Dynamic modeling method and device for multi-axle steering multi-articulated vehicle

Abstract

The invention provides a dynamics modeling method and device for a multi-axis steering multi-hinged vehicle, and the method comprises the steps: determining the motion freedom degree of the vehicle according to the structure of the multi-axis steering multi-hinged vehicle, and determining a generalized coordinate corresponding to the motion freedom degree of the vehicle; determining a dynamic coordinate system and vehicle parameters according to the generalized coordinates; determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the whole vehicle parameters, and establishing a Lagrange equation by deriving the dynamic energy; external force borne by the vehicle is determined according to the generalized coordinates, the dynamic coordinate system and the whole vehicle parameters, and generalized force corresponding to the Lagrange equation is solved according to the external force and the virtual work principle; and establishing a vehicle dynamics model according to the generalized force and a Lagrange equation. According to the method, the precision and complexity of the vehicle dynamics model are effectively balanced, the model is high in interpretability and expansibility, the method can be used for model simulation analysis, the real vehicle test cost is reduced, and a model basis is provided for controller design.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit, and provides a dynamic modeling method and device for a multi-axle steering multi-articulated vehicle. Background Art

[0002] With the rapid advancement of urbanization, traditional means of transportation can no longer meet the growing travel demand. Public transportation such as buses, although popular, has unsatisfactory passenger capacity and operating speed. Rail transit tools such as subways and light rails can provide more efficient travel services, but they face the problems of long construction periods and high costs. The intelligent rail express system connects multiple carriages into a "train" through articulation technology to enhance bus capacity. However, due to the complex structure and motion characteristics of articulated vehicles, the design of controllers has become extremely difficult, and there is an urgent need to establish an accurate dynamic model to adapt to practical applications. Currently, most methods rely on the Newton-Euler method, perform independent force analysis on each carriage, and construct force / moment balance equations based on the Newton-Euler equations. When dealing with articulated vehicles using this method, it is necessary to model the binding forces between carriages, making the modeling process extremely complex. In addition, existing technologies often rely on a large number of simplifying assumptions, such as ignoring the body width and assuming a small articulation angle, etc. These assumptions deviate from the actual situation, resulting in the model accuracy not meeting the control requirements. Summary of the Invention

[0003] The present invention provides a dynamic modeling method and device for a multi-axle steering multi-articulated vehicle, which are used to solve the defects of complex vehicle dynamic modeling and low model accuracy in the prior art. The present invention effectively balances the accuracy and complexity of the vehicle dynamic model, has strong model interpretability and expandability, can be used for model simulation analysis, reduces the cost of real vehicle testing, and provides a model basis for controller design.

[0004] The present invention provides a dynamic modeling method for a multi-axle steering multi-articulated vehicle, including: determining the vehicle motion degrees of freedom according to the structure of the multi-axle steering multi-articulated vehicle, and determining the generalized coordinates corresponding to the vehicle motion degrees of freedom; determining the dynamic coordinate system and vehicle parameters according to the generalized coordinates; determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and establishing the Lagrange equation by taking the derivative of the dynamic energy; determining the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solving the generalized forces corresponding to the Lagrange equation according to the external forces and the principle of virtual work; establishing the vehicle dynamic model according to the generalized forces and the Lagrange equation.

[0005] A dynamic modeling method for a multi-axle steering multi-articulated vehicle provided by the present invention, wherein the dynamic coordinate system includes a world coordinate system, a vehicle coordinate system, and a tire coordinate system; the vehicle parameters include the distances between vehicle key points, vehicle angles, vehicle mass, and vehicle speed; the vehicle key points include each steering axle of the vehicle, the mass centers of each carriage, the articulation points between carriages, the virtual articulation point in front of the leading vehicle, and the virtual articulation point behind the trailing vehicle; the vehicle angles include the yaw angles of each carriage, the steering angles of each steering axle, the side slip angles of each tire, and the sideslip angle of the vehicle.

[0006] A dynamic modeling method for a multi-axle steering multi-articulated vehicle provided by the present invention, the Lagrange equation is: ; wherein, M is the mass matrix, C is the centrifugal force and Coriolis force matrix, is the generalized coordinate, is the first derivative of, is the second derivative of, is the generalized force.

[0007] A dynamic modeling method for a multi-axle steering multi-articulated vehicle provided by the present invention, the generalized force is: ; wherein, is the generalized force calculated through tire forces, k is the total number of vehicle rotation axes, i is the current vehicle rotation axis label, is the force on each tire in the world coordinate system, is the position of each tire, is the transformation matrix from the world coordinate system to the tire coordinate system, is the force on each tire in the tire coordinate system.

[0008] A dynamic modeling method for a multi-axle steering multi-articulated vehicle provided by the present invention, before establishing the vehicle dynamic model according to the generalized force and the Lagrange equation, further includes: solving the tire force according to a preset tire model, and using the tire force as the external force to solve the generalized force; solving the articulation angle damping force according to a preset articulation angle damping model, so as to establish the vehicle dynamic model according to the articulation angle damping force.

[0009] A dynamic modeling method for a multi-axle steering multi-articulated vehicle provided by the present invention, the vehicle dynamic model is: ; where M is the mass matrix, and C is the centrifugal force and Coriolis force matrix, is the generalized coordinate, is the first derivative of, is the second derivative of, is the generalized force calculated from the tire forces, is the influence of the articulated angle damper on the change of the articulated angle.

[0010] The present invention also provides a dynamic modeling device for a multi-axle steering multi-articulated vehicle, including: a first module for determining the vehicle motion degrees of freedom according to the structure of the multi-axle steering multi-articulated vehicle and determining the generalized coordinates corresponding to the vehicle motion degrees of freedom; a second module for determining the dynamic coordinate system and the vehicle parameters according to the generalized coordinates; a third module for determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and establishing the Lagrangian equation by taking the derivative of the dynamic energy; a fourth module for determining the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solving the generalized forces corresponding to the Lagrangian equation according to the external forces and the virtual work principle; a fifth module for establishing a vehicle dynamic model according to the generalized forces and the Lagrangian equation.

[0011] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where when the processor executes the computer program, it implements the dynamic modeling method for a multi-axle steering multi-articulated vehicle as described in any one of the above.

[0012] The present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the dynamic modeling method for a multi-axle steering multi-articulated vehicle as described in any one of the above.

[0013] The present invention also provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the dynamic modeling method for a multi-axle steering multi-articulated vehicle as described in any one of the above.

[0014] A dynamic modeling method and device for a multi-axle steering multi-articulated vehicle provided by the present invention. The method includes: determining the vehicle motion degrees of freedom according to the structure of the multi-axle steering multi-articulated vehicle, and determining the generalized coordinates corresponding to the vehicle motion degrees of freedom; determining the dynamic coordinate system and vehicle parameters according to the generalized coordinates; determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and establishing the Lagrangian equation by taking the derivative of the dynamic energy; determining the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solving the generalized forces corresponding to the Lagrangian equation according to the external forces and the principle of virtual work; establishing a vehicle dynamic model according to the generalized forces and the Lagrangian equation. The present invention effectively balances the accuracy and complexity of the vehicle dynamic model, has strong model interpretability and expandability, can be used for model simulation analysis, reduces the cost of real vehicle testing, and provides a model basis for controller design. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0016] Figure 1 It is a schematic flow chart of the dynamic modeling method for a multi-axle steering multi-articulated vehicle provided by the present invention.

[0017] Figure 2 It is a schematic diagram of the principle of selecting generalized coordinates provided by the present invention.

[0018] Figure 3 It is a schematic diagram of the dynamic coordinate system provided by the present invention.

[0019] Figure 4 It is a schematic diagram of the vehicle parameters provided by the present invention.

[0020] Figure 5 It is a schematic diagram of the structure of the dynamic modeling device for a multi-axle steering multi-articulated vehicle provided by the present invention.

[0021] Figure 6 It is a schematic diagram of the structure of the electronic device provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] The following further describes in detail the embodiments of the present invention in conjunction with the drawings. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0023] With the acceleration of the urbanization process in China, traditional means of transportation have been difficult to meet the growing travel needs of people. Public transportation such as buses has a low passenger capacity and a low operating speed, while rail transit tools such as subways and light rails can provide efficient travel services, but they have a long construction period and a high cost. The intelligent rail express system uses an articulated method to connect multiple carriages in series to form a "train" to improve bus capacity. However, due to its complex vehicle structure, it is difficult to analyze the motion characteristics of articulated vehicles, and the controller design is difficult. A suitable dynamic model needs to be established to meet the actual needs. Most of the existing methods are based on the Newton-Euler method, which analyzes the forces on different carriages separately and establishes force / moment balance equations according to the Newton-Euler equations. Therefore, when dealing with the articulated vehicle structure, it is necessary to model the binding forces between different carriages, and the modeling process is very cumbersome. At the same time, the existing technology usually uses a large number of assumptions to simplify the modeling process, such as ignoring the body width and assuming a small articulation angle, which does not conform to the actual situation, and the model accuracy cannot meet the control requirements. Most of the models established by the existing technology can only be applied to specific structures, with unclear physical meanings, and the established models are obscure and difficult to be used to analyze the vehicle motion characteristics.

[0024] Please refer to Figure 1 , Figure 1 which is a schematic flow chart of the dynamic modeling method for multi-axis steering multi-articulated vehicles provided by the present invention.

[0025] To solve the technical problems existing in the prior art, the present invention provides a dynamic modeling method for multi-axis steering multi-articulated vehicles, including: 101: Determine the vehicle motion degrees of freedom according to the structure of the multi-axis steering multi-articulated vehicle, and determine the generalized coordinates corresponding to the vehicle motion degrees of freedom.

[0026] In this embodiment, the vehicle motion degrees of freedom are determined according to the vehicle structure, the generalized coordinates of the dynamic vehicle system are established, the influence of the binding forces is eliminated, and the modeling process is simplified; Please refer to Figure 2 , Figure 2 which is a schematic diagram of the principle of generalized coordinate selection provided by the present invention.

[0027] The structural parameters of an articulated vehicle are reflected in the number of carriages, the number of steering axles of each carriage, the length of each carriage, and the distance from each steering axle to the centroid of the corresponding carriage. The degrees of freedom of vehicle movement need to be selected according to the modeling requirements and the vehicle's own movement characteristics, and are related to the number of carriages of the vehicle. The structure of an articulated vehicle is complex and has a large number of degrees of freedom. However, when establishing a vehicle dynamics model, it is necessary to consider the model requirements to simplify the equations. When the purpose is to analyze the basic movement laws of the vehicle and facilitate the design of the steering controller, the roll and pitch movements of the vehicle can be ignored, and a vehicle dynamics model including the degrees of freedom of longitudinal and lateral movements and yaw movement can be established. Assuming that the vehicle has n carriages, when only considering the planar movement of the vehicle, the vehicle has n + 2 degrees of freedom. The generalized coordinates of the vehicle dynamics model are the basis in the Lagrangian dynamics method and need to be reasonably selected to correspond to the degrees of freedom of vehicle movement, so as to establish a dynamics model with the least number of states and equations.

[0028] When selecting the generalized coordinates, any position of the first carriage can be combined with the yaw angles of each carriage to form complete generalized coordinates. Since the degrees of freedom of the system are the same, this position can be selected as the centroid, the position of the virtual articulation point, etc., which will not affect the establishment of the model.

[0029] 102: Determine the dynamics coordinate system and the vehicle parameters according to the generalized coordinates.

[0030] As a preferred embodiment, the dynamics coordinate system includes a world coordinate system, a vehicle coordinate system, and a tire coordinate system; the vehicle parameters include the distances between key points of the vehicle, the vehicle angles, the vehicle mass, and the vehicle speed; the key points of the vehicle include each steering axle of the vehicle, the centroid of each carriage, the articulation points between carriages, the virtual articulation point in front of the leading vehicle, and the virtual articulation point behind the trailing vehicle; the vehicle angles include the yaw angles of each carriage, the steering angles of each steering axle, the sideslip angles of each tire, and the sideslip angle of the vehicle.

[0031] Please refer to Figure 3 , Figure 3 , which is a schematic diagram of the dynamics coordinate system provided by the present invention.

[0032] In this embodiment, three coordinate systems are mainly involved in the dynamics of an articulated vehicle, namely the world coordinate system (inertial coordinate system), the vehicle coordinate system, and the tire coordinate system. The coordinate system concept is represented by the variable upper left superscript. "w" represents the world coordinate system (inertial system), "v" represents the vehicle coordinate system, and "t" represents the tire coordinate system. The vehicle coordinate system is fixed in front of the vehicle unit, and the forward direction of the vehicle is the x-axis. The tire coordinate system is fixed on each tire, and the forward direction of the tire is the x-axis. All coordinate systems follow the definition method of the right-hand coordinate system.

[0033] Please refer to Figure 4 , Figure 4 , which is a schematic diagram of the vehicle parameters provided by the present invention.

[0034] The key points of the vehicle mainly include the positions of the steering axles of the vehicle, the centroid positions of each carriage, the articulation points between the carriages, and the virtual articulation points in front of the leading vehicle and behind the trailing vehicle. Among them, the letter "A" represents the midpoint of each steering axle of the vehicle, "J" represents the virtual and real articulation points, and "G" represents the centroid of the carriage. The distance between two points is represented by l a,b a and b are arbitrary vehicle positions. The angles involved in the vehicle dynamics model mainly include the yaw angles of each carriage, the steering angles of each steering axle, the sideslip angles of each tire, and the sideslip angles at the corresponding positions of the vehicle, which are represented by , , and respectively. To further distinguish the positions of each carriage, the subscripts i and j are used to represent the i-th steering axle and the j-th carriage. Among them, for the articulation points, J1 represents the virtual articulation point in front of the leading vehicle, and J2 to J n represent the real articulation points between the carriages respectively. The input of the dynamics model is the same as the generalized coordinates, which are the longitudinal and lateral positions of the midpoint in front of the leading vehicle, and the yaw angles of each carriage unit. Assuming there are n carriages, that is: ; Among them, is the generalized coordinate, is the abscissa of the virtual articulation point in front of the leading vehicle, is the ordinate of the virtual articulation point in front of the leading vehicle, is the yaw angle of the first carriage, is the yaw angle of the n-th carriage.

[0035] The input is the steering angles of the steering axles of the vehicle. Assuming there are k steering axles, that is: ; Among them, is the steering angle of the first steering axle, is the steering angle of the k-th steering axle.

[0036] 103: Determine the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and establish the Lagrangian equation by taking the derivative of the dynamic energy.

[0037] In this embodiment, the dynamic energy of the vehicle mainly includes kinetic energy and potential energy. Considering that the movement of the articulated vehicle under study in the vertical ground direction is not obvious, the change in potential energy can be ignored. The speeds of each carriage can be calculated through the generalized coordinates and the basic kinematic relationships, and then the kinetic energy can be calculated using the kinetic energy formula.

[0038] ; where T is the kinetic energy, m1 is the mass of the first carriage, m2 is the mass of the second carriage, and m n is the mass of the nth carriage, I1 is the moment of inertia of the first carriage in the vertical direction, I2 is the moment of inertia of the second carriage in the vertical direction, and I n is the moment of inertia of the nth carriage in the vertical direction. is the square of the speed of the first carriage, is the square of the speed of the second carriage, is the square of the speed of the nth carriage, is the square of the derivative of the yaw angle of the first carriage, is the square of the derivative of the yaw angle of the second carriage, is the square of the derivative of the yaw angle of the nth carriage.

[0039] The Lagrangian function L is composed of energy, that is , and the Lagrange equation is obtained by taking the derivative of the Lagrangian function with respect to the generalized coordinates and their derivatives: ; After ignoring the potential energy V, it can be converted to: .

[0040] For the process of planning and modeling, which is convenient for expanding to any vehicle structure, the dynamic equation needs to be presented in matrix form, and the centroid velocity of each carriage can be represented by generalized coordinates. ; The carriage mass and moment of inertia are represented by matrices D1 and D2 respectively, and the kinetic energy is represented in matrix form as: ; where the mass matrix M is defined as: ; Substituting into the Lagrange equation gives: ; where R is an auxiliary matrix defined by oneself and similar to the P matrix. Thus, the centrifugal force and Coriolis force matrix C can be defined as: ; As a preferred embodiment, the Lagrange equation is: ; where M is the mass matrix, C is the centrifugal force and Coriolis force matrix, is the generalized coordinate, is the first derivative of, is the second derivative of, is the generalized force.

[0041] When solving the mass matrix and the Coriolis matrix, the accumulation method can be chosen to replace the auxiliary matrices such as P and R, and the combination of multiple carriages can be achieved through accumulation. Similarly, the calculation of kinetic energy and its derivative can be completed. There are many representation methods for the calculation of kinetic energy here, not limited to the method of auxiliary matrices, but the principle is the same.

[0042] 104: Determine the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solve the generalized force corresponding to the Lagrange equation according to the external forces and the principle of virtual work.

[0043] In this embodiment, the external forces acting on the vehicle are determined, the force application positions are represented using generalized coordinates, and the generalized force of the vehicle system is solved according to the principle of virtual work; the external forces acting on the articulated vehicle are mainly tire forces, and the carriages are also affected by the articulated angle dampers. Therefore, it is necessary to calculate the positions of each tire using generalized coordinates, which can be obtained through the position of the articulated point and the basic kinematic relationship.

[0044] ; where, are the positions of each articulated point, is the yaw angle of the i-th carriage, is the (longitudinal) distance from the j-th articulated point to the center of the i-th rotating shaft.

[0045] The right side of the Lagrangian dynamics equation is the generalized force / moment of the system, which can be calculated through the principle of virtual work; As a preferred embodiment, the generalized force is: ; where, is the generalized force calculated through the tire force, k is the total number of vehicle rotating shafts, i is the current vehicle rotating shaft label, are the forces on each tire in the world coordinate system, are the positions of each tire, is the transformation matrix from the world coordinate system to the tire coordinate system, are the forces on each tire in the tire coordinate system.

[0046] The transformation matrix can be obtained by multiplying the transformation matrix from the world coordinate system to the vehicle coordinate system and the transformation matrix from the vehicle coordinate system to the tire coordinate system, and these two transformation matrices are respectively related to the heading angle of each carriage and the steering angle of each tire: ; where, is the transformation matrix from the world coordinate system to the vehicle coordinate system, is the transformation matrix from the vehicle coordinate system to the tire coordinate system, is the yaw angle of the j-th carriage, is the steering angle of the i-th steering axle.

[0047] As a preferred embodiment, before establishing the vehicle dynamics model according to the generalized force and Lagrange equation, it further includes: solving the tire force according to the preset tire model, and using the tire force as an external force to solve the generalized force; solving the articulation angle damping force according to the preset articulation angle damping model, so as to establish the vehicle dynamics model according to the articulation angle damping force.

[0048] In this embodiment, the tire force and the articulation angle damping moment are respectively solved according to the tire model and the articulation angle damping model, and the Lagrange equation is integrated to obtain the articulated vehicle dynamics model in matrix form.

[0049] To simplify the modeling difficulty and capture the main dynamic characteristics of the system, a linear tire model and a single-track model are selected to calculate the tire force. Among them, the longitudinal force of the tire can be solved according to the current longitudinal driving torque and the tire radius r to obtain: ; The lateral force of the tire is mainly calculated based on the linear tire model. Assuming that the lateral force of the tire has a linear relationship with the tire sideslip angle, it can be calculated through the sideslip stiffness and the sideslip angle to obtain: ; The tire sideslip angle can be calculated by calculating the angle between the tire speed direction and the movement direction, and can be decomposed into the body sideslip angle and the steering angle : ; Among them, the body sideslip angle is the angle between the movement speeds of the corresponding points of the tire. The actual movement speed of the tire needs to be calculated according to the generalized coordinates and their derivatives. The tire orientation and the steering angles of each axis are related to the carriage orientation (yaw angle). The single-track model assumes that there is a virtual tire in the middle of each axis of the vehicle, and the forces on both sides of the tire are replaced by the forces on this tire. Considering that the accuracy loss caused by the actual single-track model can be ignored, the single-track model is selected to calculate the tire force to simplify the solution of the tire force.

[0050] Since the present invention clearly gives the application range of the tire model, and only the tire force needs to be calculated to complete the solution of the generalized force of the system, the use of a non-linear tire model can also complete the model construction here.

[0051] The articulated angle damper is a common device to prevent the rapid change of the articulation angle of articulated vehicles. The resulting dynamic characteristics can be directly calculated through the actuator model and are represented by in the dynamic equation, which is mainly related to the derivative of the generalized coordinates, that is, the yaw angular velocity of each carriage.

[0052] 105: Establish a vehicle dynamic model according to the generalized force and Lagrange equation.

[0053] As a preferred embodiment, the vehicle dynamic model is: ; where M is the mass matrix, C is the centrifugal force and Coriolis force matrix, is the generalized coordinate, is the first derivative of is the second derivative of is the generalized force calculated through the tire force, is the influence of the articulated angle damper on the change of the articulated angle.

[0054] From the perspective of input and output, the input variables of the dynamic model include the basic state variables, that is, the longitudinal and lateral positions of the midpoint in front of the leading vehicle, and the yaw angles of each carriage unit, as well as their derivatives (velocity and angular velocity), and the control variables, that is, the steering angles of each axle. The output variables include the longitudinal and lateral accelerations of the midpoint in front of the leading vehicle, and the angular accelerations of each carriage. Through the acceleration at the next moment, the prediction of the vehicle motion state can be iteratively realized.

[0055] The present invention uses the Lagrangian dynamics method as the basis for dynamic modeling. By selecting appropriate generalized coordinates and directly starting from the energy perspective without considering the mutual influence of internal forces in the system, it is not necessary to solve the interaction forces between carriages, that is, the constraint forces, eliminating the influence of the constraint forces and reducing the modeling difficulty. The established generalized coordinates correspond to the degrees of freedom of the system motion. By analyzing the main characteristics of the articulated vehicle motion, on the one hand, the external forces on the vehicle are deeply analyzed to accurately solve the tire forces, and on the other hand, the degrees of freedom such as the pitch of the vehicle are selectively ignored, focusing on the lateral motion characteristics of the vehicle, effectively balancing the accuracy and complexity of the model.

[0056] The present invention establishes a modeling process for articulated vehicles with clear physical meanings and distinct parameter symbols. By clearly defining the required physical coordinate systems and the parameter symbols of each position, angle, and velocity, the interpretability of the vehicle model is ensured, and the vehicle modeling process can be accurately expressed. At the same time, since the variable conversion relationships between the carriages are clarified, it is convenient to expand the vehicle dynamics model to any vehicle structure. The model expansion can be completed by expanding the generalized coordinates and supplementing the formulas accordingly, providing a model basis for the analysis of the dynamic characteristics of articulated vehicles and the design of controllers.

[0057] The present invention represents the Lagrangian dynamics model in matrix form, analyzes the actual meanings of each matrix, and simplifies the originally complex modeling process into standardized modeling steps through the design of numerous auxiliary matrices. It can be used for multi - formation vehicles with any structure, greatly reducing the cost of real - vehicle testing, improving the vehicle debugging efficiency, providing a model basis for controller design, and having a wider range of applications. Using the matrix form can greatly reduce the number of equations and simplify the repetitive processes, making the modeling process more concise and clear.

[0058] The following describes the dynamic modeling device for multi - axis - steering multi - articulated vehicles provided by the present invention. The dynamic modeling device for multi - axis - steering multi - articulated vehicles described below can be mutually referred to corresponding to the dynamic modeling method for multi - axis - steering multi - articulated vehicles described above.

[0059] Please refer to Figure 5 , Figure 5 , which is a schematic structural diagram of the dynamic modeling device for multi - axis - steering multi - articulated vehicles provided by the present invention.

[0060] The present invention also provides a dynamic modeling device for multi - axis - steering multi - articulated vehicles, including: a first module 501, configured to determine the vehicle motion degrees of freedom according to the structure of the multi - axis - steering multi - articulated vehicle and determine the generalized coordinates corresponding to the vehicle motion degrees of freedom; a second module 502, configured to determine the dynamic coordinate system and the vehicle - wide parameters according to the generalized coordinates; a third module 503, configured to determine the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system, and the vehicle - wide parameters, and establish the Lagrangian equation by taking the derivative of the dynamic energy; a fourth module 504, configured to determine the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system, and the vehicle - wide parameters, and solve the generalized forces corresponding to the Lagrangian equation according to the external forces and the virtual work principle; a fifth module 505, configured to establish the vehicle dynamics model according to the generalized forces and the Lagrangian equation.

[0061] Figure 6 Illustrates a schematic structural diagram of an electronic device, as Figure 6As shown in the figure, the electronic device may include: a processor 601, a communications interface 602, a memory 603, and a communication bus 604. Among them, the processor 601, the communications interface 602, and the memory 603 complete communication with each other through the communication bus 604. The processor 601 may call the logical instructions in the memory 603 to execute a dynamic modeling method for a multi-axle steering multi-articulated vehicle. The method includes: determining the vehicle's degrees of freedom of movement according to the structure of the multi-axle steering multi-articulated vehicle, and determining the generalized coordinates corresponding to the vehicle's degrees of freedom of movement; determining the dynamic coordinate system and the vehicle's overall parameters according to the generalized coordinates; determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system, and the vehicle's overall parameters, and establishing the Lagrange equation by taking the derivative of the dynamic energy; determining the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system, and the vehicle's overall parameters, and solving the generalized forces corresponding to the Lagrange equation according to the external forces and the principle of virtual work; and establishing a vehicle dynamic model according to the generalized forces and the Lagrange equation.

[0062] In addition, when the logical instructions in the above-mentioned memory 603 can be implemented in the form of software functional units and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the related technology, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods in various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0063] An embodiment of the present invention discloses a computer program product. The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the dynamic modeling method for a multi-axis steering multi-articulated vehicle provided in each of the above method embodiments. The method includes: determining the vehicle motion degrees of freedom according to the structure of the multi-axis steering multi-articulated vehicle, and determining the generalized coordinates corresponding to the vehicle motion degrees of freedom; determining the dynamic coordinate system and vehicle parameters according to the generalized coordinates; determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and establishing the Lagrangian equation by taking the derivative of the dynamic energy; determining the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solving the generalized forces corresponding to the Lagrangian equation according to the external forces and the principle of virtual work; establishing a vehicle dynamic model according to the generalized forces and the Lagrangian equation.

[0064] On the other hand, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is configured to execute the dynamic modeling method for a multi-axis steering multi-articulated vehicle provided in each of the above embodiments. The method includes: determining the vehicle motion degrees of freedom according to the structure of the multi-axis steering multi-articulated vehicle, and determining the generalized coordinates corresponding to the vehicle motion degrees of freedom; determining the dynamic coordinate system and vehicle parameters according to the generalized coordinates; determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and establishing the Lagrangian equation by taking the derivative of the dynamic energy; determining the external forces acting on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solving the generalized forces corresponding to the Lagrangian equation according to the external forces and the principle of virtual work; establishing a vehicle dynamic model according to the generalized forces and the Lagrangian equation.

[0065] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0066] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the related technology, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic modeling method for a multi-axle steering multi-articulated vehicle, characterized in that: include: Determining the vehicle's degrees of freedom of motion according to the structure of the multi-axle steering multi-articulated vehicle, and determining the generalized coordinates corresponding to the vehicle's degrees of freedom of motion; Determine the dynamic coordinate system and vehicle parameters according to the generalized coordinates; Determining the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the whole vehicle parameters, and establishing the Lagrangian equation by deriving the dynamic energy; Determine the external force on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solve the generalized force corresponding to the Lagrange equation according to the external force and virtual work principle; A vehicle dynamics model is established according to the generalized force and the Lagrange equation.

2. The dynamic modeling method for a multi-axle steering multi-articulated vehicle according to claim 1, characterized in that: The dynamic coordinate system includes the world coordinate system, the vehicle coordinate system and the tire coordinate system; the whole vehicle parameters include the distance between the key points of the vehicle, the vehicle angle, the vehicle mass and the vehicle speed; the key points of the vehicle include the steering axes of the vehicle, the center of mass of each car body, the hinge points between the cars, the virtual hinge point in front of the leading car and the virtual hinge point behind the trailing car; the vehicle angle includes the yaw angle of each car body, the steering angle of each steering axis, the sideslip angle of each tire and the sideslip angle of the vehicle.

3. The dynamic modeling method for a multi-axle steering multi-articulated vehicle according to claim 1, characterized in that: The Lagrange equation is: ； Where M is the mass matrix, C is the centrifugal force and Coriolis force matrix, is the generalized coordinate, for The first derivative of for The second-order derivative of is the generalized force.

4. The dynamic modeling method for a multi-axle steering multi-articulated vehicle according to claim 3 is characterized in that: The generalized force is: ； in, is the generalized force calculated from the tire force, k is the total number of rotating shafts of the vehicle, i is the current vehicle axis label, is the force on each tire in the world coordinate system, For each tire position, is the transformation matrix from the world coordinate system to the tire coordinate system, is the force on each tire in the tire coordinate system.

5. The dynamic modeling method for a multi-axle steering multi-articulated vehicle according to claim 4, characterized in that: Before establishing the vehicle dynamics model according to the generalized force and the Lagrange equation, the method further includes: Solving the tire force according to a preset tire model, using the tire force as the external force to solve the generalized force; The articulation angle damping force is solved according to a preset articulation angle damping model to suggest the vehicle dynamics model according to the articulation angle damping force.

6. The dynamic modeling method for a multi-axle steering multi-articulated vehicle according to any one of claims 1 to 5, characterized in that: The vehicle dynamics model is: ； Where M is the mass matrix, C is the centrifugal force and Coriolis force matrix, is the generalized coordinate, for The first derivative of for The second-order derivative of is the generalized force calculated from the tire force, is the effect of the hinge angle damper on the hinge angle change.

7. A dynamic modeling device for a multi-axle steering multi-articulated vehicle, characterized in that: include: The first module is used to determine the vehicle movement freedom according to the structure of the multi-axle steering multi-articulated vehicle, and determine the generalized coordinates corresponding to the vehicle movement freedom; The second module is used to determine the dynamic coordinate system and vehicle parameters according to the generalized coordinates; A third module is used to determine the dynamic energy of the vehicle according to the generalized coordinates, the dynamic coordinate system and the whole vehicle parameters, and establish the Lagrangian equation by deriving the dynamic energy; The fourth module is used to determine the external force on the vehicle according to the generalized coordinates, the dynamic coordinate system and the vehicle parameters, and solve the generalized force corresponding to the Lagrange equation according to the external force and the principle of virtual work; The fifth module is used to establish a vehicle dynamics model based on the generalized force and the Lagrange equation.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the program, the dynamic modeling method for a multi-axle steering multi-articulated vehicle is implemented as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the dynamic modeling method for a multi-axle steering multi-articulated vehicle as claimed in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the dynamic modeling method for a multi-axle steering multi-articulated vehicle as claimed in any one of claims 1 to 6 is implemented.

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