplary embodiment;

[0073] Figure 4 is a diagram showing the introduction of a recursive terminal sliding film in the embodiment of the present application to improve the trajectory tracking control structure of the autonomous vehicle;

[0074] Figure 5 is a comparison chart of the lateral stability of RITSMC compared with ITSMC and SMC in the embodiment of the present application;

[0075] Figure 6 is a comparison chart of the controller output of RITSMC compared with ITSMC and SMC in the embodiment of the present application;

[0076] Figure 7 is a comparison chart of the trajectory tracking accuracy of RITSMC compared with ITSMC and SMC in the embodiment of the present application;

[0077] Figure 8This is a comparison chart of the lateral errors of RITSMC compared to ITSMC and SMC in the embodiments of the present invention;

[0078] Figure 9 This is a comparison chart of steering stability of RITSMC, ITSMC, and SMC in an embodiment of the present invention. Detailed Implementation

[0079] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0080] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings. The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure of the invention, components and arrangements of specific examples are described below. Furthermore, reference numerals and / or letters may be repeated in different examples. This repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. It should be noted that the components illustrated in the drawings are not necessarily drawn to scale. Descriptions of well-known components, processing techniques, and processes are omitted in this invention to avoid unnecessarily limiting the invention.

[0081] like Figure 1 As shown in the figure, an embodiment of the present invention provides a trajectory tracking control method for autonomous vehicles based on recursive sliding mode, comprising the following steps:

[0082] The vehicle's state variables are determined using vehicle kinematic and vehicle dynamic models.

[0083] The lateral error and heading error are combined to form the mapping error, and the second derivative of the mapping error is solved to obtain the state variables required by the intelligent controller.

[0084] By combining the power integral sliding mode function and the recursive function, a recursive sliding surface is obtained;

[0085] An adaptive control algorithm is used to adjust the error control parameters on the recursive sliding surface online.

[0086] An exponential reaching law is used to design a recursive sliding mode controller.

[0087] As one possible implementation of this embodiment, the vehicle dynamics model is as follows:

[0088]

[0089] Where β is the vehicle's slip angle; γ is the vehicle's yaw rate; m is the vehicle's total mass; v x It is the longitudinal speed of the vehicle; I zis the yaw inertia moment of the vehicle; a, b are the distances from the center of gravity of the vehicle to the front and rear axles; F fl ,F fr is the lateral force of the left tire of the front axle of the vehicle; F rl ,F rr is the lateral force of the right tire of the front axle of the vehicle. As the vehicle passes through different road sections at different speeds, the sideslip angle and the yaw rate of the vehicle will be too large or too small, so that the vehicle loses stability.

[0090] In the process of path tracking, the tire force of the vehicle is also a key factor. In order to fully represent the cornering characteristics of the tire, the following estimation method of the nonlinear tire lateral force is adopted:

[0091]

[0092] wherein C fl , C fr are the cornering stiffness of the left and right tires of the front axle of the vehicle; C rl , C rr are the cornering stiffness of the left and right tires of the rear axle of the vehicle; α f , α r are the sideslip angles of the front and rear axles of the vehicle. According to the small-angle approximation method, the sideslip angle of the tire can be expressed in the following form:

[0093]

[0094] wherein δ f is the front wheel steering angle of the vehicle; β is the sideslip angle of the vehicle; γ is the yaw rate of the vehicle; a, b are the distances from the center of gravity of the vehicle to the front and rear axles; v x is the longitudinal speed of the vehicle.

[0095] According to the above, the total cornering stiffness of the front axle k1 and the total cornering stiffness of the rear axle k2 are:

[0096]

[0097] wherein C fl , C fr are the cornering stiffness of the left and right tires of the front axle of the vehicle; C rl , C rr are the cornering stiffness of the left and right tires of the rear axle of the vehicle.

[0098] As a possible implementation manner of the embodiment, the vehicle kinematics model specifically comprises:

[0099]

[0100] wherein e mis the mapping error to integrate the lateral error e and the heading error ψ, x m is the constant projection distance; φ, φ r are the vehicle heading angle and the reference path heading angle, respectively, v x is the longitudinal speed of the vehicle v y is the lateral speed of the vehicle, d is the distance traveled by the vehicle along the reference path.

[0101] According to the small angle approximation, the e m and ψ are derived as follows:

[0102]

[0103] where e m is the mapping error to integrate the lateral error e and the heading error ψ, x m is the constant projection distance; φ, φ r are the vehicle heading angle and the reference path heading angle, respectively, v x is the longitudinal speed of the vehicle v y is the lateral speed of the vehicle, d is the distance traveled by the vehicle along the reference path.

[0104] The second order derivative of the heading error ψ and the second order derivative of the lateral error e are obtained from the above equation:

[0105]

[0106] where γ is the yaw rate of the vehicle; ρ is the path curvature; is the lateral acceleration of the vehicle; is the longitudinal acceleration of the vehicle; v x is the longitudinal speed of the vehicle; d is the distance traveled by the vehicle along the reference path.

[0107] As a possible implementation manner of the embodiment, the mapping error e m is expressed as a function as follows:

[0108]

[0109] where d e represents the disturbance uncertainty; δ f is the front wheel steering angle of the vehicle; k1, k2 are the total front and rear side stiffness of the vehicle, respectively; ρ is the path curvature; a, b are the distances from the center of gravity of the vehicle to the front and rear axles, respectively; I z is the yaw inertia moment of the vehicle; e is the lateral error; ψ is the heading error; is the lateral acceleration of the vehicle; is the longitudinal acceleration of the vehicle; α ris the vehicle rear axle side slip angle; d is the distance traveled by the vehicle along the reference path; and γ is the yaw rate of the vehicle.

[0110] As a possible implementation manner of the embodiment, the power integral sliding mode function and the recursive function are combined to obtain a recursive sliding mode surface, including:

[0111] The recursive integral terminal sliding mode function is defined as:

[0112]

[0113] wherein σ is an integral terminal sliding mode function:

[0114]

[0115] wherein ζ>1; q, p are two positive odd numbers; and the initial value The adaptive law is used to update the control parameters in real time online; The expression of σ is:

[0116]

[0117] wherein η1, η2, η3 are positive adaptive gains.

[0118] As a possible implementation manner of the embodiment, the recursive sliding mode controller is:

[0119]

[0120] wherein ε1, ε2>0 are two normal numbers to be designed; is an online estimated terminal sliding mode controller parameter. In order to ensure the convergence of the system, the value of ε1 must be greater than the upper limit value of the disturbance uncertainty d e , that is,

[0121] ε1>D≥|d e |

[0122] wherein ε1, D are constants greater than 0; and d e is an external disturbance.

[0123] As a possible implementation manner of the embodiment, the correction condition of σ is:

[0124]

[0125]

[0126]

[0127] wherein, alpha e >0, alpha σ >0 is a positive parameter.

[0128] As a possible implementation of the present embodiment, the boundary layer condition of the recursive sliding mode controller is:

[0129]

[0130] wherein, delta > 0 is the thickness of the boundary layer. When selecting the value of delta, both the tracking accuracy and the control stability should be considered.

[0131] The present application proposes a RITSMC trajectory tracking control strategy. Firstly, by introducing the ITSMC algorithm and the recursive function, the influence of unknown external disturbance on the trajectory tracking accuracy and lateral stability of the autonomous vehicle can be effectively suppressed. Compared with the existing SMC and ITSMC, this control strategy has fast convergence and strong stability, and can achieve excellent performance in a limited time. Secondly, the adaptive algorithm is introduced to realize the real-time online update of the error control parameters of the recursive sliding mode surface, and the adaptive algorithm and the conversion function are further modified in the region, which effectively improves the trajectory tracking accuracy and lateral stability of the autonomous vehicle. Therefore, the present application provides an efficient and reliable solution for the trajectory tracking control of autonomous vehicles.

[0132] In order to design an efficient intelligent control algorithm for autonomous vehicles, the present application fully considers the kinematic model and the dynamic model of the vehicle to reflect the trajectory tracking ability of the vehicle in actual driving. The kinematic model describes the basic motion characteristics such as position, speed and acceleration of the vehicle in motion, while the dynamic model considers the influence of external forces and torques on the vehicle, so as to more truly reflect the motion state of the vehicle.

[0133] Designing a recursive sliding mode surface to construct an intelligent controller can overcome the instability of traditional sliding mode methods under unknown external disturbances. The recursive sliding mode surface can quickly and stably track the desired trajectory, while achieving better robustness and fast response performance. This provides precise, reliable and safe trajectory tracking performance for autonomous vehicles, and has important application value.

[0134] An adaptive algorithm is designed to realize online updating of error control parameters, error power integral control parameters and recursive control parameters on the integral terminal sliding mode surface, so that the intelligent controller can dynamically adjust the control parameters to adapt to different driving scenes and complex environments, and realize the optimal control effect. Compared with the traditional fixed control method, this method has higher adaptability and robustness, can effectively improve the tracking accuracy and stability of the autonomous vehicle, and reduces the difficulty of control parameter adjustment. Through online updating of the control parameters, the adaptive algorithm can automatically adjust the control strategy to cope with environmental changes and vehicle dynamics changes, so as to realize better control performance in actual driving.

[0135] The dead zone correction is added to the adaptive algorithm, which can avoid the oscillation of the error in a small range, effectively reduce the shaking of the vehicle during driving, especially for complex environments and greater uncertainty, which can further improve the stability and robustness of the system. Therefore, the adaptive algorithm with dead zone correction of the present application can effectively cope with the influence of complex environment and various uncertain factors, and improve the performance and stability of the autonomous vehicle.

[0136] A boundary layer technique is introduced to prevent the system from entering the chattering state. This technique limits the output of the switching function within the boundary layer range and uses a switching function to gradually reduce the controller output, thereby avoiding the chattering phenomenon of the system. This method can effectively improve the stability and control accuracy of the autonomous vehicle;

[0137] As shown in Figure 2 The embodiment of the present application provides a trajectory tracking control system for an autonomous vehicle based on a recursive sliding mode, which comprises:

[0138] A state quantity determination module is configured to determine the state quantity of the vehicle by using a vehicle kinematics model and a vehicle dynamics model;

[0139] A mapping error solving module is configured to combine the lateral error and the heading error to form a mapping error, and solve the second derivative of the mapping error to obtain the state quantity required by the intelligent controller;

[0140] A function combination module is configured to combine the power integral sliding mode function and the recursive function to obtain a recursive sliding mode surface;

[0141] An online adjustment module is configured to adjust the error control parameters on the recursive sliding mode surface by using an adaptive control algorithm;

[0142] A controller design module is configured to design a recursive sliding mode controller by using an exponential reaching law.

[0143] The application introduces RITSMC to improve the process of trajectory tracking of an autonomous vehicle, including: constructing a controlled object model through a vehicle dynamics model and a kinematics model, designing a recursive terminal sliding surface, introducing an adaptive algorithm, designing a recursive terminal controller, compensating and correcting the adaptive algorithm and a conversion function, proving the stability of the intelligent controller using Lyapunov function, and analyzing simulation results.

[0144] 1) As shown in the controlled object model constructed from the vehicle kinematics model and the dynamics model, the vehicle motion is studied from a geometric perspective. When the vehicle travels at low speed on the road surface, the dynamics problems such as vehicle lateral and longitudinal stability do not need to be considered, and in this case, the RITSMC control designed by using the model to control the autonomous vehicle has good performance. Figure 3

[0145] The established vehicle dynamics model is:

[0146]

[0147] Wherein, β is the slip angle of the vehicle; γ is the yaw rate of the vehicle; m is the total mass of the vehicle; v x is the longitudinal speed of the vehicle; I z is the yaw inertia moment of the vehicle; a, b are the distances from the center of gravity of the vehicle to the front axle and the rear axle; F fl , F fr are the lateral forces of the left and right tires of the front axle of the vehicle; F rl , F rr are the lateral forces of the left and right tires of the rear axle of the vehicle. As the vehicle travels at different speeds through different road sections, the side slip angle and yaw rate of the vehicle will be too large or too small, thereby causing the vehicle to lose stability.

[0148] In the process of path tracking, the tire force of the vehicle is also a key factor. In order to fully represent the turning characteristics of the tire, the following estimation method of nonlinear tire lateral force is adopted:

[0149]

[0150] Wherein, C fl , C fr are the turning stiffness of the left and right tires of the front axle of the vehicle; C rl , C rr are the turning stiffness of the left and right tires of the rear axle of the vehicle; α f , α r are the side slip angles of the front axle and the rear axle of the vehicle. According to the small angle approximation method, the side slip angle of the tire can be expressed in the following form:

[0151] ​

[0152] where δ f is the front wheel steering angle of the vehicle; β is the slip angle of the vehicle; γ is the yaw rate of the vehicle; a, b are the distances from the center of gravity of the vehicle to the front and rear axles; v x is the longitudinal speed of the vehicle.

[0153] From the above, the total steering stiffness of the front axle k1 and the total steering stiffness of the rear axle k v are obtained as follows:

[0154]

[0155] where C fl , C fr are the steering stiffness of the left and right tires of the front axle of the vehicle, respectively; C rl , C rr are the steering stiffness of the left and right tires of the rear axle of the vehicle, respectively.

[0156] The kinematic model of the vehicle is established as follows:

[0157]

[0158] where e m is the mapping error to integrate the lateral error e and the heading error ψ, x m is the constant projection distance; φ, φ r are the vehicle heading angle and the reference path heading angle, respectively, v x is the longitudinal speed of the vehicle v y is the lateral speed of the vehicle, and d is the distance traveled by the vehicle along the reference path.

[0159] According to the small angle approximation method, the derivatives of e m and ψ are obtained as follows:

[0160]

[0161] where e m is the mapping error to integrate the lateral error e and the heading error ψ, x m is the constant projection distance; φ, φ r are the vehicle heading angle and the reference path heading angle, respectively, v x is the longitudinal speed of the vehicle v y is the lateral speed of the vehicle, and d is the distance traveled by the vehicle along the reference path.

[0162] From the above, the second derivative of the heading error ψ and the second derivative of the lateral error e are obtained as follows:

[0163]

[0164] where γ is the yaw rate of the vehicle; ρ is the path curvature; is the lateral acceleration of the vehicle; is the longitudinal acceleration of the vehicle; v x is the longitudinal speed of the vehicle; d is the distance traveled by the vehicle along the reference path.

[0165] the mapping error e m is expressed as a function of:

[0166]

[0167] where k1, k2 are the total cornering stiffness of the front and rear axles of the vehicle, respectively; a, b are the distances from the center of gravity of the vehicle to the front and rear axles, respectively; I z is the yaw inertia of the vehicle; ρ is the path curvature; δ f is the front wheel steering angle of the vehicle; d e is the external disturbance; e is the lateral error; ψ is the heading error; is the lateral acceleration of the vehicle; is the longitudinal acceleration of the vehicle; α r is the rear axle side slip angle of the vehicle; d is the distance traveled by the vehicle along the reference path; γ is the yaw rate of the vehicle.

[0168] 2) Selecting an appropriate sliding mode surface can help achieve accurate trajectory tracking and stability control of autonomous vehicles, thereby improving the driving safety and comfort of the vehicle.

[0169] First, the recursive integral terminal sliding mode function is defined as:

[0170]

[0171] where the integral terminal sliding mode function σ is given by:

[0172]

[0173] where ζ > 1; q, p are two positive odd numbers; the initial value is updated in real time by the adaptive law.

[0174] 3) To further reduce the trajectory tracking deviation, an adaptive algorithm is introduced to adjust the error control parameters in the recursive sliding mode surface. This adaptive algorithm has the characteristics of automatically adjusting the controller parameters, which can adjust online and dynamically adapt to changes in the external environment, and to a certain extent, improve the robustness and control accuracy of the system. It is expressed as follows:

[0175]

[0176] Wherein, η1, η2, η3 are positive adaptive gains.

[0177] 4) Design recursive terminal controller. The controller has ITSMC and adaptive algorithm, in order to make tracking error fast convergence, the control rate is designed as:

[0178]

[0179] Wherein, ε1, ε2>0 are two normal numbers needing design; Is the terminal sliding mode controller parameter estimated online. In order to ensure the convergence of the system, the value of ε1 must be greater than the upper limit value of disturbance uncertainty d e , that is

[0180]

[0181] Wherein, ε1, D is a constant greater than 0; d e Is external disturbance.

[0182] The scheme described in the application is illustrated by specific examples as follows:

[0183] Figure 4 The recursive terminal sliding film is introduced in the embodiment of the application to improve the automatic driving vehicle trajectory tracking control structure diagram. Wherein: β is the slip angle of the vehicle; γ is the yaw rate of the vehicle; v x Is the longitudinal speed of the vehicle; ρ is the path curvature; X0 is the reference longitudinal position; Y0 is the reference lateral position; Is the lateral acceleration of the vehicle; Is the longitudinal acceleration of the vehicle; d is the distance passed by the vehicle along the reference path; ψ is the heading error; α r Is the rear axle side slip angle of the vehicle; δ f Is the front wheel steering angle of the vehicle; d e Represents the disturbance uncertainty.

[0184] 1) The target function is composed of exponential approach law and recursive terminal sliding surface. The reference trajectory is generated by parameter equation:

[0185]

[0186] Wherein: Y r , x, φ r Respectively, the reference lateral position, the reference longitudinal position and the reference heading angle of the unmanned vehicle in the process of driving. The selection of the parameter value in the trajectory model is r1=0.096(x-60)-1.2, r2=0.096(x-120)-1.2, d m1 =25, d m2 =25, d n1 =3.6, dn2 = 3.6.

[0187] 2) The system designed in the present application takes the lateral deviation between the actual driving trajectory of the vehicle and the reference trajectory as a performance indicator. The smaller the lateral deviation between the actual driving trajectory of the vehicle and the reference trajectory, the higher the accuracy of the vehicle tracking trajectory.

[0188] 3) The present application designs a recursive terminal sliding mode controller to improve the trajectory tracking step of the autonomous vehicle:

[0189] ① Design the state quantity required for the intelligent controller. First, use the vehicle kinematic model and vehicle dynamic model to express the vehicle state quantity, including the vehicle's position, speed, distance, etc. information; second, use the lateral error and heading error to integrate the mapping error, and by solving the second derivative of the mapping error, the state quantity required for the design of the intelligent controller is obtained. These state quantities will be used as the input of the controller to achieve precise control of the vehicle.

[0190] ② Design recursive sliding surface. Recursive sliding surface can gradually reduce the error in the vehicle's motion process through the combination of recursive function and power integral sliding function. Through the combination of recursive function and power integral sliding function, the control equation of recursive sliding surface can be obtained, so as to achieve the purpose of vehicle tracking reference trajectory. Compared with the traditional sliding mode control method, recursive sliding surface has better stability and robustness, and can achieve precise control of the vehicle in complex environment.

[0191] ③ Design recursive controller. The present experiment selects exponential reaching law to design the controller, which has the advantages of fast convergence speed and accurate tracking of reference trajectory. At the same time, the output of the controller has good robustness, which can maintain stable control effect when facing external unknown disturbance. The characteristic of exponential reaching law is that it can quickly eliminate error, so that the system can quickly converge to the reference trajectory. Therefore, this controller can quickly and accurately track the reference trajectory, which can further improve the driving stability and precision of the autonomous vehicle.

[0192] 4) Lateral acceleration comparison chart. As shown in Figure 5 , the peak value of lateral acceleration generated by SMC controlled vehicle is the largest, and the stability is the worst. The peak value of lateral acceleration generated by ITSMC controlled vehicle is smaller than that of SMC controlled vehicle, but it will still reduce the stability of the vehicle. The lateral acceleration fluctuation and peak value change of RITSMC controlled vehicle are the smallest, and the control effect is the best, which is most consistent with the actual driving requirements of the vehicle.

[0193] 5) Comparison of controller output, as Figure 6As shown in the front wheel angle change, the RITSMC control vehicle shows the best stability, with the smallest peak and smoothness without fluctuations. In contrast, the SMC control vehicle has a larger front wheel angle when turning, with slight fluctuations, while the ITSMC control vehicle has a smaller peak and fluctuations in the front wheel angle change.

[0194] 6) Trajectory tracking accuracy comparison chart. As shown in Figure 7 , the SMC and ITSMC control vehicles generate the farthest actual trajectory from the reference trajectory Ref when changing lanes, while the RITSMC control vehicle generates the closest trajectory to the reference trajectory. This indicates that the RITSMC control vehicle has precise trajectory tracking performance when changing lanes, allowing it to travel according to the ideal trajectory, thereby improving driving safety.

[0195] 7) Lateral deviation comparison chart. As shown in Figure 8 , the RITSMC controller performs best in terms of lateral error, with the smallest peak and better stability. In contrast, the ITSMC controller still has a large error compared to the SMC controller. Therefore, the RITSMC controller has better trajectory tracking performance and higher driving stability, and can be better applied to automatic driving vehicle control systems.

[0196] 8) Slip angle comparison chart. As shown in Figure 9 , the RITSMC controller can effectively reduce the fluctuation of the vehicle's center side angle, showing more excellent lateral stability control performance. At the same time, the SMC controller produces the largest fluctuation of the center side angle, which cannot meet the stability requirements of vehicle driving; the ITSMC controller has relatively good performance, but still has a certain degree of side angle fluctuation. Therefore, in practical applications, we should choose the RITSMC controller to achieve more accurate and stable vehicle control.

[0197] The application aims to solve the problem of trajectory tracking of an autonomous vehicle affected by external unknown disturbances, and provides an autonomous vehicle trajectory tracking control method based on a kinematic model and a two-degree-of-freedom vehicle dynamics model. The method combines a recursive integral terminal sliding mode controller and an adaptive algorithm. The recursive integral terminal sliding mode controller has nonlinear and adaptive characteristics, which can effectively suppress disturbances and maintain system stability; and the adaptive algorithm can further improve control performance by adjusting the parameters of the recursive controller online. In addition, the application also uses Lyapunov functions to prove the stability of the system, which has a theoretical guarantee. Simulation results show that, compared with traditional sliding mode control methods, the application can better suppress external disturbances, has higher real-time performance, and the control parameter adjustment is simpler. In complex road conditions, the application can significantly improve the trajectory tracking accuracy and lateral stability of the autonomous vehicle, and has wide applicability and application value.

[0198] The computer device provided by the embodiment of the application comprises a processor, a memory and a bus, the memory stores machine readable instructions executable by the processor, when the device is running, the processor and the memory communicate through the bus, and the processor executes the machine readable instructions to perform the steps of any of the above-mentioned recursive sliding mode based autonomous vehicle trajectory tracking control methods.

[0199] Specifically, the memory and the processor can be general memory and processor, which are not specifically limited here, and when the processor runs the computer program stored in the memory, the above-mentioned recursive sliding mode based autonomous vehicle trajectory tracking control method can be executed.

[0200] Those skilled in the art can understand that the structure of the computer device does not constitute a limitation on the computer device, and can comprise more or fewer components than the illustration, or combine certain components, or split certain components, or different component arrangements.

[0201] In some embodiments, the computer device can further include a touch screen which can be used to display a graphical user interface (e.g., a start interface of an application) and receive user operations for the graphical user interface (e.g., a start operation for the application). The specific touch screen can include a display panel and a touch panel. The display panel can be configured in the form of an LCD (Liquid Crystal Display), an OLED (Organic Light-Emitting Diode), etc. The touch panel can collect contact or non-contact operations of a user thereon or therearound and generate pre-set operation instructions, for example, operations of the user using a finger, a stylus or any suitable object or accessory on or near the touch panel. In addition, the touch panel can include two parts of a touch detection device and a touch controller. The touch detection device detects the touch position and posture of the user and detects signals generated by the touch operation and transmits the signals to the touch controller. The touch controller receives the touch information from the touch detection device and converts the touch information into information that can be processed by the processor and sends the information to the processor. In addition, the touch controller can receive and execute commands from the processor. In addition, the touch panel can be implemented in various types such as a resistive type, a capacitive type, an infrared type and a surface acoustic wave type, and can be implemented in any technology developed in the future. Further, the touch panel can cover the display panel. The user can operate on or near the touch panel covering the display panel according to the graphical user interface displayed on the display panel. After the touch panel detects the operation thereon or therearound, the touch panel transmits the operation to the processor to determine the user input. Then, the processor provides corresponding visual output on the display panel in response to the user input. In addition, the touch panel and the display panel can be implemented as two independent components or can be integrated.

[0202] Corresponding to the above-mentioned application starting method, the embodiment of the present application further provides a storage medium, and the storage medium stores a computer program. When the computer program is run by a processor, the steps of any of the above-mentioned automatic driving vehicle trajectory tracking control methods based on recursive sliding mode are executed.

[0203] The application starting device provided by the embodiment of the present application can be specific hardware on the device or software or firmware installed on the device, etc. The device provided by the embodiment of the present application has the same implementation principle and technical effects as the above-mentioned method embodiments. For brevity and conciseness, the part of the device embodiment not mentioned in the description can refer to the corresponding content in the above-mentioned method embodiments. Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system, device and unit described above can refer to the corresponding process in the above-mentioned method embodiments, which will not be described herein.

[0204] Those skilled in the art will appreciate that embodiments of the application can be supplied as a method, a system, or a computer program product. Accordingly, the application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the application can be in the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk memory, CD-ROMs, optical storage media, etc.) embodying computer readable program code.

[0205] In the embodiments provided by the present application, it should be understood that the disclosed apparatus and method can be implemented in other manners. The embodiments described above are merely exemplary, and the division of the modules is merely logical function division, and there can be other division manners in actual implementation. For example, a plurality of modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed coupling or direct coupling or communication connection between modules can be indirect coupling or communication connection through some interfaces, and can be electrical, mechanical or other forms.

[0206] The modules illustrated as separated components can or can not be physically separated, and the components illustrated as modules can or can not be physical modules, i.e., can be located in one place, or can be distributed on a plurality of network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the embodiments.

[0207] In addition, each functional module in the embodiments provided by the present application can be integrated in a processing module, or each module can exist physically independently, or two or more modules can be integrated in one module.

[0208] The present application is described with reference to flowcharts and / or block diagrams of methods, apparatus (system) and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one flow or a plurality of flows and / or blocks Figure 1 The apparatus for implementing the functions specified in one flow or a plurality of flows and / or blocks.

[0209] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flow Figure 1 one or more flows and / or blocks Figure 1 one or more blocks or multiple blocks.

[0210] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions executed on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 one or more flows and / or blocks Figure 1 one or more blocks or multiple blocks.

[0211] Finally, it should be noted that the above-mentioned embodiments are merely used to illustrate the technical solutions of the present application, rather than limit the present application. Although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalent replaced without departing from the spirit and scope of the present application, and any modification or equivalent replacement should be covered in the protection scope of the claims of the present application.

Claims

1. A trajectory tracking control method for autonomous vehicles based on recursive sliding mode, characterized in that, Includes the following steps: The vehicle's state variables are determined using vehicle kinematic and vehicle dynamic models. The lateral error and heading error are combined to form the mapping error, and the second derivative of the mapping error is solved to obtain the state variables required by the intelligent controller. By combining the power integral sliding mode function and the recursive function, a recursive sliding surface is obtained; An adaptive control algorithm is used to adjust the error control parameters on the recursive sliding surface online. A recursive sliding mode controller is designed using the exponential reaching law; The recursive sliding mode controller is: in, , >0 represents two positive numbers that need to be designed; , , These are the parameters of the terminal sliding mode controller estimated online; The value of depends on the disturbance uncertainty. The upper bound value, that is: in, D is a constant greater than 0; It is external interference; The boundary layer conditions of the recursive sliding mode controller are: in, It is the boundary layer thickness; The , , The correction condition is: in, It is a positive parameter.

2. The autonomous vehicle trajectory tracking control method based on recursive sliding mode according to claim 1, characterized in that, The vehicle dynamics model is as follows: in, It is the vehicle's slip angle; ω is the yaw rate of the vehicle; m is the total mass of the vehicle. It is the longitudinal speed of the vehicle; It is the vehicle's yaw moment of inertia; It is the distance from the vehicle's center of gravity to the front and rear axles; , It is the lateral force of the left and right tires on the front axle of the vehicle; , These are the lateral forces of the left and right tires on the rear axle of the vehicle.

3. The autonomous vehicle trajectory tracking control method based on recursive sliding mode according to claim 2, characterized in that, The vehicle kinematic model specifically includes: in, It is the mapping error that integrates the lateral error. With heading error , It is a constant projection distance; , These are the vehicle heading angle and the reference path heading angle, It is the vehicle's lateral speed. It is the vehicle's longitudinal speed. It is the distance traveled by the vehicle along the reference path.

4. The autonomous vehicle trajectory tracking control method based on recursive sliding mode according to claim 3, characterized in that, The mapping error The function expression is: in, This represents uncertainty caused by disturbances; It is the steering angle of the vehicle's front wheels; , These are the total lateral stiffness of the front axle and the total lateral stiffness of the rear axle of the vehicle. It is the path curvature; a and b are the distances from the vehicle's center of gravity to the front and rear axles, respectively. is the vehicle's yaw moment of inertia; e is the lateral error; It is a heading error; It is the vehicle's lateral acceleration; It is the vehicle's longitudinal acceleration; It is the rear axle slip angle of the vehicle; It is the distance the vehicle travels along the reference path; It is the yaw rate of the vehicle.

5. The autonomous vehicle trajectory tracking control method based on recursive sliding mode according to claim 4, characterized in that, The method of combining the power integral sliding mode function and the recursive function to obtain the recursive sliding surface includes: The recursive integral terminal sliding mode function is defined as follows: in, For the sliding mode function of the integrator terminal: in, ; , Two positive odd numbers; initial value ; , , The control parameters are updated online in real time for the adaptive law; , , The expression is: in, , , It is a positive adaptive gain.

6. A trajectory tracking control system for autonomous vehicles based on recursive sliding mode, characterized in that, include: The state variable determination module is used to determine the state variables of the vehicle using the vehicle kinematics model and the vehicle dynamics model. The mapping error solving module is used to combine the lateral error and the heading error to form the mapping error, and solve the second derivative of the mapping error to obtain the state variables required by the intelligent controller. The function combination module is used to combine power integral sliding mode functions and recursive functions to obtain recursive sliding surfaces; The online adjustment module is used to adjust the error control parameters on the recursive sliding surface online using an adaptive control algorithm; The controller design module is used to design recursive sliding mode controllers using the exponential reaching law; The recursive sliding mode controller is: in, , >0 represents two positive numbers that need to be designed; , , These are the parameters of the terminal sliding mode controller estimated online; The value of depends on the disturbance uncertainty. The upper bound value, that is: in, D is a constant greater than 0; It is external interference; The boundary layer conditions of the recursive sliding mode controller are: in, It is the boundary layer thickness; The , , The correction condition is: in, It is a positive parameter.

7. A computer device, characterized in that, The system includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor communicates with the memory via the bus, and the processor executes the machine-readable instructions to perform the steps of the recursive sliding mode-based autonomous vehicle trajectory tracking control method as described in any one of claims 1-5.

8. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, performs the steps of the recursive sliding mode-based autonomous vehicle trajectory tracking control method as described in any one of claims 1-5.

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