A metal wheel six-force output method and system based on a magic formula

Abstract

The application belongs to the field of data processing, and discloses a metal wheel six-component force output method and system based on a magic formula, which comprises the following steps: obtaining a plurality of discrete working condition points of a target metal wheel, and performing curve generation processing and preprocessing on the plurality of discrete working condition points to obtain a preprocessed curve; performing parameter identification processing on the preprocessed curve by using an MF model to obtain an initial parameter set, and performing parameter quality processing on the initial parameter set to obtain a target parameter set; performing continuous mapping processing on the plurality of discrete working condition points according to the target parameter set to obtain a target mapping model; obtaining current working condition data, and inputting the current working condition data into the target mapping model to obtain a metal wheel six-component force output result. The target mapping model is constructed, and the six-component force output result of the metal wheel can be accurately and efficiently output.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method, system, terminal, and computer-readable storage medium for outputting six components of force in a metal wheel based on a magic formula. Background Technology

[0002] Metal elastic wheels are used in scenarios such as lunar rovers and exploration robots, facing low gravity, low or variable friction, loose particulate media, and complex terrain. The dynamics simulation and control of the whole vehicle requires the mechanical output of the interaction between the wheel and the ground, which is usually described by six components of force.

[0003] However, most existing six-component force calculation methods are only applicable to rubber pneumatic tires and are not well adapted to the structure or ground contact characteristics of metal elastic wheels, resulting in inaccurate output of the six-component force.

[0004] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0005] The main objective of this invention is to provide a method, system, terminal, and computer-readable storage medium for outputting six components of force for metal wheels based on the magic formula. This aims to solve the problem that most existing six-component force calculation methods are only applicable to rubber pneumatic tires and are not well adapted to the structural or grounding characteristics of metal elastic wheels, resulting in inaccurate output of the six-component force.

[0006] To achieve the above objectives, the present invention provides a method for outputting six components of force in a metal wheel based on a magic formula. The method includes the following steps: Multiple discrete operating points of the target metal wheel are obtained, and curve generation and preprocessing are performed on the multiple discrete operating points to obtain a preprocessed curve. The preprocessed curve is subjected to parameter identification processing using the MF model to obtain an initial parameter set, and the initial parameter set is subjected to parameter quality processing to obtain a target parameter set. Based on the target parameter set, a target mapping model is obtained by continuously mapping multiple discrete operating points. The current working condition data is acquired and input into the target mapping model to obtain the six-component force output result of the metal wheel.

[0007] Optionally, the method for outputting six components of force for a metal wheel based on the magic formula, wherein obtaining multiple discrete operating points of the target metal wheel and performing curve generation and preprocessing on the multiple discrete operating points to obtain a preprocessed curve specifically includes: The target metal wheel is identified, and multiple discrete operating points of the target metal wheel are obtained. The discrete operating point data includes operating variables, excitation variables, and environmental or state variables. The operating condition variables include vertical load and outward tilt angle; the excitation variables include slip ratio and sideslip angle; and the environmental or state variables include temperature, settlement degree, and contact radius. Based on the discrete operating condition data, a discrete curve corresponding to each discrete operating condition point is constructed to obtain the discrete operating condition curve. The discrete operating condition curve is preprocessed to obtain a preprocessed curve. The preprocessing includes unit unification processing, coordinate direction convention processing, outlier removal processing, smoothing processing, and zero point or offset checking processing.

[0008] Optionally, the method for outputting six components of force in a metal wheel based on the magic formula, wherein the use of the MF model to perform parameter identification processing on the preprocessed curve to obtain an initial parameter set specifically includes: Determine the MF model and input the preprocessed curve into the MF model; The preprocessed curve is subjected to parameter identification processing using the magic formula in the MF model to obtain an initial parameter set, wherein the initial parameter set includes stiffness factor parameters, shape factor parameters, peak factor parameters, and curvature factor parameters. The expression for the initial parameter set is: ; in, For the initial parameter set, For stiffness factor parameters, For shape factor parameters, For peak factor parameters, For curvature factor parameters, For preprocessing curves, It is a vertical drift.

[0009] Optionally, the metal wheel six-component force output method based on the magic formula includes parameter quality processing, parameter boundary constraint processing, phased sequential fitting processing, multi-initial value optimization processing, and parameter quality control processing. The step of performing parameter quality processing on the initial parameter set to obtain the target parameter set specifically includes: Determine the preset parameter boundaries, and perform parameter boundary constraint processing on each parameter in the initial parameter set according to the preset parameter boundaries to obtain the first parameter set; A preset fitting order is determined, and the first parameter set is subjected to a phased sequential fitting process according to the preset fitting order to obtain a second parameter set; The preset fitting order, from first to last, is stiffness factor parameter fitting, peak factor parameter fitting, shape factor parameter fitting, and curvature factor parameter fitting. The second parameter set is subjected to multiple initial value optimization processing to obtain the third parameter set; The third parameter set is subjected to parameter quality control processing to obtain the target parameter set.

[0010] Optionally, the method for outputting six components of force for metal wheels based on the magic formula, wherein the step of continuously mapping multiple discrete working points according to the target parameter set to obtain a target mapping model specifically includes: A preset continuous mapping model is determined, wherein the preset continuous mapping model includes a regression model or an interpolation model; The regression models include linear regression models, multinomial regression models, regression models with regularization terms, kernel regression models, radial basis function regression models, Gaussian Process regression models, and neural network regression models. The interpolation models include piecewise linear interpolation models, spline interpolation models, bilinear or bicubic interpolation models, and interpolation models based on Delaunay triangulation. The target parameter set is input into the preset continuous mapping model, and the target parameter set is continuously mapped and modeled through the preset continuous mapping model to obtain the target mapping model.

[0011] Optionally, the method for outputting six components of force for metal wheels based on the magic formula, wherein the step of continuously mapping multiple discrete working points according to the target parameter set to obtain a target mapping model, further includes: Perform quadratic surface regression on the target mapping model to obtain the parametric quadratic surface corresponding to each parameter in the target parameter set; The expression for the parametric quadratic surface is as follows: ; in, The parametric quadratic surface corresponding to each parameter. The vertical load is... The outward tilt angle is... , All are coefficients of quadratic terms. and All are coefficients of linear terms. This is a constant term.

[0012] Optionally, the method for outputting the six components of force on a metal wheel based on the magic formula, wherein acquiring current working condition data and inputting the current working condition data into the target mapping model to obtain the output result of the six components of force on the metal wheel specifically includes: Obtain the current operating condition data and input the current operating condition data into the target mapping model to obtain the current parameter set; The current parameter set is input into the MF model, and the six-component force output result of the metal wheel is output.

[0013] Furthermore, to achieve the above objectives, the present invention also provides a six-component force output system for metal wheels based on a magic formula, wherein the six-component force output system for metal wheels based on a magic formula includes: The discrete working condition point processing module is used to acquire multiple discrete working condition points of the target metal wheel, and to perform curve generation and preprocessing on the multiple discrete working condition points to obtain a preprocessed curve. The parameter processing module is used to perform parameter identification processing on the preprocessed curve using the MF model to obtain an initial parameter set, and to perform parameter quality processing on the initial parameter set to obtain a target parameter set. The mapping model generation module is used to perform continuous mapping processing on multiple discrete working points according to the target parameter set to obtain a target mapping model. The six-component force output module is used to acquire the current working condition data and input the current working condition data into the target mapping model to obtain the six-component force output result of the metal wheel.

[0014] Furthermore, to achieve the above objectives, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a magic formula-based metal wheel six-component force output program stored in the memory and executable on the processor, wherein when the magic formula-based metal wheel six-component force output program is executed by the processor, it implements the steps of the magic formula-based metal wheel six-component force output method as described above.

[0015] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a metal wheel six-component force output program based on the magic formula, and when the metal wheel six-component force output program based on the magic formula is executed by a processor, it implements the steps of the metal wheel six-component force output method based on the magic formula as described above.

[0016] In this invention, multiple discrete operating points of the target metal wheel are acquired, and curve generation and preprocessing are performed on these discrete operating points to obtain preprocessed curves. A mean-factor (MF) model is used to identify parameters in the preprocessed curves to obtain an initial parameter set, and parameter quality processing is performed on the initial parameter set to obtain a target parameter set. Continuous mapping processing is then performed on the multiple discrete operating points based on the target parameter set to obtain a target mapping model. Current operating condition data is acquired and input into the target mapping model to obtain the six-component force output result of the metal wheel. This invention acquires the curves corresponding to the discrete operating points of the metal wheel, fits the curves to obtain multiple fitting parameters, and then performs quality control on the fitting parameters to construct a target mapping model. This target mapping model can accurately and efficiently output the six-component force output result of the metal wheel. Attached Figure Description

[0017] Figure 1 This is a flowchart of a preferred embodiment of the metal wheel six-component force output method based on the magic formula of the present invention; Figure 2 This is a schematic diagram illustrating the influence of parameter B (stiffness factor) on the shape of the magic formula curve in a preferred embodiment of the six-component force output method for metal wheels based on the magic formula of the present invention. Figure 3 This is a schematic diagram illustrating the influence of parameter C (shape factor) on the shape of the magic formula curve in a preferred embodiment of the six-component force output method for metal wheels based on the magic formula of the present invention. Figure 4 This is a schematic diagram illustrating the influence of parameter D (peak factor) on the shape of the magic formula curve in a preferred embodiment of the six-component force output method for metal wheels based on the magic formula of the present invention. Figure 5 This is a schematic diagram illustrating the influence of parameter E (curvature factor) on the shape of the magic formula curve in a preferred embodiment of the six-component force output method for metal wheels based on the magic formula of the present invention. Figure 6 This is a structural diagram of a preferred embodiment of the metal wheel six-component force output system based on the magic formula of the present invention; Figure 7 This is a structural diagram of a preferred embodiment of the terminal of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0019] Metallic elastic wheels are used in scenarios such as lunar rovers and exploration robots, facing low gravity, low or variable friction, loose particulate media, and complex terrain. Vehicle dynamics simulation and control (including traction control, braking, path tracking, and stability) requires the mechanical output of the wheel-ground interaction, typically described using six force components, including: longitudinal force. F x Lateral force F y Normal force F z Overturning torque M x Rolling resistance torque M y , backing torque M z .in, F x , F y , M z It has the greatest impact on the vehicle's traction, lateral handling stability, and steering return characteristics, and is also related to slip ratio. k Side slip angle α outward tilt angle c and vertical load F z There is a strong nonlinear relationship between them.

[0020] In engineering, both accuracy (i.e., conforming to test / simulation data) and speed (i.e., applicable to real-time / quasi-real-time simulation of vehicle multibody dynamics) are required. Furthermore, it is desirable to be able to quickly reuse the data under different wheel types, different lunar soil parameters, and different mission conditions. Therefore, a configurable and encapsulated six-component force output method is needed.

[0021] Existing technologies include: 1. Semi-empirical tire model: The Pacejka magic formula (i.e. MF model) and UniTire are mature for rubber pneumatic tires, but they are not well adapted to the structural / ground contact characteristics of metal elastic wheels.

[0022] 2. High-precision numerical methods: Finite element / discrete element method and its coupling with multibody dynamics offer high precision but have high computational costs, making them unsuitable for rapid iteration and large-scale working condition scanning.

[0023] 3. Lookup table interpolation: Sampling and interpolating for finite operating conditions is simple to implement in engineering, but it is difficult to balance accuracy, smoothness and range expansion.

[0024] The disadvantages of existing technologies are as follows: 1. Limited applicability: Discrete fitting / table lookup often only covers a limited range of applications. F z , cThe model needs to be re-collected and rebuilt when the task conditions change or the wheel type is updated.

[0025] 2. The fitting of MF parameters is unstable: B , C , D , E With strong parameter coupling, one-time nonlinear fitting of all parameters is prone to getting trapped in local optima or producing physically unreasonable parameters.

[0026] 3. Lack of "arbitrary working condition input" interface: The lack of a parameter prediction mechanism from discrete working conditions to continuous working conditions leads to complex simulation calls.

[0027] To address the aforementioned problems, this invention proposes a method for outputting six components of force in a metal wheel based on a magic formula. F x , F y , M z Core output (longitudinal force) F x Lateral force F y , backing torque M z The methods include: 1. At discrete operating points (by ( F z , c (Construction) Acquisition of curve data (i.e., the preprocessed curve in this invention): k - F x , α - F y , α - M z ; 2. For each discrete operating point, the parameters are obtained by fitting using MF (stiffness factor parameter). B (i.e., the stiffness factor parameter in this invention) 、C (i.e., the shape factor parameter in this invention) 、D (i.e., the peak factor parameter in this invention) 、E (i.e., the curvature factor parameter in this invention), and through parameter boundary constraints + staged sequential fitting (i.e., according to...) BDC (Fitting in sequence) + multi-start optimization + amplitude / zero alignment to improve stability; 3. Obtained from discrete operating conditions B、C、D、E Further analysis of operating condition variables ( F z , cEstablish a continuous mapping (preferably using quadratic surface regression) to obtain B ( F z , c ), C ( F z , c ), D ( F z , c ), E ( F z , c ), that is, the target mapping model; 4. Within the dataset coverage area, for any input ( F z , c , k , α (i.e., current operating condition data) Quickly calculate and output F x , F y , M z It also provides a strategy for handling superdomain inputs.

[0028] Results: With configurable applicability, it can achieve fast, smooth and encapsulated core six-component force output, significantly reducing refitting / reconstruction costs.

[0029] The preferred embodiment of the present invention describes a method for outputting six components of force in a metal wheel based on a magic formula, such as... Figure 1 As shown, the method for outputting six components of force in a metal wheel based on the magic formula includes the following steps: Step S10: Obtain multiple discrete working points of the target metal wheel, and perform curve generation and preprocessing on the multiple discrete working points to obtain a preprocessed curve.

[0030] The overall structure of this invention progresses from discrete to continuous computation, and then to online computation. The method of this invention can be broken down into two main chains: 1. Offline calibration link (modeling / training), the implementation process is as follows: discrete working condition data → MF parameter identification → parameter quality control → continuous mapping of parameters with working conditions → generation of deployable model (coefficient / parameter file); 2. Online call chain (inference / simulation), the implementation process is as follows: input any working condition → query / calculate BCDE (And drift term) → Substitute into MF → Output F x , F y , Mz (Extendable to six-part force).

[0031] The logical relationship between the two links is as follows: the online call strictly depends on the "parameter mapping model / coefficients" produced by the offline calibration, and the applicable domain of the online output is constrained by the coverage domain of the offline calibration data (this domain can be expanded by adding data and re-regressed to achieve a "configurable range").

[0032] Specifically, a target metal wheel is identified, and multiple discrete operating points of the target metal wheel are obtained. The discrete operating point data includes operating variables, excitation variables, and environmental or state variables. The operating variables include vertical load and camber angle. The excitation variables include slip ratio and sideslip angle. The environmental or state variables include temperature, indentation degree, and contact radius.

[0033] This invention acquires or constructs a dataset of wheel-ground interaction between a metal wheel (i.e., the target metal wheel in this invention) and multiple discrete operating conditions (i.e., discrete operating condition data in this invention), wherein the discrete operating conditions are at least determined by vertical loads. F z With outward tilt c The dataset consists of, and at least contains, longitudinal forces. F x Lateral force F y , backing torque M z One of the factors with slip ratio k or side deflection angle α The curve showing the change.

[0034] The data sources for the wheel-ground interaction dataset in this invention include experimental data, discrete element simulation data, finite element simulation data, or combinations thereof, and the units, coordinate systems, and symbols of the different data sources are standardized before parameter identification.

[0035] Input variable grouping (i.e., discrete operating condition data grouping) divides the variables into three groups for easier subsequent hierarchical modeling: 1. Operating condition variables (determining parameter mapping) include: vertical load. F z and outward tilt c (This may also include: speed) v Equivalent friction m Soil parameter set s and wheel type parameter set w ); 2. The incentive variables (which determine the horizontal axis of the curve) include: slip ratio. k (For longitudinal force curves), sideslip angle α (Used for lateral force / correction moment curves); 3. Environmental / state variables (optional as compensation terms) include: temperature, degree of settlement, and contact radius. Re If such variables have a significant impact, they can be used as independent variables in the extended mapping or as post-processing terms in the output.

[0036] It is understood that the discrete data in this invention is mainly obtained from simulation data, with each working condition corresponding to a set of simulations and simulation data.

[0037] The output variable is: F x ( F z , c , k ), F y ( F z , c , α ), M z ( F z , c , α In fact, only the Magic Formula (MF) fits the data. F x , F y , M z , M x and M y There is no corresponding fitted curve; you can directly use the formula in the Magic Formula (MF) to find it.

[0038] This invention defines a "configurable range," which (i.e., applicable range) is not defined as a fixed numerical interval, but rather as: determined by the coverage domain Ω of the calibration dataset, and is configurable or extensible, expressed as: Ω=Ω Fz，γ ×Ω κ ×Ω α ; Where Ω represents the applicable scope / coverage of the model, which is "the set of operating conditions covered by the calibration data"; Ω Fz，γ In order to be in F z and c Coverage area in these two dimensions (a 2D region); Ω κ slip ratio k The allowable range (usually an interval); Ω α Side slip angle α The allowed range (usually a range);F z This is a vertical load. c The outward tilt angle (inclination angle); k It is the slip ratio (longitudinal slip); α It is the sideslip angle (lateral slip angle).

[0039] The above formula means combining the various subdomains into a higher-dimensional domain. In other words, a complete set of "usable working conditions" consists of three parts: 1. A two-dimensional covering domain Ω of load and outward tilt. Fz，γ Slip ratio allowable range Ω κ Side slip angle allowable range Ω α , Just enter ( F z , c , k , α If a value falls within all three of these ranges, it is considered to be within Ω. In the engineering implementation, the boundaries (or convex hull / mesh) of Ω need to be saved for online determination of whether the domain is exceeded.

[0040] Based on the discrete operating condition data, a discrete curve corresponding to each discrete operating condition point is constructed to obtain the discrete operating condition curve.

[0041] The first step is to obtain the set of discrete operating point values. The expression for the set of discrete operating point values ​​is: G ={( F z , i , c j Each operating point should correspond to at least three types of curve data: {( k , F x )}、{( α , F y )}as well as{( α , M z )}.

[0042] in, G ={( F z , i , c j )} represents the set of discrete operating point values, with subscripts... i , j This indicates that several discrete combination points were taken at different vertical load settings and different outward tilt angle settings; k , F x ) indicates a fixed operating point ( Fz , i , c j The longitudinal force curve data collected under the following conditions is: Input k Output F x ; ( α , F y () represents a pair of lateral force curve data, the input is... α The output is F y ; ( α , M z This indicates a pair of data for the aligning torque curve; the input is... α The output is M z .

[0043] Logical relationship: Only when each ( F z , i , c j All of these can yield a set of MF parameters (i.e.) B、C、D、 E) is necessary to subsequently address ( F z , c Therefore, the coverage quality of discrete operating points directly determines the reliability and configurable range of the "continuous mapping".

[0044] This is a regressive data processing approach, and the implementation steps are as follows: 1. First, select the set of discrete operating points. G (e.g., different) F z , c Scattered data).

[0045] 2. At each discrete operating point ( F z , i , c j The following requires three types of curve data (i.e., the preprocessed curves in this invention): F x -k curve, F y -α curve, M z -α curve.

[0046] 3. For each operating point, perform parametric fitting (using MF) on these curves to obtain a set of parameters (i.e., the initial parameter set in this invention, such as...). B, C, D, E wait).

[0047] Only when each discrete point ( F z , i , c j Only when a stable set of parameters is obtained can these parameters be used as samples in the next step to analyze (the data). F z , c Perform continuous interpolation.

[0048] The discrete operating condition curve is preprocessed to obtain a preprocessed curve. The preprocessing includes unit unification processing, coordinate direction convention processing, outlier removal processing, smoothing processing, and zero point or offset checking processing.

[0049] The data preprocessing process is as follows: 1. Standardize units and coordinate directions (standardization) α positive direction, Fy positive direction, k 1. Define the method); 2. Remove and smooth out anomalies; 3. Perform zero-point / bias checks ( k When =0, F x Is it close to 0? α When =0, F y , M z Is it close to 0?

[0050] In other words, this invention requires processing the discrete data points to be processed. The coordinate direction only needs to be defined as the positive direction, and obviously irregular data points in the discrete data are removed. Smoothing processing refers to selecting appropriate discrete data for fitting based on the curve trend.

[0051] The zero-point offset check process is as follows: when k When = 0, determine F x Is it close to 0, when α When = 0, determine F y , M z Whether it is close to 0, otherwise horizontal or vertical slippage will occur.

[0052] Logical relationship: The purpose of preprocessing is to ensure that the objective function is interpretable, the parameters do not diverge, and the parameters are comparable under different operating conditions during the subsequent MF parameter identification.

[0053] Step S20: The preprocessed curve is subjected to parameter identification processing using the MF model to obtain an initial parameter set. The initial parameter set is then subjected to parameter quality processing to obtain a target parameter set. The parameter quality processing includes parameter boundary constraint processing, staged sequential fitting processing, multi-initial-value optimization processing, and parameter quality control processing.

[0054] This invention employs the MF equation to identify parameters of the curve corresponding to each discrete operating point, thereby obtaining a set of MF parameters corresponding to that discrete operating point. The set of MF parameters includes at least... B , C , D , E One of the steps; further, parameter quality control is performed on the obtained MF parameter set to remove or reduce the weight of abnormal parameter samples.

[0055] In this invention, curve parametric fitting adopts the magic formula parametric form, and the parameter set includes... B , C , D , E At least one of the following and an optional bias parameter.

[0056] Specifically, an MF model is determined, and the preprocessed curve is input into the MF model; the preprocessed curve is subjected to parameter identification processing through the magic formula in the MF model to obtain an initial parameter set, wherein the initial parameter set includes stiffness factor parameters, shape factor parameters, peak factor parameters, and curvature factor parameters; The expression for the initial parameter set is: ; in, For the initial parameter set, For stiffness factor parameters, For shape factor parameters, For peak factor parameters, For curvature factor parameters, For preprocessing curves, It is a vertical drift.

[0057] Regarding the selection of the MF model and the meaning of its parameters (laying the groundwork for the subsequent "sequential fitting"), we first need to determine the basic MF form. For any output Y, the expression is: ; ; in, , For initial data, The type of the input variable;D The peak / saturation value scale (directly determines the force / moment amplitude); B For small input segment stiffness (strongly correlated with slope near zero); C For the overall shape (determines the "degree of bending / saturation speed"); E For curvature details and nonlinear corrections (which are prone to divergence and require constraints / postfitting); S h , S v For bias and drift (used for zero-point alignment and asymmetry compensation), where, S h For the horizontal drift of the curve, S v It is a vertical drift.

[0058] Logical relationship: It is necessary to understand what each parameter "controls" in order to design a stable staged fitting, thereby ensuring the success rate of fitting discrete working point and improving the usability of subsequent regression mapping.

[0059] for B、C、D、E The influence of parameters is analyzed as follows: First, in order to deeply understand the regulatory role of various parameters in the magic tire model on the shape of the mechanical response curve, this invention examines the parameters. B (Stiffness factor) C (shape factor) D (Peak factor) and E The effect of changes in the curvature factor on the output curve.

[0060] like Figure 2 As shown: B The parameters determine the slope of the initial segment of the curve, i.e., the response speed when the input variable (slip ratio or sideslip angle) is small. B The larger the value, the steeper the initial part of the curve, reflecting that the system is more sensitive to small disturbances; B When the value is small, the response is slower, and the force changes more gradually with the input.

[0061] like Figure 3 As shown: C The parameters control the overall shape and steepness of the curve. Larger... C The value makes the curve sharper, and the changes near the peak more concentrated; C When the value is small, the response curve becomes smoother and flatter, exhibiting a wider force-input distribution characteristic.

[0062] like Figure 4 As shown: D The parameters directly determine the peak amplitude of the output force or torque, that is, the highest point of the curve. DThe larger the value, the stronger the output force, reflecting the enhanced maximum interaction capacity between the wheel and the ground; this parameter is closely related to the structural stiffness and ground contact capability of the wheel.

[0063] like Figure 5 As shown: E Parameters affect the asymmetry and tilt / sag characteristics of the output curve. When E When >0, the curve tilts slightly forward, and the peak appears earlier; when E When the value is less than 0, the curve tilts backward, exhibiting stronger nonlinear hysteresis characteristics. This is often used to describe the "hysteresis grip" or hysteresis mechanical effect of wheels on soft terrain.

[0064] Furthermore, for discrete operating condition MF parameter identification (core: stability, repeatability), an objective function and weighting strategy are required. A loss is defined for each curve, expressed as: ;in, ; Formula meaning: From all candidate parameters Find a set of values ​​that minimizes the sum of the weighted squared errors between the "model output" and the "data observation". Indicates the parameter Optimize (find the optimal parameters); Indicates to N The sum of the errors of each sampling point / data point; Indicates the first n Input Below is the actual output given by the data (obtained by measurement or simulation); Indicates the first n Input Below, the MF model (or parametric model) uses parameters The calculated output. The square in the formula is used to prevent positive and negative errors from canceling each other out; Indicates the first n The weights of each data point control the importance of that point in the fit.

[0065] Determine the preset parameter boundaries, and perform parameter boundary constraint processing on each parameter in the initial parameter set according to the preset parameter boundaries to obtain the first parameter set.

[0066] The expression for the parameter boundary constraint (configurable) is as follows: ; The parameter boundaries are automatically generated by empirical, statistical, or prior fitting methods and are configurable.

[0067] A preset fitting order is determined, and the first parameter set is subjected to a phased sequential fitting process according to the preset fitting order to obtain a second parameter set; wherein, the preset fitting order is, in order from first to last, stiffness factor parameter fitting, peak factor parameter fitting, shape factor parameter fitting, and curvature factor parameter fitting. The parameter identification in this invention adopts a staged sequential fitting strategy, according to... B → D → C → E The parameters are updated sequentially, and upper and lower bound constraints are set for the parameters at least in one stage.

[0068] Staged sequential fitting BDC The process is as follows: 1. Initialization: D Initial value: Take the absolute value of the peak / saturation value of the data (corrected by sign); S v Initial value: Take the mean value near x=0 (usually 0 or approximately 0); B Initial value: estimated from the slope near zero (or given multiple initial values); 2. Fitting B (locking C , D , E (or given a coarse value): Objective: To match the slope near zero with the initial growth segment, avoiding premature fitting. E This causes the curve to become distorted.

[0069] 3. Fitting D : Objective: Align peak / saturation values ​​to ensure correct amplitude.

[0070] 4. Fitting C : Objective: Adjust the overall shape to ensure a smooth transition zone.

[0071] 5. Fitting E : Objective: To make final corrections to curvature and details, and to check... E Is it approaching the boundary? (If it is, trigger reinitialization or reduce the degree of freedom.)

[0072] The second parameter set is subjected to multiple initial value optimization processing to obtain the third parameter set.

[0073] In this invention, multiple initial value optimization is used to identify parameters for each discrete working point, and the parameter set that satisfies the minimum error and meets the preset physical consistency condition is selected from multiple candidate results.

[0074] The process of multi-start optimization (to improve robustness) is as follows: repeat the above fitting process KKK times (with different initial values / perturbations) for each working point, and select the set of parameters that has the minimum loss and satisfies the physical constraints.

[0075] The third parameter set is subjected to parameter quality control processing to obtain the target parameter set.

[0076] The parameter quality control in this invention includes at least one or a combination of the following criteria: fitting error threshold, peak error threshold, zero error threshold, slope error threshold, parameter edge criterion, and monotonicity / singularity criterion.

[0077] Furthermore, the parameter quality control (QC) in this invention includes the following: Output fitting quality metrics for each discrete operating point, including: R2 or normalized RMSE; peak error, zero-point error, slope error, and whether the parameters touch the boundary (if they are close to the boundary, they are marked as low confidence).

[0078] Logical relationship: The role of QC is to "determine whether this operating point should proceed to the next regression step." Without QC, a small number of bad fits will significantly worsen the regression. B ( F z , c Surfaces such as curved surfaces cause overall distortion in the output under any online operating condition.

[0079] Step S30: Perform continuous mapping processing on multiple discrete working points according to the target parameter set to obtain the target mapping model.

[0080] This invention constructs a continuous mapping model of MF parameters with respect to operating condition variables based on parameter samples obtained through quality control, enabling MF parameters to be derived from any input operating condition (…). F z , c The value is calculated through regression and / or interpolation, wherein the continuous mapping model in this invention is a deployable model.

[0081] Specifically, a preset continuous mapping model is determined, wherein the preset continuous mapping model includes a regression model or an interpolation model; the regression model includes a linear regression model, a multinomial regression model, a regression model with a regularization term, a kernel regression model, a radial basis function regression model, a Gaussian Process regression model, and a neural network regression model; the interpolation model includes a piecewise linear interpolation model, a spline interpolation model, a bilinear or bicubic interpolation model, and an interpolation model based on Delaunay triangulation; the target parameter set is input into the preset continuous mapping model, and the target parameter set is continuously mapped and modeled through the preset continuous mapping model to obtain the target mapping model.

[0082] The continuous mapping model in this invention is a regression model and / or an interpolation model. The regression model includes at least one of linear regression, multinomial regression, regression with regularization, kernel regression, radial basis function regression, Gaussian Process regression, or neural network regression. The interpolation model includes at least one of piecewise linear interpolation, spline interpolation, bilinear / bicubic interpolation, and interpolation based on Delaunay triangulation.

[0083] The continuous mapping model in this invention models parameters separately, so that... B ( F z , Y ), C ( F z , Y ), D ( F z , Y ), E ( F z , Y The outputs are respectively from the corresponding regression or interpolation models. Parameter mapping: that is, from discrete... BCDE Convert to continuous BCDE .

[0084] For the regression object and dimension, this invention applies a different type of output ( F x , F y , M z By establishing mappings respectively, we obtain: B = B ( F z , c ), C = C ( F z, c ), D=D ( F z , c ), E=E ( F z , c The rationale for this is that the parameters for longitudinal and lateral / alignment directions typically differ, and modeling them separately provides greater stability.

[0085] The continuous mapping model set in this invention requires setting weights for parameter samples during construction. These weights are determined by the quality control results or by the sample density of discrete operating points.

[0086] Furthermore, quadratic surface regression is performed on the target mapping model to obtain the parametric quadratic surface corresponding to each parameter in the target parameter set.

[0087] The expression for the parametric quadratic surface is as follows: ; in, The parametric quadratic surface corresponding to each parameter. The vertical load is... The outward tilt angle is... , All are coefficients of quadratic terms. and All are coefficients of linear terms. This is a constant term.

[0088] Furthermore, by adding a regular expression, the expression becomes: Used to prevent overfitting when data is sparse.

[0089] in, For data fitting terms, The target quantity observed in the data (e.g., a parameter value, a force / torque, etc.); The predicted value given by the model (from the input) n and parameters a (Calculated); The summation of squared errors indicates that the overall prediction should fit the data as closely as possible.

[0090] in, For regularization terms, Let be the parameter vector to be fitted. It usually refers to the square of the L2 norm, expressed as: Where λ≥0 represents the regularization strength (hyperparameter); λ=0 represents degeneration into ordinary least squares fitting; the larger λ is, the smoother and more conservative the model is, but it may be underfitting.

[0091] By introducing a regularization term, this invention can solve the problem of data overfitting, making the model smoother and the values ​​more stable, which is especially useful when the independent variables are highly correlated.

[0092] Step S40: Obtain the current working condition data and input the current working condition data into the target mapping model to obtain the six-component force output result of the metal wheel.

[0093] This invention allows for online input of arbitrary operating condition data ( Fz , c , k , α First, the MF parameters are calculated using the continuous mapping model, and then the MF parameters are substituted into the MF equations to calculate the results. Fx ( Fz , c , k ), Fy ( Fz , c , α ), Mz ( Fz , c , α ).

[0094] This invention is based on the above Fx , Fy , Mz And the additional output model outputs six components of the metal wheel force, said six components of the force including at least ( F z , F y , F z , M x , M y , M z ),in, F z The input is obtained from vertical dynamics or contact models, and M x and M y It is obtained from the output of the mapping model or from the calculation of force and lever arm.

[0095] Furthermore, the present invention outputs six component forces and applicable domain indicator information, wherein the applicable domain indicator information is obtained by determining the domain of the offline calibration data coverage Ω and the domain of the online input working condition.

[0096] Specifically, the current working condition data is acquired and input into the target mapping model to obtain the current parameter set; the current parameter set is input into the MF model to output the six-component force output result of the metal wheel.

[0097] It is understood that in this invention, the coverage area Ω is determined by the set of discrete operating points. M y The rolling resistance torque mapping model is output from the rolling resistance torque mapping model. F z , c and equivalent rolling radius Re At least one of them is an independent variable. In this invention... M x Output from the lateral force application point lever arm mapping model, the lever arm mapping model is based on F z and c At least one of them is an independent variable.

[0098] The steps for online calculation are as follows: 1. Input check: Read current operating condition data ( F z , c , k , α ), and determine whether it is within Ω; 2. Calculation parameters: obtained from the regression model. B , C , D , E ; 3. Substitute into the MF model: using k have to F x ;use α have to F y , M z .

[0099] Furthermore, the six component forces are solved and completed as follows: F z As input, the output can be given directly or by the suspension model; M y Mapped by rolling resistance coefficient cr ( F z , c , )get; M xObtained by simplification or fitting mapping of lateral force application point / pressure distribution; Their common logic remains: discrete data → parameterization / mapping → fast online output.

[0100] In addition, possible modifications to this invention include: 1. It is possible that quadratic surfaces will no longer be used and interpolation will be used instead, so it should be described as "continuous mapping (regression / interpolation / surface mapping, etc.)", with quadratic surfaces being the preferred embodiment; 2. May not be needed B , C , D , E Instead, it uses a different set of parameters, so it should be summarized as "full parameter set / shape parameter set" and support phased and gradual optimization based on parameter sensitivity; 3. It is possible to change the operating condition variables from ( F z , c If we change it to another combination, it should be expressed as "the working condition variables include at least one of vertical load and outward tilt angle, and can be extended to at least two of the following: load, outward tilt, speed, friction, soil parameters and wheel type parameters"; 4. May only output F x , F y Without output M z Therefore, it is necessary to M z As an independent and optional core output, it is written and implemented by covering the "expandable output of other component forces / torques", thus forming a broad coverage and implementation support for the method chain as a whole.

[0101] Furthermore, such as Figure 6 As shown, based on the above-mentioned method for outputting six components of force to a metal wheel based on the magic formula, the present invention also provides a system for outputting six components of force to a metal wheel based on the magic formula, wherein the system for outputting six components of force to a metal wheel based on the magic formula includes: The discrete working condition point processing module 51 is used to acquire multiple discrete working condition points of the target metal wheel, and to perform curve generation processing and preprocessing on the multiple discrete working condition points to obtain a preprocessed curve. The parameter processing module 52 is used to perform parameter identification processing on the preprocessed curve using the MF model to obtain an initial parameter set, and to perform parameter quality processing on the initial parameter set to obtain a target parameter set. The mapping model generation module 53 is used to perform continuous mapping processing on multiple discrete working points according to the target parameter set to obtain a target mapping model. The six-component force output module 54 is used to acquire the current working condition data and input the current working condition data into the target mapping model to obtain the six-component force output result of the metal wheel.

[0102] Furthermore, such as Figure 7 As shown, based on the above-mentioned method and system for outputting six-component force of a metal wheel based on the magic formula, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 7 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0103] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, SmartMediaCard (SMC), SecureDigital (SD) card, or FlashCard. Furthermore, the memory 20 may include both internal and external storage devices. The memory 20 is used to store application software and various types of data installed on the terminal, such as program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a six-component force output program 40 for a metal wheel based on a magic formula. This six-component force output program 40 can be executed by the processor 10 to implement the six-component force output method for a metal wheel based on a magic formula in this application.

[0104] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the metal wheel six-component force output method based on the magic formula.

[0105] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen, etc. The display 30 is used to display information on the terminal and to display a visual user interface.

[0106] In one embodiment, when the processor 10 executes the magic formula-based metal wheel six-component force output program 40 in the memory 20, it implements the steps of the magic formula-based metal wheel six-component force output method as described above.

[0107] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a six-component force output program for a metal wheel based on a magic formula, and when the six-component force output program for a metal wheel based on a magic formula is executed by a processor, it implements the steps of the six-component force output method for a metal wheel based on a magic formula as described above.

[0108] In summary, this invention provides a method, system, terminal, and storage medium for outputting the six components of force for a metal wheel based on the Magic Formula. The method includes: acquiring multiple discrete operating points of the target metal wheel, and performing curve generation and preprocessing on the multiple discrete operating points to obtain a preprocessed curve; using the Magic Formula model to perform parameter identification processing on the preprocessed curve to obtain an initial parameter set, and performing parameter quality processing on the initial parameter set to obtain a target parameter set; performing continuous mapping processing on the multiple discrete operating points according to the target parameter set to obtain a target mapping model; acquiring current operating data, and inputting the current operating data into the target mapping model to obtain the output result of the six components of force for the metal wheel. This invention acquires the curves corresponding to the discrete operating points of the metal wheel, fits the curves to obtain multiple fitting parameters, and then performs quality control on the fitting parameters to construct a target mapping model. The target mapping model can accurately and efficiently output the output result of the six components of force for the metal wheel.

[0109] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal that includes that element.

[0110] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The computer-readable storage medium can be a memory, magnetic disk, optical disk, etc.

[0111] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for outputting six components of force in a metal wheel based on a magic formula, characterized in that, The method for outputting six components of force in a metal wheel based on the magic formula includes: Multiple discrete operating points of the target metal wheel are obtained, and curve generation and preprocessing are performed on the multiple discrete operating points to obtain a preprocessed curve. The preprocessed curve is subjected to parameter identification processing using the MF model to obtain an initial parameter set, and the initial parameter set is subjected to parameter quality processing to obtain a target parameter set. The parameter quality processing includes parameter boundary constraint processing, phased sequential fitting processing, multi-initial-value optimization processing, and parameter quality control processing. The step of performing parameter quality processing on the initial parameter set to obtain the target parameter set specifically includes: Determine the preset parameter boundaries, and perform parameter boundary constraint processing on each parameter in the initial parameter set according to the preset parameter boundaries to obtain the first parameter set; A preset fitting order is determined, and the first parameter set is subjected to a phased sequential fitting process according to the preset fitting order to obtain a second parameter set; The preset fitting order, from first to last, is stiffness factor parameter fitting, peak factor parameter fitting, shape factor parameter fitting, and curvature factor parameter fitting. The second parameter set is subjected to multiple initial value optimization processing to obtain the third parameter set; The multi-initial-value optimization process involves repeatedly fitting the process a preset number of times for each operating point and selecting a set of parameters that minimizes the loss and satisfies the physical constraints. The third parameter set is subjected to parameter quality control processing to obtain the target parameter set; Parameter quality control includes at least one or a combination of the following criteria: fitting error threshold, peak error threshold, zero error threshold, slope error threshold, parameter edge criterion, and monotonicity or singularity criterion; Based on the target parameter set, a target mapping model is obtained by continuously mapping multiple discrete operating points. The step of continuously mapping multiple discrete operating points according to the target parameter set to obtain a target mapping model further includes: Perform quadratic surface regression on the target mapping model to obtain the parametric quadratic surface corresponding to each parameter in the target parameter set; The expression for the parametric quadratic surface is as follows: ； in, The parametric quadratic surface corresponding to each parameter. For vertical loads, Outward tilt angle, , All are coefficients of quadratic terms. and All are coefficients of linear terms. For constant terms; Adding a regular expression, the expression is: ； in, For data fitting terms, The target quantity observed in the data. The predicted value given by the model, For regularization terms, Let be the parameter vector to be fitted. The squared L2 norm, where λ≥0 indicates the regularization strength; The current working condition data is acquired and input into the target mapping model to obtain the six-component force output result of the metal wheel.

2. The method for outputting six components of force in a metal wheel based on the magic formula according to claim 1, characterized in that, The process of acquiring multiple discrete operating points of the target metal wheel and performing curve generation and preprocessing on these discrete operating points to obtain a preprocessed curve specifically includes: The target metal wheel is identified, and multiple discrete operating points of the target metal wheel are obtained. The discrete operating point data includes operating variables, excitation variables, and environmental or state variables. The operating condition variables include vertical load and outward tilt angle; the excitation variables include slip ratio and sideslip angle; and the environmental or state variables include temperature, settlement degree, and contact radius. Based on the discrete operating condition data, a discrete curve corresponding to each discrete operating condition point is constructed to obtain the discrete operating condition curve. The discrete operating condition curve is preprocessed to obtain a preprocessed curve. The preprocessing includes unit unification processing, coordinate direction convention processing, outlier removal processing, smoothing processing, and zero point or offset checking processing.

3. The method for outputting six components of force in a metal wheel based on the magic formula according to claim 1, characterized in that, The process of using the MF model to perform parameter identification on the preprocessed curve to obtain an initial parameter set specifically includes: Determine the MF model and input the preprocessed curve into the MF model; The preprocessed curve is subjected to parameter identification processing using the magic formula in the MF model to obtain an initial parameter set, wherein the initial parameter set includes stiffness factor parameters, shape factor parameters, peak factor parameters, and curvature factor parameters. The expression for the initial parameter set is: ； in, For the initial parameter set, For stiffness factor parameters, For shape factor parameters, For peak factor parameters, For curvature factor parameters, For preprocessing curves, It is a vertical drift.

4. The method for outputting six components of force in a metal wheel based on the magic formula according to claim 1, characterized in that, The step of continuously mapping multiple discrete operating points according to the target parameter set to obtain the target mapping model specifically includes: A preset continuous mapping model is determined, wherein the preset continuous mapping model includes a regression model or an interpolation model; The regression models include linear regression models, multinomial regression models, regression models with regularization terms, kernel regression models, radial basis function regression models, Gaussian Process regression models, and neural network regression models. The interpolation models include piecewise linear interpolation models, spline interpolation models, bilinear or bicubic interpolation models, and interpolation models based on Delaunay triangulation. The target parameter set is input into the preset continuous mapping model, and the target parameter set is continuously mapped and modeled through the preset continuous mapping model to obtain the target mapping model.

5. The method for outputting six components of force in a metal wheel based on the magic formula according to claim 1, characterized in that, The process of acquiring current operating condition data and inputting it into the target mapping model to obtain the six-component force output result of the metal wheel specifically includes: Obtain the current operating condition data and input the current operating condition data into the target mapping model to obtain the current parameter set; The current parameter set is input into the MF model, and the six-component force output result of the metal wheel is output.

6. A six-component force output system for metal wheels based on a magic formula, characterized in that, The six-component force output system for metal wheels based on the magic formula is used to implement the six-component force output method for metal wheels based on the magic formula as described in any one of claims 1-5, wherein the six-component force output system for metal wheels based on the magic formula includes: The discrete working condition point processing module is used to acquire multiple discrete working condition points of the target metal wheel, and to perform curve generation and preprocessing on the multiple discrete working condition points to obtain a preprocessed curve. The parameter processing module is used to perform parameter identification processing on the preprocessed curve using the MF model to obtain an initial parameter set, and to perform parameter quality processing on the initial parameter set to obtain a target parameter set. The mapping model generation module is used to perform continuous mapping processing on multiple discrete working points according to the target parameter set to obtain a target mapping model. The six-component force output module is used to acquire the current working condition data and input the current working condition data into the target mapping model to obtain the six-component force output result of the metal wheel.

7. A terminal, characterized in that, The terminal includes: a memory, a processor, and a magic formula-based metal wheel six-component force output program stored in the memory and executable on the processor. When the magic formula-based metal wheel six-component force output program is executed by the processor, it implements the steps of the magic formula-based metal wheel six-component force output method as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a six-component force output program for a metal wheel based on a magic formula, which, when executed by a processor, implements the steps of the six-component force output method for a metal wheel based on a magic formula as described in any one of claims 1-5.

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