Trajectory tracking control method for single automated valet parking robot

Abstract

The application relates to a trajectory tracking control method of a single automatic valet parking robot, which comprises the following steps: establishing a kinematic model of a parking AGV; establishing a dynamic model of the parking AGV; designing a sliding mode controller based on a nonlinear disturbance observer; taking the disturbance value estimated by the nonlinear disturbance observer as an input signal of the sliding mode controller; converting the motor torque output by the sliding mode controller into the motor speed; outputting the motor speed to the kinematic model of the parking AGV; and outputting the required speed of the four Mecanum wheels from the kinematic model of the parking AGV, so as to realize trajectory tracking control. The application firstly analyzes the kinematic model of the parking AGV and the dynamic model of the parking AGV, considers the interference of the load-carrying universal wheel on the movement of the parking AGV, estimates the disturbance force and torque generated by the load-carrying universal wheel by using a nonlinear disturbance observer, and realizes the tracking of the reference trajectory of the parking AGV in combination with a non-singular terminal sliding mode controller. The application can track the reference trajectory well, and the tracking stability is improved by 42% to 68%.

Description

Technical Field

[0001] This invention relates to the field of intelligent control technology for valet parking robot platforms, and in particular to a trajectory tracking control method for a single automatic valet parking robot. Background Technology

[0002] In recent years, my country's car ownership has continued to grow. At the same time, the amount of land available for urban development and parking lot construction is constantly decreasing, leading to a series of parking problems such as difficulty finding parking spaces, insufficient parking spaces, and frequent parking accidents. To make the most of the limited urban parking space and park vehicles safely and efficiently, an increasing number of Smart Parking Systems (SPS) have been proposed. Currently, Smart Parking Systems can be divided into two categories: direct and indirect. One type involves equipping smart vehicles with Automated Parking Systems (APS), allowing the vehicles to automatically complete the parking task. This direct approach is suitable for a wide range of parking scenarios and requires minimal parking infrastructure. However, its drawbacks include limited space utilization and high demands on the intelligence level of the vehicles themselves. The second approach utilizes Automated Guided Vehicles (AGVs) to automatically and indirectly fulfill parking needs. Compared to Automatic Parking System (APS), the Automated Valet Parking (AVP) system uses AGVs to automatically transport vehicles. These AGVs can move omnidirectionally to any location and do not require a high level of vehicle intelligence. Furthermore, since it eliminates the need to reserve space for opening and closing doors and vehicle entry / exit for each parking space, and because AGVs are more mobile than traditional vehicles, they effectively improve parking space utilization. Additionally, with AGVs, users only need to drive their cars to the parking lot pick-up area, saving time and improving parking safety.

[0003] Currently, AVP systems based on parking AGVs have significant advantages, which has attracted great attention from relevant researchers. Many types and forms of parking AGVs have been developed. Among them, the omnidirectional motion clamping parking AGV has been widely used because of the advantage that the tire clamping arm can automatically clamp the wheels and lift the vehicle without the help of any other equipment.

[0004] Based on the parking AGV platform, researchers have conducted extensive research on parking space allocation, path planning, and positioning. However, trajectory tracking control of parking AGVs has received little attention. Although some research has been conducted on trajectory tracking control of omnidirectional moving parking AGVs, with sliding mode control being widely used in trajectory tracking control of omnidirectional moving parking AGVs, most studies have not considered the impact of external disturbances on the control system. This results in poor trajectory tracking performance and weak robustness. Summary of the Invention

[0005] To address the issues of poor trajectory tracking performance and weak robustness in omnidirectional mobile parking AGVs, the present invention aims to provide a trajectory tracking control method for a single automated valet parking robot that enables the parking AGV to accurately track the desired trajectory while estimating and eliminating the impact of external disturbances on trajectory tracking, thereby improving the robustness of the tracking process.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a trajectory tracking control method for a single automated valet parking robot, the method comprising the following sequential steps:

[0007] (1) Establish the kinematic model of the parking AGV;

[0008] (2) Establish a dynamic model for the parking AGV;

[0009] (3) Based on the kinematic model and dynamic model of the parking AGV, a sliding membrane controller based on a nonlinear disturbance observer is designed. The disturbance value estimated by the nonlinear disturbance observer is used as the input signal of the sliding membrane controller. The output motor torque of the sliding membrane controller is converted into motor speed and then output to the kinematic model of the parking AGV. The kinematic model of the parking AGV outputs the required speed of the four Mecanum wheels to realize trajectory tracking control.

[0010] Step (1) specifically refers to:

[0011] The parking AGV is a Mecanum wheel omnidirectional moving platform. It is the global coordinate system of the parking AGV; Parking AGV vehicle coordinate system; It is the origin of the coordinate system of the parking AGV and the center point of the four Mecanum wheels; It is the core of the parking AGV; The linear velocities corresponding to the centers of each Mecanum wheel, i=1,2,3,4, , Let the radius of the Mecanum wheel be 1. The corresponding rotational angular velocity of each Mecanum wheel; The tangential speed corresponding to the grounding roller of each Mecanum wheel; The yaw rate of the parking AGV; Let the heading angle be the AGV's heading angle. The inverse kinematics equation of the AGV is obtained as follows:

[0012] (1)

[0013] In the formula: For the speed at the center of the vehicle body The velocity component of the shaft; For the speed at the center of the vehicle body The velocity component of the shaft; It is half the distance between the centers of the two Mecanum wheels on the left and right sides; It is half the distance between the centers of the two Mecanum wheels in the longitudinal direction; Equation (1) is the kinematic model of the parking AGV;

[0014] Rewrite equation (1) as equation (2):

[0015] (2)

[0016] In the formula: The rotational angular velocity of the Mecanum wheel; ,in, and These are the lower edges of the parking AGV's body coordinate system. , velocity components; The yaw rate in the coordinate system of the parking AGV body;

[0017] Define the Jacobian matrix for:

[0018] (3)

[0019] The forward kinematic equations of the parking AGV are obtained as follows;

[0020] (4)

[0021] In the formula: ;

[0022] Establish the coordinate transformation equations between the parking AGV's vehicle coordinate system and the global coordinate system. Based on the motion relationship, the coordinate transformation formula is as follows:

[0023] (5)

[0024] In the formula: ,in, , The parking AGV is positioned at the lower edge of the global coordinate system. , velocity components; The yaw rate of the parking AGV in the global coordinate system; ; Expressed as follows; The heading angle in the coordinate system of the parking AGV body;

[0025] (6)

[0026] By combining equations (1) to (6), we obtain The conversion relationship between the speed of the parking AGV and the speed of the AGV is as follows;

[0027] (7)

[0028] In the formula, This is the coordinate transformation matrix;

[0029] Due to the origin of the parking AGV coordinates and center of mass Theoretically, they do not coincide. After analysis, the origin of the parking AGV coordinates is expressed by the following formula. and center of mass The speed relationship between them:

[0030] (8)

[0031] In the formula: , The centroids along , The velocity component of the shaft; , The centroids To the origin The horizontal and vertical distances;

[0032] Finally, by combining equations (5) to (8), we obtain the following equation;

[0033] (9).

[0034] Step (2) specifically refers to: establishing the dynamic model of the parking AGV using the Lagrange method to obtain the Lagrange function of the parking AGV. As shown in the following formula:

[0035] (10)

[0036] In the formula: For parking AGVs to circle Moment of inertia of the shaft; The overall vehicle weight of the parking AGV; Let be the moment of inertia of the Mecanum wheel; For parking AGVs to circle The yaw rate of the shaft; , The parking AGV is positioned at the lower edge of the global coordinate system. , velocity components; , , , For the rotational angular velocity of each Mecanum wheel;

[0037] Then, combining equations (9) and (10), and considering the Lagrange function... Taking the derivative, we obtain the dynamic model of the parking AGV, as shown in the following equation:

[0038] (11)

[0039] In the formula:

[0040] (12)

[0041] (13)

[0042] (14)

[0043] in, ,in , , The parking AGV is positioned at the lower edge of the global coordinate system. , , The acceleration; For generalized force and torque, , They are parking AGVs along , Generalized force components of the axis; For parking AGVs to circle Generalized torque of the shaft, Let the radius of the Mecanum wheel be 1. It is half the distance between the centers of the two Mecanum wheels on the left and right sides; It is half the distance between the centers of the two Mecanum wheels in the longitudinal direction; , The centroids To the origin The horizontal and vertical distances; The heading angle of the parking AGV. The yaw rate of the parking AGV in the global coordinate system; The yaw rate is given in the coordinate system of the parking AGV.

[0044] Step (3) specifically includes the following sequential steps:

[0045] (3a) Design a nonlinear disturbance observer: Combine the disturbance forces and torques generated by all the load-bearing casters into an equivalent disturbance force and torque, expressed as:

[0046] (15)

[0047] In the formula: , They are respectively the parking AGVs , The equivalent disturbance force of the shaft; For parking AGVs The equivalent disturbance torque of the shaft;

[0048] Based on the dynamic model of the parking AGV, the generalized forces and torques acting on the parking AGV are... To further express:

[0049] (16)

[0050] In the formula:

[0051] (17)

[0052] (18)

[0053] in, The driving torque of the Mecanum wheel; The frictional force acting on the Mecanum wheel, , The additional equivalent disturbance force and torque generated by the load-bearing casters; The heading angle of the parking AGV. It is half the distance between the centers of the two Mecanum wheels on the left and right sides; It is half the distance between the centers of the two Mecanum wheels in the longitudinal direction; , , , For the rotational angular velocity of each Mecanum wheel;

[0054] Because of the center of gravity of the parking AGV Very close to the parking AGV center Assuming each Mecanum wheel has the same load, the frictional force on each Mecanum wheel can be expressed as:

[0055] (19)

[0056] In the formula: It is the acceleration due to gravity; Let be the coefficient of friction between the Mecanum wheel and the ground, and take . ; The overall vehicle weight of the parking AGV;

[0057] The nonlinear perturbation observer is represented as:

[0058] (20)

[0059] In the formula:

[0060] (twenty one) (twenty two)

[0061] (twenty three)

[0062] (twenty four)

[0063] in, It is an auxiliary variable; It is disturbance force and torque The estimated value; The tuning matrix of the perturbation observer. ;

[0064] By combining equations (23) and (24), we obtain for:

[0065] (25)

[0066] Define the observer error for:

[0067] (26)

[0068] Assumption:

[0069] (27)

[0070] The final result is:

[0071] (28)

[0072] (3b) Design of the synovial controller:

[0073] First, define the tracking error as:

[0074] (29)

[0075] In the formula: This provides the position information of the reference trajectory in the global coordinate system. This refers to the position information of the actual trajectory in the global coordinate system. These represent the errors in the X and Y directions and the heading angle in the global coordinate system, respectively.

[0076] The sliding surface of the sliding membrane controller is designed as follows:

[0077] (30)

[0078] In the formula: Design parameters for the synovial controller and ensure they meet the requirements. ,Pick ; Design a matrix for the sliding diaphragm controller, and take... ;

[0079] Differentiating equation (30) yields:

[0080] (31)

[0081] In the formula:

[0082] By satisfying the exponential reaching law in the equation of synovial dynamics, we get:

[0083] (32)

[0084] In the formula: Let be the positive definite gain matrix of the switching surface of the diaphragm controller, and The smaller the value, the slower the approach speed. The larger the value, the greater the speed at which the motion point reaches the switching surface, resulting in greater jitter. ;

[0085] Combining equations (29) and (30), we get:

[0086] (33)

[0087] Finally, by combining equations (11), (16), and (31), we obtain:

[0088] (34).

[0089] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows: The present invention addresses the trajectory tracking problem of parking AGVs by proposing a sliding membrane controller based on a nonlinear disturbance observer. Firstly, based on the analysis of the kinematic and dynamic models of the parking AGV, the interference of the load-bearing omnidirectional wheel on the parking AGV's motion is considered. Then, a nonlinear disturbance observer is used to estimate the disturbance force and torque generated by the load-bearing omnidirectional wheel. Finally, a non-singular terminal sliding membrane controller is combined to achieve the parking AGV tracking the reference trajectory. The results show that, compared with the traditional non-singular sliding membrane controller, the present invention can track the reference trajectory very well, and the tracking stability is improved by 42% to 68%. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the overall structure of the parking AGV;

[0091] Figure 2 This is the circuit block diagram of a parking AGV;

[0092] Figure 3 It is the kinematic model of the parking AGV;

[0093] Figure 4 This is a schematic diagram of a sliding membrane controller based on a nonlinear disturbance observer;

[0094] Figure 5 This is a schematic diagram of disturbance analysis for load-bearing casters;

[0095] Figure 6 This is a schematic diagram of the lateral error in linear tracking;

[0096] Figure 7 This is a schematic diagram of the lateral error in circular tracking. Detailed Implementation

[0097] A trajectory tracking control method for a single automated valet parking robot, the method comprising the following sequential steps:

[0098] (1) Establish the kinematic model of the parking AGV;

[0099] (2) Establish a dynamic model for the parking AGV;

[0100] (3) Based on the kinematic model and dynamic model of the parking AGV, a sliding membrane controller based on a nonlinear disturbance observer is designed. The disturbance value estimated by the nonlinear disturbance observer is used as the input signal of the sliding membrane controller. The output motor torque of the sliding membrane controller is converted into motor speed and then output to the kinematic model of the parking AGV. The kinematic model of the parking AGV outputs the required speed of the four Mecanum wheels 10 to realize trajectory tracking control.

[0101] Step (1) specifically refers to:

[0102] The parking AGV is a typical Mecanum wheel omnidirectional mobile platform, such as... Figure 3 As shown in the picture, along the way It is the global coordinate system of the parking AGV; Parking AGV vehicle coordinate system; It is the origin of the coordinate system of the parking AGV and the center point of the four Mecanum wheels 10; It is the core of the parking AGV; The linear velocities corresponding to the centers of each Mecanum wheel, i=1,2,3,4, , For a Mecanum wheel with a radius of 10, The corresponding rotational angular velocity of each Mecanum wheel 10; The tangential speed corresponding to the grounding roller of each Mecanum wheel 10; The yaw rate of the parking AGV; Let the heading angle be the AGV's heading angle. The inverse kinematics equation of the AGV is obtained as follows:

[0103] (1)

[0104] In the formula: For the speed at the center of the vehicle body The velocity component of the shaft; For the speed at the center of the vehicle body The velocity component of the shaft; It is half the distance between the centers of the two Mecanum wheels 10 on the left and right sides; It is half the center distance between the two Mecanum wheels 10 in the longitudinal direction; Equation (1) is the kinematic model of the parking AGV;

[0105] To facilitate subsequent trajectory control, equation (1) is rewritten as equation (2):

[0106] (2)

[0107] In the formula: The rotational angular velocity of the Mecanum wheel 10; ,in, and These are the lower edges of the parking AGV's body coordinate system. , velocity components; The yaw rate in the coordinate system of the parking AGV body;

[0108] Define the Jacobian matrix for:

[0109] (3)

[0110] The forward kinematic equations of the parking AGV are obtained as follows;

[0111] (4)

[0112] In the formula: ;

[0113] For subsequent trajectory tracking, coordinate transformation equations between the parking AGV's vehicle coordinate system and the global coordinate system must be established. Based on the motion relationship, the coordinate transformation formula is as follows:

[0114] (5)

[0115] In the formula: ,in, , The parking AGV is positioned at the lower edge of the global coordinate system. , velocity components; The yaw rate of the parking AGV in the global coordinate system; ; Expressed as follows; The heading angle in the coordinate system of the parking AGV body;

[0116] (6)

[0117] By combining equations (1) to (6), we obtain The conversion relationship between the speed of the parking AGV and the speed of the AGV is as follows;

[0118] (7)

[0119] In the formula, This is the coordinate transformation matrix;

[0120] Due to the origin of the parking AGV coordinates and center of mass Theoretically, they do not coincide. After analysis, the origin of the parking AGV coordinates is expressed by the following formula. and center of mass The speed relationship between them:

[0121] (8)

[0122] In the formula: , The centroids along , The velocity component of the shaft; , The centroids To the origin The horizontal and vertical distances;

[0123] Finally, by combining equations (5) to (8), we obtain the following equation;

[0124] (9).

[0125] Step (2) specifically refers to: establishing the dynamic model of the parking AGV using the Lagrange method to obtain the Lagrange function of the parking AGV. As shown in the following formula:

[0126] (10)

[0127] In the formula: For parking AGVs to circle Moment of inertia of the shaft; The overall vehicle weight of the parking AGV; Let be the moment of inertia of Mecanum wheel 10; For parking AGVs to circle The yaw rate of the shaft; , The parking AGV is positioned at the lower edge of the global coordinate system. , velocity components; , , , For the rotational angular velocity of each Mecanum wheel;

[0128] Then, combining equations (9) and (10), and considering the Lagrange function... Taking the derivative, we obtain the dynamic model of the parking AGV, as shown in the following equation:

[0129] (11)

[0130] In the formula:

[0131] (12)

[0132] (13)

[0133] (14)

[0134] in, ,in , , The parking AGV is positioned at the lower edge of the global coordinate system. , , The acceleration; For generalized force and torque, , They are parking AGVs along , Generalized force components of the axis; For parking AGVs to circle Generalized torque of the shaft, For a Mecanum wheel with a radius of 10, It is half the distance between the centers of the two Mecanum wheels 10 on the left and right sides; It is half the distance between the centers of the two Mecanum wheels 10 in the longitudinal direction; , The centroids To the origin The horizontal and vertical distances; The heading angle of the parking AGV. The yaw rate of the parking AGV in the global coordinate system; The yaw rate is given in the coordinate system of the parking AGV.

[0135] Step (3) specifically includes the following sequential steps:

[0136] To achieve precise tracking control performance and strong anti-interference robustness, a sliding mode controller based on a nonlinear disturbance observer was designed, the structure of which is as follows: Figure 4 As shown, based on steps (1) and (2), the influence of disturbance force on trajectory tracking is further analyzed, and a nonlinear disturbance observer is designed to estimate the disturbance force and torque. Then, based on the designed disturbance observer, a control method of sliding mode controller based on nonlinear disturbance observer is proposed to track the reference trajectory. Figure 4 The parking AGV in the text includes the kinematic model and the dynamic model of the parking AGV.

[0137] Because the clamping arm of the parking AGV is equipped with load-bearing casters 12, such as Figure 5 As shown, when the curvature of the parking AGV trajectory changes, the load-bearing universal wheel 12 will swing, which will exert additional disturbance force and torque on the parking AGV. This effect cannot be ignored, especially when the load is large.

[0138] (3a) Design a nonlinear disturbance observer: Combine the disturbance forces and torques generated by all the load-bearing casters 12 into an equivalent disturbance force and torque, expressed as:

[0139] (15)

[0140] In the formula: , They are respectively the parking AGVs , The equivalent disturbance force of the shaft; For parking AGVs The equivalent disturbance torque of the shaft;

[0141] Considering the unknown dynamic disturbance forces and frictional forces, based on the dynamic model of the parking AGV, the generalized forces and torques acting on the parking AGV are... To further express:

[0142] (16)

[0143] In the formula:

[0144] (17)

[0145] (18)

[0146] in, The driving torque of Mecanum wheel 10; The frictional force acting on Mecanum wheel 10 , The additional equivalent disturbance force and torque generated by the load-bearing caster 12; The heading angle of the parking AGV. It is half the distance between the centers of the two Mecanum wheels 10 on the left and right sides; It is half the distance between the centers of the two Mecanum wheels 10 in the longitudinal direction; , , , For the rotational angular velocity of each Mecanum wheel;

[0147] Because of the center of gravity of the parking AGV Very close to the parking AGV center Assuming each Mecanum wheel 10 has the same load, the frictional force on each Mecanum wheel 10 can be expressed as:

[0148] (19)

[0149] In the formula: It is the acceleration due to gravity; Let be the coefficient of friction between Mecanum wheel 10 and the ground, taken as... ; The overall vehicle weight of the parking AGV;

[0150] To accurately estimate the disturbance force and torque generated by the load-bearing caster 12, the proposed nonlinear disturbance observer is expressed as follows:

[0151] (20)

[0152] In the formula:

[0153] (twenty one) (twenty two)

[0154] (twenty three)

[0155] (twenty four)

[0156] in, It is an auxiliary variable; It is disturbance force and torque The estimated value; The tuning matrix of the perturbation observer. ;

[0157] By combining equations (23) and (24), we obtain for:

[0158] (25)

[0159] Define the observer error for:

[0160] (26)

[0161] Assumption:

[0162] (27)

[0163] The final result is:

[0164] (28)

[0165] (3b) Design of the synovial controller:

[0166] Design a sliding diaphragm controller to achieve trajectory tracking of parking AGVs, and combine it with a nonlinear disturbance observer. Specifically, use the disturbance value estimated by the nonlinear disturbance observer as the input signal of the sliding diaphragm controller to improve the robustness of trajectory tracking of parking AGVs under uncertain disturbances.

[0167] First, define the tracking error as:

[0168] (29)

[0169] In the formula: This provides the position information of the reference trajectory in the global coordinate system. This refers to the position information of the actual trajectory in the global coordinate system. These represent the errors in the X and Y directions and the heading angle in the global coordinate system, respectively.

[0170] The sliding surface of the sliding membrane controller is designed as follows:

[0171] (30)

[0172] In the formula: Design parameters for the synovial controller and ensure they meet the requirements. ,Pick ; Design a matrix for the sliding diaphragm controller, and take... ;

[0173] Differentiating equation (30) yields:

[0174] (31)

[0175] In the formula:

[0176] By satisfying the exponential reaching law in the equation of synovial dynamics, we get:

[0177] (32)

[0178] In the formula: Let be the positive definite gain matrix of the switching surface of the diaphragm controller, and The smaller the value, the slower the approach speed. The larger the value, the greater the speed at which the motion point reaches the switching surface, resulting in greater jitter. ;

[0179] Combining equations (29) and (30), we get:

[0180] (33)

[0181] Finally, by combining equations (11), (16), and (31), we obtain:

[0182] (34).

[0183] like Figure 1As shown, the parking AGV consists of a frame 1, a rear clamping arm 2, a front clamping arm 3, four Mecanum wheels 10, two push rod motors 7, a push rod motor mounting base 8, four travel motors 9, and a coupling 11. When the parking AGV moves to the bottom of the car, the rear clamping arm 2 is horizontally extended under the drive of the rear unfolding motor 13, and the front clamping arm 3 is folded and unfolded under the drive of the front unfolding motor 6. The front clamping arm 3 is fixed to the slider 5 by bolts, and the slider 5 can move on the guide rail 4. Finally, with the assistance of the push rod motor 7, the front clamping arm 3 and the rear clamping arm 2 clamp the car tires and lift the car. At the same time, the load-bearing casters 12 under the clamping arms bear most of the weight of the car.

[0184] like Figure 2 As shown, the lidar and inertial navigation sensors upload point cloud data and data such as the heading angle / yaw rate of the parking AGV to the industrial control computer. The industrial control computer then uses this data to build a map of the surrounding environment. The industrial control computer then sends the AGV's pose information to the electronic control unit (ECU). The ECU then sends a torque signal to the motor driver according to the corresponding control strategy, thereby controlling the parking AGV to move according to the planned trajectory.

[0185] This invention addresses the trajectory tracking problem of parking AGVs by proposing a sliding membrane controller based on a nonlinear disturbance observer. First, based on the analysis of the kinematic and dynamic model of the parking AGV, the interference of the load-bearing omnidirectional wheels 12 on the AGV's motion is considered. Then, a nonlinear disturbance observer is used to estimate the disturbance force and torque generated by the load-bearing omnidirectional wheels 12. Finally, a non-singular terminal sliding membrane controller is combined to achieve AGV tracking of the reference trajectory. Results show that compared with traditional non-singular sliding membrane controllers, this invention can track the reference trajectory much better, and the tracking stability is improved by 42% to 68%. Figure 6 , Figure 7 As shown.

[0186] In summary, this invention addresses the trajectory tracking problem of parking AGVs by proposing a sliding membrane controller based on a nonlinear disturbance observer. First, based on the analysis of the kinematic and dynamic models of the parking AGV, the interference of the load-bearing omnidirectional wheels on the AGV's motion is considered. Then, a nonlinear disturbance observer is used to estimate the disturbance force and torque generated by the load-bearing omnidirectional wheels. Finally, a non-singular terminal sliding membrane controller is combined to achieve AGV tracking of the reference trajectory. Results show that, compared with traditional non-singular sliding membrane controllers, this invention can track the reference trajectory much better, and the tracking stability is improved by 42% to 68%.

Claims

1. A trajectory tracking control method for a single automated valet parking robot, characterized in that: The method includes the following steps in sequence: (1) Establish the kinematic model of the parking AGV; (2) Establish a dynamic model for the parking AGV; (3) Based on the kinematic model and dynamic model of the parking AGV, a sliding mode controller based on a nonlinear disturbance observer is designed. The disturbance value estimated by the nonlinear disturbance observer is used as the input signal of the sliding mode controller. The motor torque output by the sliding mode controller is converted into motor speed and then output to the kinematic model of the parking AGV. The kinematic model of the parking AGV outputs the required speed of the four Mecanum wheels to realize trajectory tracking control. Step (3) specifically includes the following sequential steps: (3a) Design a nonlinear disturbance observer: Combine the disturbance forces and torques generated by all the load-bearing casters into an equivalent disturbance force and torque, expressed as: （15） In the formula: F cy They are respectively the parking AGVs , The equivalent disturbance force of the shaft; For parking AGVs The equivalent disturbance torque of the shaft; Based on the dynamic model of the parking AGV, the generalized forces and torques acting on the parking AGV are... To further express: （16） In the formula: （17） （18） in, The driving torque of the Mecanum wheel; The frictional force acting on the Mecanum wheel, , The additional equivalent disturbance force and torque generated by the load-bearing casters; The heading angle of the parking AGV. It is half the distance between the centers of the two Mecanum wheels on the left and right sides; It is half the distance between the centers of the two Mecanum wheels in the longitudinal direction; , , , For the rotational angular velocity of each Mecanum wheel; Each Mecanum wheel has the same load, therefore the frictional force on each Mecanum wheel is expressed as: （19） In the formula: It is the acceleration due to gravity; Let be the coefficient of friction between the Mecanum wheel and the ground, and take . ; The overall vehicle weight of the parking AGV; The nonlinear perturbation observer is represented as: （20） In the formula: （21） （22） （23） （24） in, It is an auxiliary variable; It is disturbance force and torque The estimated value; The tuning matrix of the perturbation observer. ; By combining equations (23) and (24), we obtain for: （25） Define the observer error for: （26） set up: （27） The final result is: （28） (3b) Design of sliding mode controller: First, define the tracking error as: （29） In the formula: This provides the position information of the reference trajectory in the global coordinate system. This refers to the position information of the actual trajectory in the global coordinate system. These represent the errors in the X and Y directions and the heading angle in the global coordinate system, respectively. The sliding surface of the sliding mode controller is designed as follows: （30） In the formula: Design parameters for the sliding mode controller and ensure they meet the requirements. ,Pick ; Design a matrix for the sliding mode controller, and take... ; Differentiating equation (30) yields: （31） In the formula: , Let the sliding mode dynamics equations satisfy the exponential reaching law, we get: （32） In the formula: Let be the positive definite gain matrix of the switching surface of the sliding mode controller, and The smaller the value, the slower the approach speed. The larger the value, the greater the speed at which the motion point reaches the switching surface, resulting in greater jitter. ; Combining equations (29) and (30), we get: （33） Finally, by combining equations (11), (16), and (31), we obtain: （34）； Step (1) specifically refers to: The parking AGV is a Mecanum wheel omnidirectional moving platform. It is the global coordinate system of the parking AGV; Parking AGV vehicle coordinate system; It is the origin of the coordinate system of the parking AGV and the center point of the four Mecanum wheels; It is the core of the parking AGV; The linear velocities corresponding to the centers of each Mecanum wheel, i=1,2,3,4, , Let the radius of the Mecanum wheel be 1. The corresponding rotational angular velocity of each Mecanum wheel; The tangential speed corresponding to the grounding roller of each Mecanum wheel; The yaw rate of the parking AGV; Let the heading angle be the AGV's heading angle. The inverse kinematics equation of the AGV is obtained as follows: （1） In the formula: For the speed at the center of the vehicle body The velocity component of the shaft; For the speed at the center of the vehicle body The velocity component of the shaft; It is half the distance between the centers of the two Mecanum wheels on the left and right sides; It is half the distance between the centers of the two Mecanum wheels in the longitudinal direction; Equation (1) is the kinematic model of the parking AGV; Rewrite equation (1) as equation (2): （2） In the formula: The rotational angular velocity of the Mecanum wheel; ,in, and These are the lower edges of the parking AGV's body coordinate system. , velocity components; The yaw rate in the coordinate system of the parking AGV body; Define the Jacobian matrix for: （3） The forward kinematic equations of the parking AGV are obtained as follows; （4） In the formula: ; Establish the coordinate transformation equations between the parking AGV's vehicle coordinate system and the global coordinate system. Based on the motion relationship, the coordinate transformation formula is as follows: （5） In the formula: ,in, , The parking AGV is positioned at the lower edge of the global coordinate system. , velocity components; The yaw rate of the parking AGV in the global coordinate system; ; Expressed as follows; The heading angle in the coordinate system of the parking AGV body; （6） By combining equations (1) to (6), we obtain The conversion relationship between the speed of the parking AGV and the speed of the AGV is as follows; （7） In the formula, This is the coordinate transformation matrix; After analysis, the origin of the parking AGV coordinates can be expressed by the following formula. and center of mass The speed relationship between them: （8） In the formula: , The centroids along , The velocity component of the shaft; , The centroids To the origin The horizontal and vertical distances; Finally, by combining equations (5) to (8), we obtain the following equation; （9）。 2. The trajectory tracking control method for a single automated valet parking robot according to claim 1, characterized in that: Step (2) specifically refers to: establishing the dynamic model of the parking AGV using the Lagrange method to obtain the Lagrange function of the parking AGV. As shown in the following formula: （10） In the formula: For parking AGVs to circle Moment of inertia of the shaft; The overall vehicle weight of the parking AGV; Let be the moment of inertia of the Mecanum wheel; For parking AGVs to circle The yaw rate of the shaft; , The parking AGV is positioned at the lower edge of the global coordinate system. , velocity components; , , , For the rotational angular velocity of each Mecanum wheel; Then, combining equations (9) and (10), and considering the Lagrange function... Taking the derivative, we obtain the dynamic model of the parking AGV, as shown in the following equation: （11） In the formula: （12） （13） （14） in, ,in , , The parking AGV is positioned at the lower edge of the global coordinate system. , , The acceleration; For generalized force and torque, , They are parking AGVs along , Generalized force components of the axis; For parking AGVs to circle Generalized torque of the shaft, Let the radius of the Mecanum wheel be 1. It is half the distance between the centers of the two Mecanum wheels on the left and right sides; It is half the distance between the centers of the two Mecanum wheels in the longitudinal direction; , The centroids To the origin The horizontal and vertical distances; The heading angle of the parking AGV. The yaw rate of the parking AGV in the global coordinate system; The yaw rate is given in the coordinate system of the parking AGV.

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