Wheeled vehicle dynamics modeling method and system based on Li group Li algebra

Abstract

The invention discloses a wheeled vehicle dynamics modeling method and system based on Lie group Lie algebra, and relates to the technical field of vehicle dynamics modeling, and the method comprises the steps: carrying out the simplification processing of a target vehicle system structure, and obtaining a vehicle hinge system; based on the Lie group Lie algebra theory, constructing a speed recursion relation of the system; establishing a dynamic model of each rigid body in the system, and determining a mechanical state quantity recursive relation of the system by taking the kinematics state quantity of each rigid body in the system at the current moment as input; according to the inertia and the bias force of the hinged body, the acceleration recursion relation of the system is calculated through a conversion operator; and according to the speed recursion relation, the mechanical state quantity recursion relation and the acceleration recursion relation of the system, a vehicle recursion mechanical model of the target vehicle system structure is obtained. According to the method, the Lie group Lie algebra is adopted, and the recursive mechanical algorithm is applied to perform dynamic modeling on the wheeled vehicle, so that the calculation precision is ensured, and the solving efficiency of the dynamic model is improved.

Description

Technical Field

[0001] The present application relates to the technical field of vehicle dynamics modeling, and in particular to a wheeled vehicle dynamics modeling method and system based on Lie group and Lie algebra. Background Art

[0002] With the development of modern information technology, the research and development process of automobiles has also been improved and optimized under the integration of interdisciplinary technologies. Different from the traditional research and development model based on real vehicle experiments, the vehicle virtual prototype technology can effectively shorten the automobile product development cycle, reduce development costs, and improve product quality and market competitiveness by discovering problems in advance and predicting product performance. At the same time, it also enables automobile product development to better adapt to market demand and the changing needs of consumers, and has a very broad application prospect. The use of virtual prototypes to simulate vehicles under different working conditions can efficiently evaluate the driving performance of the vehicle. In the process of simulation, the subsequent vehicle motion control algorithm can also be closed-loop corrected and improved, which can effectively shorten the research and development cycle and experimental costs. As the basis for system analysis and control, the establishment of a high-precision vehicle dynamics model is the basis for ensuring the effectiveness and feasibility of simulation, and it is also of great significance for the development and improvement of vehicle performance.

[0003] However, as the requirements for accuracy and real-time performance of vehicle virtual prototype technology continue to increase, the existing vehicle dynamics models cannot take into account both refinement and real-time performance due to their low computational efficiency and cannot meet the needs of real-time simulation. Summary of the invention

[0004] The purpose of this application is to provide a wheeled vehicle dynamics modeling method and system based on Lie group Lie algebra, which can improve the calculation efficiency of the dynamics model while ensuring the calculation accuracy.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] In a first aspect, the present application provides a wheeled vehicle dynamics modeling method based on Lie group Lie algebra, comprising:

[0007] Get the target vehicle system structure.

[0008] The target vehicle system structure is simplified to obtain a simplified vehicle articulation system; the rigid bodies in the vehicle articulation system include a vehicle body, a suspension system and wheels; the constraints between the rigid bodies in the vehicle articulation system are articulation constraints; a set number of virtual bodies and virtual joints are provided in the vehicle articulation system; the virtual bodies and virtual joints are used to describe the movement of the vehicle articulation system relative to a ground reference system; the parent-child structural relationship of the motion chain in the vehicle articulation system is determined according to the articulation structure.

[0009] Based on the Lie group and Lie algebra theory, a velocity recursion relationship of a vehicle articulated system is constructed; the velocity recursion relationship is used to solve the kinematic state quantity of each rigid body in the vehicle articulated system.

[0010] A dynamic model of each rigid body in the vehicle articulated system is established, and the kinematic state of each rigid body in the vehicle articulated system at the current moment is used as input to determine the recursive relationship of the mechanical state of the vehicle articulated system; the recursive relationship of the mechanical state includes the recursive relationship between the inertia of the articulated body and the bias force.

[0011] According to the inertia of the articulated body and the bias force, the acceleration recursion relationship of the vehicle articulated system is calculated through a transformation operator; the acceleration recursion relationship is composed of the acceleration recursion relationship of the articulated joint and the rigid body.

[0012] According to the velocity recursive relationship, the mechanical state quantity recursive relationship and the acceleration recursive relationship of the vehicle articulated system, a vehicle recursive dynamics model of the target vehicle system structure is obtained.

[0013] In a second aspect, the present application provides a wheeled vehicle dynamics modeling system based on Lie group Lie algebra, comprising:

[0014] The acquisition module is used to acquire the target vehicle system structure.

[0015] A simplification processing module is used to simplify the target vehicle system structure to obtain a simplified vehicle articulation system; the rigid bodies in the vehicle articulation system include a vehicle body, a suspension system and wheels; the constraints between the rigid bodies in the vehicle articulation system are articulation constraints; a set number of virtual bodies and virtual joints are provided in the vehicle articulation system; the virtual bodies and virtual joints are used to describe the movement of the vehicle articulation system relative to a ground reference system; the parent-child structural relationship of the motion chain in the vehicle articulation system is determined according to the articulation structure.

[0016] The velocity recursion relationship construction module is used to construct the velocity recursion relationship of the vehicle articulated system based on the Lie group and Lie algebra theory; the velocity recursion relationship is used to solve the kinematic state quantity of each rigid body in the vehicle articulated system.

[0017] The mechanical state quantity recursive relationship construction module is used to establish the dynamic model of each rigid body in the vehicle articulated system, and determine the recursive relationship of the mechanical state quantity of the vehicle articulated system with the kinematic state quantity of each rigid body in the vehicle articulated system at the current moment as input; the mechanical state quantity recursive relationship includes the recursive relationship between the inertia of the articulated body and the bias force.

[0018] The acceleration recursive relationship building module is used to calculate the acceleration recursive relationship of the vehicle articulated system according to the inertia of the articulated body and the bias force through the transformation operator; the acceleration recursive relationship is composed of the acceleration recursive relationship of the articulated joint and the rigid body.

[0019] The vehicle recursive dynamics model building module is used to obtain the vehicle recursive dynamics model of the target vehicle system structure according to the velocity recursive relationship, mechanical state quantity recursive relationship and acceleration recursive relationship of the vehicle articulated system.

[0020] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0021] The present application provides a wheeled vehicle dynamics modeling method and system based on Lie group Lie algebra, the method comprising: obtaining and simplifying the vehicle system structure to reduce the complexity of the system; setting up virtual bodies and virtual joints in the system to describe the movement of the vehicle relative to the ground; determining the parent-child relationship of the kinematic chain according to the articulated structure, and clarifying the kinematic connection between the components in the system; constructing the velocity recursive relationship of the vehicle articulated system based on the Lie group Lie algebra theory to solve the kinematic state quantity of each rigid body; establishing the dynamic model of each rigid body, and determining the recursive relationship of the mechanical state quantity; calculating the acceleration recursive relationship of the vehicle articulated system through the transformation operator; integrating the velocity recursive relationship, the mechanical state quantity recursive relationship and the acceleration recursive relationship to obtain the vehicle recursive dynamics model of the target vehicle system structure. The present application uses Lie group Lie algebra to describe the motion posture of each component of the vehicle, and models the vehicle system based on recursive dynamics. This method can improve the calculation efficiency while ensuring the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0023] Figure 1 A flowchart of a wheeled vehicle dynamics modeling method based on Lie group and Lie algebra is provided in accordance with an embodiment of the present application.

[0024] Figure 2 A schematic diagram of a kinematic chain tree structure provided in one embodiment of the present application.

[0025] Figure 3 A schematic diagram of a vehicle articulation system provided in accordance with an embodiment of the present application.

[0026] Figure 4 A schematic diagram of the structure of a wheeled vehicle dynamics modeling system based on Lie group and Lie algebra provided in one embodiment of the present application. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0028] The purpose of this application is to provide a wheeled vehicle dynamics modeling method and system based on Lie group Lie algebra, which can improve the calculation efficiency of the dynamics model while ensuring the calculation accuracy.

[0029] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0030] Embodiment 1

[0031] like Figure 1 As shown, this embodiment provides a wheeled vehicle dynamics modeling method based on Lie group Lie algebra, including:

[0032] Step 101: Obtain the target vehicle system structure.

[0033] Step 102: Simplify the target vehicle system structure to obtain a simplified vehicle articulation system; the rigid bodies in the vehicle articulation system include a vehicle body, a suspension system and wheels; the constraints between the rigid bodies in the vehicle articulation system are articulation constraints; a set number of virtual bodies and virtual joints are provided in the vehicle articulation system; the virtual bodies and virtual joints are used to describe the movement of the vehicle articulation system relative to a ground reference system; the parent-child structural relationship of the motion chain in the vehicle articulation system is determined according to the articulation structure.

[0034] Step 103: Based on the Lie group and Lie algebra theory, a velocity recursion relationship of the vehicle articulated system is constructed; the velocity recursion relationship is used to solve the kinematic state quantity of each rigid body in the vehicle articulated system.

[0035] Step 104: Establish a dynamic model of each rigid body in the vehicle articulated system, and use the kinematic state of each rigid body in the vehicle articulated system at the current moment as input to determine the recursive relationship of the mechanical state of the vehicle articulated system; the recursive relationship of the mechanical state includes the recursive relationship between the inertia of the articulated body and the bias force.

[0036] Step 105: Calculate the acceleration recursive relationship of the vehicle articulation system according to the inertia of the articulated body and the bias force through a transformation operator; the acceleration recursive relationship is composed of the acceleration recursive relationship of the articulated joint and the rigid body.

[0037] Step 106: Obtain a vehicle recursive dynamics model of the target vehicle system structure according to the velocity recursive relationship, the mechanical state quantity recursive relationship and the acceleration recursive relationship of the vehicle articulation system.

[0038] In some embodiments, when step 102 is executed, the specific steps may be as follows:

[0039] The main structure of the vehicle system is simplified into the body, suspension system and wheels. The body of the target vehicle can include six degrees of freedom: longitudinal, lateral, vertical, roll, pitch and yaw. Each wheel includes two degrees of freedom: vertical bounce and rotation. For multi-axle vehicles, the number of wheels can be increased to expand the model.

[0040] According to the simplified structure of the vehicle, the complex constraints between rigid bodies are simplified to hinge constraints, and the hinge coordinates are used as the generalized coordinates q to describe the relative motion of adjacent rigid bodies. Specifically, the complex constraints between rigid bodies refer to the motion constraints and mechanical constraints of vehicle components under complex contact relationships. For example, the constraints between the vehicle body and the suspension include the rigid connection of multiple rods, the elastic connection of the shock absorber, etc. In this embodiment, the above contact relationship is simplified and processed as only two types of hinge constraints, namely, prismatic hinges and rotary hinges.

[0041] Since the vehicle articulated system has no part directly connected to the base (ground reference system) during movement, in order to describe the movement of the vehicle system relative to the ground reference system, such as Figure 3 As shown, five virtual bodies with zero mass and six virtual joints are added to the vehicle body, namely three rotational joints and three translational joints. The hinge coordinates of the virtual joints describe the movement of the vehicle body relative to the ground reference system. The added virtual joints connect the vehicle body reference system (body mass center) and the ground reference system (base) in a chain structure.

[0042] According to the articulated structure of the adjacent rigid bodies, the parent-child structural relationship of the kinematic chain is determined, that is, the tree hierarchy of the vehicle motion transmission relationship is determined step by step starting from the ground base. According to the obtained connection relationship, Figure 2 In this patent, the recursive process from the base (ground) to the tire is recorded as outward recursive process, and the reverse is recorded as inward recursive process.

[0043] According to the structure and degrees of freedom of the articulated system, the relative motion relationship of adjacent rigid bodies and the form of kinematic hinges are determined, and the Jacobian matrix S of each articulated joint is confirmed one by one according to the articulated form. i .

[0044] For prismatic hinges, S i The spinor expression is:

[0045]

[0046] For a rotary joint, S i The spinor expression is:

[0047]

[0048] The simplified processing of the vehicle system structure is completed so far. Taking the 8x8 vehicle as an example, the following is obtained: Figure 3 The vehicle articulation system is shown.

[0049] In some embodiments, when executing step 103, the specific steps may be as follows:

[0050] According to the connection mode of the articulated joints and the initial positions of each rigid body in the vehicle articulated system, the rotation transformation matrix of the adjacent rigid body coordinate system and the translation transformation matrix of the adjacent rigid body coordinate system are determined based on the Lie group and Lie algebra theory.

[0051] According to the rotation transformation matrix and the translation transformation matrix, the coordinate transformation matrix of the relative motion of adjacent rigid bodies is determined.

[0052] According to the parent-child structural relationship of the kinematic chain in the vehicle articulated system and the coordinate transformation matrix, the velocity recursive relationship of the vehicle articulated system is determined based on the recursive dynamics of the articulated body.

[0053] Specifically, according to the articulated joint connection mode and the initial position of the rigid body input by the vehicle articulated system, the rotation transformation matrix of the adjacent rigid body coordinate system is determined as:

[0054] R=R x R y R z (3).

[0055]

[0056] Among them, θ is the rotation angle of the adjacent articulated joint coordinate system, which is determined according to the initial position of the rigid body input by the model.

[0057] According to the determined articulated joint connection mode and the initial position of the rigid body input by the model, the translation transformation matrix of the adjacent rigid body coordinate system is determined as:

[0058]

[0059] Where L x , L y , L z It is the projection of the radius vector of the adjacent articulated joint on the rigid body coordinate system, which is determined according to the initial position of the rigid body input by the model.

[0060] According to the rotation transformation matrix and the translation transformation matrix, the coordinate transformation matrix T that comprehensively describes the relative motion of adjacent rigid bodies can be obtained as follows:

[0061]

[0062] Based on the recursive dynamics of the articulated body, according to the kinematic chain structure and the determined coordinate transformation matrix, the outward recursive expression of the articulated system velocity is:

[0063]

[0064] Where V i is the velocity vector of rigid body i, Ad is the adjoint operator of the Lie group, defined as:

[0065]

[0066] In the formula, T is the coordinate transformation matrix, and h is the transformed vector, which can be understood as the velocity vector V i , S i is the Jacobian matrix of the articulated joint, q i It is the generalized coordinate of the articulated joint, representing the translation or rotation angle of the corresponding joint.

[0067] At this point, the velocity recursive relationship of the vehicle system is constructed to solve the kinematic state quantities of each component in the articulated system.

[0068] In some embodiments, when executing step 104, the specific steps may be as follows:

[0069] 1) Establishing the dynamic model of each rigid body in the vehicle articulated system, specifically including:

[0070] According to the slip rate calculation formula And the side slip angle calculation formula A tire dynamics model in the vehicle articulated system is established; wherein v wx is the longitudinal velocity of the wheel, ω is the angular velocity of the wheel, R w is the wheel rolling radius, v wy is the lateral speed of the wheel.

[0071] Specifically, tires are critical components of a vehicle, and the force that affects the movement of the entire vehicle during driving is mainly generated by the interaction between the tires and the ground. This embodiment considers the interaction between the vehicle body and the tire, and uses the magic formula as an example to calculate the tire's slip rate, side slip angle, and six-component force.

[0072] In this embodiment, the Pacejka tire model is selected, and the tire test data is fitted using a trigonometric function combination formula according to the tire parameters, and the tire force and tire torque are fully expressed in a set of formulas. The tire parameters, slip rate, side slip angle and vertical load of the vehicle are input into the vehicle dynamics model, and the tire force of each wheel of the target vehicle is output.

[0073] Y(x)=Dsin{Carctan[Bx-E(Bx-arctan(Bx))]} (9).

[0074] Where Y(x) represents tire force or torque, x represents slip rate or sideslip angle, and B, C, D, and E are coefficients obtained by fitting based on vertical load, tire parameters, etc.

[0075] 2) Construct a suspension dynamics model, including:

[0076] According to the suspension spring force calculation formula F 1i =K si d i 、Suspension damping force calculation formula F 2i =C di v i 、Suspension auxiliary anti-roll force calculation formula And the suspension anti-roll force calculation formula The suspension dynamics model in the vehicle articulated system is established; wherein, F 1i is the spring force, K si is the elastic stiffness of the suspension, d i is the compression of the suspension, F 2i is the damping force, C di is the damping coefficient of the suspension, v i is the compression speed of the suspension, F 3i The K ri is the auxiliary anti-roll stiffness of the suspension, Δd i is the difference in suspension compression on both sides, D i is the wheelbase, F 4i is the anti-roll force, F yi is the tire lateral force, Δz i represents the vertical displacement of the tire, Δy i Indicates the lateral displacement of the tire.

[0077] Specifically, this embodiment uses parametric modeling to calculate the suspension force based on the K&C characteristics. Since the vehicle model of this patent assumes that the tire has only vertical bounce and rotation along the axis relative to the vehicle body, it can be obtained that there is only a vertical force transmitted by the suspension between the vehicle body and the tire, which is obtained by the suspension elastic force F 1i , damping force F 2i , auxiliary anti-roll force F 3i , anti-roll force F 4i Each part is superimposed. Therefore, the suspension force expression under K&C characteristic correction is:

[0078] F i =F 1i +F 2i +F 3i +F4i (10).

[0079] Where, spring force F 1i is the force of the spring on the wheel center position, the damping force F 2i is the damping force acting on the wheel center position, and the suspension auxiliary anti-roll force F 3i The anti-roll force F is the equivalent vertical force acting on the left and right suspensions due to the twisting of the lateral stabilizer bar caused by the body roll. 4i The roll center is regarded as a virtual force transmission point between the wheel and the vehicle body. The vertical force generated by the roll center in the process of transmitting torque to the vehicle body is equivalent to the vertical force at the connection point between the suspension and the vehicle body. It can be calculated based on the position of the roll center.

[0080] Among them, the aerodynamic model of the vehicle articulation system is constructed, including:

[0081] Specifically, the air resistance and air torque values ​​of a vehicle are usually summarized as being proportional to the dynamic pressure of the relative velocity of the airflow. According to the formula and An aerodynamic model of the vehicle articulation system is established; wherein C i is the air resistance coefficient, ρ is the air density, A is the frontal area of ​​the vehicle, L is the wheelbase, F ai is the air resistance, M ai is the air torque.

[0082] In some embodiments, when executing step 104, specifically including

[0083] After constructing the recursive relationship of the vehicle system speed, based on the Lie group and Lie algebra theory, the transformation of the articulated body inertia and bias force of adjacent rigid bodies is calculated through the transformation operator. The specific steps of the recursion are as follows:

[0084] 1) Recursively solve the inertia of the hinged body:

[0085] The inertia of the joint of a rigid body represents the rotational inertia of the system containing this rigid body under the influence of other adjacent rigid bodies and joint dynamics. According to the recursive dynamics of the joint, the inertia of the joint from the end of the kinematic chain to the rigid body can be obtained as:

[0086]

[0087] in, J is the inertia of the articulated body, which means the coupled inertia of the rigid body as a part of the articulated system; i is the moment of inertia matrix, the specific expression is J ixx , J iyy , J izz Represents the moment of inertia around the xyz axis, Jixy , J iyz , J ixz is the inertia product, I is the unit matrix, C is the sub-joint body set of rigid body i in the kinematic chain, τ i is the driving torque of each articulated joint, S i is the Jacobian matrix of the articulated joint, the subscript j corresponds to j∈C, z i is the constraint force of the hinge joint.

[0088] 2) Recursively solve the bias force inward:

[0089] According to the solved forces of each component, the external force input F of the hinge system is i ext According to recursive dynamics, the bias force of the joint can be obtained as:

[0090]

[0091] where τ i is the driving torque of each articulated joint, ad * is the adjoint operator of Lie algebra, expressed as F i ext is the external force vector input of the articulated body. For the tire, substitute the tire force and suspension force required above, and for the body, substitute the air resistance and suspension force required above.

[0092] 3) Recursively solve the joint constraint force inward:

[0093] According to the inertia of the articulated body and the bias force as input, the constraint force of each articulated joint can be obtained as:

[0094]

[0095] In some embodiments, when executing step 105, the specific steps may be as follows:

[0096] Solve the acceleration recursion relation of the system:

[0097] After obtaining the inertia and constraint force of the articulated body, the recursive relationship between the acceleration of the articulated joint and the rigid body is calculated through the transformation operator. The specific recursive steps are:

[0098] 1) Recursively solve the acceleration of each articulated joint:

[0099] According to the dynamics of the articulated body, the outward recursive formula for the acceleration of each articulated joint is:

[0100]

[0101] 2) Recursively solve the velocity of each rigid body:

[0102] The acceleration of each rigid body in the vehicle system is recursively solved, and the formula is:

[0103]

[0104] In the formula, is the first-order derivative of the velocity vector of rigid body i, that is, the acceleration vector of rigid body i.

[0105] At this point, the acceleration recursive relationship of the system is completed, and the construction of the vehicle recursive dynamics model is realized.

[0106] In addition, after the construction of the vehicle recursive dynamics model is realized, it also includes integral iteration and output of vehicle state quantity, specifically:

[0107] By inputting the partial observation data and control data of the current vehicle state into the dynamics model, the future vehicle state can be predicted based on the numerical integration method, and it also serves as the input for subsequent iterations of the vehicle dynamics model. Using the vehicle dynamics model of this patent, the displacement, speed, angular velocity, acceleration and other information of the target vehicle in various directions, as well as the vertical bounce and rotation of the wheels can be output.

[0108] Embodiment 2

[0109] like Figure 4 As shown, this embodiment provides a wheeled vehicle dynamics modeling system based on Lie group Lie algebra, including:

[0110] The acquisition module 401 is used to acquire the target vehicle system structure.

[0111] The simplification processing module 402 is used to simplify the target vehicle system structure to obtain a simplified vehicle articulation system; the rigid bodies in the vehicle articulation system include a vehicle body, a suspension system and wheels; the constraints between the rigid bodies in the vehicle articulation system are articulation constraints; the vehicle articulation system is provided with a set number of virtual bodies and virtual joints; the virtual bodies and virtual joints are used to describe the movement of the vehicle articulation system relative to the ground reference system; the parent-child level structural relationship of the motion chain in the vehicle articulation system is determined according to the articulation structure.

[0112] The velocity recursive relationship construction module 403 is used to construct a velocity recursive relationship of the vehicle articulated system based on the Lie group and Lie algebra theory; the velocity recursive relationship is used to solve the kinematic state quantity of each rigid body in the vehicle articulated system.

[0113] The mechanical state quantity recursive relationship construction module 404 is used to establish the dynamic model of each rigid body in the vehicle articulated system, and determine the recursive relationship of the mechanical state quantity of the vehicle articulated system with the kinematic state quantity of each rigid body in the vehicle articulated system at the current moment as input; the mechanical state quantity recursive relationship includes the recursive relationship between the inertia of the articulated body and the bias force.

[0114] The acceleration recursive relationship building module 405 is used to calculate the acceleration recursive relationship of the vehicle articulated system according to the inertia of the articulated body and the bias force through the transformation operator; the acceleration recursive relationship is composed of the acceleration recursive relationship of the articulated joint and the rigid body.

[0115] The vehicle recursive dynamics model building module 406 is used to obtain a vehicle recursive dynamics model of the target vehicle system structure according to the velocity recursive relationship, mechanical state quantity recursive relationship and acceleration recursive relationship of the vehicle articulation system.

[0116] In summary, this application has the following technical effects:

[0117] The present application provides a wheeled vehicle dynamics algorithm, which uses Lie group Lie algebra to describe the motion posture of each vehicle component, and models the vehicle system based on recursive dynamics. This method can improve the calculation efficiency while ensuring the calculation accuracy, and make the dynamic simulation have better real-time performance, which creates favorable conditions for the construction of simulation models and vehicle driving performance analysis in the development of wheeled vehicle systems, and has high promotion and application value.

[0118] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0119] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A wheeled vehicle dynamics modeling method based on Lie group Lie algebra, characterized in that: The wheeled vehicle dynamics modeling method based on Lie group Lie algebra comprises: Obtaining the target vehicle system structure; The target vehicle system structure is simplified to obtain a simplified vehicle articulation system; the rigid bodies in the vehicle articulation system include a vehicle body, a suspension system and wheels; the constraints between the rigid bodies in the vehicle articulation system are articulation constraints; a set number of virtual bodies and virtual joints are provided in the vehicle articulation system; the virtual bodies and virtual joints are used to describe the movement of the vehicle articulation system relative to a ground reference system; the parent-child structural relationship of the kinematic chain in the vehicle articulation system is determined according to the articulation structure; Based on the Lie group and Lie algebra theory, a velocity recursion relationship of a vehicle articulated system is constructed; the velocity recursion relationship is used to solve the kinematic state quantity of each rigid body in the vehicle articulated system; Establishing a dynamic model of each rigid body in the vehicle articulated system, and taking the kinematic state of each rigid body in the vehicle articulated system at the current moment as input, determining a recursive relationship of the mechanical state of the vehicle articulated system; the recursive relationship of the mechanical state includes a recursive relationship of the inertia of the articulated body and the bias force; According to the inertia of the articulated body and the bias force, the acceleration recursive relationship of the vehicle articulated system is calculated by the transformation operator; the acceleration recursive relationship is composed of the acceleration recursive relationship of the articulated joint and the rigid body; According to the velocity recursive relationship, the mechanical state quantity recursive relationship and the acceleration recursive relationship of the vehicle articulated system, a vehicle recursive dynamics model of the target vehicle system structure is obtained.

2. A wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 1, characterized in that: The degrees of freedom of the vehicle body in the vehicle articulation system include longitudinal, lateral, vertical, roll, pitch and yaw; the degrees of freedom of the wheels in the vehicle articulation system include vertical bounce and rotation.

3. A wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 2, characterized in that: After simplifying the target vehicle system structure to obtain a simplified vehicle articulation system, the method further includes: According to the rigid body structure and degree of freedom of the vehicle articulated system, determine the relative motion relationship of adjacent rigid bodies and the form of kinematic hinges; According to the form of kinematic hinge, determine the Jacobian matrix S of each articulated joint i ; The articulated joint is a hinged connection between two adjacent rigid bodies.

4. The wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 3, characterized in that: The Jacobian matrix S i The formula expression is: For a prismatic hinge, the Jacobian matrix S i The spinor expression is: For a revolute joint, the Jacobian matrix S i The spinor expression is:

5. The wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 4, characterized in that: Based on the Lie group and Lie algebra theory, the velocity recursion relationship of the vehicle articulated system is constructed, including: According to the connection mode of the articulated joints and the initial positions of each rigid body in the vehicle articulated system, based on the Lie group and Lie algebra theory, the rotation transformation matrix of the adjacent rigid body coordinate system and the translation transformation matrix of the adjacent rigid body coordinate system are determined; According to the rotation transformation matrix and the translation transformation matrix, the coordinate transformation matrix of the relative motion of adjacent rigid bodies is determined; According to the parent-child structural relationship of the kinematic chain in the vehicle articulated system and the coordinate transformation matrix, the velocity recursive relationship of the vehicle articulated system is determined based on the recursive dynamics of the articulated body.

6. The wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 5, characterized in that: The formula expression of the speed recursion relationship of the vehicle articulation system is: Among them, V i is the velocity vector of rigid body i, Ad is the adjoint operator of the Lie group, R = R x R y R z , θ is the rotation angle of the adjacent articulated joint coordinate system, L x , L y , L z is the projection of the radius vector of the adjacent articulated joint on the rigid body coordinate system; S i is the Jacobian matrix of the articulated joint, q i are the generalized coordinates of the articulated joint.

7. A wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 6, characterized in that: The dynamic model of each rigid body in the vehicle articulated system is established, specifically including: According to the slip rate calculation formula And the side slip angle calculation formula A tire dynamics model in the vehicle articulated system is established; wherein v wx is the longitudinal velocity of the wheel, ω is the angular velocity of the wheel, R w is the wheel rolling radius, v wy is the lateral speed of the wheel; According to the suspension spring force calculation formula F 1i =K si d i 、Suspension damping force calculation formula F 2i =C di v i 、Suspension auxiliary anti-roll force calculation formula And the suspension anti-roll force calculation formula The suspension dynamics model in the vehicle articulated system is established; wherein, F 1i is the spring force, K si is the elastic stiffness of the suspension, d i is the compression of the suspension, F 2i is the damping force, C di is the damping coefficient of the suspension, v i is the compression speed of the suspension, F 3i The K ri is the auxiliary anti-roll stiffness of the suspension, Δd i is the difference in suspension compression on both sides, F 4i is the anti-roll force, F yi is the tire lateral force, Δz i represents the vertical displacement of the tire, Δy i Indicates the lateral displacement of the tire, D i is the wheelbase; According to the formula and An aerodynamic model of the vehicle articulation system is established; wherein C i is the air resistance coefficient, ρ is the air density, A is the frontal area of ​​the vehicle, L is the wheelbase, F ai is the air resistance, M ai is the air torque.

8. The wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 7, characterized in that: The recursive relationship between the inertia of the articulated body and the bias force specifically includes: The formula expression of the recursive relationship of the articulated body inertia is: The recursive relationship of the bias force is expressed as follows: in, is the inertia of the joint, J i is the moment of inertia matrix, I is the identity matrix, C is the sub-joint set of rigid body i in the kinematic chain, τ i is the driving torque of each articulated joint, S i is the Jacobian matrix of the articulated joint, the subscript j corresponds to the summation sign j∈C, and zi is the constraint force of the articulated joint.

9. The wheeled vehicle dynamics modeling method based on Lie group and Lie algebra according to claim 8, characterized in that: According to the inertia of the articulated body and the bias force, the acceleration recursive relationship of the vehicle articulated system is calculated by transforming the operator, including: According to the formula Calculate the recursive relationship of the acceleration of the articulated joints in the vehicle articulated system; According to the formula Calculate the recursive relationship for the acceleration of the rigid body in the vehicle's articulated system.

10. A wheeled vehicle dynamics modeling system based on Lie group Lie algebra, characterized in that: include: An acquisition module, used for acquiring a target vehicle system structure; A simplification processing module is used to simplify the target vehicle system structure to obtain a simplified vehicle articulation system; the rigid bodies in the vehicle articulation system include a vehicle body, a suspension system and wheels; the constraints between the rigid bodies in the vehicle articulation system are articulation constraints; a set number of virtual bodies and virtual joints are provided in the vehicle articulation system; the virtual bodies and virtual joints are used to describe the movement of the vehicle articulation system relative to a ground reference system; the parent-child structural relationship of the kinematic chain in the vehicle articulation system is determined according to the articulation structure; A velocity recursive relationship construction module is used to construct a velocity recursive relationship of a vehicle articulated system based on the Lie group and Lie algebra theory; the velocity recursive relationship is used to solve the kinematic state quantity of each rigid body in the vehicle articulated system; A mechanical state quantity recursive relationship building module is used to establish a dynamic model of each rigid body in the vehicle articulated system, and determine the mechanical state quantity recursive relationship of the vehicle articulated system by taking the kinematic state quantity of each rigid body in the vehicle articulated system at the current moment as input; the mechanical state quantity recursive relationship includes the recursive relationship of the articulated body inertia and the bias force; An acceleration recursive relationship building module is used to calculate the acceleration recursive relationship of the vehicle articulated system through a transformation operator according to the inertia of the articulated body and the bias force; the acceleration recursive relationship is composed of the acceleration recursive relationship of the articulated joint and the rigid body; The vehicle recursive dynamics model building module is used to obtain the vehicle recursive dynamics model of the target vehicle system structure according to the velocity recursive relationship, mechanical state quantity recursive relationship and acceleration recursive relationship of the vehicle articulation system.

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