Unmanned ground vehicle off-road path planning method based on stability margin field

Abstract

This application proposes an off-road path planning method for unmanned ground vehicles based on a stability margin field. The method includes: constructing a normalized 3D failure envelope proxy model library, which includes proxy models for 3D failure envelopes corresponding to various environmental parameters; calculating the normalized demand force vector required for contact components to maintain their motion state based on the terrain features and preset motion state of the area to be planned; retrieving the corresponding proxy model from the proxy model library according to the environmental parameters of the area to be planned, calculating the minimum geometric distance from the normalized demand force vector to the 3D failure envelope, and defining a 3D stability margin based on the minimum geometric distance; constructing a comprehensive cost map based on the 3D stability margin; and searching for the optimal path within the comprehensive cost map. This method can plan off-road paths for unmanned ground vehicles while considering the interaction mechanics between the unmanned ground vehicle and the ground and anticipating instability risks.

Description

Technical Field

[0001] This application relates to the field of unmanned ground vehicle technology, and in particular to an off-road path planning method for unmanned ground vehicles based on a stability margin field. Background Technology

[0002] Unmanned ground vehicles (UGVs) are increasingly used in fields such as wilderness rescue and planetary exploration. The operating environments of UGVs are mostly unstructured terrains such as soft soil and sand, and the interaction between UGVs and the ground is highly nonlinear and complex. In unstructured off-road environments, the mobility of UGVs depends not only on geometric passability but also on mechanical passability—that is, avoiding instability phenomena such as getting stuck, slipping, and overturning. Mechanical passability has become a key bottleneck restricting the off-road performance of UGVs.

[0003] Existing off-road path planning technologies for unmanned ground vehicles (UGVs) rely on terrain geometry or semantic information for path planning. However, they lack quantitative assessments of the mechanical characteristics of the interaction between UGVs and the ground, making it impossible to predict instability risks or differentiate path safety levels. Therefore, an important research direction is to develop off-road paths for UGVs that consider the mechanical characteristics of their interaction with the ground, can predict instability risks, and can differentiate path safety levels. Summary of the Invention

[0004] The purpose of this application is to at least solve the problem of planning off-road paths for unmanned ground vehicles, considering the interaction mechanics between unmanned ground vehicles and the ground, being able to predict instability risks, and being able to distinguish path safety levels. This purpose is achieved through the following technical solution: This application proposes a method for off-road path planning for unmanned ground vehicles based on a stability margin field, including: A numerical simulation environment for the interaction between the contact component and the contact medium is established. Multi-condition virtual loading tests are conducted in the numerical simulation environment to obtain a mathematical model of the three-dimensional failure envelope surface, wherein the three-dimensional failure envelope surface represents the ultimate force boundary between the contact component and the contact medium. Construct a normalized proxy model library for the three-dimensional failure envelope surface, the proxy model library including proxy models for the three-dimensional failure envelope surface corresponding to various environmental parameters; Based on the terrain features and preset motion state of the area to be planned, the required force vector for the contact component to maintain the motion state is calculated, and the required force vector is normalized to obtain the normalized required force vector. Based on the environmental parameters of the area to be planned, the proxy model of the corresponding three-dimensional failure envelope surface in the proxy model library is retrieved, the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface is calculated, and the three-dimensional stability margin is defined based on the minimum geometric distance. A risk cost function is constructed based on the three-dimensional stability margin, a distance cost function is constructed based on the minimum geometric distance, and a comprehensive cost map is constructed based on the risk cost function and the distance cost function. A comprehensive cost map is constructed based on the three-dimensional stability margin, and the optimal path is searched within the comprehensive cost map.

[0005] This application establishes a numerical simulation environment for the interaction between contact components and the contact medium, obtains a mathematical model of the three-dimensional failure envelope surface, and constructs a surrogate model library to achieve a quantitative assessment of the mechanical properties of unmanned ground vehicles interacting with the ground. By solving the normalized demand force vector and calculating its minimum geometric distance to the failure envelope surface, a three-dimensional stability margin is defined, enabling accurate prediction of vehicle instability risks in unstructured terrain. Based on the three-dimensional stability margin, a risk cost function and a distance cost function are constructed to form a comprehensive cost map, allowing path planning to consider both mechanical safety and path efficiency. This enables path planning to take into account quantitative mechanical assessment, prediction of instability risks, and differentiation of path safety levels, significantly improving the mobility and operational safety of unmanned ground vehicles in off-road environments.

[0006] In some embodiments, the step of establishing a numerical simulation environment for the interaction between the contact component and the contact medium, conducting multi-condition virtual loading tests in the numerical simulation environment, and obtaining a mathematical model of the three-dimensional failure envelope surface includes: A soil particle bed model based on discrete particles is established for the target soil characteristics, and the soil particle bed model is used as the contact medium. The walking mechanism model of the unmanned ground vehicle is imported into the soil particle bed model, and the walking mechanism model of the unmanned ground vehicle is used as the contact component to form the numerical simulation environment. In the numerical simulation environment, the contact component is planned using the Latin hypercube sampling method, and the contact component is subjected to working condition loading on the contact medium. A three-dimensional set of stress data points characterizing the critical failure state of the contact medium is collected, and the three-dimensional set of stress data points is normalized to obtain a normalized set of failure data points. The normalized failure data point set is reconstructed using a mathematical fitting method to obtain a mathematical model of the three-dimensional failure envelope surface.

[0007] In some embodiments, the step of acquiring a three-dimensional stress data point set characterizing the critical failure state of the contact medium, and normalizing the three-dimensional stress data point set to obtain a normalized failure data point set includes: Collect a set of three-dimensional stress data points characterizing the critical failure state of the contact medium. ,in, For the first The maximum horizontal traction force at the critical state of contact medium failure for each data point. For the first The maximum vertical force at the critical failure state of the contact medium at each data point. For the first The maximum bending moment at the critical failure state of the contact medium at each data point. It is a positive integer; Select the three-dimensional force data point set The largest vertical force and the global mechanical reference value Recorded as ,in The characteristic width of the contact component; The normalized failure data point set is calculated using the following formula ( ):

[0008] in, For the first The normalized value of the maximum horizontal traction force at the critical state of contact medium failure for each data point. For the first The normalized value of the maximum vertical force at the critical failure state of the contact medium for each data point. For the first The normalized value of the maximum bending moment of the critical state of failure of the contact medium at each data point.

[0009] In some embodiments, the step of reconstructing the normalized failure data point set using a mathematical fitting method to obtain a mathematical model of the three-dimensional failure envelope surface includes: Least squares ellipsoid fitting is used to reconstruct the surface of the normalized failure data point set, and a mathematical model of the three-dimensional failure envelope surface in the following form is constructed. :

[0010] in, All are shape parameters. All are indices. The offset of the center of the three-dimensional failure envelope surface on the vertical load axis.

[0011] In some embodiments, the step of constructing a normalized proxy model library for the three-dimensional failure envelope surface includes: Select a set of environmental parameters that affect the passage capability of the contact component. ={ }; M typical discrete soil parameter nodes were selected from the set of environmental parameters.

[0012] Based on the discrete soil parameter nodes, the contact component is planned using the Latin hypercube sampling method, and the contact component is subjected to working condition loading on the contact medium. Collect the set of ultimate stress points of the contact medium. The set of ultimate stress points characterizes the critical failure state of the contact medium based on the discrete soil parameter nodes; According to the set of limit stress points And the mathematical model of the three-dimensional failure envelope surface, for each discrete soil parameter node The corresponding hyperellipsoid shape coefficient vector To solve, where, To and Corresponding shape parameters , To and Corresponding shape parameters , To and Corresponding shape parameters , To and Corresponding index , To and Corresponding index , To and Corresponding index , for The corresponding center offset of the three-dimensional failure envelope surface on the vertical load axis ; Discrete soil parameter nodes Using the index key, with the hyperellipsoid shape coefficient vector For numerical values, construct the proxy model library. .

[0013] In some embodiments, the step of solving the required force vector for the contact component to maintain the motion state based on the terrain features and preset motion state of the area to be planned, and normalizing the required force vector to obtain a normalized required force vector, includes: Extract the terrain geometry features of each grid node in the area to be planned, including the slope angle and roll angle, and obtain the environmental parameter label of the node; A reference motion state is set for the contact component. The reference motion state is used to characterize the expected mobility performance index of the unmanned ground vehicle in off-road missions. The reference motion state includes a preset cruising speed and a preset maximum acceleration. Based on the aforementioned terrain geometry and reference motion state, the normalized demand force vector required to maintain the motion state is obtained by inverse solving the force balance equation. The normalized demand force vector includes longitudinal traction force, vertical support force, and overturning moment.

[0014] In some embodiments, the step of obtaining the normalized required force vector to maintain the motion state by inverse solving the force balance equation based on the terrain geometry and reference motion state includes: The longitudinal traction force is calculated according to the following formula. :

[0015] in, The weight allocated to the contact components, It is the acceleration due to gravity. For rolling resistance, The preset maximum acceleration; The vertical support force is calculated according to the following formula. :

[0016] in, The slope angle; The overturning moment is calculated according to the following formula. :

[0017] in, It is a lateral force. The effective height from the contact point to the torque reference center. For vertical loads, Load eccentricity caused by structural design; The grid nodes are obtained using the following formula. Absolute demand force vector :

[0018] The demand force vector is expressed by the following formula. Normalization is performed to obtain the normalized demand force vector. : .

[0019] In some embodiments, the step of retrieving the surrogate model of the corresponding three-dimensional failure envelope surface from the surrogate model library based on the environmental parameters of the area to be planned, calculating the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface, and defining the three-dimensional stability margin based on the minimum geometric distance includes: Based on the soil physical parameters of the grid nodes, adjacent parameter nodes are retrieved in the proxy model library, and the three-dimensional failure envelope proxy model parameters corresponding to the grid nodes are calculated by weighted interpolation. The reconstructed three-dimensional failure envelope is obtained based on the proxy model parameters. Find the minimum Euclidean distance from the normalized demand force vector to the reconstructed three-dimensional failure envelope surface; Determine the positional relationship between the normalized demand force vector and the reconstructed three-dimensional failure envelope surface; Based on the fact that the normalized demand force vector is located inside the three-dimensional failure envelope, the three-dimensional stability margin is defined as the positive value of the minimum Euclidean distance; Based on the fact that the normalized demand force vector is located at the boundary or outside of the three-dimensional failure envelope, the three-dimensional stability margin is defined as the negative value of the minimum Euclidean distance.

[0020] In some embodiments, the step of retrieving adjacent parameter nodes in the surrogate model library based on the soil physical parameters of the grid node, calculating the 3D failure envelope surrogate model parameters corresponding to the grid node through weighted interpolation, and obtaining the reconstructed 3D failure envelope based on the surrogate model parameters includes: Obtain the soil physical parameters for each of the grid nodes. ; In the proxy model library Searching for the soil physical parameters The parameter node whose Euclidean distance is closest; The shape coefficient vector of the retrieved parameter node is used according to the following formula. Model coefficients for the grid nodes Perform weighted interpolation calculations:

[0021] in, The model coefficients of the grid nodes Corresponding shape parameters The value, The model coefficients of the grid nodes Corresponding shape parameters The value, The model coefficients of the grid nodes Corresponding shape parameters The value, The model coefficients of the grid nodes Corresponding index The value, The model coefficients of the grid nodes Corresponding index The value, The model coefficients of the grid nodes Corresponding index The value, The model coefficients of the grid nodes The corresponding center offset of the three-dimensional failure envelope surface on the vertical load axis The value; Will Substitute into mathematical model In order to obtain the reconstructed three-dimensional failure envelope surface. :

[0022] The step of finding the minimum Euclidean distance from the normalized demand force vector to the reconstructed three-dimensional failure envelope surface includes: The normalized demand force vector is calculated using the following formula. Minimum Euclidean distance to the reconstructed three-dimensional failure envelope surface :

[0023] in, To reconstruct the three-dimensional failure envelope surface any point; The step of determining the positional relationship between the normalized demand force vector and the reconstructed three-dimensional failure envelope surface includes: The normalized demand force vector Substitute the coordinates of the points into To obtain the calculated value ; according to It is determined that the normalized demand force vector is located inside the three-dimensional failure envelope surface; according to It is determined that the normalized demand force vector is located outside the three-dimensional failure envelope surface; according to It is determined that the normalized demand force vector is located at the boundary of the three-dimensional failure envelope. The step of defining the three-dimensional stability margin as a positive value of the minimum Euclidean distance based on the fact that the normalized demand force vector lies inside the three-dimensional failure envelope surface includes: Based on the fact that the normalized demand force vector lies within the three-dimensional failure envelope, a three-dimensional stability margin is defined. First three-dimensional stability margin for ; The step of defining the three-dimensional stability margin as the negative of the minimum Euclidean distance based on the normalized demand force vector being located at or outside the three-dimensional failure envelope facing the boundary boundary includes: The three-dimensional stability margin is defined based on whether the normalized demand force vector is located at or outside the three-dimensional failure envelope, facing the boundary or outside. The second three-dimensional stability margin value for .

[0024] In some embodiments, the steps of constructing a risk cost function based on the three-dimensional stability margin, constructing a distance cost function based on the minimum geometric distance, and constructing a comprehensive cost map based on the risk cost function and the distance cost function include: Based on the fact that the normalized demand force vector is located at or outside the three-dimensional failure envelope, a risk cost function is constructed using the following formula: First cost function :

[0025] Based on the fact that the normalized demand force vector lies within the three-dimensional failure envelope, the risk cost function is constructed using the following formula. The second cost function : ;or,

[0026] in, For adjustment coefficients, The preset risk weight coefficient is used to adjust the sensitivity of the planning algorithm to mechanical stability. To prevent small quantities with a denominator of zero; The total cost function for each node is generated using the following formula. And form a comprehensive cost map;

[0027] in, To the grid node Three-dimensional stability margin , This is a safety weight used to adjust the sensitivity to mechanical risks; Efficiency weights are used to adjust the sensitivity to path length. The distance cost function is used to characterize the distance the vehicle travels to the node. Required path length cost; and / or, The step of constructing a comprehensive cost map based on the three-dimensional stability margin and searching for the optimal path in the comprehensive cost map includes: Establish a search graph containing all the grid nodes within the planning area, and maintain the actual cumulative cost, heuristic estimated cost, and total evaluation cost including the actual cumulative cost and the heuristic estimated cost for each grid node; The search step includes: defining an open list and adding the raster nodes. Add the starting point to the open list; traverse the neighboring nodes of the grid node with the minimum total evaluation cost, filter out the neighboring nodes with a three-dimensional stability margin greater than 0, and add them to the open list; calculate the actual cumulative cost of the neighboring nodes with a three-dimensional stability margin greater than 0. Repeat the search steps until the endpoint is added to the open list. Backtrack from the endpoint to the starting point to obtain the initial optimal path. Smooth the initial optimal path to obtain the optimal path. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings are only used to illustrate preferred embodiments and are not intended to limit this application.

[0029] Figure 1 This is a schematic diagram of an off-road path planning method for unmanned ground vehicles based on a stability margin field, according to an embodiment of this application. Figure 2 This is a schematic diagram illustrating the interaction between the contact component and the contact medium in an embodiment of this application; Figure 3 This is a schematic diagram of the three-dimensional failure envelope surface according to an embodiment of this application; Figure 4 This is a schematic diagram illustrating the longitudinal traction force, vertical support force, and overturning moment in an embodiment of this application. Figure 5 This is a schematic diagram illustrating the principle of three-dimensional stability margin calculation in an embodiment of this application; Figure 6 This is a schematic diagram comparing the path planning of this application embodiment with the path planning of traditional geometric planning. Detailed Implementation

[0030] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0031] To enable those skilled in the art to better understand the technical solutions in the embodiments of this application, and to make the above-mentioned objectives, features and advantages of the embodiments of this application more apparent and understandable, the technical solutions in the embodiments of this application will be further described in detail below with reference to the accompanying drawings.

[0032] While exemplary embodiments of the present application are shown in the accompanying drawings, it should be understood that the embodiments of the present application can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the embodiments of the present application and to fully convey the scope of the embodiments of the present application to those skilled in the art.

[0033] It should be noted that, unless otherwise stated, the technical or scientific terms used in the embodiments of this application should have the ordinary meaning understood by those skilled in the art to which the embodiments of this application pertain.

[0034] Unmanned ground vehicles (UGVs) are increasingly used in fields such as wilderness rescue and planetary exploration. The operating environments of UGVs are mostly unstructured terrains such as soft soil and sand, and the interaction between UGVs and the ground is highly nonlinear and complex. In unstructured off-road environments, the mobility of UGVs depends not only on geometric passability but also on mechanical passability—that is, avoiding instability phenomena such as getting stuck, slipping, and overturning. Mechanical passability has become a key bottleneck restricting the off-road performance of UGVs.

[0035] Existing off-road path planning technologies for unmanned ground vehicles (UGVs) rely on terrain geometry or semantic information for path planning. However, they lack quantitative assessments of the mechanical characteristics of the interaction between UGVs and the ground, making it impossible to predict instability risks or differentiate path safety levels. Therefore, an important research direction is to develop off-road paths for UGVs that consider the mechanical characteristics of their interaction with the ground, can predict instability risks, and can differentiate path safety levels.

[0036] To address the challenge of planning off-road paths for unmanned ground vehicles (UGVs) while considering the interaction mechanics between the UUV and the ground, predicting instability risks, and differentiating path safety levels, this application proposes an UUV off-road path planning method based on a stability margin field. This method enables the planning of UUV off-road paths while considering the interaction mechanics between the UUV and the ground, predicting instability risks, and differentiating path safety levels. This application was supported by the National Natural Science Foundation of China (Grant No. 52172365) and the Jilin University Graduate Innovation Fund.

[0037] The following describes, with reference to the accompanying drawings, an embodiment of the unmanned ground vehicle off-road path planning method based on a stability margin field.

[0038] like Figure 1 As shown in the figure, the off-road path planning method for unmanned ground vehicles based on a stability margin field in this application includes: S100. Establish a numerical simulation environment for the interaction between the contact component and the contact medium. Conduct virtual loading tests under multiple working conditions in the numerical simulation environment to obtain a mathematical model of the three-dimensional failure envelope surface. The three-dimensional failure envelope surface represents the ultimate force boundary between the contact component and the contact medium. S200. Construct a normalized surrogate model library for the three-dimensional failure envelope surface. The surrogate model library includes surrogate models for the three-dimensional failure envelope surface corresponding to various environmental parameters. S300. Based on the terrain features and preset motion state of the area to be planned, solve the required force vector for the contact component to maintain the motion state, and normalize the required force vector to obtain the normalized required force vector. S400. Based on the environmental parameters of the area to be planned, retrieve the corresponding surrogate model of the three-dimensional failure envelope surface from the surrogate model library, calculate the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface, and define the three-dimensional stability margin based on the minimum geometric distance. S500: Construct a risk cost function based on the three-dimensional stability margin, construct a distance cost function based on the minimum geometric distance, and construct a comprehensive cost map based on the risk cost function and the distance cost function; S600: Construct a comprehensive cost map based on three-dimensional stability margin, and search for the optimal path in the comprehensive cost map.

[0039] The unmanned ground vehicle off-road path planning method of this application embodiment can be executed by the on-board controller of the unmanned ground vehicle, an independent industrial control computer or server.

[0040] S100. Establish a numerical simulation environment for the interaction between the contact component and the contact medium. Conduct virtual loading tests under multiple working conditions in the numerical simulation environment to obtain a mathematical model of the three-dimensional failure envelope surface. The three-dimensional failure envelope surface represents the ultimate force boundary between the contact component and the contact medium.

[0041] Numerical simulation environments can be built using discrete element analysis (DEM) software or multibody dynamics simulation software. In these environments, contact components can be modeled as rigid or flexible bodies with specific geometries and material properties, while the contact medium can be modeled as a medium with specific mechanical parameters. Within the numerical simulation environment, loads of different directions and magnitudes can be applied to the contact components to simulate their stress conditions under various working conditions. By systematically changing the load conditions, multi-condition virtual loading tests are conducted to record the critical stress state when the contact medium experiences macroscopic failure (e.g., shear failure, excessive compaction deformation, etc.). This allows for the acquisition of a series of data points characterizing the ultimate stress boundary. Based on these data points, a mathematical model of the three-dimensional failure envelope can be obtained through data processing and curve fitting methods. The three-dimensional failure envelope intuitively characterizes the ultimate bearing capacity between the contact component and the contact medium under different stress combinations, providing a foundation for subsequent stability assessments.

[0042] In some embodiments, the steps of establishing a numerical simulation environment for the interaction between contact components and contact media, conducting multi-condition virtual loading tests in the numerical simulation environment, and obtaining a mathematical model of the three-dimensional failure envelope include: To address the specific characteristics of the target soil, a soil particle bed model based on discrete particles was established, and this model was used as the contact medium. The walking mechanism model of the unmanned ground vehicle is imported into the soil particle bed model, and the walking mechanism model of the unmanned ground vehicle is used as the contact component to form a numerical simulation environment. In the numerical simulation environment, the contact components are planned using the Latin hypercube sampling method, and the contact components are subjected to working conditions on the contact medium. A three-dimensional set of stress data points characterizing the critical state of failure of the contact medium is collected, and the three-dimensional set of stress data points is normalized to obtain a normalized set of failure data points. A mathematical model of the three-dimensional failure envelope surface is obtained by reconstructing the surface of the normalized failure data point set using mathematical fitting.

[0043] like Figure 2As shown, a walking mechanism model of an unmanned ground vehicle is imported into a soil particle bed model and used as a contact component to form a numerical simulation environment. As an example, this can be achieved by importing the vehicle's CAD model into the simulation software and assigning it rigid or flexible body properties; alternatively, a simplified geometric model, such as a parametric representation of tracks or wheels, can be used, but its key dimensions, mass distribution, and kinematic characteristics must be preserved to ensure the accuracy of the mechanical interaction. Using the unmanned ground vehicle's walking mechanism model as a contact component clarifies its active interaction role in the simulation. As an example, this can be achieved by defining the kinematics and dynamics of the unmanned ground vehicle, enabling it to apply preset forces, torques, or displacements in the simulation, and to physically contact the contact medium and generate reaction forces; alternatively, the unmanned ground vehicle can be configured as a controllable entity in the simulation, capable of executing specific motion trajectories and monitoring its interaction forces with the environment. Integrating the soil particle bed model and the walking mechanism model into a unified simulation platform to form a numerical simulation environment provides a computational framework for physical interaction between the soil particle bed model and the walking mechanism model. As an example, this can be achieved by using commercial simulation software (such as Adams, RecurDyn, EDEM, etc.) or open-source physics engines (such as Chrono, Bullet, etc.); or, a custom simulation framework can be developed, which includes core modules such as collision detection, mechanics calculation, and motion update.

[0044] As an example, soil particles are composed of spherical or non-spherical composite particles, and the contact model between particles is the Hertz-Mindlin with Bonding contact model to simulate the cohesion and internal friction angle characteristics of loose soil.

[0045] In a numerical simulation environment, the contact components are planned using the Latin hypercube sampling method, and then subjected to load conditions on the contact medium. Specifically, the Latin hypercube sampling method is used to plan the contact components to efficiently explore a multi-dimensional parameter space to comprehensively cover various possible working conditions. This can be achieved by defining the range of key motion parameters of the contact components (such as velocity, load, attitude angle, steering angle, etc.) and then using the Latin hypercube sampling algorithm to generate sampling points uniformly distributed in these parameter spaces; alternatively, by combining experience, denser sampling can be performed in critical areas known to potentially lead to failure, thereby improving the ability to capture critical behaviors while reducing unnecessary simulation iterations. Loading the contact components onto the contact medium involves simulating the driving or operating process of an unmanned ground vehicle under different stress conditions in the simulation. This can be achieved by applying preset force, displacement, or velocity boundary conditions to the contact components in the simulation to simulate the vehicle's stress under different slopes, steering, acceleration, or deceleration conditions; or by controlling the motion trajectory and attitude of the contact components to make them contact the soil particle bed model and recording the resulting interaction forces.

[0046] A three-dimensional stress data point set characterizing the critical state of failure of the contact medium is collected, and then normalized to obtain a normalized failure data point set. Specifically, the purpose of collecting the three-dimensional stress data point set characterizing the critical state of failure of the contact medium is to obtain the mechanical response data of the soil when it reaches its bearing limit. As an example, this can be achieved by monitoring the interaction forces between the contact component and the soil in real time during the simulation (such as horizontal traction force, vertical support force, bending moment, etc.), and recording the corresponding three-dimensional mechanical data when the soil undergoes significant plastic deformation, shear failure, a sharp decrease in bearing capacity, or reaches a preset failure criterion (such as maximum shear stress, maximum deformation); or by analyzing the inflection point or plateau region of the force-displacement curve to determine the critical point of soil transition from elastic deformation to plastic deformation or failure, and collecting the corresponding stress data at this point. The normalization of the three-dimensional stress data point set aims to eliminate the dimensional influence of mechanical data under different working conditions, making different data comparable and facilitating subsequent mathematical fitting. As an example, this can be achieved by dividing the collected three-dimensional mechanical data by the reference force or reference size; or, statistical standardization methods, such as Z-score standardization or Min-Max standardization, can be used to map the data to a specific numerical range to ensure that data of different dimensions have the same weight in model building.

[0047] like Figure 3As shown, a mathematical model of the three-dimensional failure envelope surface is obtained by reconstructing the normalized failure data point set using mathematical fitting. Specifically, the surface reconstruction of the normalized failure data point set using mathematical fitting aims to transform discrete failure data points into continuous mathematical expressions, thereby describing the entire failure boundary. As an example, this can be achieved by using traditional mathematical methods such as polynomial fitting, radial basis function (RBF) fitting, and spline fitting to find the function form that best fits the discrete data points; or by using machine learning methods, such as support vector machine regression (SVR), Gaussian process regression, or neural networks, to learn the complex nonlinear relationships between data points and construct a model that can predict the failure boundary under arbitrary input conditions, thus obtaining the mathematical model of the three-dimensional failure envelope surface to quantify the ultimate stress boundary between the contact component and the contact medium. The mathematical model can be an explicit functional expression, such as the hyperellipsoid equation, whose parameters can be determined through the fitting process; or it can be an implicit function or a parameterized surface representation capable of describing complex and irregular failure boundary shapes.

[0048] This application's embodiments can efficiently and accurately establish a numerical simulation environment for the interaction between contact components and the contact medium, and obtain a mathematical model of the three-dimensional failure envelope surface. By establishing a soil particle bed model based on discrete particles and importing the walking mechanism model of the unmanned ground vehicle, a highly realistic numerical simulation environment is formed, which can realistically reflect the complex nonlinear interaction between the vehicle and the soil, significantly improving simulation accuracy. The Latin hypercube sampling method is used to plan and load contact components under multiple working conditions, effectively covering a broad working space, ensuring data comprehensiveness while greatly improving simulation efficiency. By collecting and normalizing the three-dimensional stress data of the failure critical state, the standardization and comparability of the data are ensured, providing a data foundation for subsequent model construction. Mathematical fitting is used to reconstruct the surface of the normalized data, transforming the discrete simulation results into a continuous, quantifiable three-dimensional failure envelope surface mathematical model, providing a precise quantitative tool for the mechanical passability assessment of unmanned ground vehicles. The embodiments of this application systematically solve the problems of insufficient accuracy and low efficiency of traditional methods in simulating real soil and vehicle interaction, covering multiple working conditions, and generating reliable mathematical models, and provide a foundation for subsequent off-road path planning based on stability margin fields.

[0049] In some embodiments, the step of acquiring a three-dimensional stress data point set characterizing the critical state of failure of the contact medium, and normalizing the three-dimensional stress data point set to obtain a normalized failure data point set includes: Acquire a three-dimensional set of stress data points characterizing the critical state of failure of the contact medium. ,in, For the first The maximum horizontal traction force at the critical state of contact medium failure for each data point. For the first The maximum vertical force at the critical failure state of the contact medium at each data point. For the first The maximum bending moment at the critical failure state of the contact medium at each data point. It is a positive integer; Select three-dimensional force data point set The largest vertical force and the global mechanical reference value Recorded as ,in The characteristic width of the contact component; The normalized failure data point set is calculated using the following formula ( ):

[0050] in, For the first The normalized value of the maximum horizontal traction force at the critical state of contact medium failure for each data point. For the first The normalized value of the maximum vertical force at the critical failure state of the contact medium for each data point. For the first The normalized value of the maximum bending moment at the critical failure state of the contact medium at each data point.

[0051] Acquire a three-dimensional set of stress data points characterizing the critical state of failure of the contact medium. It can acquire raw data on the mechanical limits of the contact medium under various load conditions. The critical failure state refers to the point at which the contact medium, under applied force, is about to undergo significant deformation, slippage, or collapse, leading to vehicle instability or immobility. Three-dimensional force data point set. The maximum horizontal traction force, maximum vertical force, and maximum bending moment that the contact medium could withstand before failure were recorded. As an example, a three-dimensional force data point set was provided. Failure points can be obtained by systematically applying loads and observing the failure points in a numerical simulation environment (e.g., simulating the interaction between the walking mechanism and the soil particle bed using the discrete element method or the finite element method). As other examples, they can also be obtained through physical experiments, such as using a test bench to press the physical contact parts into a soil tank and applying forces or torques until failure is observed, with peak data recorded by sensors.

[0052] Select three-dimensional force data point set The largest vertical force and the global mechanical reference value Recorded as This establishes a unified reference standard for subsequent normalization processing.

[0053] By each component Divide by its corresponding The reference values ​​in the data are all converted to dimensionless quantities, eliminating the influence of different units and magnitudes in the original data. This allows for direct comparison of data points and provides a suitable data format for subsequent mathematical fitting algorithms. The normalized data points characterize the geometry of the failure envelope, independent of the absolute magnitude of the force. As an example, iterative calculations can be performed on all data points using a batch script (e.g., using Python or MATLAB).

[0054] This application's embodiments effectively address the issue of inconsistent dimensions in the original data by normalizing the collected three-dimensional stress data point set. This eliminates the dimensional differences in the original data, enabling subsequent mathematical fitting algorithms to more accurately and robustly reconstruct the three-dimensional failure envelope. Furthermore, the normalized failure envelope allows for a unified comparison of failure boundaries under different working conditions, improving the model's accuracy and versatility in representing the ultimate stress boundary of the contact medium. This provides a more reliable and accurate foundation for subsequent off-road path planning for unmanned ground vehicles based on a stability margin field.

[0055] In some embodiments, the step of reconstructing a surface from a normalized set of failure data points using mathematical fitting to obtain a mathematical model of the three-dimensional failure envelope includes: Least squares ellipsoid fitting is used to reconstruct the surface of the normalized failure data point set, and a mathematical model of the three-dimensional failure envelope surface in the following form is constructed. :

[0056] in, All are shape parameters. All are indices. This represents the center offset of the three-dimensional failure envelope surface on the vertical load axis.

[0057] like Figure 3 As shown, the mathematical model employs a super-ellipsoid form, providing a highly flexible and parameterizable mathematical expression to accurately describe the failure envelope in three-dimensional space. This allows the model to adapt to various complex, non-standard failure boundaries by adjusting its internal parameters. As an example, nonlinear regression analysis can be used, employing fitting algorithms (such as the Levenberg-Marquardt algorithm or genetic algorithms) to solve for the unknown parameters in the model, enabling the mathematical model to best fit the normalized failure data point set.

[0058] This application employs a least-squares ellipsoid fitting method to reconstruct the surface of the normalized failure data point set and constructs a three-dimensional failure envelope surface model with a specific mathematical form. The three-dimensional failure envelope surface mathematical model constructed in this application not only possesses high flexibility and accuracy but also provides a reliable and continuous mathematical foundation for subsequent three-dimensional stability margin calculations. This significantly improves the accuracy and reliability of stability margin assessment, thereby providing a basis for path planning of unmanned ground vehicles in unstructured off-road environments. It effectively avoids errors in predicting instability risks due to model inaccuracies, thus enhancing the safety and reliability of path planning.

[0059] S200. Construct a normalized surrogate model library for the three-dimensional failure envelope surface. The surrogate model library includes surrogate models for the three-dimensional failure envelope surface corresponding to various environmental parameters.

[0060] A representative combination of environmental parameters is pre-selected, and for each combination, the process of establishing the numerical simulation environment and obtaining the mathematical model of the three-dimensional failure envelope surface is repeated. The three-dimensional failure envelope surface models obtained under different environmental parameters are normalized and parameterized. For example, the core parameters of each failure envelope surface model can be extracted to form a compact surrogate model. The surrogate models and their corresponding environmental parameters are stored in a database, forming a surrogate model library. By querying or interpolating this surrogate model library, the three-dimensional failure envelope surface model under the corresponding environment can be quickly obtained, improving evaluation efficiency.

[0061] By constructing a normalized 3D failure envelope model library, the 3D failure envelope model under the corresponding environment can be quickly obtained by querying or interpolating the surrogate model library. This avoids the need for detailed numerical simulation calculations for each environmental parameter, reduces data storage and computation, and improves evaluation efficiency.

[0062] In some embodiments, the step of constructing a surrogate model library of normalized three-dimensional failure envelope surfaces includes: Select the set of environmental parameters that affect the passage capability of the contact components ={ }; M typical discrete soil parameter nodes were selected from the environmental parameter set.

[0063] Based on discrete soil parameter nodes, the contact components are planned using the Latin hypercube sampling method, and the contact components are subjected to working condition loading on the contact medium. Collect the set of ultimate stress points of the contact medium The ultimate stress point set characterizes the critical state of contact medium failure under discrete soil parameter nodes; According to the limit force set The mathematical model of the three-dimensional failure envelope surface is used for each discrete soil parameter node. The corresponding hyperellipsoid shape coefficient vector To solve, where, To and Corresponding shape parameters , To and Corresponding shape parameters , To and Corresponding shape parameters , To and Corresponding index , To and Corresponding index , To and Corresponding index , for The corresponding center offset of the three-dimensional failure envelope surface on the vertical load axis ; Discrete soil parameter nodes Using the index key, with the hyperellipsoid shape coefficient vector For numerical values, build a proxy model library. .

[0064] Select the set of environmental parameters that affect the passage capability of the contact components ={ Environmental parameter set This refers to the set of environmental factors that influence the mechanical properties of the interaction between the contact components of an unmanned ground vehicle and the contact medium. The environment affects the mechanical response of the contact medium, thus impacting the vehicle's mobility and stability. For example, for soil, environmental parameters might include physical and mechanical parameters such as soil moisture content, density, particle size distribution, internal friction angle, and cohesion. By selecting key parameters, the complexity of the off-road environment can be comprehensively characterized, providing fundamental data for subsequent mechanical assessments. As an example, empirical methods can be used, combined with actual operational data of unmanned ground vehicles under different terrains, to identify soil physical parameters that significantly affect mobility; alternatively, sensitivity analysis can be used to perturb various environmental parameters in a numerical simulation environment, assessing their impact on the force response of the contact components, thereby selecting key environmental parameters.

[0065] M typical discrete soil parameter nodes were selected from the set of environmental parameters. Discrete soil parameter nodes Discrete soil parameter nodes refer to M representative, discrete parameter combinations selected from a continuous environmental parameter space. Since environmental parameters are typically continuously changing, directly simulating or modeling all possible parameter combinations is impractical. Therefore, by selecting a limited number of typical discrete nodes, computational costs and data storage can be significantly reduced while ensuring model coverage and accuracy. Discrete soil parameter nodes should represent the main trends and extreme cases in the environmental parameter space. For example, uniform sampling or stratified sampling methods can be used to divide the range of environmental parameter values ​​into several intervals, and representative values ​​can be selected as discrete nodes within each interval; alternatively, data mining techniques such as cluster analysis can be used to analyze historical environmental data, identify clusters of environmental parameters with similar mechanical properties, and select a central point or representative point from each cluster as a discrete node.

[0066] The contact components are planned using the Latin hypercube sampling method based on discrete soil parameter nodes, and then subjected to load conditions on the contact medium. The Latin hypercube sampling method is a hierarchical random sampling technique that ensures the generation of uniformly distributed sample points in a multidimensional parameter space, thus efficiently covering the entire design space. This method of planning contact components (such as tracks or wheels of unmanned ground vehicles) using the Latin hypercube sampling method and subjecting them to load conditions on the contact medium is used to plan the virtual loading conditions of contact components (such as tracks or wheels of unmanned ground vehicles) when interacting with the contact medium (such as a soil particle bed). This sampling method allows for a systematic exploration of the response of contact components under different motion states and stress conditions, thereby obtaining comprehensive mechanical data. Load conditions refer to simulating the process of applying various mechanical loads to the contact medium by the contact components in a numerical simulation environment to reproduce the complex stress conditions that may be encountered in actual off-road driving. As an example, in simulation software, parameters such as the motion trajectory, velocity, acceleration, and contact angle with the contact medium of the contact component can be set, and a series of loading condition combinations can be generated using the Latin hypercube sampling algorithm. Then, the simulation of these conditions can be performed one by one. Alternatively, parametric modeling can be used to take the kinematic and dynamic parameters of the contact component as input, and combine them with Latin hypercube sampling to generate different input combinations to drive the numerical simulation model to perform calculations to simulate different loading conditions.

[0067] Collect the set of ultimate stress points of the contact medium The ultimate stress point set characterizes the critical failure state of the contact medium based on the discrete soil parameter nodes. This refers to the discrete soil parameter nodes. The ultimate stress point set is a three-dimensional set of stress points obtained through load simulation, characterizing the critical state of failure of the contact medium (such as plastic deformation, shear failure, compaction, etc.). The ultimate stress point set typically includes mechanical quantities such as horizontal traction force, vertical force, and bending moment when the contact component and the contact medium reach their ultimate bearing capacity. Collecting the ultimate stress point set is the foundation for constructing the three-dimensional failure envelope. For example, during numerical simulation, the stress, strain, or deformation within the contact medium can be monitored in real time. When a preset failure criterion is reached (e.g., shear stress exceeds the shear strength of the soil, or plastic strain reaches a certain threshold), the interaction force between the contact component and the contact medium is recorded. Alternatively, iterative simulation can be used to gradually increase the load or motion intensity of the contact component until macroscopic failure phenomena occur in the contact medium (e.g., a sharp increase in slippage rate, settlement exceeding a threshold), and the mechanical data at this point is recorded.

[0068] According to the set of limit stress points And the mathematical model of the three-dimensional failure envelope surface, for each discrete soil parameter node The corresponding hyperellipsoid shape coefficient vector The solution is then performed. The collected discrete limit force point set is obtained through data fitting. Mapping onto a predefined three-dimensional failure envelope mathematical model, thereby determining the model's performance under specific soil parameters. The specific shape parameters are as follows. Hyperellipsoid shape coefficient vector. It contains key parameters describing the shape and position of the hyperellipsoid. Solving for the hyperellipsoid shape coefficient vector allows for the representation of complex mechanical failure boundaries using concise mathematical parameters.

[0069] As an example, the nonlinear least squares method can be used to analyze the collected set of limit stress points. Substituting the model into the three-dimensional failure envelope surface mathematical model, and iteratively solving using an optimization algorithm, the error between the model's predicted values ​​and the actual data points is minimized, thus obtaining the optimal shape coefficient vector. Alternatively, global optimization algorithms such as genetic algorithms and particle swarm optimization can be used to search for the optimal shape coefficient vector within a preset parameter range in order to better fit complex ultimate stress data.

[0070] Discrete soil parameter nodes Using the index key, with the hyperellipsoid shape coefficient vector For numerical values, build a proxy model library. Proxy model library It is a structured data storage collection that stores each discrete soil parameter node. With the corresponding hyperellipsoid shape coefficient vector Establish a connection. As an index key, it can quickly find or interpolate the corresponding failure envelope surface model parameters based on the current environmental parameters. As numerical values, they store all the information describing the geometry of the failure envelope surface. (Building a proxy model library) This enables rapid, on-demand access to the 3D failure envelope surface under different environmental conditions, avoiding time-consuming real-time simulation calculations during path planning. For example, a hash table or dictionary data structure can be used to store the proxy model library, where... As a key, As a value, it enables fast lookup; alternatively, these proxy model libraries can be stored in relational or non-relational databases, with indexes used to optimize query performance and support more complex parameter retrieval and management.

[0071] This application embodiment, by systematically discretizing environmental parameters and constructing a proxy model library, can efficiently generate accurate mechanical models in complex and variable off-road environments, improving the real-time performance of mechanical assessment. Due to the use of accurately parameterized proxy models, the accuracy of stability margin calculation is further improved, providing a more reliable and safer foundation for path planning of unmanned ground vehicles in complex off-road environments.

[0072] S300. Based on the terrain features and preset motion state of the area to be planned, solve the required force vector for the contact component to maintain the motion state, and normalize the required force vector to obtain the normalized required force vector.

[0073] The terrain features of the area to be planned can be geometrically analyzed using local elevation maps constructed from onboard sensors or known global digital elevation models. Preset motion states can be set according to the mission requirements of the unmanned ground vehicle, such as setting the vehicle's desired speed, acceleration, or turning radius. Combining terrain features and motion states, the mechanical components required by the contact components under the current terrain and motion requirements, including support force, traction force, and overturning resistance bending moment, can be calculated in reverse. These mechanical components collectively constitute the required force vector. Normalizing the required force vector allows for comparison with the normalized three-dimensional failure envelope at the same scale, providing fundamental data for risk prediction and facilitating subsequent stability assessments.

[0074] In some embodiments, the step of solving the required force vector for the contact component to maintain the motion state based on the terrain features of the area to be planned and a preset motion state, and normalizing the required force vector to obtain a normalized required force vector, includes: Extract the terrain geometry features of each grid node in the area to be planned. The terrain geometry features include the slope angle and roll angle. Also obtain the environmental parameter labels for that node. The reference motion state of the contact component is set. The reference motion state is used to characterize the expected maneuverability performance index of the unmanned ground vehicle in off-road missions. The reference motion state includes the preset cruise speed and the preset maximum acceleration. Based on the terrain geometry and reference motion state, the normalized demand force vector required to maintain the motion state is obtained by inverse solution of the force balance equation. The normalized demand force vector includes longitudinal traction force, vertical support force and overturning moment.

[0075] The topographic geometric features of each grid node in the area to be planned are extracted, including slope angle and roll angle. Environmental parameter labels for each node are also obtained, providing accurate data input for subsequent demand force vector calculations. Slope angle and roll angle are geometric parameters describing terrain undulation and tilt, directly affecting the stress state of vehicles. Environmental parameter labels provide information on the physical properties of the terrain, such as soil type and moisture content. For example, the slope angle and roll angle of each grid node can be obtained through LiDAR scanning, stereo vision systems, or high-precision digital elevation model (DEM) data. Environmental parameter labels can be queried and correlated through remote sensing image analysis, soil sensor data, or pre-established regional environmental databases. Alternatively, inertial measurement units (IMUs) combined with GPS can be used to measure local slope angles and roll angles in real time during vehicle operation. Environmental parameter labels can be obtained through manual surveying, geological mapping analysis, or machine learning-based image recognition techniques to classify terrain surface features.

[0076] The reference motion state of the contact components is set. This reference motion state characterizes the expected maneuverability of the unmanned ground vehicle in off-road missions. It includes a preset cruise speed and a preset maximum acceleration. The reference motion state defines the performance target the unmanned ground vehicle is expected to achieve in off-road missions and forms the basis for calculating the required forces to maintain this motion state. The preset cruise speed and preset maximum acceleration are key indicators for measuring vehicle maneuverability, directly determining the inertial forces and drag that the vehicle needs to overcome in specific terrains. The reference motion state can be set according to specific mission requirements and vehicle design parameters. The preset cruise speed and preset maximum acceleration can be manually entered by the operator, loaded from a preset configuration file according to the mission type, or analyzed from historical operational data of the unmanned ground vehicle.

[0077] Based on terrain geometry and reference motion state, the normalized required force vector to maintain motion state is obtained through inverse solution of the force balance equation. This normalized required force vector includes longitudinal traction force, vertical support force, and overturning moment, transforming terrain information and motion targets into specific mechanical requirements. By inversely solving the force balance equation, the mechanical response that contact components of an unmanned ground vehicle need to obtain from the ground under specific terrain and motion states can be calculated scientifically and accurately. Normalization allows direct comparison of mechanical quantities with a normalized three-dimensional failure envelope, thereby assessing stability margin. Longitudinal traction force, vertical support force, and overturning moment are key physical quantities describing the mechanical state of the interaction between the unmanned ground vehicle and the ground, comprehensively reflecting the vehicle's stability and maneuverability. The inverse solution of the force balance equation can be based on the vehicle's dynamics model. For example, a simplified vehicle-terrain interaction model can be established, considering factors such as gravity, inertial force, rolling resistance, and air resistance, and combined with the terrain's slope angle and roll angle. The required longitudinal traction force, vertical support force, and overturning moment can be obtained by solving linear or nonlinear equations. Normalization is performed according to a preset baseline mechanical value. Alternatively, more complex finite element analysis (FEA) or multibody dynamics (MBD) simulation software can be used, taking terrain geometry and reference motion states as input, and using iterative calculations or optimization algorithms to deduce the mechanical components required to maintain the motion state. Normalization can use the maximum possible force value or the vehicle's own weight as a reference baseline.

[0078] The embodiments of this application extract slope angle and roll angle as terrain geometric features and obtain environmental parameter labels, providing comprehensive and accurate input for the calculation of demand force vectors, reducing errors caused by incomplete or inaccurate terrain information. Setting preset cruising speed and preset maximum acceleration as reference motion states ensures that the calculation of demand force vectors is closely integrated with the actual mission requirements and expected maneuverability of unmanned ground vehicles, guaranteeing the rationality of motion state index settings. Employing inverse kinematics of force balance equations ensures the scientific validity and consistency of demand force vector calculations from a physical principle perspective, thereby improving the accuracy of demand force vectors. The normalized demand force vector includes longitudinal traction force, vertical support force, and overturning moment. After normalization, the mechanical components can be directly compared with the normalized three-dimensional failure envelope, laying the foundation for accurate subsequent stability margin assessment, thus improving the safety and reliability of path planning. Therefore, it is possible to more accurately query and calculate stability margins in the proxy model library, making the unmanned ground vehicle off-road path planning method based on the stability margin field in this application embodiment more refined and reliable in assessing the mechanical passability of unmanned ground vehicles.

[0079] like Figure 4As shown, in some embodiments, the step of obtaining the normalized required force vector to maintain the motion state by inverse solving the force balance equation based on terrain geometry features and a reference motion state includes: Calculate the longitudinal traction force using the following formula. :

[0080] in, To allocate weight to the contact components, It is the acceleration due to gravity. For rolling resistance, The preset maximum acceleration; Calculate the vertical support force using the following formula. :

[0081] in, The slope angle; Calculate the overturning moment using the following formula. :

[0082] in, It is a lateral force. The effective height from the contact point to the torque reference center. For vertical loads, Load eccentricity caused by structural design; The grid nodes are obtained using the following formula. Absolute demand force vector :

[0083] The demand force vector is obtained through the following formula. Normalization is performed to obtain the normalized demand force vector. : .

[0084] The embodiments of this application accurately calculate the mechanical parameters required for unmanned ground vehicles to maintain their motion state, thereby improving the comprehensiveness and reliability of mechanical assessment. As a result, when searching for the optimal path in the comprehensive cost map, it is possible to more reliably predict and avoid instability risks, significantly improving the safety of path planning.

[0085] S400. Based on the environmental parameters of the area to be planned, retrieve the corresponding surrogate model of the three-dimensional failure envelope surface from the surrogate model library, calculate the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface, and define the three-dimensional stability margin based on the minimum geometric distance.

[0086] Environmental parameters of the area to be planned can be sensed in real time through sensors (such as soil moisture sensors and soil type identification systems) or preset through a geographic information system. Based on the acquired environmental parameters, the best-matching surrogate model is searched in a pre-built surrogate model library, or a failure envelope surrogate model obtained through interpolation is selected. Through the corresponding three-dimensional failure envelope model, the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope can be obtained. The minimum geometric distance reflects the safety margin between the current demand force vector and the ultimate bearing capacity. Based on this minimum geometric distance, a three-dimensional stability margin can be defined. For example, when the demand force vector is located inside the failure envelope, the stability margin is defined as a positive value, indicating that the vehicle is in a stable state; when the demand force vector is located at the boundary or outside the failure envelope, the stability margin is defined as zero or a negative value, indicating that the vehicle is in a critical or unstable state.

[0087] By setting a three-dimensional stability margin, the mechanical stability of a vehicle under current operating conditions can be quantified, providing a key risk assessment indicator for path planning.

[0088] like Figure 5 As shown, in some embodiments, the steps of retrieving the corresponding surrogate model of the three-dimensional failure envelope surface from the surrogate model library based on the environmental parameters of the area to be planned, calculating the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface, and defining the three-dimensional stability margin based on the minimum geometric distance include: Based on the soil physical parameters of the grid nodes, the adjacent parameter nodes are retrieved in the surrogate model library. The surrogate model parameters of the three-dimensional failure envelope surface corresponding to the grid nodes are calculated by weighted interpolation. The reconstructed three-dimensional failure envelope surface is obtained based on the surrogate model parameters. Find the minimum Euclidean distance from the normalized demand force vector to the reconstructed 3D failure envelope surface; Determine the positional relationship between the normalized demand force vector and the reconstructed three-dimensional failure envelope surface; Based on the fact that the normalized demand force vector lies inside the three-dimensional failure envelope, the three-dimensional stability margin is defined as the positive value of the minimum Euclidean distance. Based on the fact that the normalized demand force vector is located on the boundary or outside of the three-dimensional failure envelope, the three-dimensional stability margin is defined as the negative value of the minimum Euclidean distance.

[0089] Soil physical parameters refer to quantitative indicators that describe the mechanical and physical properties of soil, such as soil moisture content, density, cohesion, internal friction angle, and particle size distribution. Soil physical parameters directly affect the soil's bearing capacity and deformation characteristics, thus determining the mobility and stability of unmanned ground vehicles under different soil conditions.

[0090] Retrieving neighboring parameter nodes refers to finding, within the surrogate model library, several stored parameter nodes that are closest to or most relevant to the soil physical parameters of the current raster node. As an example, this can be achieved by calculating distances in the parameter space to determine the most representative surrogate model data for the current environmental parameters.

[0091] Weighted interpolation is a method that estimates the 3D failure envelope surrogate model parameters of the current grid node by linearly or nonlinearly combining adjacent parameter nodes and their corresponding surrogate model parameters with different weights. Commonly used interpolation methods include inverse distance weighted interpolation, radial basis function interpolation, and kriging interpolation. Interpolation can generate continuous and smooth model parameters based on a finite number of discrete data points.

[0092] Reconstructing the three-dimensional failure envelope surface refers to dynamically constructing a three-dimensional failure envelope surface that matches the soil physical parameters of the current grid node by using surrogate model parameters obtained through weighted interpolation and combining them with a preset mathematical model form. This allows the failure envelope surface to accurately reflect the mechanical failure boundary under a specific local environment.

[0093] The minimum Euclidean distance is the shortest straight-line distance between the point represented by the normalized demand force vector in three-dimensional mechanical space and any point on the reconstructed three-dimensional failure envelope surface. As an example, the minimum Euclidean distance can be solved using numerical methods (such as gradient descent or Lagrange multiplier methods) or geometric methods. The minimum Euclidean distance result quantifies the margin between the vehicle's current mechanical requirements and the soil's ultimate bearing capacity.

[0094] When the normalized demand force vector lies within the three-dimensional failure envelope, it indicates that the mechanical load currently required by the unmanned ground vehicle is far less than the ultimate bearing capacity of the soil, and the unmanned ground is in a safe and stable state. In this case, the calculated minimum Euclidean distance is defined as a positive three-dimensional stability margin, thus providing an indicator for subsequent evaluation.

[0095] When the normalized demand force vector is located at or outside the critical boundary of the three-dimensional failure envelope, it indicates that the mechanical load currently required on the unmanned ground has reached or exceeded the ultimate bearing capacity of the soil, and vehicles are at risk of getting stuck, skidding, or overturning. In this case, the calculated minimum Euclidean distance is defined as a negative three-dimensional stability margin, thus providing an indicator for subsequent evaluation.

[0096] The embodiments of this application can calculate the three-dimensional stability margin through the soil physical parameters of the grid nodes. The three-dimensional stability margin can provide a clear and quantitative basis for the subsequent construction of the risk cost function, which significantly improves the reliability and safety of path planning.

[0097] In some embodiments, the step of reconstructing the three-dimensional failure envelope surface proxy model parameters corresponding to the grid nodes by retrieving adjacent parameter nodes in the proxy model library based on the soil physical parameters of the grid nodes, calculating the proxy model parameters based on the weighted interpolation, and obtaining the reconstructed three-dimensional failure envelope surface based on the proxy model parameters includes: Obtain the soil physical parameters for each grid node. ; In the proxy model library Searching for soil physical parameters The parameter node whose Euclidean distance is closest; The shape coefficient vector of the retrieved parameter nodes is used as follows: Model coefficients for grid nodes Perform weighted interpolation calculations:

[0098] in, For the model coefficients of the grid nodes Corresponding shape parameters The value, For the model coefficients of the grid nodes Corresponding shape parameters The value, For the model coefficients of the grid nodes Corresponding shape parameters The value, For the model coefficients of the grid nodes Corresponding index The value, For the model coefficients of the grid nodes Corresponding index The value, For the model coefficients of the grid nodes Corresponding index The value, For the model coefficients of the grid nodes The corresponding center offset of the three-dimensional failure envelope surface on the vertical load axis The value; Will Substitute into mathematical model In order to obtain the reconstructed three-dimensional failure envelope surface. :

[0099] The steps for finding the minimum Euclidean distance from the normalized demand force vector to the reconstructed 3D failure envelope include: The normalized demand force vector is calculated using the following formula. Minimum Euclidean distance to the reconstructed 3D failure envelope surface :

[0100] in, To reconstruct the three-dimensional failure envelope surface any point; The steps for determining the positional relationship between the normalized demand force vector and the reconstructed three-dimensional failure envelope surface include: Normalized demand force vector Substitute the coordinates of the points into To obtain the calculated value ; according to The normalized demand force vector is determined to be located inside the three-dimensional failure envelope surface. according to The normalized demand force vector is determined to be located outside the three-dimensional failure envelope surface; according to The normalized demand force vector is located at the boundary of the three-dimensional failure envelope. Based on the fact that the normalized demand force vector lies inside the three-dimensional failure envelope, the steps to define the three-dimensional stability margin as a positive value of the minimum Euclidean distance include: Based on the fact that the normalized demand force vector lies inside the three-dimensional failure envelope, a three-dimensional stability margin is defined. First three-dimensional stability margin for ; The steps for defining the three-dimensional stability margin as the negative of the minimum Euclidean distance, based on the normalized demand force vector being located at or outside the three-dimensional failure envelope facing the boundary or external surface, include: The three-dimensional stability margin is defined based on whether the normalized demand force vector is located at the boundary or outside of the three-dimensional failure envelope. The second three-dimensional stability margin value for .

[0101] Obtain the soil physical parameters for each grid node. This provides fundamental environmental data input for subsequent model reconstruction, ensuring that the reconstructed model accurately reflects the actual terrain features. For example, soil physical parameters of the current grid nodes can be collected in real time using soil sensors (such as soil moisture sensors, soil density sensors, and soil shear strength sensors) mounted on unmanned ground vehicles; alternatively, soil physical parameters can be queried based on the geographical location of the grid nodes using a pre-established Geographic Information System (GIS) database; or, soil type and state can be estimated through remote sensing image analysis or machine learning models to obtain... .

[0102] In the proxy model library Searching for the soil physical parameters The parameter node with the closest Euclidean distance can be identified from a pre-built library of discrete surrogate models, finding one or more reference points that most closely match the soil physical parameters of the current raster node, thus providing a data foundation for subsequent interpolation calculations. As an example, the calculation can be performed on the... With the proxy model library All discrete soil parameter nodes The Euclidean distance between the nodes is used, and the node with the smallest distance is selected as the nearest parameter node; alternatively, to improve retrieval efficiency, spatial index structures such as Kd-trees and ball trees can be used to index the proxy model library. Preprocessing is performed to quickly locate and The parameter node with the closest Euclidean distance.

[0103] Weighted interpolation allows model parameters to smoothly adapt to the specific soil parameters of the current grid node, overcoming the limitations of directly using discrete node parameters. For example, linear interpolation methods can be used, based on... The shape coefficient vector is obtained by weighting the distances between the retrieved neighboring parameter nodes. Alternatively, more complex interpolation methods such as radial basis function (RBF) interpolation and Kriging interpolation can be used to obtain smoother and more accurate interpolation results, further improving the adaptability of model parameters.

[0104] Using the accurate model coefficients obtained through interpolation, a personalized three-dimensional failure envelope surface suitable for the current soil conditions of the grid nodes is dynamically constructed.

[0105] This application's embodiments effectively address the model mismatch problem that may arise when discrete proxy model libraries handle continuously changing real-world environmental parameters by introducing a weighted interpolation mechanism. This is achieved by obtaining the soil physical parameters of each grid node. The system retrieves the nearest parameter nodes to ensure that the starting point for interpolation calculations is highly relevant to the actual environment. Based on this, model coefficients adapted to the specific soil parameters of the current grid node are obtained through weighted interpolation. This approach achieves a smooth transition and adaptive adjustment of model parameters, avoiding the rigid matching of discrete node coefficients. Finally, by substituting the precise interpolation coefficients into the mathematical model, a high-fidelity reconstructed 3D failure envelope surface can be obtained. Therefore, a matching three-dimensional failure envelope can be dynamically generated based on the soil environment, which significantly improves the accuracy of three-dimensional failure envelope reconstruction and enhances the robustness of mechanical risk assessment in off-road path planning for unmanned ground vehicles.

[0106] S500: Construct a risk cost function based on the three-dimensional stability margin, construct a distance cost function based on the minimum geometric distance, and construct a comprehensive cost map based on the risk cost function and the distance cost function.

[0107] This risk cost function aims to translate the vehicle's mechanical stability into costs in path planning. For example, when the three-dimensional stability margin is positive, the risk cost can be a function that decreases as the margin increases, indicating that the more stable the path, the lower the risk and the smaller the cost. When the three-dimensional stability margin is zero or negative, the risk cost can be set to an extremely high value or infinity to prevent the vehicle from entering the relevant area. A distance cost function can be constructed based on the minimum geometric distance. This function is typically related to factors such as path length, travel time, or energy consumption, and is used to measure path efficiency. Finally, the risk cost function and the distance cost function are weighted and combined to construct a comprehensive cost map. In the comprehensive cost map, each potential waypoint is assigned a comprehensive cost, which considers both mechanical stability and path efficiency, providing a comprehensive evaluation criterion for path planning algorithms.

[0108] In some embodiments, the steps of constructing a risk cost function based on a three-dimensional stability margin, constructing a distance cost function based on a minimum geometric distance, and constructing a comprehensive cost map based on the risk cost function and the distance cost function include: Based on the fact that the normalized demand force vector is located at or outside the three-dimensional failure envelope facing the boundary, the risk cost function is constructed using the following formula. First cost function :

[0109] Based on the fact that the normalized demand force vector lies within the three-dimensional failure envelope, the risk cost function is constructed using the following formula. The second cost function : ;or,

[0110] in, For adjustment coefficients, The preset risk weight coefficient is used to adjust the sensitivity of the planning algorithm to mechanical stability. To prevent small quantities with a denominator of zero; The total cost function for each node is generated using the following formula. And form a comprehensive cost map;

[0111] in, For grid nodes Three-dimensional stability margin , This is a safety weight used to adjust the sensitivity to mechanical risks; Efficiency weights are used to adjust the sensitivity to path length. The distance cost function is used to characterize the distance the vehicle travels to the node. Cost of the required path length.

[0112] The first cost function can set an infinitely high risk cost for the mechanically unstable areas that unmanned ground vehicles may encounter during off-road driving, fundamentally eliminating any path selection that may lead to vehicle instability.

[0113] The second cost function quantifies the risk cost of unmanned ground vehicles within a mechanically stable region. This second cost function allows for fine-grained differentiation of different levels of stability within a safe range, thereby guiding the path planning algorithm to prioritize safer areas.

[0114] use When. The larger, The closer the risk margin is to zero, the lower the risk cost. This simulates the non-linear decrease in risk with increasing safety margin, causing risk to increase rapidly in areas with small safety margins and to level off in areas with large safety margins. This avoids overly conservative approaches while ensuring safety. At that time, The larger the denominator, the smaller the risk cost, providing an intuitive way to quantify risk. Risk is inversely proportional to stability margin, meaning that risk increases sharply when the stability margin approaches zero, and gradually decreases when the stability margin is large. The second cost function can effectively distinguish different levels of stability within a safe region, providing a refined risk assessment for path planning.

[0115] Total cost function Each grid node Mechanical risk cost With distance cost Weighted combinations are used to form a comprehensive evaluation index, which is then used to construct a comprehensive cost map. The total cost function achieves a balance between safety and efficiency. This is achieved through adjustments... and The relative size of the path can be dynamically adjusted according to specific task requirements (e.g., prioritizing safety in extreme terrain and efficiency in flat terrain). This can be simply represented as the distance from the starting point to the current node. The cumulative path length, or from the current node The heuristic distance to the destination. Furthermore, It can also be defined as a vehicle moving from the previous node to the current node. The required energy consumption, time cost, or other efficiency-related metrics. Therefore, the total cost function... It can flexibly integrate multiple optimization objectives, so that the comprehensive cost map not only reflects mechanical stability, but also takes into account other important path planning factors, such as fuel consumption or task completion time.

[0116] This application defines a risk cost function, constructs a comprehensive cost function, and establishes a search graph to facilitate efficient planning of safe paths in subsequent steps while considering mechanical stability. By setting the first cost function to infinity, the selection of unstable nodes is completely avoided. Simultaneously, by employing an exponential decay function or its reciprocal in the second cost function, the positive impact of the safety margin is quantified, solving the problem of how to finely adjust risk sensitivity within the safe region. When generating the total cost function, risk cost and distance cost are combined, and safety and efficiency are balanced through weighting coefficients, enabling the comprehensive cost map to reflect multi-objective optimization needs. Establishing a search graph and maintaining the actual cumulative cost, heuristically estimated cost, and total evaluated cost solves the problem of efficiently managing node information in complex environments, providing a data foundation for heuristic search.

[0117] S600: Construct a comprehensive cost map based on three-dimensional stability margin, and search for the optimal path in the comprehensive cost map.

[0118] Searching for the optimal path in the comprehensive cost map ensures that the planned path is not only geometrically feasible but also mechanically stable, thereby effectively preventing unmanned ground vehicles from getting stuck, slipping, or overturning during off-road driving, and improving the vehicle's off-road capability and safety in complex unstructured terrain.

[0119] As an example, graph search algorithms (such as A* algorithm, Dijkstra's algorithm) or sampling algorithms (such as RRT* algorithm) can be used to search for the optimal path from the starting point to the ending point.

[0120] In some embodiments, the step of constructing a comprehensive cost map based on a three-dimensional stability margin and searching for the optimal path in the comprehensive cost map includes: Establish a search graph containing all grid nodes within the planning area, and maintain the actual cumulative cost, heuristic estimated cost, and total evaluation cost including the maintenance of actual cumulative cost and heuristic estimated cost for each grid node; The search steps include: defining an open list and adding raster nodes. Add the starting point to the open list; traverse the neighboring nodes of the grid node with the minimum total evaluation cost, filter out the neighboring nodes with a 3D stability margin greater than 0, and add them to the open list; calculate the actual cumulative cost of the neighboring nodes with a 3D stability margin greater than 0. Repeat the search steps until the endpoint is added to the open list. Backtrack from the endpoint to the starting point to obtain the initial optimal path. Smooth the initial optimal path to obtain the optimal path.

[0121] A search graph containing all grid nodes within the planning area is established. For each grid node, an actual cumulative cost, a heuristic estimated cost, and a total evaluation cost including both are maintained. This provides the necessary data structures and evaluation mechanisms for path search algorithms (such as the A* algorithm). The search graph is a discretized representation of the planning area, with each grid node representing a potential vehicle location, providing a foundation for efficient heuristic search. The actual cumulative cost records the actual path cost from the starting point to the current grid node. The heuristic estimated cost is an estimate of the minimum cost from the current grid node to the destination. The total evaluation cost is used to evaluate the priority of nodes during the search process. Maintaining the cost allows the search algorithm to effectively explore the search space and avoid unnecessary computation. The search graph can be constructed using data structures such as two-dimensional arrays or adjacency lists to represent grid nodes and their connections. Each grid node object can contain its coordinates, a parent node pointer, and storage fields for the three costs mentioned above. Through structured data management, the path search algorithm can quickly access and update node information, thereby improving search efficiency.

[0122] An open list is defined, and the starting point of each grid node is added to the open list. The neighboring nodes of the grid node with the minimum total evaluated cost are traversed, and neighboring nodes with a 3D stability margin greater than 0 are selected and added to the open list. The actual cumulative cost of the neighboring nodes with a 3D stability margin greater than 0 is calculated. The open list stores a set of nodes to be explored, usually sorted by total evaluated cost. Its purpose is to efficiently find the optimal path while ensuring mechanical stability. First, the starting point is added to the open list. In each iteration, the node with the minimum total evaluated cost is taken from the open list and expanded. When traversing the neighboring nodes of this node, only those neighboring nodes with a 3D stability margin greater than 0 (i.e., in a safe region) are considered. For these selected safe nodes, their actual cumulative cost from the starting point to themselves is calculated and added to the open list. This ensures that the path always avoids unstable regions. The open list is usually implemented using a priority queue to ensure that the node with the minimum total evaluated cost is retrieved efficiently each time. Understandably, when calculating the actual cumulative cost to adjacent nodes, the movement cost from the current node to the adjacent node is considered, and this cost can be determined based on the total cost function mentioned above. Through iterative and filtering processes, paths from the starting point to the ending point that meet the mechanical stability requirements can be gradually selected.

[0123] The search steps are repeated until the endpoint is added to the open list. The initial optimal path is then obtained by backtracking from the endpoint back to the starting point. This initial optimal path is smoothed to obtain the optimal path. The search continues until the endpoint node is added to the open list and ultimately selected for expansion. The expansion of the endpoint means that a path from the starting point to the endpoint has been found. At this point, the initial optimal path is obtained by backtracking from the endpoint node along its parent node pointers back to the starting point. The backtracking mechanism allows for efficient path reconstruction because each node records its best predecessor node during the search process. The initial optimal path typically consists of a series of discrete grid nodes, which are then smoothed. Smoothing can be achieved through various methods, such as fitting path points with B-spline curves or Bézier curves, or adjusting the coordinates of path points through iterative averaging or window filtering to eliminate sharp corners and generate a continuous, gently curvatured final optimal path that conforms to vehicle kinematic constraints, thereby improving the executability of the path and the comfort of vehicle driving.

[0124] like Figure 6 As shown, this application achieves efficient planning of safe paths based on mechanical stability by performing a search step. This ensures that the planned path not only minimizes the travel distance but also effectively guarantees the mechanical stability of unmanned ground vehicles under varying terrain and soil conditions, significantly reducing the risk of instability events such as getting stuck, skidding, and overturning in unstructured environments.

[0125] In some specific embodiments, the step of constructing a comprehensive cost map based on the three-dimensional stability margin and searching for the optimal path in the comprehensive cost map further includes: Define a shutdown list, which is used to store the evaluated raster nodes.

[0126] This application embodiment establishes a numerical simulation environment for the interaction between contact components and the contact medium, obtains a mathematical model of the three-dimensional failure envelope surface, and constructs a surrogate model library to achieve a quantitative assessment of the mechanical characteristics of unmanned ground vehicles interacting with the ground. By solving the normalized demand force vector and calculating its minimum geometric distance to the failure envelope surface, a three-dimensional stability margin is defined, thereby enabling accurate prediction of the vehicle's instability risk in unstructured terrain. Based on the three-dimensional stability margin, a risk cost function and a distance cost function are constructed to form a comprehensive cost map, enabling path planning to take into account both mechanical safety and path efficiency. This allows path planning to consider mechanical quantitative assessment, instability risk prediction, and path safety level differentiation, significantly improving the mobility and operational safety of unmanned ground vehicles in off-road environments.

[0127] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable storage medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), and read-only memory (ROM). Erasable Programmable Read-Only Memory (EPROM) Only memory (or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM, Compact Disc Read-Only Memory). (Only Memory). Furthermore, the computer-readable storage medium can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0128] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0129] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus 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 apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0130] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the apparatus embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0131] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0132] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for off-road path planning for unmanned ground vehicles based on a stability margin field, characterized in that, include: A numerical simulation environment for the interaction between the contact component and the contact medium is established. Multi-condition virtual loading tests are conducted in the numerical simulation environment to obtain a mathematical model of the three-dimensional failure envelope surface, wherein the three-dimensional failure envelope surface represents the ultimate force boundary between the contact component and the contact medium. Construct a normalized proxy model library for the three-dimensional failure envelope surface, the proxy model library including proxy models for the three-dimensional failure envelope surface corresponding to various environmental parameters; Based on the terrain features and preset motion state of the area to be planned, the required force vector for the contact component to maintain the motion state is calculated, and the required force vector is normalized to obtain the normalized required force vector. Based on the environmental parameters of the area to be planned, the proxy model of the corresponding three-dimensional failure envelope surface in the proxy model library is retrieved, the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface is calculated, and the three-dimensional stability margin is defined based on the minimum geometric distance. A risk cost function is constructed based on the three-dimensional stability margin, a distance cost function is constructed based on the minimum geometric distance, and a comprehensive cost map is constructed based on the risk cost function and the distance cost function. A comprehensive cost map is constructed based on the three-dimensional stability margin, and the optimal path is searched within the comprehensive cost map.

2. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 1, characterized in that, The steps of establishing a numerical simulation environment for the interaction between the contact component and the contact medium, conducting multi-condition virtual loading tests in the numerical simulation environment, and obtaining the mathematical model of the three-dimensional failure envelope surface include: A soil particle bed model based on discrete particles is established for the target soil characteristics, and the soil particle bed model is used as the contact medium. The walking mechanism model of the unmanned ground vehicle is imported into the soil particle bed model, and the walking mechanism model of the unmanned ground vehicle is used as the contact component to form the numerical simulation environment. In the numerical simulation environment, the contact component is planned using the Latin hypercube sampling method, and the contact component is subjected to working condition loading on the contact medium. A three-dimensional set of stress data points characterizing the critical failure state of the contact medium is collected, and the three-dimensional set of stress data points is normalized to obtain a normalized set of failure data points. The normalized failure data point set is reconstructed using a mathematical fitting method to obtain a mathematical model of the three-dimensional failure envelope surface.

3. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 2, characterized in that, The step of collecting a three-dimensional stress data point set characterizing the critical failure state of the contact medium, and normalizing the three-dimensional stress data point set to obtain a normalized failure data point set includes: Collect a set of three-dimensional stress data points characterizing the critical failure state of the contact medium. ,in, For the first The maximum horizontal traction force at the critical state of contact medium failure for each data point. For the first The maximum vertical force at the critical failure state of the contact medium at each data point. For the first The maximum bending moment at the critical failure state of the contact medium at each data point. It is a positive integer; Select the three-dimensional force data point set The largest vertical force and the global mechanical reference value Recorded as ,in The characteristic width of the contact component; The normalized failure data point set is calculated using the following formula ( ): in, For the first The normalized value of the maximum horizontal traction force at the critical state of contact medium failure for each data point. For the first The normalized value of the maximum vertical force at the critical failure state of the contact medium for each data point. For the first The normalized value of the maximum bending moment of the critical state of failure of the contact medium at each data point.

4. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 3, characterized in that, The step of reconstructing the normalized failure data point set using a mathematical fitting method to obtain the mathematical model of the three-dimensional failure envelope surface includes: Least squares ellipsoid fitting is used to reconstruct the surface of the normalized failure data point set, and a mathematical model of the three-dimensional failure envelope surface in the following form is constructed. : in, All are shape parameters. All are indices. The offset of the center of the three-dimensional failure envelope surface on the vertical load axis.

5. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 4, characterized in that, The step of constructing a normalized proxy model library for the three-dimensional failure envelope surface includes: Select a set of environmental parameters that affect the passage capability of the contact component. ={ }; M typical discrete soil parameter nodes were selected from the set of environmental parameters. Based on the discrete soil parameter nodes, the contact component is planned using the Latin hypercube sampling method, and the contact component is subjected to working condition loading on the contact medium. Collect the set of ultimate stress points of the contact medium. The set of ultimate stress points characterizes the critical failure state of the contact medium based on the discrete soil parameter nodes; According to the set of limit stress points And the mathematical model of the three-dimensional failure envelope surface, for each discrete soil parameter node The corresponding hyperellipsoid shape coefficient vector To solve, where, To and Corresponding shape parameters , To and Corresponding shape parameters , To and Corresponding shape parameters , To and Corresponding index , To and Corresponding index , To and Corresponding index , for The corresponding center offset of the three-dimensional failure envelope surface on the vertical load axis ; Discrete soil parameter nodes Using the index key, with the hyperellipsoid shape coefficient vector For numerical values, construct the proxy model library. .

6. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 5, characterized in that, The step of calculating the required force vector for the contact component to maintain its motion state based on the terrain features and preset motion state of the area to be planned, and then normalizing the required force vector to obtain a normalized required force vector, includes: Extract the terrain geometry features of each grid node in the area to be planned, including the slope angle and roll angle, and obtain the environmental parameter label of the node; A reference motion state is set for the contact component. The reference motion state is used to characterize the expected mobility performance index of the unmanned ground vehicle in off-road missions. The reference motion state includes a preset cruising speed and a preset maximum acceleration. Based on the aforementioned terrain geometry and reference motion state, the normalized demand force vector required to maintain the motion state is obtained by inverse solving the force balance equation. The normalized demand force vector includes longitudinal traction force, vertical support force, and overturning moment.

7. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 6, characterized in that, The step of obtaining the normalized required force vector to maintain the motion state by inverse solving the force balance equation based on the terrain geometry and reference motion state includes: The longitudinal traction force is calculated according to the following formula. : in, The weight allocated to the contact components, It is the acceleration due to gravity. For rolling resistance, The preset maximum acceleration; The vertical support force is calculated according to the following formula. : in, The slope angle; The overturning moment is calculated according to the following formula. : in, It is a lateral force. The effective height from the contact point to the torque reference center. For vertical loads, Load eccentricity caused by structural design; The grid nodes are obtained using the following formula. Absolute demand force vector : The demand force vector is expressed by the following formula. Normalization is performed to obtain the normalized demand force vector. : 。 8. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 7, characterized in that, The steps of retrieving the surrogate model corresponding to the three-dimensional failure envelope surface from the surrogate model library based on the environmental parameters of the area to be planned, calculating the minimum geometric distance from the normalized demand force vector to the three-dimensional failure envelope surface, and defining the three-dimensional stability margin based on the minimum geometric distance include: Based on the soil physical parameters of the grid nodes, adjacent parameter nodes are retrieved in the proxy model library, and the three-dimensional failure envelope proxy model parameters corresponding to the grid nodes are calculated by weighted interpolation. The reconstructed three-dimensional failure envelope is obtained based on the proxy model parameters. Find the minimum Euclidean distance from the normalized demand force vector to the reconstructed three-dimensional failure envelope surface; Determine the positional relationship between the normalized demand force vector and the reconstructed three-dimensional failure envelope surface; Based on the fact that the normalized demand force vector is located inside the three-dimensional failure envelope, the three-dimensional stability margin is defined as the positive value of the minimum Euclidean distance; Based on the fact that the normalized demand force vector is located at the boundary or outside of the three-dimensional failure envelope, the three-dimensional stability margin is defined as the negative value of the minimum Euclidean distance.

9. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 8, characterized in that, The step of retrieving adjacent parameter nodes in the surrogate model library based on the soil physical parameters of the grid nodes, calculating the 3D failure envelope surrogate model parameters corresponding to the grid nodes through weighted interpolation, and obtaining the reconstructed 3D failure envelope based on the surrogate model parameters includes: Obtain the soil physical parameters for each of the grid nodes. ; In the proxy model library Searching for the soil physical parameters The parameter node whose Euclidean distance is closest; The shape coefficient vector of the retrieved parameter node is used according to the following formula. Model coefficients for the grid nodes Perform weighted interpolation calculations: in, The model coefficients of the grid nodes Corresponding shape parameters The value, The model coefficients of the grid nodes Corresponding shape parameters The value, The model coefficients of the grid nodes Corresponding shape parameters The value, The model coefficients of the grid nodes Corresponding index The value, The model coefficients of the grid nodes Corresponding index The value, The model coefficients of the grid nodes Corresponding index The value, The model coefficients of the grid nodes The corresponding center offset of the three-dimensional failure envelope surface on the vertical load axis The value; Will Substitute into mathematical model In order to obtain the reconstructed three-dimensional failure envelope surface : The step of finding the minimum Euclidean distance from the normalized demand force vector to the reconstructed three-dimensional failure envelope surface includes: The normalized demand force vector is calculated using the following formula. Minimum Euclidean distance to the reconstructed three-dimensional failure envelope surface : in, To reconstruct the three-dimensional failure envelope surface any point; The step of determining the positional relationship between the normalized demand force vector and the reconstructed three-dimensional failure envelope surface includes: The normalized demand force vector Substitute the coordinates into To obtain the calculated value ; according to It is determined that the normalized demand force vector is located inside the three-dimensional failure envelope surface; according to It is determined that the normalized demand force vector is located outside the three-dimensional failure envelope surface; according to It is determined that the normalized demand force vector is located at the boundary of the three-dimensional failure envelope. The step of defining the three-dimensional stability margin as a positive value of the minimum Euclidean distance based on the fact that the normalized demand force vector lies inside the three-dimensional failure envelope surface includes: Based on the fact that the normalized demand force vector lies within the three-dimensional failure envelope, a three-dimensional stability margin is defined. First three-dimensional stability margin for ； The step of defining the three-dimensional stability margin as the negative of the minimum Euclidean distance based on the normalized demand force vector being located at or outside the three-dimensional failure envelope facing the boundary boundary includes: The three-dimensional stability margin is defined based on whether the normalized demand force vector is located at or outside the three-dimensional failure envelope, facing the boundary or outside. The second three-dimensional stability margin value for 。 10. The off-road path planning method for unmanned ground vehicles based on a stability margin field according to claim 9, characterized in that, The steps of constructing a risk cost function based on the three-dimensional stability margin, constructing a distance cost function based on the minimum geometric distance, and constructing a comprehensive cost map based on the risk cost function and the distance cost function include: Based on the fact that the normalized demand force vector is located at or outside the three-dimensional failure envelope, a risk cost function is constructed using the following formula: First cost function : Based on the fact that the normalized demand force vector lies within the three-dimensional failure envelope, the risk cost function is constructed using the following formula. The second cost function : ;or, in, For adjustment coefficients, The preset risk weight coefficient is used to adjust the sensitivity of the planning algorithm to mechanical stability. To prevent small quantities with a denominator of zero; The total cost function for each node is generated using the following formula. And form a comprehensive cost map; in, To the grid node Three-dimensional stability margin , This is a safety weight used to adjust the sensitivity to mechanical risks; Efficiency weights are used to adjust the sensitivity to path length. The distance cost function is used to characterize the distance the vehicle travels to the node. Required path length cost; The step of constructing a comprehensive cost map based on the three-dimensional stability margin and searching for the optimal path in the comprehensive cost map includes: Establish a search graph containing all the grid nodes within the planning area, and maintain the actual cumulative cost, heuristic estimated cost, and total evaluation cost including the actual cumulative cost and the heuristic estimated cost for each grid node; The search step includes: defining an open list and adding the raster nodes. Add the starting point to the open list; traverse the neighboring nodes of the grid node with the minimum total evaluation cost, filter out the neighboring nodes with a three-dimensional stability margin greater than 0, and add them to the open list; calculate the actual cumulative cost of the neighboring nodes with a three-dimensional stability margin greater than 0. Repeat the search steps until the endpoint is added to the open list. Backtrack from the endpoint to the starting point to obtain the initial optimal path. Smooth the initial optimal path to obtain the optimal path.

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