A predictive control-based method and system for reversing path tracking control of articulated vehicles
By constructing a mathematical model of the reversing condition of the articulated vehicle and nonlinear predictive control, the reversing path tracking control of the articulated vehicle was realized, which solved the problem of the inability to track the reversing path in the existing technology, reduced costs and improved control accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF SCI & TECH BEIJING
- Filing Date
- 2023-10-16
- Publication Date
- 2026-05-26
AI Technical Summary
Existing model predictive control-based articulated vehicle path tracking control methods cannot achieve reverse path tracking control.
A hardware platform for bidirectional driving of an articulated steering vehicle is constructed, with the front axle of the original articulated vehicle serving as the de facto rear axle. A mathematical model of the reversing working condition is established, and a nonlinear predictive control method with multiple aiming points is adopted to perform predictive control in order to achieve reversing path tracking.
It solves the problem of reversing path tracking control of articulated vehicles in the existing technology, which is low-cost and effective, and avoids collision with the tunnel wall and alignment problems of the work object.
Smart Images
Figure CN117389143B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of motion control technology for unmanned vehicles, and in particular to a method and system for reversing path tracking control of an articulated vehicle based on predictive control. Background Technology
[0002] Articulated steering vehicles are often simply referred to as articulated cars. Considering that articulated cars are multi-constraint systems, and that model predictive control can effectively handle system constraints, there are currently some research results on path tracking control of articulated cars based on model predictive control (Bai G, Liu L, Meng Y, et al. Path tracking of mining vehicles based on nonlinear model predictive control[J]. Applied Sciences,2019,9(7):1372; Meng Yu, Gan Xin, Bai Guoxing. Path tracking predictive control of underground mining articulated cars based on pre-aiming distance[J]. Journal of Engineering Science,2019,41(5):662-671.). In these research results, the control point of the model predictive controller is the center of the front axle of the articulated car, which can only complete the path tracking control when moving forward. However, articulated cars usually need to have bidirectional driving capabilities, and the existing research results do not consider the case of reversing, so they cannot realize path tracking control when reversing. Summary of the Invention
[0003] This invention provides a method and system for reversing path tracking control of articulated vehicles based on predictive control, which solves the problem that existing articulated vehicle path tracking control methods based on model predictive control cannot achieve reversing path tracking control.
[0004] To achieve the aforementioned objectives, the present invention provides the following technical solution: a method for reversing path tracking control of an articulated vehicle based on predictive control, characterized in that the steps include:
[0005] S1. Construct a hardware platform for bidirectional travel of the articulated steering vehicle, and use the original articulated vehicle's front axle as the de facto rear axle.
[0006] S2. Construct a mathematical model for reversing operation;
[0007] S3. Based on the hardware platform and the mathematical model of the reversing condition, predictive control is performed on the articulated steering vehicle to complete the reversing path tracking control of the articulated vehicle based on predictive control.
[0008] Preferably, in step S1, constructing a hardware platform for bidirectional travel of the articulated steering vehicle, with the original articulated vehicle's front axle serving as the de facto rear axle, includes:
[0009] Install a path tracking control system in articulated steering vehicles;
[0010] The path tracking control system sets the forward direction of the reference path of the articulated steering vehicle to the reverse direction.
[0011] Obtain the heading angle given by the path planning system and align the heading angle.
[0012] Preferably, the heading angle is aligned, including:
[0013] The heading angle given by the path planning system is processed according to the following formula (1):
[0014]
[0015] Where θ represents the heading angle, the subscript p represents the positioning system, the subscript ar represents the actual rear axle, and the subscript ref represents the reference value;
[0016] Take the heading angle of the rear axle as the absolute value of the difference between the original front axle heading angle and the heading angle of the reference path, whichever is increased or decreased by 180°.
[0017] The longitudinal velocity, hinge angle, and hinge angular velocity given by the positioning system are simultaneously reversed.
[0018] Preferably, in step S2, constructing a mathematical model for the reversing operation includes:
[0019] Based on the transformation results of the front and rear axles, and the motion relationship between the front and rear axles of the articulated steering vehicle, the mathematical model of the reversing condition is obtained as shown in the following formula (2):
[0020]
[0021] Where x represents the horizontal axis, y represents the vertical axis, v represents the longitudinal velocity, γ represents the hinge angle, ω represents the angular velocity, l represents the distance from the axle to the hinge point, the subscript of represents the original front axle, and the subscript or represents the original rear axle.
[0022] Preferably, in step S3, predictive control of the articulated steering vehicle is performed based on the hardware platform and the mathematical model of the reversing condition, including:
[0023] A nonlinear predictive control method with multiple aiming points is adopted;
[0024] Based on the nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted to obtain the predictive model.
[0025] The predictive model is used to solve the control problem. The obtained articulated angular velocity is inverted and transmitted to the controlled articulated vehicle to achieve reversing path tracking control.
[0026] Preferably, based on a nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted, including:
[0027] By substituting the mathematical model of the reversing condition of the articulated steering vehicle into the nonlinear predictive control method, an abstract model as shown in the following formula (3) is obtained:
[0028]
[0029] in,
[0030] A predictive control-based reversing path tracking control system for articulated vehicles, the system being used in the aforementioned predictive control-based reversing path tracking control method for articulated vehicles, the system comprising:
[0031] The platform construction module is used to build a hardware platform for bidirectional travel of the articulated steering vehicle, using the original articulated vehicle's front axle as the de facto rear axle.
[0032] The mathematical model building module is used to build mathematical models of reversing conditions;
[0033] The predictive control module is used to perform predictive control on the articulated steering vehicle based on the hardware platform and the mathematical model of the reversing condition, and to complete the reversing path tracking control of the articulated vehicle based on predictive control.
[0034] Preferably, the platform building module is used to set up a path tracking control system in an articulated steering vehicle;
[0035] The path tracking control system sets the forward direction of the reference path of the articulated steering vehicle to the reverse direction.
[0036] Obtain the heading angle given by the path planning system and align the heading angle.
[0037] Preferably, the heading angle is aligned, including:
[0038] The heading angle given by the path planning system is processed according to the following formula (1):
[0039]
[0040] Where θ represents the heading angle, the subscript p represents the positioning system, the subscript ar represents the actual rear axle, and the subscript ref represents the reference value;
[0041] Take the heading angle of the rear axle as the absolute value of the difference between the original front axle heading angle and the heading angle of the reference path, whichever is increased or decreased by 180°.
[0042] The longitudinal velocity, hinge angle, and hinge angular velocity given by the positioning system are simultaneously reversed.
[0043] Preferably, the mathematical model construction module is used to obtain the mathematical model of the reversing condition as shown in the following formula (2) based on the transformation results of the front and rear axles and the motion relationship between the front and rear axles of the articulated steering vehicle:
[0044]
[0045] Where l represents the distance from the axle to the articulation point, the subscript of represents the original front axle, and the subscript or represents the original rear axle.
[0046] On the one hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the above-described predictive control-based articulated vehicle reversing path tracking control method.
[0047] On the one hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, the at least one instruction being loaded and executed by a processor to implement the above-described articulated vehicle reversing path tracking control method based on predictive control.
[0048] The above technical solution has at least the following advantages compared with the existing technology:
[0049] The above solution, by setting up a hardware platform, establishing a mathematical model of the articulated vehicle under reversing conditions, and designing a multi-predictive-point nonlinear model predictive control algorithm, can solve the problem that existing articulated vehicle path tracking control systems based on model predictive control cannot complete reversing path tracking control. Compared with the technical solution of adding a positioning system to the rear axle, the cost is lower. Attached Figure Description
[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0051] Figure 1 This is a schematic flowchart of the articulated vehicle reversing path tracking control method based on predictive control provided in an embodiment of the present invention;
[0052] Figure 2 This is a schematic diagram of the positioning system layout provided in an embodiment of the present invention;
[0053] Figure 3 This is a schematic diagram of the positioning system in the forward direction provided in an embodiment of the present invention;
[0054] Figure 4This is a schematic diagram of parameter transformation provided in an embodiment of the present invention;
[0055] Figure 5 This is a block diagram of a predictive control-based reversing path tracking control system for articulated vehicles provided in an embodiment of the present invention;
[0056] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation
[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0058] This invention addresses the problem that existing articulated vehicle path tracking control methods based on model predictive control cannot achieve reverse path tracking control, and provides an articulated vehicle reverse path tracking control method and system based on predictive control.
[0059] like Figure 1 As shown, this embodiment of the invention provides a predictive control-based reversing path tracking control method for articulated vehicles, which can be implemented by electronic devices. Figure 1 The flowchart shown is for a reversing path tracking control method for articulated vehicles based on predictive control. The processing flow of this method may include the following steps:
[0060] S101. Construct a hardware platform for bidirectional travel of the articulated steering vehicle, using the original articulated vehicle's front axle as the de facto rear axle.
[0061] In one feasible implementation, in an articulated steering vehicle path tracking control system, the positioning system should provide the abscissa, ordinate, and heading angle of the front axle center in the global coordinate system, the longitudinal velocity and yaw rate in the front axle coordinate system, and the hinge angle and hinge rate at the hinge point. In existing articulated steering vehicle path tracking control systems, the positive longitudinal direction of the front axle coordinate system is the forward direction of the front vehicle body, the positive lateral direction is to the left of the forward direction of the front vehicle body, and the positive directions of the heading angle, yaw rate, hinge angle, and hinge rate are counterclockwise. The hinge angle refers to the difference between the heading angle of the front vehicle body and the heading angle of the rear vehicle body.
[0062] In reverse operation, the forward direction of the reference path provided by the path planning system should first be aligned with the reverse direction of the articulated vehicle. At this point, the difference between the forward direction of the reference path and the heading angle provided by the positioning system is too large. If the heading angle provided by the positioning system is used directly, the articulated steering vehicle will turn around, potentially leading to collisions with the tunnel wall or failure to align the working mechanism with the work object. Furthermore, in reverse operation, the original front axle effectively becomes the rear axle.
[0063] In one feasible implementation, step S101 involves constructing a hardware platform for bidirectional movement of the articulated steering vehicle, using the original articulated vehicle's front axle as the de facto rear axle, including:
[0064] Install a path tracking control system in articulated steering vehicles;
[0065] The path tracking control system sets the forward direction of the reference path of the articulated steering vehicle to the reverse direction.
[0066] Obtain the heading angle given by the path planning system and align the heading angle.
[0067] Preferably, the heading angle is aligned, including:
[0068] The heading angle given by the path planning system is processed according to the following formula (1):
[0069]
[0070] Where θ represents the heading angle, the subscript p represents the positioning system, the subscript ar represents the actual rear axle, and the subscript ref represents the reference value;
[0071] Take the heading angle of the rear axle as the absolute value of the difference between the original front axle heading angle and the heading angle of the reference path, whichever is increased or decreased by 180°.
[0072] In one feasible implementation, since the forward direction is reversed, the longitudinal velocity, hinge angle, and hinge angular velocity provided by the positioning system also need to be reversed:
[0073]
[0074] In the formula, v represents the longitudinal velocity, γ represents the hinge angle, and ω represents the angular velocity.
[0075] Considering that the longitudinal speed given by the positioning system is negative when the articulated steering vehicle is reversing, the longitudinal speed is calculated as a positive value in the above process, which is the path tracking control algorithm solution process.
[0076] The longitudinal velocity, hinge angle, and hinge angular velocity given by the positioning system are simultaneously reversed. For example... Figure 2This is a schematic diagram of the positioning system layout provided in an embodiment of the present invention; as shown. Figure 3 This is a schematic diagram of the positioning system provided in an embodiment of the present invention in the forward direction; as shown. Figure 4 This is a schematic diagram of parameter transformation provided in an embodiment of the present invention.
[0077] S102. Construct a mathematical model for reversing operation;
[0078] In one feasible implementation, the original front axle becomes the de facto rear axle in the reversing condition, so the kinematic model of the articulated steering vehicle needs to be re-derived.
[0079] The theoretical basis stems from existing research (Bai G, Liu L, Meng Y, et al. Path tracking of mining vehicles based on nonlinear model predictive control[J]. Applied Sciences, 2019, 9(7): 1372), namely, the motion relationship between the front and rear axles of articulated steering vehicles:
[0080]
[0081] In the formula, l represents the distance from the axle to the articulation point. In the above formula, the distances from the front axle and the rear axle to the articulation point are the actual distances from the front axle and the rear axle to the articulation point.
[0082] Considering that the control point is the actual rear axle, we take θ. r The model output is:
[0083]
[0084] Let the center of the rear axle be the control point, that is:
[0085]
[0086] In the formula, the subscript c represents a control point.
[0087] We can obtain:
[0088]
[0089] In the formula, x represents the horizontal coordinate and y represents the vertical coordinate.
[0090] In one feasible implementation, based on the transformation results of the front and rear axles and the motion relationship between the front and rear axles of the articulated steering vehicle, a mathematical model for the reversing condition is obtained as shown in the following formula (2):
[0091]
[0092] Where l represents the distance from the axle to the articulation point, the subscript of represents the original front axle, and the subscript or represents the original rear axle.
[0093] S103. Based on the hardware platform and the mathematical model of reversing conditions, predictive control is performed on the articulated steering vehicle to complete the reversing path tracking control of the articulated vehicle based on predictive control.
[0094] In one feasible implementation, a nonlinear predictive control method with multiple aiming points is employed;
[0095] Based on the nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted to obtain the predictive model.
[0096] The predictive model is used to solve the control problem. The obtained articulated angular velocity is inverted and transmitted to the controlled articulated vehicle to achieve reversing path tracking control.
[0097] Preferably, based on a nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted, including:
[0098] By substituting the mathematical model of the reversing condition of the articulated steering vehicle into the nonlinear predictive control method, an abstract model as shown in the following formula (3) is obtained:
[0099]
[0100] in,
[0101] In one feasible implementation, since the above model is a critically stable model, the control algorithm must adopt nonlinear model predictive control with multiple aiming points (Bai G, Liu L, Meng Y, et al. Path tracking of mining vehicles based on nonlinear model predictive control[J]. Applied Sciences, 2019, 9(7): 1372).
[0102] Based on this control method, substituting the above mathematical model of the reversing condition of the articulated steering vehicle, the model can first be abstracted into the following formula (3):
[0103]
[0104] in,
[0105] By discretizing the model using the Euler method, the prediction model can be obtained.
[0106]
[0107] Where t represents the actual time, t+k represents the k-th iteration at that time, T is the iteration period, c is the control time domain, and p is the prediction time domain.
[0108] In one feasible implementation, the Euler method can also be replaced by the fourth-order Runge-Kutta method:
[0109] Substitute the predicted values obtained from the prediction model into the following penalty function.
[0110]
[0111] st-ω γpmax ≤ω γp ≤ω γpmax
[0112] -γ pmax ≤γ p ≤γ pmax
[0113] Where Q is the weight matrix
[0114]
[0115] Generally, q x q y q θ All values are 1. The value is 0.
[0116] After solving the nonlinear model predictive control, the obtained articulated angular velocity is inverted and transmitted to the controlled articulated vehicle to achieve reversing path tracking control. Specifically, the actual longitudinal velocity executed by the articulated vehicle is also negative to achieve reversing.
[0117] This invention provides a method for adjusting the parameters of a multi-prediction nonlinear model predictive controller. When the number of prediction steps (also known as the prediction time domain) of the controller is short, the controller error may diverge. In this case, extending the number of prediction steps to pT≥5 can stabilize the control system, but excessive extension will lead to a large residual error. Specifically, the prediction step value that can ensure stability is related to parameters such as the size of the articulated vehicle, vehicle speed, control cycle, articulation angle constraint, and articulation angular velocity constraint, and has strong nonlinear characteristics. For now, the optimal value can only be achieved through manual adjustment.
[0118] Figure 5 This is a schematic diagram of a predictive control-based reversing path tracking control system for articulated vehicles according to the present invention. The system 200 is used in the above-mentioned predictive control-based reversing path tracking control method for articulated vehicles, and the system 200 includes:
[0119] Platform construction module 210 is used to build a hardware platform for bidirectional travel of the articulated steering vehicle, using the original articulated vehicle's front axle as the de facto rear axle.
[0120] Mathematical model building module 220 is used to build a mathematical model of the reversing operation;
[0121] The predictive control module 230 is used to perform predictive control on the articulated steering vehicle based on the hardware platform and the mathematical model of the reversing condition, and to complete the reversing path tracking control of the articulated vehicle based on predictive control.
[0122] Preferably, the platform construction module 210 is used to set up a path tracking control system in an articulated steering vehicle;
[0123] The path tracking control system sets the forward direction of the reference path of the articulated steering vehicle to the reverse direction.
[0124] Obtain the heading angle given by the path planning system and align the heading angle.
[0125] Preferably, the heading angle is aligned, including:
[0126] The heading angle given by the path planning system is processed according to the following formula (1):
[0127]
[0128] Where θ represents the heading angle, the subscript p represents the positioning system, the subscript ar represents the actual rear axle, and the subscript ref represents the reference value;
[0129] Take the heading angle of the rear axle as the absolute value of the difference between the original front axle heading angle and the heading angle of the reference path, whichever is increased or decreased by 180°.
[0130] The longitudinal velocity, hinge angle, and hinge angular velocity given by the positioning system are simultaneously reversed.
[0131] Preferably, the mathematical model construction module 220 is used to obtain the mathematical model of the reversing condition as shown in the following formula (2) based on the transformation results of the front and rear axles and the motion relationship between the front and rear axles of the articulated steering vehicle:
[0132]
[0133] Where l represents the distance from the axle to the articulation point, the subscript of represents the original front axle, and the subscript or represents the original rear axle.
[0134] Preferably, the predictive control module 230 is used to employ a nonlinear predictive control method with multiple aiming points;
[0135] Based on the nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted to obtain the predictive model.
[0136] The predictive model is used to solve the control problem. The obtained articulated angular velocity is inverted and transmitted to the controlled articulated vehicle to achieve reversing path tracking control.
[0137] Preferably, based on a nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted, including:
[0138] By substituting the mathematical model of the reversing condition of the articulated steering vehicle into the nonlinear predictive control method, an abstract model as shown in the following formula (3) is obtained:
[0139]
[0140] in,
[0141] In this embodiment of the invention, by setting up a hardware platform, establishing a mathematical model of the articulated vehicle under reversing conditions, and designing a multi-predictive-point nonlinear model predictive control algorithm, the present invention can solve the problem that existing articulated vehicle path tracking control systems based on model predictive control cannot complete reversing path tracking control. Compared with the technical solution of adding a positioning system to the rear axle, the cost is lower.
[0142] Figure 6 This is a schematic diagram of the structure of an electronic device 300 provided in an embodiment of the present invention. The electronic device 300 can vary considerably due to differences in configuration or performance. It may include one or more central processing units (CPUs) 301 and one or more memories 302. The memories 302 store at least one instruction, which is loaded and executed by the processors 301 to implement the steps of the following predictive control-based articulated vehicle reversing path tracking control method:
[0143] S1. Construct a hardware platform for bidirectional travel of the articulated steering vehicle, and use the original articulated vehicle's front axle as the de facto rear axle.
[0144] S2. Construct a mathematical model for reversing operation;
[0145] S3. Based on the hardware platform and the mathematical model of the reversing condition, predictive control is performed on the articulated steering vehicle to complete the reversing path tracking control of the articulated vehicle based on predictive control.
[0146] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions that can be executed by a processor in a terminal to complete the aforementioned predictive control-based articulated vehicle reversing path tracking control method. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device.
[0147] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.
Claims
1. A method for reversing path tracking control of an articulated vehicle based on predictive control, characterized in that, The method steps include: S1. Construct a hardware platform for bidirectional travel of the articulated steering vehicle, and use the original articulated vehicle's front axle as the de facto rear axle. Step S1 includes: Install a path tracking control system in articulated steering vehicles; The path tracking control system sets the forward direction of the reference path of the articulated steering vehicle to the reverse driving direction. Obtain the heading angle given by the path planning system and perform alignment processing on the heading angle; The process of aligning the heading angle includes: The heading angle given by the path planning system is processed according to the following formula (1): （1） in, Indicates the heading angle, subscript Indicates the positioning system, subscript Indicates the actual rear axle, subscript Indicates a reference value; Take the heading angle of the rear axle as the absolute value of the difference between the original front axle heading angle and the heading angle of the reference path, whichever is increased or decreased by 180°. The longitudinal velocity, hinge angle, and hinge angular velocity given by the positioning system are simultaneously reversed in the opposite direction; S2. Construct a mathematical model for reversing operation; The construction of the mathematical model for reversing operation includes: Based on the transformation results of the front and rear axles, and the motion relationship between the front and rear axles of the articulated steering vehicle, the mathematical model of the reversing condition is obtained as shown in the following formula (2): （2） in, Indicates longitudinal velocity. Indicates the hinge angle. Indicates angular velocity; Represents the x-axis, Represents the ordinate; Indicates the distance from the axle to the articulation point, subscript Indicates the original front axle, subscript Indicates the original rear axle; S3. Based on the hardware platform and the mathematical model of the reversing condition, predictive control is performed on the articulated steering vehicle to complete the reversing path tracking control of the articulated vehicle based on predictive control.
2. The method according to claim 1, characterized in that, In step S3, based on the hardware platform and the mathematical model of the reversing condition, predictive control is performed on the articulated steering vehicle, including: A nonlinear predictive control method with multiple aiming points is adopted; Based on the aforementioned nonlinear predictive control method, the mathematical model of the reversing condition of the articulated steering vehicle is substituted to obtain the predictive model. The prediction model is solved for control, and the obtained articulated angular velocity is inverted and transmitted to the controlled articulated vehicle to achieve reversing path tracking control.
3. The method according to claim 2, characterized in that, The nonlinear predictive control method, by substituting the mathematical model of the reversing condition of the articulated steering vehicle into the method, obtains a predictive model, including: Substituting the mathematical model of the reversing condition of the articulated steering vehicle into the nonlinear predictive control method, we obtain the abstract model as shown in the following formula (3): （3）； in, .
4. A reversing path tracking control system for an articulated vehicle based on predictive control, characterized in that, The system is used in the articulated vehicle reversing path tracking control method based on predictive control as described in any one of claims 1 to 3, the system comprising: The platform construction module is used to build a hardware platform for bidirectional travel of the articulated steering vehicle, using the original articulated vehicle's front axle as the de facto rear axle. The platform construction module is used to set up a path tracking control system in an articulated steering vehicle; The path tracking control system sets the forward direction of the reference path of the articulated steering vehicle to the reverse driving direction. Obtain the heading angle given by the path planning system and perform alignment processing on the heading angle; The process of aligning the heading angle includes: The heading angle given by the path planning system is processed according to the following formula (1): （1） in, Indicates the heading angle, subscript Indicates the positioning system, subscript Indicates the actual rear axle, subscript Indicates a reference value; Take the heading angle of the rear axle as the absolute value of the difference between the original front axle heading angle and the heading angle of the reference path, whichever is increased or decreased by 180°. The longitudinal velocity, hinge angle, and hinge angular velocity given by the positioning system are simultaneously reversed in the opposite direction; The mathematical model building module is used to build mathematical models of reversing conditions; The mathematical model construction module is used to obtain the mathematical model of the reversing condition as shown in the following formula (2) based on the transformation results of the front and rear axles and the motion relationship between the front and rear axles of the articulated steering vehicle: （2） in, Indicates the distance from the axle to the articulation point, subscript Indicates the original front axle, subscript Indicates the original rear axle; The predictive control module is used to perform predictive control on the articulated steering vehicle based on the hardware platform and the mathematical model of the reversing condition, and to complete the reversing path tracking control of the articulated vehicle based on predictive control.