A Method and System for Tracking Articulated Mining Cars Based on Linear Model Prediction

Abstract

This invention belongs to the technical field of path tracking, specifically relating to a path tracking method and system for articulated mining vehicles based on linear model prediction. It aims to solve the problem that existing control schemes struggle to balance accuracy and real-time performance. The method includes: obtaining the kinematic model of the articulated mining vehicle; simplifying the kinematic model; further simplifying it by fixing the nominal wheelbase and performing piecewise linearization of the articulation angles to obtain a linearized state variable model, which is then discretized to obtain a prediction model; constructing an initial function based on the prediction model and a reference path point sequence in the local coordinate system, and transforming the initial function into a standard quadratic form to obtain an objective function; determining the optimal control input for the articulated mining vehicle at the current moment by solving the objective function; and controlling the articulated mining vehicle according to the optimal control input. This method can simultaneously achieve both accuracy and real-time performance, effectively improving the path tracking effect.

Description

Technical Field

[0001] This invention belongs to the technical field of path tracking, specifically relating to a path tracking method and system for mine articulated vehicles based on linear model prediction. Background Technology

[0002] Mining articulated cars employ an active bending steering system with both the front and rear bodies, which effectively reduces the minimum turning radius. However, this also results in complex motion characteristics, making path tracking control challenging. Model Predictive Control (MPC), as an advanced control strategy, has gradually emerged in the field of path tracking control for mining articulated cars in recent years.

[0003] Among various methods of MPC (Multi-Level Predictive Control), Linear Model Predictive Control (LMPC) has the advantage of high computational efficiency and can quickly respond to control requirements, making it suitable for scenarios with high real-time requirements. However, most existing LMPCs use error model linearization or Jacobi model linearization methods, which make it difficult to fully utilize the detailed information of the reference path ahead of the articulated mine vehicle, resulting in poor accuracy in complex path tracking tasks. Although LMPC based on nonlinear compensation Jacobi linearization can introduce multiple aiming points ahead of the vehicle, the model error generated during the linearization process is difficult to obtain, and the controller needs to perform nonlinear model iteration and transmit a large amount of data obtained from the iteration, resulting in poor real-time performance. Therefore, existing LMPCs suffer from the problem of not being able to balance accuracy and real-time performance; that is, traditional LMPC has poor accuracy, while LMPC based on nonlinear compensation has poor real-time performance. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, namely the difficulty in balancing accuracy and real-time performance when applying existing path control schemes based on linear model predictive control to articulated mine vehicles, thus affecting their application effectiveness, this invention, in its first aspect, proposes a path tracking method for articulated mine vehicles based on linear model predictive control, the method comprising:

[0005] Obtain the kinematic model of the mining articulated vehicle;

[0006] Based on the physical law that the motion of the mining articulated car relative to the current vehicle body coordinate system in the prediction time domain conforms to the small angle assumption, the kinematic model is simplified to obtain a preliminary simplified model.

[0007] Based on the physical law that the articulation angle of a mining articulated car has a limited range of variation in the prediction time domain, the nominal wheelbase in the prediction time domain is fixed, the articulation angle in the prediction time domain is piecewise linearized, and the preliminary simplified model is further simplified to obtain the linearized state variable model of the mining articulated car.

[0008] The linearized state variable model is discretized to obtain a prediction model based on the linearized state variable model. The initial value of the prediction model is [0 0 γ]. T γ is the hinge angle;

[0009] Based on the prediction model and the reference path point sequence of the articulated mine vehicle in the local coordinate system, an initial function is constructed, and the initial function is transformed by a standard quadratic form to obtain an objective function. By solving the objective function, the optimal control input of the articulated mine vehicle at the current moment is determined. The reference path point sequence of the articulated mine vehicle in the local coordinate system is obtained by selecting the reference path point sequence corresponding to the prediction time domain on the preset reference path, based on the reference path reference point of the articulated mine vehicle in the global coordinate system, and then transforming the reference path point sequence corresponding to the global coordinate system to the local coordinate system.

[0010] The mining articulated car is controlled according to the optimal control input.

[0011] In some preferred embodiments, the kinematic model is simplified based on the physical laws that the motion of the mining articulated car relative to the current vehicle coordinate system conforms to the small-angle assumption, including:

[0012] Based on the small-angle assumption, the kinematic model is simplified. The preliminary simplified model after simplification satisfies: ;

[0013] In the formula, The rate of change of the x-coordinate of the center of the front axle of the mining articulated vehicle. Let v be the rate of change of the longitudinal coordinate of the center of the front axle of the mining articulated truck, and v be the travel speed of the mining articulated truck. This refers to the heading angle of the mining articulated vehicle. The rate of change of the heading angle of the mining articulated vehicle. This refers to the distance between the front axle and the articulation point of the mining articulated vehicle. This refers to the distance between the rear axle and the articulation point of the mining articulated vehicle. Hinged angle, Let ω be the rate of change of the hinge angle, and ω be the hinge angular velocity.

[0014] In some preferred embodiments, the physical law that the articulation angle of a mining articulated car varies only within the prediction time domain is further simplified by fixing the nominal wheelbase within the prediction time domain, performing piecewise linearization on the articulation angle within the prediction time domain, and further simplifying the preliminary simplified model, including:

[0015] Determine the nominal wheelbase for the curing process, wherein the nominal wheelbase satisfies: ;

[0016] In the formula, m is a constant value corresponding to the nominal wheelbase. This refers to the distance from the front axle to the articulation point of the mining articulated vehicle. γ is the distance from the rear axle of the mining articulated car to the articulation point, and γ is the articulation angle.

[0017] Based on the nominal wheelbase, the hinge angle in the prediction time domain is piecewise linearized, and the preliminary simplified model is further simplified. The simplified preliminary simplified model satisfies: ;

[0018] In the formula, m is the nominal wheelbase and n is the proportional value;

[0019] The proportional value n is calculated from the current articulation angle and sine value of the mining articulated car, and the calculation process of the proportional value n satisfies: .

[0020] In some preferred embodiments, the discretization of the linearized state variable model includes:

[0021] Determine the vector form of the linearized state variable model;

[0022] Based on the vector form of the linearized state variable model, the linearized state variable model is discretized using the Euler method, satisfying: ;

[0023] In the formula, To predict all predicted states of the mining articulated car in the time domain, Here is the state transition matrix. This is the state transition matrix after discretization. The control input matrix after discretization. To control the input matrix, Here, t represents time t, c represents the number of control steps, and p represents the number of prediction steps. For state vectors, The value is [0 0 γ]T.

[0024] In some preferred embodiments, the vector form of the linearized state variable model satisfies: ;

[0025] In the formula, For state vectors, For the input vector, Here is the state transition matrix. The input matrix is ​​y, which is the ordinate of the center of the front axle of the mining articulated vehicle.

[0026] In some preferred embodiments, the reference path point sequence of the mining articulated vehicle in a preset local coordinate system is obtained by the following method:

[0027] A reference point is determined, which is the point closest to the center of the front axle of the mining articulated vehicle in a preset reference path;

[0028] Based on the aforementioned reference point, multiple target points are determined according to a preset reference path to obtain the reference path point sequence of the mining articulated vehicle, satisfying the following: ;

[0029] In the formula, For global reference path information, This refers to the state vector of the reference path point in the global coordinate system. These represent the x-coordinate, y-coordinate, and heading angle of the reference path point in the global coordinate system. For a moment, for The value corresponding to the predicted quantity at time i. To predict the number of steps;

[0030] The reference path point sequence is transformed to obtain the reference path point sequence of the mining articulated vehicle in a preset local coordinate system.

[0031] In some preferred embodiments, the coordinate transformation of the reference path point sequence satisfies: ;

[0032] In the formula, , These are the ordinate and heading angle of the reference path point in the local coordinate system, respectively. Let x, y, and y coordinates be the x-coordinate, y-coordinate, and heading angle of the center of the front axle of the mining articulated vehicle at time t in the global coordinate system.

[0033] In some preferred embodiments, the process of constructing the objective function includes:

[0034] Construct an initial function that satisfies: ;

[0035] In the formula, Q and R are preset weight matrices to be determined;

[0036] The initial function is transformed using a quadratic form to obtain the objective function, which satisfies: ;

[0037] In the formula, H and G are quadratic parameters, Ω is the dynamic matrix, and N(t) is the compensation term.

[0038] In some preferred embodiments, determining the optimal control input of the mining articulated car at the current moment by solving the objective function includes:

[0039] Based on the prediction model, solve the objective function and determine the sequence of input values ​​that minimizes the objective function;

[0040] The first input value in the input value sequence is determined to be the optimal control input for the mining articulated vehicle at the current moment.

[0041] A second aspect of the present invention provides a path tracking system for articulated mine vehicles based on linear model prediction, the system comprising:

[0042] The data acquisition module is used to acquire the kinematic model of the mining articulated car;

[0043] The first simplification module is used to simplify the kinematic model based on the physical law that the motion of the mining articulated car relative to the current vehicle body coordinate system in the prediction time domain conforms to the small angle assumption, and to obtain a preliminary simplified model.

[0044] The second simplification module is used to obtain the linearized state variable model of the mining articulated car by solidifying the nominal wheelbase in the prediction time domain, performing piecewise linearization on the articulated angle in the prediction time domain, and further simplifying the preliminary simplified model based on the physical law that the articulated angle of the mining car changes within a limited range in the prediction time domain.

[0045] The model building module is used to discretize the linearized state variable model to obtain a prediction model based on the linearized state variable model. The initial value of the prediction model is [0 0 γ]T, where γ is the hinge angle.

[0046] The constraint solving module is used to construct an initial function based on the prediction model and the reference path point sequence of the articulated mine vehicle in the local coordinate system, and to obtain an objective function by performing a standard quadratic transformation on the initial function. By solving the objective function, the optimal control input of the articulated mine vehicle at the current moment is determined. The reference path point sequence of the articulated mine vehicle in the local coordinate system is obtained by selecting the reference path point sequence corresponding to the prediction time domain on the preset reference path based on the reference path reference point of the articulated mine vehicle in the global coordinate system, and then transforming the reference path point sequence corresponding to the global coordinate system to the local coordinate system.

[0047] The vehicle control module is used to control the mining articulated car according to the optimal control input.

[0048] The beneficial effects of this invention are:

[0049] Based on the method proposed in this invention, a linearized model of the articulated vehicle is constructed by employing a small-angle assumption model linearization method that differs from that of general linear model predictive control. Then, a predictive model based on the linearized model is constructed. By using a reference path coordinate transformation method in the prediction time domain that is different from that of general linear model predictive control, a reference path point sequence in the local coordinate system is obtained. Based on this, an initial form similar to nonlinear model predictive control is constructed, but it can ultimately be transformed into a standard quadratic optimization objective function unique to linear model predictive control. Finally, compared with other control methods such as linear model predictive control and nonlinear model predictive control, the goal of simultaneously ensuring the accuracy and real-time performance of the mine vehicle path tracking control is achieved. Attached Figure Description

[0050] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0051] Figure 1 This is a flowchart illustrating a path tracking method for mine articulated vehicles based on linear model prediction, as proposed in an embodiment of the present invention.

[0052] Figure 2 This is a schematic diagram of a mine articulated vehicle path tracking system based on linear model prediction proposed in an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the structure of a computer system used to implement the methods and system embodiments of this application. Detailed Implementation

[0054] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0055] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0056] To more clearly illustrate the method proposed in this invention, the following is combined with... Figure 1 The steps in the embodiments of the present invention are described in detail below. Please refer to... Figure 1 ,like Figure 1 As shown, the first embodiment of the present invention provides a path tracking method for mine articulated vehicles based on linear model prediction, comprising:

[0057] Step S10: Obtain the kinematic model of the mining articulated vehicle;

[0058] Step S20: Based on the physical law that the motion of the mining articulated car relative to the current vehicle body coordinate system in the prediction time domain conforms to the small angle assumption, the kinematic model is simplified to obtain a preliminary simplified model.

[0059] Step S30: Based on the physical law that the articulation angle of the mining articulated car has a limited range of variation in the prediction time domain, the nominal wheelbase in the prediction time domain is solidified, the articulation angle in the prediction time domain is piecewise linearized, and the preliminary simplified model is further simplified to obtain the linearized state variable model of the mining articulated car.

[0060] Step S40: Discretize the linearized state variable model to obtain a prediction model based on the linearized state variable model. The initial value of the prediction model is [0 0 γ]. T γ is the hinge angle;

[0061] Step S50: Based on the prediction model and the reference path point sequence of the articulated mine vehicle in the local coordinate system, an initial function is constructed, and the initial function is transformed by a standard quadratic form to obtain an objective function. By solving the objective function, the optimal control input of the articulated mine vehicle at the current moment is determined. The reference path point sequence of the articulated mine vehicle in the local coordinate system is obtained by selecting the reference path point sequence corresponding to the prediction time domain on the preset reference path based on the reference path reference point of the articulated mine vehicle in the global coordinate system, and then transforming the reference path point sequence corresponding to the global coordinate system to the local coordinate system.

[0062] Step S60: Control the mining articulated car according to the optimal control input.

[0063] Those skilled in the articulation will understand that, due to the low operating speed of the mining articulated truck and the short prediction time domain of the controller, the initial value of the heading angle θ in the local coordinate system of the vehicle body is 0, and the change range is very small, which fully meets the small angle assumption. Based on this, it can be assumed that in the vehicle body coordinate system, the following conditions are met: ;

[0064] Therefore, the kinematic model of the articulated vehicle can be simplified to: ;

[0065] In the formula, The rate of change of the x-coordinate of the center of the front axle of the mining articulated vehicle. Let v be the rate of change of the longitudinal coordinate of the center of the front axle of the mining articulated truck, and v be the travel speed of the mining articulated truck. This refers to the heading angle of the mining articulated vehicle. The rate of change of the heading angle of the mining articulated vehicle. This refers to the distance between the front axle and the articulation point of the mining articulated vehicle. This refers to the distance between the rear axle and the articulation point of the mining articulated vehicle. Hinged angle, Let ω be the rate of change of the hinge angle, and ω be the hinge angular velocity.

[0066] And for Considering that γ changes relatively little over a shorter prediction time domain, The overall value changes relatively little, so it can be treated as a constant value within each control cycle. Let:

[0067] , where m is the nominal wheelbase.

[0068] for Its value varies considerably. If we also consider that the upper limit of the articulation angle of some articulated vehicles can reach 50°, it does not perfectly meet the small angle assumption. Therefore, we can make the following assumption: ;

[0069] Where n is the proportion, its value is calculated from the current hinge angle and its sine value: ;

[0070] Thus, the articulated vehicle model can be simplified to: .

[0071] In some embodiments, for path tracking control, speed can be considered constant, thus simplifying the linearized model by eliminating one dimension, resulting in the following representation: .

[0072] In some embodiments, the aforementioned linearized model can be abstracted into the following vector form: ;

[0073] In the formula, For state vectors, For the input vector, Here is the state transition matrix. The input matrix is ​​y, which is the ordinate of the center of the front axle of the mining articulated vehicle.

[0074] Based on this, by discretizing using the Euler method, all predicted states of the mining articulated vehicle in the time domain can be obtained, and finally, they can be expressed in matrix form as follows: ;

[0075] In the formula, To predict all predicted states of the mining articulated car in the time domain, Here is the state transition matrix. This is the state transition matrix after discretization. The control input matrix after discretization. To control the input matrix, Here, t represents time t, c represents the number of control steps, and p represents the number of prediction steps. For state vectors, The value is [0 0 γ]T.

[0076] In the above embodiment, the point closest to the center of the front axle of the mining articulated vehicle is selected as the reference point on the reference path of the mining articulated vehicle. This embodiment does not limit the specific selection process.

[0077] It is easy to understand that in this embodiment, the reference path in the prediction time domain is transferred to the local coordinate system corresponding to the vehicle body. On the one hand, the small angle assumption can only be valid in the vehicle body coordinate system. On the other hand, since the path tracking control technology is an absolute navigation technology, the reference path is generally a discrete point sequence information in the global coordinate system. Only the reference path in the prediction time domain is converted to ensure real-time performance.

[0078] The specific steps include: first, selecting a reference path reference point in the global coordinate system, that is, the point on the reference path closest to the articulated vehicle; then, based on this point and the principle of taking points at equal intervals, selecting a series of reference path points in the prediction time domain on the reference path in the global coordinate system; and then transferring the series of reference path points in the prediction time domain into the time-varying local coordinate system.

[0079] Based on this baseline, points are taken forward along the reference path. The distance between each point should be equal to the product of the vehicle speed and the iteration period. A total of p points are taken to form the reference path point sequence: ;

[0080] In the formula, the subscript ref represents reference information, and the subscript G represents information in the global coordinate system. Accordingly, For global reference path information, This refers to the state vector of the reference path point in the global coordinate system. These represent the x-coordinate, y-coordinate, and heading angle of the reference path point in the global coordinate system. For a moment, for The value corresponding to the predicted quantity at time i. To predict the number of steps;

[0081] Finally, perform coordinate transformation on the reference point list: ;

[0082] In the formula, , These are the ordinate and heading angle of the reference path point in the local coordinate system, respectively. Let x, y, and y coordinates be the x-coordinate, y-coordinate, and heading angle of the center of the front axle of the mining articulated vehicle at time t in the global coordinate system.

[0083] Finally, the reference path point sequence in the vehicle's local coordinate system can be obtained: ;

[0084] In this embodiment, the initial form of the objective function (i.e., the initial function mentioned above) is the same as that of a typical nonlinear model predictive control objective function: ;

[0085] In the formula, Q and R are weight matrices. For the state tracking error term, To control input penalty items, To predict the vehicle state sequence in the time domain (p steps in the future), The target state sequence (p steps in the future) of the reference path in the local coordinate system;

[0086] The objective function can be transformed into the standard quadratic form specific to linear model predictive control: ;

[0087] In the formula, H and G are the parameters of the quadratic form. Let N(t) be a dynamic matrix, and let N(t) be the compensation term.

[0088] Under the preset constraints, the sequence of input values ​​that minimizes the above optimization objective function is solved. The first value is the optimal control input generated by the mine car path tracking controller based on linear model predictive control. Based on this optimal control input, the control strategy of the mine articulated car at the current time is determined, thereby realizing the control process of the mine articulated car.

[0089] Although the steps in the above embodiments are described in the above order, those skilled in the art will understand that in order to achieve the effect of this embodiment, different steps do not need to be executed in such an order. They can be executed simultaneously (in parallel) or in a reverse order. These simple variations are all within the protection scope of this invention.

[0090] The second embodiment of this invention proposes a mine articulated car path tracking system based on linear model prediction. This system can be a software module, comprising several instructions stored in memory. A processor can access this memory, call the instructions, and execute them to complete the mine articulated car path tracking method based on linear model prediction described in the various embodiments above. In some embodiments, the mine articulated car path tracking system based on linear model prediction can also be constructed from hardware devices. For example, the system can be constructed from one or more chips, which can coordinate with each other to complete the mine articulated car path tracking method based on linear model prediction described in the various embodiments above. Furthermore, the mine articulated car path tracking system based on linear model prediction can also be constructed from various logic devices, such as general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), microcontrollers, ARM (AcornRISC) or other programmable logic devices, discrete gate or transistor logic, discrete hardware components, or any combination of these components.

[0091] Please refer to Figure 2 , Figure 2 The diagram shows the structure of the mine articulated car path tracking system based on linear model prediction. The system includes:

[0092] Data acquisition module 210 is used to acquire the kinematic model of the mining articulated car;

[0093] The first simplification module 220 is used to simplify the kinematic model based on the physical law that the motion of the mining articulated car relative to the current vehicle body coordinate system in the prediction time domain conforms to the small angle assumption, and obtain a preliminary simplified model.

[0094] The second simplification module 230 is used to obtain the linearized state quantity model of the mining articulated car by solidifying the nominal wheelbase in the prediction time domain, performing piecewise linearization on the articulated angle in the prediction time domain, and further simplifying the preliminary simplified model based on the physical law that the articulated angle of the mining car changes within a limited range in the prediction time domain.

[0095] The model building module 240 is used to discretize the linearized state variable model to obtain a prediction model based on the linearized state variable model, wherein the initial value of the prediction model is [0 0 γ]. T γ is the hinge angle;

[0096] The constraint solving module 250 is used to construct an initial function based on the prediction model and the reference path point sequence of the mining articulated car in the local coordinate system, and to obtain an objective function by performing a standard quadratic transformation on the initial function. By solving the objective function, the optimal control input of the mining articulated car at the current moment is determined. The reference path point sequence of the mining articulated car in the local coordinate system is obtained by selecting the reference path point sequence corresponding to the prediction time domain on the preset reference path based on the reference path reference point of the mining articulated car in the global coordinate system, and then transforming the reference path point sequence corresponding to the global coordinate system to the local coordinate system.

[0097] The vehicle control module 260 is used to control the mining articulated car according to the optimal control input.

[0098] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process and related descriptions of the system described above can be found in the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0099] The following is for reference. Figure 3 It shows a schematic diagram of the structure of a computer system used to implement the methods and system embodiments of this application. Figure 3 The server shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0100] like Figure 3 As shown, the computer system includes a Central Processing Unit (CPU) 301, which can perform various appropriate actions and processes based on programs stored in Read Only Memory (ROM) 302 or programs loaded from storage section 308 into Random Access Memory (RAM) 303. The RAM 303 also stores various programs and data required for system operation. The CPU 301, ROM 302, and RAM 303 are interconnected via a bus 304. An Input / Output (I / O) interface 305 is also connected to the bus 304.

[0101] The following components are connected to I / O interface 305: an input section 306 including a keyboard, mouse, etc.; an output section 307 including a cathode ray tube (CRT), liquid crystal display (LCD), and speakers, etc.; a storage section 308 including a hard disk, etc.; and a communication section 309 including a network interface card such as a LAN (Local Area Network) card and a modem, etc. The communication section 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to I / O interface 305 as needed. Removable media 311, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 310 as needed so that computer programs read from them can be installed into storage section 308 as needed.

[0102] Specifically, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 309, and / or installed from removable medium 311. When the computer program is executed by central processing unit (CPU) 301, it performs the functions defined in the methods of this application. It should be noted that the computer-readable medium described above in this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. The computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, system, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, system, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, system, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0103] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0104] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0105] The terms “first,” “second,” etc., are used to distinguish similar objects, not to describe or indicate a specific order or sequence. The term “comprising,” or any other similar term, is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to those processes, methods, articles, or apparatus / systems.

[0106] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A path tracking method for mine articulated vehicles based on linear model prediction, characterized in that, The method includes: Obtain the kinematic model of the mining articulated vehicle; Based on the physical law that the motion of the mining articulated car relative to the current vehicle body coordinate system in the prediction time domain conforms to the small angle assumption, the kinematic model is simplified to obtain a preliminary simplified model. The kinematic model is simplified based on the physical law that the motion of the mining articulated car relative to the current vehicle coordinate system conforms to the small-angle assumption, including: Based on the small-angle assumption, the kinematic model is simplified. The preliminary simplified model after simplification satisfies: ； In the formula, The rate of change of the x-coordinate of the center of the front axle of the mining articulated vehicle. Let v be the rate of change of the longitudinal coordinate of the center of the front axle of the mining articulated truck, and v be the travel speed of the mining articulated truck. This refers to the heading angle of the mining articulated vehicle. The rate of change of the heading angle of the mining articulated vehicle. This refers to the distance between the front axle and the articulation point of the mining articulated vehicle. This refers to the distance between the rear axle and the articulation point of the mining articulated vehicle. It is the hinge angle. Let ω be the rate of change of the hinge angle, and ω be the hinge angular velocity. Based on the physical law that the articulation angle of a mining articulated car has a limited range of variation in the prediction time domain, the nominal wheelbase in the prediction time domain is fixed, the articulation angle in the prediction time domain is piecewise linearized, and the preliminary simplified model is further simplified to obtain the linearized state variable model of the mining articulated car. The physical law that the articulation angle of a mining articulated car varies only within the prediction time domain is addressed by solidifying the nominal wheelbase within the prediction time domain, performing piecewise linearization on the articulation angle within the prediction time domain, and further simplifying the preliminary simplified model, including: Determine the nominal wheelbase for the curing process, wherein the nominal wheelbase satisfies: ； In the formula, m is a constant value corresponding to the nominal wheelbase. This refers to the distance between the front axle and the articulation point of the mining articulated vehicle. This refers to the distance between the rear axle and the articulation point of the mining articulated vehicle. The hinge angle; Based on the nominal wheelbase, the hinge angle in the prediction time domain is piecewise linearized, and the preliminary simplified model is further simplified. The preliminary simplified model after further simplification satisfies: ； In the formula, m is the nominal wheelbase and n is the proportional value; The proportional value n is calculated from the current articulation angle and sine value of the mining articulated car, and the calculation process of the proportional value n satisfies: ； The linearized state variable model is discretized to obtain a prediction model based on the linearized state variable model. The initial value of the prediction model is [0 0 γ]. T γ is the hinge angle; Based on the prediction model and the reference path point sequence of the articulated mine vehicle in the local coordinate system, an initial function is constructed, and the initial function is transformed by a standard quadratic form to obtain an objective function. By solving the objective function, the optimal control input of the articulated mine vehicle at the current moment is determined. The reference path point sequence of the articulated mine vehicle in the local coordinate system is obtained by selecting the reference path point sequence corresponding to the prediction time domain on the preset reference path, based on the reference path reference point of the articulated mine vehicle in the global coordinate system, and then transforming the reference path point sequence corresponding to the global coordinate system to the local coordinate system. The mining articulated car is controlled according to the optimal control input.

2. The method for path tracking of articulated mine vehicles based on linear model prediction according to claim 1, characterized in that, The discretization process of the linearized state variable model includes: Determine the vector form of the linearized state variable model; Based on the vector form of the linearized state variable model, the linearized state variable model is discretized using the Euler method, satisfying: ； In the formula, To predict all predicted states of the mining articulated car in the time domain, Here is the state transition matrix. This is the state transition matrix after discretization. The control input matrix after discretization. To control the input matrix, Here, t represents time t, c represents the number of control steps, and p represents the number of prediction steps. For state vectors, The value is [0 0 γ] T .

3. The method for path tracking of articulated mine vehicles based on linear model prediction according to claim 2, characterized in that, The vector form of the linearized state variable model satisfies: ； In the formula, For state vectors, For the input vector, Here is the state transition matrix. The input matrix is ​​y, which is the ordinate of the center of the front axle of the mining articulated vehicle.

4. The method for path tracking of articulated mine vehicles based on linear model prediction according to claim 1, characterized in that, The method for obtaining the reference path point sequence of the mining articulated vehicle in the preset local coordinate system is as follows: A reference point is determined, which is the point closest to the center of the front axle of the mining articulated vehicle in a preset reference path; Based on the aforementioned reference point, multiple target points are determined according to a preset reference path to obtain the reference path point sequence of the mining articulated vehicle, satisfying the following: ； In the formula, For global reference path information, This refers to the state vector of the reference path point in the global coordinate system. These represent the x-coordinate, y-coordinate, and heading angle of the reference path point in the global coordinate system. For a moment, for The value corresponding to the predicted quantity at time i. To predict the number of steps; The reference path point sequence is transformed to obtain the reference path point sequence of the mining articulated vehicle in a preset local coordinate system.

5. The method for path tracking of articulated mine vehicles based on linear model prediction according to claim 4, characterized in that, The coordinate transformation performed on the reference path point list satisfies: ； In the formula, , These are the ordinate and heading angle of the reference path point in the local coordinate system, respectively. Let x, y, and y coordinates be the x-coordinate, y-coordinate, and heading angle of the center of the front axle of the mining articulated vehicle at time t in the global coordinate system.

6. The method for path tracking of articulated mine vehicles based on linear model prediction according to claim 1, characterized in that, The process of constructing the objective function includes: Construct an initial function that satisfies: ； In the formula, Q and R are preset weight matrices to be determined. For the state tracking error term, To control input penalty items, To predict the vehicle state sequence in the time domain, This is the target state sequence of the reference path in the local coordinate system. The objective function is... The initial function is transformed using a quadratic form to obtain the objective function, which satisfies: ； In the formula, H and G are the parameters of the quadratic form. Let N(t) be the dynamic matrix, and N(t) be the compensation term. For the control sequence, t is time. To control the input matrix, Here is the state transition matrix. This is the state transition matrix after discretization. For state vectors, Let t be the state vector at time t. The value is [0 0 γ] T .

7. The method for path tracking of articulated mine vehicles based on linear model prediction according to claim 1, characterized in that, The step of determining the optimal control input of the mining articulated car at the current moment by solving the objective function includes: Based on the prediction model, solve the objective function and determine the sequence of input values ​​that minimizes the objective function; The first input value in the input value sequence is determined to be the optimal control input for the mining articulated vehicle at the current moment.

8. A path tracking system for articulated mine vehicles based on linear model prediction, characterized in that, The system includes: The data acquisition module is used to acquire the kinematic model of the mining articulated car; The first simplification module is used to simplify the kinematic model based on the physical law that the motion of the mining articulated car relative to the current vehicle body coordinate system in the prediction time domain conforms to the small angle assumption, and to obtain a preliminary simplified model. The kinematic model is simplified based on the physical law that the motion of the mining articulated car relative to the current vehicle coordinate system conforms to the small-angle assumption, including: Based on the small-angle assumption, the kinematic model is simplified. The preliminary simplified model after simplification satisfies: ； In the formula, The rate of change of the x-coordinate of the center of the front axle of the mining articulated vehicle. Let v be the rate of change of the longitudinal coordinate of the center of the front axle of the mining articulated truck, and v be the travel speed of the mining articulated truck. This refers to the heading angle of the mining articulated vehicle. The rate of change of the heading angle of the mining articulated vehicle. This refers to the distance between the front axle and the articulation point of the mining articulated vehicle. This refers to the distance between the rear axle and the articulation point of the mining articulated vehicle. It is the hinge angle. ω is the rate of change of the articulation angle, and ω is the angular velocity of the articulation. The second simplification module is used to obtain the linearized state variable model of the mining articulated car by solidifying the nominal wheelbase in the prediction time domain, performing piecewise linearization on the articulation angle in the prediction time domain, and further simplifying the preliminary simplified model based on the physical law that the change of the articulation angle of the mining articulated car is limited in the prediction time domain. The physical law that the articulation angle of a mining articulated car varies only within the prediction time domain is addressed by solidifying the nominal wheelbase within the prediction time domain, performing piecewise linearization on the articulation angle within the prediction time domain, and further simplifying the preliminary simplified model, including: Determine the nominal wheelbase for the curing process, wherein the nominal wheelbase satisfies: ； In the formula, m is a constant value corresponding to the nominal wheelbase. This refers to the distance between the front axle and the articulation point of the mining articulated vehicle. This refers to the distance between the rear axle and the articulation point of the mining articulated vehicle. The hinge angle; Based on the nominal wheelbase, the hinge angle in the prediction time domain is piecewise linearized, and the preliminary simplified model is further simplified. The preliminary simplified model after further simplification satisfies: ； In the formula, m is the nominal wheelbase and n is the proportional value; The proportional value n is calculated from the current articulation angle and sine value of the mining articulated car, and the calculation process of the proportional value n satisfies: ； The model building module is used to discretize the linearized state variable model to obtain a prediction model based on the linearized state variable model. The initial value of the prediction model is [0 0 γ]. T γ is the hinge angle; The constraint solving module is used to construct an initial function based on the prediction model and the reference path point sequence of the articulated mine vehicle in the local coordinate system, and to obtain an objective function by performing a standard quadratic transformation on the initial function. By solving the objective function, the optimal control input of the articulated mine vehicle at the current moment is determined. The reference path point sequence of the articulated mine vehicle in the local coordinate system is obtained by selecting the reference path point sequence corresponding to the prediction time domain on the preset reference path based on the reference path reference point of the articulated mine vehicle in the global coordinate system, and then transforming the reference path point sequence corresponding to the global coordinate system to the local coordinate system. The vehicle control module is used to control the mining articulated car according to the optimal control input.

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