An off-road vehicle low-energy path tracking control method and system

Abstract

The application discloses a kind of off-road vehicle low-energy consumption path tracking control method and system, method includes: establishing two-axis off-road vehicle equivalent simplified dynamics model, four-wheel ground effect is equivalent to front, rear axle concentrated tire force;Based on the equivalent simplified model, an expert database and a steady-state response database are constructed, a data-driven compensation model is trained to learn the expert steering rule and compensate for model prediction errors;Tire slip energy consumption is introduced into the optimization objective, and the optimal control amount is selected by combining the path tracking error and the vehicle stability index to comprehensively evaluate the candidate steering control amount.The application reduces the online calculation burden of the model while improving the prediction accuracy in complex off-road conditions, achieving a coordinated optimization of path tracking accuracy and tire slip energy consumption, and is suitable for autonomous driving control of vehicles in complex off-road scenarios such as soft soil, gravel road or low adhesion unpaved road.

Description

Technical Field

[0001] This invention relates to the field of off-road vehicle path tracking technology, and in particular to a low-energy path tracking control method and system for off-road vehicles. Background Technology

[0002] Autonomous driving control for off-road vehicles typically includes environmental perception, terrain recognition, path planning, speed planning, and path tracking. One approach focuses on acquiring surrounding environmental information through lidar, visual sensors, or integrated navigation systems, then combining this information with path search, rule-based judgment, or fuzzy control methods to generate a drivable path. Another approach establishes a path tracking controller based on a vehicle dynamics model, controlling the front wheel steering angle, driving torque, or braking torque to ensure the vehicle follows a predetermined trajectory as closely as possible. These methods contribute to improving the off-road capability and autonomous driving ability of vehicles.

[0003] However, the path-following problem for off-road vehicles is not simply a matter of "whether they can follow the path." Under conditions of continuous steering, low adhesion, or soft surfaces, tires will exhibit significant lateral and longitudinal slippage. The vehicle frequently adjusts its steering to correct trajectory errors, resulting in additional tire slippage energy consumption. Control methods that only focus on path errors and do not incorporate tire slippage energy consumption into their evaluation may allow the vehicle to complete the path-following process, but this may be accompanied by a significant amount of ineffective slippage and substantial tire slippage energy consumption.

[0004] Existing technologies include: The invention patent titled "A Reconfigurable Wheeled and Tracked Universal Distributed Drive Unmanned Vehicle and Its Control Method" (patent application number: CN115107904B) classifies off-road conditions by acquiring three-dimensional spatial information, vehicle status information, and road scene information. Based on collision risk, path search results, and weighted evaluation results, it generates a target planning path, enabling the unmanned vehicle to complete path travel in scenarios such as soft off-road surfaces, hard mountain roads, or paved roads. The focus of this solution is on off-road condition identification, path planning, and passability control. The invention patent titled "An Automatic Identification and Control System and Method for Unmanned Off-Road Vehicles Crossing Ditches" (patent application number: CN109808509A) acquires obstacle information around the vehicle through image processing and information fusion. Combined with the vehicle's pose, it determines the size of the ditch and crossing conditions. When the crossing conditions are met, it generates a crossing path, path points, and speed information. Then, the path tracking module controls the steering wheel angle and drive wheel torque, enabling the off-road vehicle to complete the ditch crossing task. This solution is mainly aimed at specific negative obstacle scenarios, focusing on solving the problems of obstacle identification, crossing path generation, and path execution.

[0005] During path tracking, off-road vehicles often encounter slippage between the tires and the ground due to the prevalence of soft soil, gravel, or low-adhesion unpaved surfaces. This slippage occurs when the vehicle corrects its steering angle according to the target path, causing relative sliding in the tire contact area. Consequently, some driving energy is converted into frictional energy loss between the tire and the ground, increasing the energy consumption due to ineffective tire slippage during path tracking. Furthermore, the dynamic response of off-road vehicles is significantly affected by changes in road surface adhesion, vehicle attitude disturbances, and tire slippage. Using only a fixed, simplified equivalent model for vehicle state prediction can easily lead to discrepancies between the model predictions and the actual vehicle response, resulting in inaccurate steering control. Consequently, the controller struggles to simultaneously achieve both path tracking accuracy and reduced tire slippage energy consumption. Therefore, existing off-road vehicle path tracking control methods still suffer from insufficient model prediction accuracy under complex conditions, inaccurate steering control, and difficulty in effectively reducing tire slippage energy consumption. Summary of the Invention

[0006] The purpose of this invention is to provide a low-energy path tracking control method and system for off-road vehicles based on an equivalent simplified model and data-driven compensation. This reduces the online computational burden on the vehicle dynamics model under complex off-road conditions, improves the accuracy of path tracking, minimizes the impact of changes in road surface adhesion and tire slippage on the prediction results of the equivalent simplified model, and reduces energy loss caused by tire slippage while ensuring lateral error, heading error, and yaw stability.

[0007] The technical solution adopted in this invention is:

[0008] A low-energy path tracking control method for off-road vehicles includes the following steps:

[0009] S1: Establish an equivalent simplified dynamic model of a two-axle off-road vehicle, and convert the left and right wheels and wheel-ground action of the off-road vehicle into equivalent tire forces of the front axle and the rear axle, so as to obtain an equivalent simplified dynamic model for real-time control.

[0010] S2: Based on the equivalent simplified dynamic model, an expert database and a steady-state response database are constructed, and the expert database and steady-state response database are used to train the data-driven compensation model, so that the data-driven compensation model learns the expert steering control law and compensates for the prediction error of the equivalent simplified dynamic model under complex off-road conditions.

[0011] S3: Incorporate tire slip energy consumption into the path tracking control optimization objective, combine path tracking error index and vehicle stability index to comprehensively evaluate candidate steering control quantities, and select the optimal steering control quantity during real-time path tracking to achieve low-energy path tracking control for off-road vehicles.

[0012] Furthermore, the method for establishing the equivalent simplified dynamic model in step S1 is as follows:

[0013] Based on the overall vehicle weight of the two-axle off-road vehicle yaw moment of inertia Distance from front axle to center of gravity Distance from rear axle to center of gravity Longitudinal speed , centroid side slip angle yaw rate Front wheel equivalent steering angle The combined wheel-to-ground forces of the front left and front right wheels are converted into an equivalent lateral force on the front axle. The combined wheel-to-ground forces of the left and right rear wheels are converted into an equivalent lateral force on the rear axle. Establish the biaxial equivalent dynamic equation:

[0014] ;

[0015] ;

[0016] in, The rate of change of the centroid sideslip angle. Given the yaw acceleration, the front and rear axle tire slip angles can be expressed as:

[0017] ;

[0018] ;

[0019] in, This is the equivalent tire slip angle for the front axle. This is the equivalent tire slip angle for the rear axle;

[0020] Considering the adhesion coefficient, vertical load, and slip condition of the off-road surface, the equivalent tire force expressions for the front and rear axles are defined as follows:

[0021] ;

[0022] in, As axis index, Represents the front axle. Represents the rear axle; The road surface adhesion coefficient, as axis The equivalent tire slip ratio; as axis Vertical load, The unmodeled lateral force residuals are caused by soft ground, slope undulation, load transfer, and tire-soil interaction.

[0023] Establish the path tracking error dynamics equation:

[0024] ;

[0025] ;

[0026] in, For lateral error, For heading error, Let be the curvature of the target path, and ;

[0027] The For lateral error and The heading error, along with the centroid sideslip angle, constitutes the path tracking error index. and yaw rate These together constitute the vehicle stability index;

[0028] Constructing state vectors and operating condition reference quantity :

[0029] ;

[0030] ;

[0031] With equivalent front wheel steering angle As the control input, a discrete-form two-axis equivalent simplified model is obtained:

[0032] ;

[0033] Among them, among them, This is the index for the current discrete time step. For the index of the next discrete time step, To simplify the mapping function of the equivalent dynamic model, For the first The state vector of each control cycle For the first Operating condition reference values ​​for each control cycle To be applied to the first The equivalent steering angle of the front wheels for one control cycle.

[0034] Furthermore, in step S2, the expert database Build it in the following way:

[0035] ;

[0036] in, For sample index, The total number of samples; It is a combination of the current vehicle status, operating conditions, and terrain features. This may include road surface type, slope, rolling resistance estimate, vehicle pitch angle, roll angle, or terrain features identified by sensors; For experts to shift their focus to control quantities; and These represent the vehicle's state and skid energy consumption after expert control.

[0037] Furthermore, in step S2, the steady-state response database Build it in the following way:

[0038] Based on the equivalent simplified dynamic model, the vehicle's steady-state or quasi-steady-state response is obtained by traversing candidate steering angles, vehicle speeds, path curvatures, adhesion coefficients, and slip states, forming a steady-state response database.

[0039] ;

[0040] ;

[0041] in, For sample index, The total number of samples; For the first The group traverses the corresponding combination vectors of the input, and , For the first The state vector corresponding to each sample input For the first Each sample input corresponds to a working condition reference value. For the first Each sample input corresponds to a terrain feature; For the first Each sample is used to traverse the corresponding candidate front wheel equivalent turning angles; For the first Steady-state tire slip energy consumption output by the equivalent simplified dynamic model under one sample input; For the first The steady-state response vector output by the equivalent simplified dynamic model under sample input, where: For the first Steady-state centroid sideslip angle under a given sample input For the first Steady-state yaw rate under a given sample input For the first Steady-state lateral error under a given sample input For the first Steady-state heading error under a given sample input For the first Steady-state front axle equivalent tire slip ratio under a given sample input For the first Steady-state equivalent tire slip ratio of the rear axle under a sample input.

[0042] Further, in step S2, the training method of the data-driven compensation model includes:

[0043] The basic steering strategy is obtained through imitation learning, and the loss function is:

[0044] ;

[0045] For the loss function of imitation learning, For the network parameters of the data-driven compensation model, For the mapping function of the data-driven compensation model;

[0046] Residual learning is used to predict and compensate for the equivalent simplified model. The compensated state and energy consumption predictions are as follows:

[0047] ;

[0048] ;

[0049] in, The compensated state prediction value, This is the residual compensation term for state prediction. The compensated slip energy consumption prediction value, To simplify the energy consumption prediction values ​​output by the equivalent model, This is the tire slippage energy consumption residual compensation item.

[0050] Further, in step S2, the total loss function of the data-driven compensation model is:

[0051] ;

[0052] in, The length of the training sequence is the number of discrete time steps covered by a single loss calculation. For network parameters The total loss function of the data-driven compensation model with independent variables; The first one actually observed Periodic vehicle status; For actual observation of the first Periodic sliding energy consumption; This is the weighting coefficient for energy loss.

[0053] Furthermore, the method for obtaining tire slippage energy consumption in step S3 includes:

[0054] The instantaneous slip power of a tire can be expressed as a four-wheel, wheel-by-wheel calculation:

[0055] ;

[0056] in, This refers to the instantaneous tire slip power calculated wheel-by-wheel in a four-wheel configuration. For wheel indexing, The front left wheel, The front right wheel, It is the rear left wheel. It is the rear right wheel; , respectively wheels The longitudinal and lateral forces; , respectively wheels Longitudinal and lateral slip velocity relative to the ground;

[0057] Alternatively, the instantaneous tire slip power can be expressed using a two-axle equivalent calculation method as follows:

[0058] ;

[0059] in, This refers to the instantaneous tire slip power calculated using the two-axle equivalent method. as axis longitudinal force, as axis longitudinal sliding velocity, as axis Lateral force, as axis Lateral slip velocity;

[0060] The tire slip energy consumption per unit control cycle is: ;

[0061] in, This is the index of the current discrete time step, corresponding to the [number]th [time step]. One control cycle; For the first Instantaneous slip power within each control cycle, taken from or ; For the first The online tire slip energy consumption within each control cycle is used for optimization calculation of real-time path tracking control; To control cycle duration;

[0062] The base angle output by the data-driven compensation model Centered on the target, within its neighborhood, increment by a preset step size. Generate a discrete set of candidate front wheel equivalent steering angles:

[0063] ;

[0064] in, The output of the data-driven compensation model The base front wheel equivalent steering angle for each control cycle; For the first The set of candidate front wheel equivalent steering angles for each control cycle; For discrete incremental indexes; It is a positive integer used to limit the neighborhood range.

[0065] Furthermore, when the longitudinal vehicle speed is approximately constant, the tire slip energy consumption is calculated using an approximate formula for lateral slip energy consumption:

[0066] ;

[0067] in: This represents the tire slip power in the lateral direction under the two-axle equivalent calculation method.

[0068] Furthermore, the method for comprehensively evaluating the candidate steering control values ​​and selecting the optimal steering control value in step S3 is as follows:

[0069] Construct a comprehensive evaluation function:

[0070] ;

[0071] in, To determine the equivalent steering angle of the candidate front wheels The evaluation function value of the independent variable; , , , , , These are the weighting coefficients; The first prediction of the data-driven compensation model Periodic lateral error; The first prediction of the data-driven compensation model Periodic heading error; The first prediction of the data-driven compensation model Periodic centroid sideslip angle; The first prediction of the data-driven compensation model Periodic yaw rate; The first prediction of the data-driven compensation model Cyclic tire slippage energy consumption; For the first The expected yaw rate of the cycle is determined by the curvature of the target path and the vehicle speed; This is the optimal steering control value at the previous moment;

[0072] Selecting the optimal steering control value:

[0073] ;

[0074] Where argmin represents the independent variable that minimizes the function value; the optimal front wheel equivalent steering angle is... It acts on the steering system of off-road vehicles.

[0075] This invention discloses a low-energy path tracking control system for off-road vehicles, comprising:

[0076] The equivalent simplified dynamics model module is used to establish an equivalent simplified dynamics model of a two-axle off-road vehicle. It converts the left and right wheels and wheel-ground action of the off-road vehicle into equivalent tire forces on the front axle and rear axle, thus obtaining an equivalent simplified dynamics model for real-time control.

[0077] The data-driven compensation module is used to construct an expert database and a steady-state response database based on an equivalent simplified dynamic model, and to train the data-driven compensation model using the expert database and the steady-state response database, so that the data-driven compensation model learns the expert steering control law and compensates for the prediction error of the equivalent simplified dynamic model under complex off-road conditions.

[0078] The tire slip energy consumption optimization control module is used to incorporate tire slip energy consumption into the path tracking control optimization target. It combines path tracking error index and vehicle stability index to comprehensively evaluate candidate steering control quantities and select the optimal steering control quantity during real-time path tracking to achieve low-energy path tracking control for off-road vehicles.

[0079] The present invention achieves the following beneficial effects through the above technical solution:

[0080] 1. This invention proposes an equivalent simplified dynamic modeling method for path tracking control of two-axle off-road vehicles. It equates the complex four-wheel wheel-ground interaction to the concentrated tire interaction of the front and rear axles, and replaces the independent coupled description of the four wheels with the equivalent two-axle method. While retaining key state variables such as yaw motion, center of gravity lateral slip, path error and tire slip, it effectively reduces the model state dimension and online solution burden, enabling the path tracking controller to quickly obtain the vehicle's dynamic response, significantly reducing the amount of online computation, improving the real-time performance of the control system, and making the engineering deployment of this method possible in actual off-road scenarios.

[0081] 2. This invention proposes a vehicle response prediction method combining an equivalent simplified model and data-driven compensation. Using a two-axle equivalent model as the basic prediction framework, the data-driven compensation model learns the state prediction residuals and energy consumption prediction residuals under complex off-road conditions. When the vehicle is in conditions with significant changes in road surface adhesion and tire slippage, data-driven compensation can correct the prediction results in real time, effectively reducing prediction biases caused by unmodeled factors such as soft ground, slope undulations, load transfer, and tire-soil interaction. Compared to existing technologies that only use a fixed equivalent simplified model, this invention maintains physical interpretability while making the prediction results more consistent with the actual response, providing a reliable basis for the accurate generation of steering control quantities.

[0082] 3. This invention proposes a path tracking control evaluation method that considers tire slip energy consumption. By incorporating tire slip energy consumption into a comprehensive evaluation function, the controller, when selecting candidate front wheel equivalent steering angles, comprehensively evaluates the path tracking error, tire slip energy consumption, and steering angle change smoothness, rather than focusing solely on path error or stability. Compared to existing technologies, this invention can actively suppress unnecessary tire slip in each control cycle while ensuring lateral error, heading error, and yaw stability, effectively reducing ineffective slip energy consumption during continuous steering and achieving synergistic optimization of path tracking accuracy and tire slip energy consumption.

[0083] 4. This invention employs an architecture combining an equivalent simplified dynamics model and a data-driven compensation model. The equivalent simplified model provides a basic prediction framework with clear physical meaning, while the data-driven compensation model learns the unmodeled errors and prediction residuals under complex off-road conditions. The two complement each other rather than substituting for one another. Compared to a purely data-driven model, it offers better interpretability and reliability; compared to a purely physical model, it has higher prediction accuracy and adaptability to different operating conditions, demonstrating significant advantages in the safety-critical application of off-road vehicle path tracking control. Attached Figure Description

[0084] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0085] Figure 1 This is a schematic diagram of the overall flow of the control method of the present invention. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0087] This invention focuses on a two-axle off-road vehicle, with the control input being the equivalent steering angle of the front wheels. The control objective is to reduce tire slip energy consumption caused by tire lateral slip and longitudinal slip while maintaining path tracking accuracy.

[0088] Example 1: A low-energy path tracking control system for off-road vehicles, comprising an equivalent simplified dynamics model module, a data-driven compensation module, and a tire slippage energy consumption optimization control module.

[0089] The equivalent simplified dynamics model module is used to establish an equivalent simplified dynamics model for a two-axle off-road vehicle. It equates the left and right wheels and wheel-to-ground interactions of the off-road vehicle to equivalent tire forces on the front and rear axles, resulting in an equivalent simplified dynamics model for real-time control. Based on the structural parameters of the two-axle off-road vehicle (vehicle mass, yaw moment of inertia, distance from the front axle to the center of gravity, distance from the rear axle to the center of gravity, etc.), vehicle motion states (longitudinal speed, sideslip angle, yaw rate, etc.), and path tracking requirements (lateral error, heading error, target path curvature, etc.), this module synthesizes the wheel-to-ground interactions of the front left and front right wheels into an equivalent lateral force on the front axle, and the wheel-to-ground interactions of the rear left and rear right wheels into an equivalent lateral force on the rear axle, constructing the two-axle equivalent dynamic equations. This provides a fundamental dynamics model for subsequent vehicle state prediction and steering control quantity generation.

[0090] The data-driven compensation module is used to construct an expert database and a steady-state response database based on an equivalent simplified dynamics model. It then uses these databases to train the data-driven compensation model, enabling it to learn expert steering control laws and compensate for prediction errors in the equivalent simplified dynamics model under complex off-road conditions. This module collects expert steering control variables, vehicle state responses, and tire slip energy consumption under multiple operating conditions to form the expert database. Based on the equivalent simplified dynamics model, it iterates through candidate steering angles, vehicle speeds, path curvatures, adhesion coefficients, and slip states to form a steady-state response database. Through imitation learning, it obtains a basic steering strategy, and through residual learning, it compensates for the state predictions and energy consumption predictions of the equivalent simplified model.

[0091] The tire slip energy consumption optimization control module incorporates tire slip energy consumption into the path tracking control optimization objective. Combining path tracking error and vehicle stability indicators, it comprehensively evaluates candidate steering control quantities and selects the optimal steering control quantity during real-time path tracking, achieving low-energy path tracking control for off-road vehicles. This module calculates the instantaneous tire slip power and tire slip energy consumption per unit control cycle. Using the base steering angle output by the data-driven compensation model as the center, it generates a set of candidate front wheel equivalent steering angles in its neighborhood. It constructs a comprehensive evaluation function that includes lateral error, heading error, center of gravity sideslip angle, deviation of yaw rate from its expected value, tire slip energy consumption, and steering angle change smoothness. By optimizing within the candidate front wheel equivalent steering angle set, the optimal steering control quantity is selected and applied to the off-road vehicle's steering system.

[0092] Example 2, as Figure 1 As shown, a low-energy path tracking control method for off-road vehicles includes the following steps:

[0093] S1: Based on the structural parameters, vehicle motion state, and path tracking requirements of the two-axle off-road vehicle, an equivalent simplified dynamic model of the two-axle off-road vehicle is established. The left and right wheels and wheel-ground interaction of the off-road vehicle are equivalent to the equivalent tire force of the front axle and the equivalent tire force of the rear axle, thus obtaining an equivalent simplified dynamic model for real-time control, providing a basic dynamic model for subsequent vehicle state prediction and steering control quantity generation.

[0094] S2: Based on the equivalent simplified dynamic model, an expert database and a steady-state response database are constructed, and the expert database and steady-state response database are used to train the data-driven compensation model, so that the data-driven compensation model learns the expert steering control law and compensates for the prediction error of the equivalent simplified dynamic model under complex off-road conditions.

[0095] S3: Incorporate tire slip energy consumption into the path tracking control optimization objective, combine path tracking error index and vehicle stability index to comprehensively evaluate candidate steering control quantities, and select the optimal steering control quantity during real-time path tracking to achieve low-energy path tracking control for off-road vehicles.

[0096] In step S1, the method for establishing the equivalent simplified dynamic model is as follows:

[0097] Based on the overall vehicle weight of the two-axle off-road vehicle yaw moment of inertia Distance from front axle to center of gravity Distance from rear axle to center of gravity Longitudinal speed , centroid side slip angle yaw rate Front wheel equivalent steering angle The combined wheel-to-ground forces of the front left and front right wheels are converted into an equivalent lateral force on the front axle. The combined wheel-to-ground forces of the left and right rear wheels are converted into an equivalent lateral force on the rear axle. Establish the biaxial equivalent dynamic equation:

[0098] ;

[0099] ;

[0100] in, The rate of change of the centroid sideslip angle. Given the yaw acceleration, the front and rear axle tire slip angles can be expressed as:

[0101] ;

[0102] ;

[0103] in, This is the equivalent tire slip angle for the front axle. This is the equivalent tire slip angle for the rear axle;

[0104] Considering the adhesion coefficient, vertical load, and slip condition of the off-road surface, the equivalent tire force expressions for the front and rear axles are defined as follows:

[0105] ;

[0106] in, As axis index, Represents the front axle. Represents the rear axle; The road surface adhesion coefficient, as axis The equivalent tire slip ratio; as axis Vertical load, The unmodeled lateral force residuals are caused by soft ground, slope undulation, load transfer, and tire-soil interaction.

[0107] Establish the path tracking error dynamics equation:

[0108] ;

[0109] ;

[0110] in, For lateral error, For heading error, Let be the curvature of the target path, and ;

[0111] For lateral error and The heading error, along with the centroid sideslip angle, constitutes the path tracking error index. and yaw rate These together constitute the vehicle stability index;

[0112] Constructing state vectors and operating condition reference quantity :

[0113] ;

[0114] ;

[0115] With equivalent front wheel steering angle As the control input, a discrete-form two-axis equivalent simplified model is obtained:

[0116] ;

[0117] Among them, among them, This is the index for the current discrete time step. For the index of the next discrete time step, To simplify the mapping function of the equivalent dynamic model, For the first The state vector of each control cycle For the first Operating condition reference values ​​for each control cycle To be applied to the first The equivalent steering angle of the front wheels for one control cycle.

[0118] This model compresses the complex off-road wheel-ground coupled dynamics into a two-axle vehicle response model that can be computed online. It retains key states such as yaw, center of gravity sideslip, path error, and tire slippage, while avoiding the direct solution of high-dimensional nonlinear off-road dynamics models. This provides a foundational dynamic model for subsequent database construction and data-driven compensation model training.

[0119] In step S2, the expert database Build it in the following way:

[0120] ;

[0121] in, For sample index, The total number of samples; It is a combination of the current vehicle status, operating conditions, and terrain features. This may include road surface type, slope, rolling resistance estimate, vehicle pitch angle, roll angle, or terrain features identified by sensors; For experts to shift their focus to control quantities; and These are the vehicle state and skid energy consumption after expert control;

[0122] In step S2, the steady-state response database Build it in the following way:

[0123] Based on an equivalent simplified dynamic model, candidate steering angles, vehicle speeds, path curvature, adhesion coefficients, and slip states are traversed to obtain the vehicle's steady-state or quasi-steady-state responses, forming a steady-state response database.

[0124] ;

[0125] ;

[0126] in, For sample index, The total number of samples; For the first The group traverses the corresponding combination vectors of the input, and , For the first The state vector corresponding to each sample input For the first Each sample input corresponds to a working condition reference value. For the first Each sample input corresponds to a terrain feature; For the first Each sample is used to traverse the corresponding candidate front wheel equivalent turning angles; For the first Steady-state tire slip energy consumption output by the equivalent simplified dynamic model under one sample input; For the first The steady-state response vector output by the equivalent simplified dynamic model under sample input, where: For the first Steady-state centroid sideslip angle under a given sample input For the first Steady-state yaw rate under a given sample input For the first Steady-state lateral error under a given sample input For the first Steady-state heading error under a given sample input For the first Steady-state front axle equivalent tire slip ratio under a given sample input For the first Steady-state equivalent tire slip ratio of the rear axle under a sample input.

[0127] In step S2, the training method for the data-driven compensation model includes:

[0128] The data-driven compensation model can be implemented using a fully connected neural network, comprising an input layer, several hidden layers, and an output layer. The hidden layer activation function uses the ReLU function, and the network parameters θ are trained and optimized using the backpropagation algorithm. In specific implementations, radial basis function neural networks or ensemble learning models can be used as alternatives, depending on the actual needs.

[0129] A data-driven compensation model is used to learn expert steering patterns and equivalent model residuals. Imitation learning is employed to obtain the basic steering strategy, with the loss function being:

[0130] ;

[0131] For the loss function of imitation learning, For the network parameters of the data-driven compensation model, For the mapping function of the data-driven compensation model;

[0132] Residual learning is used to predict and compensate for the equivalent simplified model. The compensated state and energy consumption predictions are as follows:

[0133] ;

[0134] ;

[0135] in, The compensated state prediction value, This is the residual compensation term for state prediction. The compensated slip energy consumption prediction value, To simplify the energy consumption predictions output by the equivalent model, This is the tire slippage energy consumption residual compensation item.

[0136] In step S2, the total loss function of the data-driven compensation model is:

[0137] ;

[0138] in, The length of the training sequence is the number of discrete time steps covered by a single loss calculation. For network parameters The total loss function of the data-driven compensation model with independent variables; The first one actually observed Periodic vehicle status; For actual observation of the first Periodic sliding energy consumption; This is the weighting coefficient for energy loss.

[0139] The methods for obtaining tire slip energy consumption in step S3 include:

[0140] In the data-driven path tracing lookup process, tire slip energy consumption is used as one of the candidate steering control quantity evaluation indicators. For four-wheel off-road vehicles, the instantaneous tire slip power can be expressed as a wheel-by-wheel calculation method:

[0141] ;

[0142] in, This refers to the instantaneous tire slip power calculated wheel-by-wheel in a four-wheel configuration. For wheel indexing, The front left wheel, The front right wheel, It is the rear left wheel. It is the rear right wheel; , respectively wheels The longitudinal and lateral forces; , respectively wheels Longitudinal and lateral slip velocity relative to the ground;

[0143] Alternatively, to reduce real-time computational load, equivalent front and rear axle slip power can be used in the biaxial equivalent model. Specifically, the instantaneous tire slip power is expressed using the biaxial equivalent calculation method as follows:

[0144] ;

[0145] in, This refers to the instantaneous tire slip power calculated using the two-axle equivalent method. as axis longitudinal force, as axis longitudinal sliding velocity, as axis Lateral force, as axis Lateral slip velocity;

[0146] When the longitudinal vehicle speed is approximately constant, tire slip energy consumption can be calculated using the approximate formula for lateral slip energy consumption:

[0147] ;

[0148] in: This represents the tire slip power in the lateral direction under the two-axle equivalent calculation method.

[0149] The tire slip energy consumption per unit control cycle is: ;

[0150] in, This is the index of the current discrete time step, corresponding to the [number]th [time step]. One control cycle; For the first Instantaneous slip power within each control cycle, taken from or ; For the first The online tire slip energy consumption within each control cycle is used for optimization calculation of real-time path tracking control; To control cycle duration;

[0151] The base angle output by the data-driven compensation model Centered on the target, within its neighborhood, increment by a preset step size. Generate a discrete set of candidate front wheel equivalent steering angles:

[0152] ;

[0153] in, The output of the data-driven compensation model The base front wheel equivalent steering angle for each control cycle; For the first The set of candidate front wheel equivalent steering angles for each control cycle; For discrete incremental indexes; It is a positive integer used to limit the neighborhood range.

[0154] The method for comprehensively evaluating candidate steering control values ​​and selecting the optimal steering control value in step S3 is as follows:

[0155] Construct a comprehensive evaluation function:

[0156] ;

[0157] in, To determine the equivalent steering angle of the candidate front wheels The evaluation function value of the independent variable; , , , , , These are the weighting coefficients; The first prediction of the data-driven compensation model Periodic lateral error; The first prediction of the data-driven compensation model Periodic heading error; The first prediction of the data-driven compensation model Periodic centroid sideslip angle; The first prediction of the data-driven compensation model Periodic yaw rate; The first prediction of the data-driven compensation model Cyclic tire slippage energy consumption; For the first The expected yaw rate of the cycle is determined by the curvature of the target path and the vehicle speed; For the previous moment (the first moment) The optimal steering control quantity (period);

[0158] Selecting the optimal steering control value:

[0159] ;

[0160] Where argmin represents the independent variable that minimizes the function value; the optimal front wheel equivalent steering angle is... It acts on the steering system of off-road vehicles, enabling the vehicle to meet the requirements of lateral error, heading error and yaw stability while reducing energy loss caused by ineffective lateral and longitudinal slippage of the tires.

[0161] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Without conflict, the embodiments and features described and illustrated herein can be combined with each other. The components of the embodiments of the present invention generally described and illustrated in the accompanying drawings can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A low-energy path tracking control method for off-road vehicles, characterized in that: Includes the following steps: S1: Establish an equivalent simplified dynamic model of a two-axle off-road vehicle, and convert the left and right wheels and wheel-ground action of the off-road vehicle into equivalent tire forces of the front axle and the rear axle, so as to obtain an equivalent simplified dynamic model for real-time control. S2: Based on the equivalent simplified dynamic model, an expert database and a steady-state response database are constructed, and the expert database and steady-state response database are used to train the data-driven compensation model, so that the data-driven compensation model learns the expert steering control law and compensates for the prediction error of the equivalent simplified dynamic model under complex off-road conditions. S3: Incorporate tire slip energy consumption into the path tracking control optimization objective, combine path tracking error index and vehicle stability index to comprehensively evaluate candidate steering control quantities, and select the optimal steering control quantity during real-time path tracking to achieve low-energy path tracking control for off-road vehicles.

2. The low-energy path tracking control method for off-road vehicles according to claim 1, characterized in that: The method for establishing the equivalent simplified dynamic model in step S1 is as follows: Based on the overall vehicle weight of the two-axle off-road vehicle yaw moment of inertia Distance from front axle to center of gravity Distance from rear axle to center of gravity Longitudinal speed , centroid side slip angle yaw rate Front wheel equivalent steering angle The combined wheel-to-ground forces of the front left and front right wheels are converted into an equivalent lateral force on the front axle. The combined wheel-to-ground forces of the left and right rear wheels are converted into an equivalent lateral force on the rear axle. Establish the biaxial equivalent dynamic equation: ； ； in, The rate of change of the centroid sideslip angle. Given the yaw acceleration, the front and rear axle tire slip angles can be expressed as: ； ； in, This is the equivalent tire slip angle for the front axle. This is the equivalent tire slip angle for the rear axle. Considering the adhesion coefficient, vertical load, and slip condition of the off-road surface, the equivalent tire force expressions for the front and rear axles are defined as follows: ； in, As axis index, Represents the front axle. Represents the rear axle; The road surface adhesion coefficient, as axis The equivalent tire slip ratio; as axis Vertical load, The unmodeled lateral force residuals are caused by soft ground, slope undulation, load transfer, and tire-soil interaction. Establish the path tracking error dynamics equation: ； ； in, For lateral error, For heading error, Let be the curvature of the target path, and ; The For lateral error and The heading error, along with the centroid sideslip angle, constitutes the path tracking error index. and yaw rate These together constitute the vehicle stability index; Constructing state vectors and operating condition reference quantity : ； ； With equivalent front wheel steering angle As the control input, a discrete-form two-axis equivalent simplified model is obtained: ； Among them, among them, This is the index for the current discrete time step. For the index of the next discrete time step, To simplify the mapping function of the equivalent dynamic model, For the first The state vector of each control cycle For the first Operating condition reference values ​​for each control cycle To be applied to the first The equivalent steering angle of the front wheels for one control cycle.

3. The low-energy path tracking control method for off-road vehicles according to claim 2, characterized in that: In step S2, the expert database Build it in the following way: ； in, For sample index, The total number of samples; It is a combination of the current vehicle status, operating conditions, and terrain features. This may include road surface type, slope, rolling resistance estimate, vehicle pitch angle, roll angle, or terrain features identified by sensors; For experts to shift their focus to control quantities; and These represent the vehicle's state and skid energy consumption after expert control.

4. The low-energy path tracking control method for off-road vehicles according to claim 3, characterized in that: In step S2, the steady-state response database Build it in the following way: Based on the equivalent simplified dynamic model, the vehicle's steady-state or quasi-steady-state response is obtained by traversing candidate turning angles, vehicle speeds, path curvatures, adhesion coefficients, and slip states, forming a steady-state response database. ； ； in, For sample index, The total number of samples; For the first The group traverses the corresponding combination vectors of the input, and , For the first The state vector corresponding to each sample input For the first Each sample input corresponds to a working condition reference value. For the first Each sample input corresponds to a terrain feature; For the first Each sample is used to traverse the corresponding candidate front wheel equivalent turning angles; For the first Steady-state tire slip energy consumption output by the equivalent simplified dynamic model under one sample input; For the first The steady-state response vector output by the equivalent simplified dynamic model under sample input, where: For the first Steady-state centroid sideslip angle under a given sample input For the first Steady-state yaw rate under a given sample input For the first Steady-state lateral error under a given sample input For the first Steady-state heading error under a given sample input For the first Steady-state front axle equivalent tire slip ratio under a given sample input For the first Steady-state equivalent tire slip ratio of the rear axle under a sample input.

5. The low-energy path tracking control method for off-road vehicles according to claim 3, characterized in that: In step S2, the training method of the data-driven compensation model includes: The basic steering strategy is obtained through imitation learning, and the loss function is: ； For the loss function of imitation learning, For the network parameters of the data-driven compensation model, For the mapping function of the data-driven compensation model; Residual learning is used to predict and compensate for the equivalent simplified model. The compensated state and energy consumption predictions are as follows: ； ； in, The compensated state prediction value, This is the residual compensation term for state prediction. The compensated slip energy consumption prediction value, To simplify the energy consumption predictions output by the equivalent model, This is the tire slippage energy consumption residual compensation item.

6. The low-energy path tracking control method for off-road vehicles according to claim 5, characterized in that: In step S2, the total loss function of the data-driven compensation model is: ； in, The length of the training sequence is the number of discrete time steps covered by a single loss calculation. For network parameters The total loss function of the data-driven compensation model with independent variables; The first one actually observed Periodic vehicle status; For actual observation of the first Periodic sliding energy consumption; This is the weighting coefficient for energy loss.

7. The low-energy path tracking control method for off-road vehicles according to claim 5, characterized in that: The method for obtaining tire slip energy consumption in step S3 includes: The instantaneous slip power of a tire can be expressed as a four-wheel, wheel-by-wheel calculation: ； in, This refers to the instantaneous tire slip power calculated wheel-by-wheel in a four-wheel configuration. For wheel indexing, The front left wheel, The front right wheel, It is the rear left wheel. It is the rear right wheel; , wheel The longitudinal and lateral forces; , wheel Longitudinal and lateral slip velocity relative to the ground; Alternatively, the instantaneous tire slip power can be expressed using a two-axle equivalent calculation method as follows: ； in, This refers to the instantaneous tire slip power calculated using the two-axle equivalent method. as axis longitudinal force, as axis longitudinal sliding velocity, as axis Lateral force, as axis Lateral slip velocity; The tire slip energy consumption per unit control cycle is: ; in, This is the index of the current discrete time step, corresponding to the [number]th [time step]. One control cycle; For the first Instantaneous slip power within each control cycle, taken from or ; For the first The online tire slip energy consumption within each control cycle is used for optimization calculation of real-time path tracking control; To control cycle duration; The base angle output by the data-driven compensation model Centered on the target, within its neighborhood, increment by a preset step size. Generate a discrete set of candidate front wheel equivalent steering angles: ； in, The output of the data-driven compensation model The base front wheel equivalent steering angle for each control cycle; For the first The set of candidate front wheel equivalent steering angles for each control cycle; For discrete incremental indexes; It is a positive integer used to limit the neighborhood range.

8. The low-energy path tracking control method for off-road vehicles according to claim 7, characterized in that: When the longitudinal vehicle speed is approximately constant, the tire slip energy consumption is calculated using the approximate formula for lateral slip energy consumption: ； in: This represents the tire slip power in the lateral direction under the two-axle equivalent calculation method.

9. The low-energy path tracking control method for off-road vehicles according to claim 7, characterized in that: The method for comprehensively evaluating candidate steering control values ​​and selecting the optimal steering control value in step S3 is as follows: Construct a comprehensive evaluation function: ； in, To determine the equivalent steering angle of the candidate front wheel The evaluation function value of the independent variable; , , , , , These are the weighting coefficients; The first prediction of the data-driven compensation model Periodic lateral error; The first prediction of the data-driven compensation model Periodic heading error; The first prediction of the data-driven compensation model Periodic centroid sideslip angle; The first prediction of the data-driven compensation model Periodic yaw rate; The first prediction of the data-driven compensation model Cyclic tire slippage energy consumption; For the first The expected yaw rate of the cycle is determined by the curvature of the target path and the vehicle speed; This is the optimal steering control value at the previous moment; Selecting the optimal steering control value: ； Where argmin represents the independent variable that minimizes the function value; the optimal front wheel equivalent steering angle is... It acts on the steering system of off-road vehicles.

10. A low-energy path tracking control system for off-road vehicles, characterized in that: include: The equivalent simplified dynamics model module is used to establish an equivalent simplified dynamics model of a two-axle off-road vehicle. It converts the left and right wheels and wheel-ground action of the off-road vehicle into equivalent tire forces on the front axle and rear axle, thus obtaining an equivalent simplified dynamics model for real-time control. The data-driven compensation module is used to construct an expert database and a steady-state response database based on an equivalent simplified dynamic model, and to train the data-driven compensation model using the expert database and the steady-state response database, so that the data-driven compensation model learns the expert steering control law and compensates for the prediction error of the equivalent simplified dynamic model under complex off-road conditions. The tire slip energy consumption optimization control module is used to incorporate tire slip energy consumption into the path tracking control optimization target. It combines path tracking error index and vehicle stability index to comprehensively evaluate candidate steering control quantities and select the optimal steering control quantity during real-time path tracking to achieve low-energy path tracking control for off-road vehicles.

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