A precision working path correction method for unmanned tractor

By combining ARA* algorithm and fuzzy adaptive model predictive control algorithm with field operation data and real-time sensor information, a safe passage path is generated, which solves the problem of crop damage caused by unmanned tractors in farmland and achieves a balance between precision operation and crop protection.

CN122363316APending Publication Date: 2026-07-10
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Filing Date
2026-04-24
Publication Date
2026-07-10

AI Technical Summary

Technical Problem

Traditional unmanned tractor path correction methods fail to take into account the spatial distribution characteristics of crops in farmland, resulting in tractors directly crushing crop plants and roots during the correction process, which cannot meet the requirements of precision operation and crop protection.

Method used

The ARA* algorithm is used to optimize path planning, combined with the fuzzy adaptive model predictive control algorithm. By collecting site operation data, a baseline path model is constructed, risk assessment values ​​are calculated, safe passage paths are generated, and path deviation prediction and control are performed to achieve precise operation path correction.

Benefits of technology

While ensuring the accuracy of path correction, crop damage is avoided, thus improving the safety and stability of unmanned tractors in complex farmland environments.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention discloses a method for precise operation path correction of unmanned tractors, relating to the field of unmanned tractor technology. The method includes the following steps: collecting land operation data of the unmanned tractor; constructing a baseline operation path model for the unmanned tractor based on the land operation data; collecting real-time operation data of the unmanned tractor and calculating a risk assessment value based on the baseline operation path model; determining the operation status of the unmanned tractor based on the risk assessment value to obtain a risk quantification result; performing path planning for the unmanned tractor using an improved ARA* algorithm based on the risk quantification result to obtain a safe passage path; and predicting and controlling the path deviation of the unmanned tractor using a fuzzy adaptive model predictive control algorithm based on the safe passage path to obtain stable control commands, thereby achieving precise operation path correction for the unmanned tractor.
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Description

Technical Field

[0001] This invention relates to the field of unmanned tractor technology, specifically to a method for precise operation path correction of unmanned tractors. Background Technology

[0002] With the rapid development of modern agriculture towards large-scale, intelligent, and unmanned operations, unmanned tractors have become the core equipment for mechanized operations such as tillage, sowing, and plant protection of field crops. However, the actual operating environment of farmland has complex characteristics such as undulating terrain, uneven soil hardness, differences in crop spatial distribution, and easy obstruction of satellite positioning signals, which puts forward stringent engineering requirements for the path adaptive correction capability of unmanned tractors.

[0003] Traditional methods acquire real-time position data of the tractor through an onboard satellite positioning module, calculate the deviation between the real-time position and the preset reference path, and when the deviation reaches a preset fixed threshold, control the tractor to adjust its direction to the preset reference path along the shortest straight path, thereby achieving passive correction of the path deviation.

[0004] However, traditional methods only use the shortest straight line regression preset path as the correction principle, without taking into account the spatial distribution characteristics of farmland crops to carry out local safety passage path correction. They cannot avoid densely growing crop areas during the correction process, which causes the tractor to directly run over crop plants and roots when turning to make corrections, ultimately causing crop damage. This cannot meet the core operational requirements of unmanned tractors to balance precision operation and crop protection. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for correcting the precise operating path of unmanned tractors, thereby resolving the problems existing in the background technology.

[0006] To achieve the above objectives, the present invention provides a method for precise operation path correction of an unmanned tractor, comprising the following steps: Step S1: Collect the field operation data of the unmanned tractor and construct the operation benchmark path model of the unmanned tractor based on the field operation data; Step S2: Based on the unmanned tractor operation baseline path model, collect real-time operation data of the unmanned tractor and calculate the risk assessment value. Determine the operation status of the unmanned tractor based on the risk assessment value to obtain the risk quantification result. Step S3: Based on the risk quantification results, the unmanned tractor is used to plan a safe passage path by improving the ARA* algorithm; Step S4: Based on the safe passage path, the unmanned tractor is predicted and controlled by the fuzzy adaptive model predictive control algorithm to obtain stable control commands, thereby realizing the accurate correction of the unmanned tractor's working path.

[0007] Preferably, the process of collecting the unmanned tractor's field operation data and constructing a baseline path model for the unmanned tractor's operation based on the field operation data includes the following specific steps: Collect land operation data of unmanned tractors, including land boundary plane coordinate data, terrain distribution elevation raster data and historical operation trajectory data; The land parcels are divided into grid cells and clustered to obtain continuous operating sections; A segment digital identifier is assigned to a continuous operation segment and path control attributes are configured. The path control attributes include at least the allowed offset direction, the correction sensitivity threshold, and the safe avoidance distance. Establish a local plane coordinate system for the land parcel, and construct a reference path model for unmanned tractor operation based on the local plane coordinate system of the land parcel. The operational baseline path model consists of segment digital identifiers, plane coordinate vectors of the baseline path, and path control attributes.

[0008] Preferably, the step of collecting real-time operation data of unmanned tractors and calculating risk assessment values ​​based on the unmanned tractor operation baseline path model includes: Based on the unmanned tractor's operating baseline path model, real-time operating data is collected. The real-time operating data includes at least the tractor's real-time planar coordinates, body attitude angle, track vertical force, ground undulation elevation difference, crop height, and crop spacing. The collected real-time coordinates are compared with the baseline path coordinates to calculate the position offset. The position offset and real-time operation data are normalized and combined with the preset risk coupling weight coefficient to calculate the risk assessment value.

[0009] Preferably, the step of determining the operational status of the unmanned tractor based on the risk assessment value to obtain a risk quantification result includes the following steps: The operational risk level is determined based on the preset threshold range in which the risk assessment value falls; Based on the trend of position offset change within a continuous control cycle, a persistent offset risk flag is obtained. The real-time operation data is compared with the corresponding safety threshold to obtain the crop damage risk flag. The risk quantification results include the risk level, the persistent offset risk marker, and the crop damage risk marker.

[0010] Preferably, based on the risk quantification results, the unmanned tractor is used to perform path planning through an improved ARA* algorithm to obtain a safe passage path, as detailed below: When the risk level is high, the improved ARA* algorithm is used to plan the path for the unmanned tractor to obtain a safe passage path. When the risk level is medium and the crop damage risk flag is valid, the improved ARA* algorithm is used to plan the path for the unmanned tractor to obtain a safe passage path. Using the real-time positioning coordinates of the tractor as the starting point of the path and the nearest regression point of the current work section's benchmark path as the ending point of the path, a path search is performed within the passable area and the sparse crop safety area, and an initial correction path is generated based on the node cost function. The initial correction path is smoothly reconstructed using a third-order B-spline curve to obtain the safe passage path.

[0011] Preferably, the improved ARA* algorithm specifically includes: An adaptive initial expansion factor is calculated based on the vertical and horizontal scales of the plot and the crop density. The adaptive initial expansion factor is constrained to be no less than a preset minimum threshold. The formula for calculating the adaptive initial expansion factor is: ; in, The longitudinal length of the plot. The horizontal width of the plot. For crop density, For floor operations, This is the adaptive initial expansion factor.

[0012] Preferably, the node cost function is as follows: The node cost function includes path length normalized cost, heuristic distance normalized cost, and crop sparsity incentive term; The formula for calculating the node cost function is: ; Among them, key For nodes Total driving cost The cost of path length normalization. To inspire the cost of distance normalization, The inflation factor for the current iteration round. This represents the crop sparsity incentive weighting coefficient. This represents the normalized value of crop plant spacing.

[0013] Preferably, the method of predicting and controlling the path deviation of the unmanned tractor based on a safe passage path using a fuzzy adaptive model predictive control algorithm includes the following steps: Based on the safe passage path, a fuzzy adaptive model predictive control algorithm is used to predict and control the path deviation of the unmanned tractor. The fuzzy adaptive model predictive control algorithm takes the safe passage path vector, real-time operation data and fixed kinematic parameters of the unmanned tractor as inputs, and sets up a fuzzy adaptive module; The fuzzy adaptive module takes the lateral offset error and the reference path curvature as inputs and outputs the state weight adaptive correction coefficient and the control weight adaptive correction coefficient. The weight matrix is ​​updated based on the adaptive correction coefficients of the state weights and the adaptive correction coefficients of the control weights, resulting in the updated weight matrix.

[0014] Preferably, the step of predicting and controlling the path deviation of the unmanned tractor using the fuzzy adaptive model predictive control algorithm further includes: Calculate the predicted offset and the offset trend growth rate based on the discrete prediction model; Determine and predict the offset trend based on the offset trend growth rate; Based on the predicted offset trend and the updated weight matrix, the optimal control quantity is solved according to the rolling optimization objective function, and a stable control command is output, which includes the optimal steering angle and the optimal driving torque difference.

[0015] Preferably, the rolling optimization objective function is as follows: ; in, To perform rolling optimization of the overall objective function, j is the index of the discrete time in the prediction and control time domain, and k represents the current time. To predict the length of the time domain, The predicted state vector of the tractor at time k+j. Let k+j be the reference state vector of the safe passage. Let Q be the weighted L2 norm of the state tracking error, and Q represent the weighting dimension of the corresponding state tracking error. To control the length of the time domain, The control increment vector at time k+j To control the increment weighted L2 norm, R represents the weighted dimension of the corresponding control increment.

[0016] This invention provides a method for precise operation path correction of unmanned tractors, involving machine learning, deep learning, and process control technologies, which has the following beneficial effects: (1) The safe passage path correction method based on ARA* algorithm breaks through the limitation of traditional path correction only pursuing the shortest regression path. It combines the operational risks and crop spatial distribution to plan a dedicated safe passage, so that the path correction of unmanned tractors is no longer blind and always completes the path regression within a safe and feasible range, effectively balancing the accuracy of path correction and the safety of farmland operations.

[0017] (2) Based on the improved ARA* algorithm, the safe passage path correction algorithm further optimizes the path structure on the basis of the ARA algorithm safe passage planning. It retains the core advantage of avoiding operational risks and improves the smoothness of the path through curve smoothing, making the unmanned tractor drive more smoothly and further enhancing the practicality and operational adaptability of the safe passage path correction.

[0018] (3) Fuzzy adaptive model predictive control algorithm, which is adapted to complex operation scenarios such as undulating farmland terrain and uneven soil hardness. It achieves active control by predicting the deviation trend in advance, avoids the lag problem of passive correction, effectively curbs the occurrence of continuous deviation, and allows the unmanned tractor to maintain a stable operation trajectory in complex farmland environment. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the steps of a method for correcting the precise working path of an unmanned tractor proposed in this invention. Figure 2 This is a step hierarchy diagram of obtaining risk quantification results in the method for correcting the precise operation path of an unmanned tractor proposed in this invention; Figure 3 This is a step hierarchy diagram of obtaining stable control commands in a method for correcting the precise operation path of an unmanned tractor proposed in this invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please see Figures 1-3 The present invention provides a technical solution: a method for correcting the precise operation path of an unmanned tractor.

[0023] Step S1: Collect the field operation data of the unmanned tractor and construct the operation benchmark path model of the unmanned tractor based on the field operation data; The following steps are taken to collect field operation data for unmanned tractors and construct a baseline path model for unmanned tractor operations based on this data: The land parcel operation data includes land parcel boundary plane coordinate data, terrain distribution elevation raster data, and historical operation trajectory data. Specifically, the vehicle-mounted RTK positioning module collects the WGS-84 coordinate system latitude and longitude coordinate points of the land parcel boundary. After Gauss-Kruger plane projection transformation, the output land parcel boundary plane coordinate data with a plane position accuracy of ±0.1 meters is generated. Based on the national standard planting row spacing for mainstream field crops such as corn and wheat, the crop planting row spacing is preset to a value of L=0.7 meters. The airborne lidar module collects the terrain information of the entire land parcel area and generates terrain distribution elevation raster data with a raster resolution of 0.5 meters × 0.5 meters and an elevation measurement accuracy of ±0.02 meters.

[0024] Historical operation trajectory data is read through the vehicle-mounted non-volatile storage unit. This data is a Cartesian coordinate sequence bound to UTC timestamps, with a sampling frequency of 10Hz and a Cartesian coordinate accuracy of ±0.01 meters. The land parcels are divided into grid cells and clustered to obtain continuous operational zones, as detailed below: Using the rated operating width W=2.4 meters of the unmanned tractor as the dividing benchmark, the entire plot is divided into planar grid units with a fixed size of 1 meter × 1 meter. All grid units fully cover the plot without overlap or gaps. Based on four quantitative characteristics—terrain slope, soil firmness, crop spacing, and the number of times historical trajectory overlap is repeated—K-Means clustering is performed on the grid units. The number of clustering iterations is fixed at 20. The segment type is determined according to the preset quantitative thresholds: terrain slope ≥6° is identified as a sloping segment, soil firmness ≤1.1MPa is identified as a loose soil segment, crop spacing ≤0.14 meters is identified as a densely cropped segment, and the number of times historical trajectory overlap is ≥3 times is identified as a compacted trajectory segment. After clustering, continuous operating segments extending longitudinally along the crop rows are formed. The length of a single segment is limited to 10 meters to 40 meters. There is no spatial overlap or gap between segments, and the total number of segments N≥2.

[0025] Each continuous work segment is assigned a segment digital identifier and configured with path control attributes. Specifically, each continuous work segment is assigned a unique digital ID and configured with three quantitative path control attributes: allowed offset direction, correction sensitivity threshold, and safe avoidance distance. The allowed offset direction is limited to ±4° along the longitudinal direction of the crop row, and the lateral offset is constrained to not exceed the safe avoidance distance of the segment. The correction sensitivity is assigned in grades according to segment type: high sensitivity for sloping areas and densely cropped areas, with a corresponding offset trigger threshold e1 = ±1.5 cm; medium sensitivity for loose soil areas, with a corresponding offset trigger threshold e2 = ±3 cm; and low sensitivity for compacted track areas. Sensitivity and corresponding offset trigger threshold e3 = ±5 cm; the safe avoidance distance is dynamically set based on crop root characteristics, with a basic threshold limit of d ≥ 7 cm. This value is determined based on the maximum lateral expansion distance of the main root system of field crops, which is 6.5 cm. At the same time, it can be dynamically adjusted according to the actual lateral expansion distance of the main root system of different field crops. The adjustment rule is that the safe avoidance distance is 1.05 to 1.2 times the maximum lateral expansion distance of the main root system of the corresponding crop, and not less than the minimum operational safety threshold of 5 cm. This distance also serves as the lateral boundary constraint for safe passage path planning and the deviation limit constraint for path tracking control, realizing a unified standard for crop root protection throughout the entire operation process.

[0026] A local planar coordinate system for the land parcel is established. Based on this local planar coordinate system, a reference path model for unmanned tractor operation is constructed. Specifically, a local planar rectangular coordinate system OXY is established with the RTK positioning point at the southwest corner of the land parcel as the origin. The X-axis is set along the longitudinal direction of the crop rows, and the Y-axis is set perpendicular to the transverse direction of the crop rows. Based on this coordinate system, a reference path model for unmanned tractor operation is constructed. The model is specifically represented as follows:

[0027]

[0028] in, For the first Each segment's numerical identifier, For the first The planar coordinate vector of the baseline path for each segment, and the single coordinate point within the vector. , The numerical accuracy is ±0.01 meters. For the first Path control attribute vector for each segment To allow for offset angles, the heading angle serves as a hard constraint for path planning and tracking control. To correct the sensitivity threshold, To ensure safe avoidance distance, all elements of the vector are real constants with no fuzzy variables.

[0029] The final control system outputs the unmanned tractor's operating reference path model. The model is stored as a binary serialized file, with the file arranged in open order by segment ID. It synchronously stores the unique identifier of each segment, the reference path coordinate vector, and the control attribute vector, providing a fixed-format, high-precision spatial reference for subsequent path correction steps.

[0030] Step S2: Based on the unmanned tractor operation baseline path model, collect real-time operation data of the unmanned tractor and calculate the risk assessment value. Determine the operation status of the unmanned tractor based on the risk assessment value to obtain the risk quantification result. Based on the baseline path model for unmanned tractor operations, the onboard intelligent navigation control system of the unmanned tractor initiates the operation risk identification process, with the following steps: First, real-time operation data is collected using onboard multi-source sensors. All sensors have a fixed sampling frequency of 10Hz, and the data sampling accuracy meets the quantization calibration requirements. Specifically, the onboard RTK positioning module collects the tractor's current working plane coordinates in real time. Coordinate measurement accuracy Meters, the inertial measurement unit (IMU) collects the fuselage roll angle in real time. Pitch angle Yaw angle The angle measurement accuracy is ±0.1°, and the force sensors mounted on the left and right tracks respectively collect the vertical force on the tracks. and The force measurement range is 0~5000N, and the measurement accuracy is ±5N. The airborne lidar and vision fusion sensor synchronously collect the ground undulation elevation difference. Crop height Crop spacing The elevation difference measurement accuracy is ±0.02 meters, the crop spacing measurement accuracy is ±0.01 meters, and the control system reads the control attribute vector of the current working section output by S1. The system obtains three quantitative parameters: the allowable offset angle of the section, the correction sensitivity threshold, and the safe avoidance distance.

[0031] The collected real-time coordinates are compared with the baseline path coordinates to calculate the position offset. The calculation formula is as follows:

[0032] in, and for Real-time planar coordinates of the tractor and The coordinates of the points corresponding to the reference path in the plane. This is the offset in a two-dimensional plane.

[0033] The location offset and real-time operation data are normalized and combined with a preset risk coupling weight coefficient to calculate the risk assessment value. The formula for calculating the risk assessment value is as follows:

[0034]

[0035]

[0036] Where k1-k6 are risk coupling weight coefficients, This is the normalized value of the position offset, obtained by dividing the position offset by the maximum allowable offset. For the fuselage roll angle, The pitch angle, This is the normalized value of the attitude tilt modulus. For the maximum safe attitude angle, This is the normalized value of the track stress difference. The threshold for the difference in force on the track for safety. The normalized value of the ground undulation elevation difference is obtained by dividing the ground undulation elevation difference by the safe terrain undulation threshold. The normalized value for crop height is obtained by dividing the crop height by the maximum crop height. This is the normalized value for crop spacing, obtained by dividing the current crop spacing at the node by the maximum crop spacing in the work area. This is the risk assessment value.

[0037] It should be noted that the risk coupling weight coefficient was obtained through orthogonal experiments on field operations of field crops. Five typical operational scenarios—positional offset, attitude, stress, terrain, and crop—were selected to design the L18 (…). Orthogonal experiments were conducted, risk sample data were collected using actual machines, and range analysis and variance verification were performed using the operational safety rate as the evaluation index. Finally, values ​​were assigned based on the risk contribution of each factor. =0.35、 =0.2、 =0.15、 =0.1、 =0.1、 =0.1, the sum of all coefficients is 1 to ensure dimensional normalization.

[0038] The operational status of the unmanned tractor is determined based on the risk assessment value, resulting in a quantified risk assessment. Specifically, the low-risk threshold is defined as the risk assessment value. ≤0.2 indicates that the corresponding positional deviation, fuselage attitude, track stress, terrain undulation, and crop distribution are all within the safe operating range; the medium-risk threshold is 0.2 < ≤0.5 indicates that a single indicator is close to the safety threshold, suggesting a slight deviation or attitude anomaly. The high-risk threshold is... A value >0.5 indicates that multiple indicators have exceeded the safety threshold, posing a risk of continuous deviation, machine instability, or crop damage. Simultaneously, a deviation trend determination rule is set, which measures the deviation within three consecutive control cycles (cumulative 0.3 seconds). If the deviation continues to increase, it is considered a persistent risk of deviation. Greater than the current segment's sensitivity threshold The absolute value of the fuselage roll / pitch angle is greater than 3°, the difference in track stress is greater than 200N, and the difference in ground elevation is greater than 100N. Larger 0.1 meters, crop spacing When the distance is less than 0.14 meters (in densely cropped areas), it is determined that there is a risk of crop damage; all other working conditions are determined to have no risk of crop damage. When the above crop damage conditions are met, and at the same time any of the following situations occurs: deviation exceeds the limit, machine attitude exceeds the limit, track force difference exceeds the limit, or terrain undulation exceeds the limit, it is directly determined to be a high-risk operation and the path correction trigger command is locked. The final output is the risk quantification result. ,in, The risk level is indicated by 0 (low risk, 1 (medium risk), 2 (high risk). This is a persistent offset flag (0 for none, 1 for yes). As a crop damage risk flag (0 indicates none, 1 indicates yes), this vector is stored in the form of a new binary data frame in real time and synchronously transmitted to the subsequent path correction module, providing a unique and quantifiable risk basis for the decision on safe passage reconstruction.

[0039] Step S3: Based on the risk quantification results, the unmanned tractor is used to plan a safe passage path by improving the ARA* algorithm; The unmanned tractor's onboard intelligent navigation control system receives the risk quantification results output by S2. When the risk level is medium to high and the crop damage risk flag is 1, the system performs path planning for the unmanned tractor using an improved ARA* algorithm to obtain a safe passage path. Through adaptive expansion factor optimization, dynamic search step size adjustment, and cubic B-spline curve smoothing, a smooth correction path that does not damage the crop is generated, as detailed below: First, four types of quantitative data are input: the unmanned tractor's operating baseline path model, the real-time operating status parameter vector output by S2, ternary raster data of crop spatial distribution (raster resolution 0.5m × 0.5m, with prohibited areas assigned a value of 1, passable areas assigned a value of 0, and sparsely populated areas assigned a value of 2), and fixed kinematic parameters of the unmanned tractor chassis, including the minimum turning radius. =1.2 meters, maximum safe operating speed =1.2 m / s, the above parameters are determined according to the general design standards for unmanned tractors in farmland.

[0040] It should be noted that the specific algorithm and quantization threshold for judging the ternary raster data of crop spatial distribution are as follows: Crop point cloud, semantic segmentation, and terrain data collected by sensors are projected onto raster cells. The average crop spacing and the percentage of obstacles within each cell are statistically analyzed. Thresholds are set as follows: When the average crop spacing is ≤0.14 meters or the obstacle percentage is ≥70%, it is determined as a no-passage zone, and a value of 1 is assigned; when the average crop spacing is greater than 0.14 meters and ≤0.3 meters, it is determined as a sparse crop zone, and a value of 2 is assigned; when the average crop spacing is greater than 0.3 meters or there are no crops distributed within the raster and the obstacle percentage is less than 70%, the threshold is set as follows: The area is considered passable, and a value of 0 is assigned at this point. The control system automatically determines and completes the grid assignment for the entire area. The value of 0.14 meters is completely consistent with the judgment threshold for the dense crop section in step S1. This value is determined based on the national standard planting density of mainstream field crops such as corn and wheat. 70% is the general engineering judgment threshold for unmanned tractor operation in farmland, which is determined based on structural parameters such as the minimum turning radius and working width of the tractor chassis. The upper limit of 0.3 meters is determined based on the national standard plant spacing upper limit for sparse planting scenarios of mainstream field crops such as corn and wheat. The plant spacing of crops in this range meets the spatial requirements for the passage of unmanned tractors in farmland.

[0041] Next, the improved ARA* algorithm initialization is completed. First, the core adaptive parameters are calculated based on the plot size and crop density. The formula for calculating the adaptive initial expansion factor is:

[0042] in, The longitudinal length of the plot. The horizontal width of the plot. This represents crop density, with a value ranging from 0 to 1. For floor operations, This is the adaptive initial expansion factor.

[0043] In this formula, The average size of the plot grid reflects the spatial scale of the route planning. This is the crop density attenuation coefficient, whose physical meaning is: the denser the crops, the smaller the expansion factor, avoiding excessive path expansion and crop compression; the sparser the crops, the larger the expansion factor, improving path search speed, through max( 1) The minimum value of the expansion factor is forced to be 1 to eliminate the risk of algorithm failure; rounding up ensures that the expansion factor is a positive integer, which conforms to the path search grid planning rules. and The physical meaning of direct multiplication is to achieve dynamic coupling between plot size and crop distribution density: the spatial scale with length dimension is proportionally corrected by the dimensionless density attenuation coefficient, and finally the expansion factor benchmark value is obtained that takes into account both plot size adaptation and crop avoidance requirements. This benchmark value is rounded up and converted into an integer expansion factor that can be executed by the algorithm, which not only ensures that the path search range matches the plot size, but also avoids damage to crops through crop density adjustment.

[0044] Set the iterative decrease step size of the expansion factor Minimum convergent expansion factor Maximum search step size meters, minimum search step size Meters, dynamic step size iterative decrease Meters / time, algorithm prediction time domain Control time domain .

[0045] Then, the algorithm's core node management linked list is initialized, which consists of an OPEN table storing nodes of the path to be explored, a CLOSE table storing nodes that have been explored, and an INCONS table storing nodes that need to be re-examined due to cost updates. The maximum storage capacity of a single table is 500 nodes, and the node spatial resolution is 0.1 meters, providing a node management carrier for subsequent path search. The algorithm uses the tractor's current real-time positioning coordinates as the path start point and the nearest regression point on the section's benchmark path as the path end point. If the corrected path crosses the boundary of the current work section, it automatically updates the corresponding regression point on the next section's benchmark path as the new path end point. Path search is performed within the defined range of the sparse crop safety zone and the passable zone. All cost terms are normalized to a dimensionless interval. The node cost function calculation formula is as follows:

[0046] Among them, key For nodes Total driving cost The normalization cost for path length is calculated from the path start point to the current node. The actual driving distance is obtained by dividing the maximum planned path length. To heuristically determine the distance normalization cost, the current node... The Euclidean distance to the end point of the path is obtained by dividing the maximum planned path length. The inflation factor for the current iteration round. The crop sparsity incentive weighting coefficient (calibrated value λ=0.2, determined through field trials). This is the normalized value of crop spacing. This term is the crop sparsity incentive term, which is always non-negative. It can guide the path planning towards sparse crop areas and further reduce the probability of crop damage.

[0047] During the search process, the linked list management logic is strictly followed. The node with the lowest total cost is moved from the OPEN list to the CLOSED list. Neighboring nodes are traversed and their costs are updated. If the cost of a node in the CLOSED list decreases, it is moved to the INCONS list. After each iteration, the INCONS and OPEN lists are merged and reordered. Simultaneously, the linked list management logic is strictly followed. Update the inflation factor, according to Update the search step size until... Alternatively, once the path search is complete, an initial sequence of corrective path nodes that satisfies the traffic constraints is generated. ,in, The number of path nodes, ranging from 20 to 100, and the precision of the node planar coordinates. rice.

[0048] Using the initial correction path nodes as control points, a third-order B-spline curve is used to smoothly reconstruct the safety passage. The standard formula for the curve is:

[0049] in, These are path fitting parameters, with values ​​ranging from 0 to 1. For real-time coordinates of the safety passage, The maximum sequence number of the control point. For the first Coordinates of the initial path control points It is a third-order B-spline basis function.

[0050] The fitting process must strictly meet quantization constraints; specifically, the angle between the path heading angle and the segment reference path must not exceed the allowable offset angle. Path curvature The lateral offset of the path does not exceed the safe avoidance distance of the current segment. centimeters, rate of change of steering angle Seconds (path planning layer actuator action constraints, limiting the smoothness of steering actions).

[0051] Final output secure channel path The path point spacing is fixed at 1. The path vector, with a planar coordinate accuracy of ±0.01 meters, is stored in the form of a binary coordinate sequence refreshed at 10Hz and directly transmitted to the on-board motion control unit. This controls the tractor to travel continuously along the safe passage, smoothly returning to the work reference path without stopping or sharp turns.

[0052] Step S4: Based on the safe passage path, the unmanned tractor is predicted and controlled by the fuzzy adaptive model predictive control algorithm to obtain stable control commands, thereby realizing the accurate correction of the unmanned tractor's working path.

[0053] After completing the path correction for the safe passage, the onboard intelligent navigation control system of the unmanned tractor uses a fuzzy-adaptive model predictive control algorithm (Fuzzy-Adaptive MPC) to predict and control the unmanned tractor's path deviation. Throughout the process, it uses quantized motion constraints to suppress continuous path deviation and prevent trajectory oscillations and abrupt correction actions, as detailed below: First, input three types of standardized and quantified data, including smoothed safe passage path vectors. The collected real-time operation data and fixed kinematic parameters of the unmanned tractor, including wheelbase. Meters, wheelbase meters, maximum steering angle °, Control Week The parameters mentioned above are determined based on the design standards of unmanned farmland tractors, and the correction sensitivity threshold of the section control attributes in S1 is read simultaneously. ; The control system is based on a discrete predictive model constructed from the planar kinematics of the unmanned tractor. The state vector and control vector are as follows:

[0054]

[0055] in, For state vectors, and for The tractor's planar coordinates at any given time for Heading angle at any time for Constant driving speed For control vectors, for Turning angle at any moment for The difference in track drive torque between left and right at any given moment.

[0056] Discrete state transition equation is ,in, It is a 4x4 state transition matrix. It is a 4×2 control input matrix, and the matrix elements are uniquely determined by the kinematic parameters, with no variable ambiguity. It should be noted that the specific expressions for the state transition matrix and the control input matrix are as follows:

[0057]

[0058] in, To control the cycle, For tractor wheelbase, The traction acceleration calibration coefficients (calibrated on-site based on tractor power system characteristics and farmland soil adhesion characteristics) are used. The matrix elements are determined by the tractor's planar kinematic coupling relationship. The state transition matrix represents the natural evolution of the tractor's state over time when there is no control input. The first and second rows characterize the coupling effect of heading angle and travel speed on the planar coordinates. The third row characterizes the effect of travel speed and steering angle on the rate of change of heading angle. The fourth row characterizes the self-holding characteristic of travel speed. The control input matrix represents the regulatory effect of the control vector on the tractor's state. The element in the first column of the third row characterizes the regulatory gain of steering angle on heading angle. The element in the second column of the fourth row characterizes the regulatory gain of driving torque difference on travel speed. A fuzzy adaptive module is configured. This module has a 2-input, 2-output structure, with the input being the lateral offset error. Reference path curvature The output is the adaptive correction coefficient for the state weights. and adaptive correction coefficients for control weights Lateral offset error The fuzzy universe of discourse is [-0.1 m, 0.1 m], and the reference path curvature is... The fuzzy domain is State weight adaptive correction coefficient The fuzzy universe of discourse is [-0.2, 0.2], and the adaptive correction coefficients for the control weights are... The fuzzy universe of discourse is [-0.1, 0.1], the membership function adopts a triangular uniform distribution, the fuzzy rule base contains 25 quantized rules, and the MPC initial weight matrix is... , The weight matrix is ​​updated based on the adaptive correction coefficients of the state weights and the adaptive correction coefficients of the control weights, resulting in the updated weight matrix: , It is used to dynamically balance path tracking accuracy and driving stability.

[0059] It should be noted that the 25 quantitative rules are as follows: When lateral offset error For negative large (NB, i.e.) When the reference path curvature κ is negative (NB, i.e., ≤-0.06 meters), it is considered that the reference path curvature κ is negative (NB, i.e., ...). ≤-0.5 Then the state weight adaptive correction coefficient Take the maximum value (PB, quantized value 0.2), and control the weight adaptive correction coefficient. Take the largest value (PB, quantization value 0.1); if the reference path curvature is... For a negative value of NS, i.e., -0.5 < ≤-0.1 ),but Take the largest positive value (PB, 0.2), and the smallest positive value for ΔR (PS, 0.05); if the reference path curvature is... =Z0, i.e. -0.1 < <0.1 ),but Take the positive value (PB, 0.2). Take zero (ZO, 0); if the reference path curvature Positive small (PS, i.e., 0.1 ≤ <0.5 ),but Take the positive value (PB, 0.2). Take the smallest positive value (PS, 0.05); if the reference path curvature is... For Zhengda (PB, i.e.) ≥0.5 ),but Take the positive value (PB, 0.2). Take the positive value (PB, 0.1).

[0060] When lateral offset error For negative small (NS, i.e.) When the reference path curvature is (meters), If it is negative (NB), then Take the smallest positive value (PS, 0.1). Take the positive value (PB, 0.1); if If the value is negative (NS), then Take the smallest positive value (PS, 0.1). Take the smallest positive value (PS, 0.05); if If it is zero (ZO), then Take the smallest positive value (PS, 0.1). Take zero (ZO, 0); if If it is positive small (PS), then Take the smallest positive value (PS, 0.1). Take the smallest positive value (PS, 0.05); if If it is PB, then Take the positive smallest (PS, then) Take the positive smallest (PS), then Take the positive smallest (PS, then) Take the smallest positive value (PS, 0.1). Take the smallest positive value (PS, 0.1). Take the smallest positive value (PS, 0.05); if If it is PB, then Take the smallest positive value (PS, 0.1) Take the positive value (PB, 0.1).

[0061] When lateral offset error =Z0, i.e. -0.02 < When the curvature of the reference path is negative (NB) and the distance is less than 0.02 meters, then... Take zero (ZO, 0), R is taken as positive (PB, 0.1); if If the value is negative (NS), then Q is zero (ZO, 0). R is taken as positive minimum (PS, 0.05); if If it is zero (ZO), then Take zero (ZO, 0), Take zero (ZO, 0); if If it is positive small (PS), then Take zero (ZO, 0), Take the smallest positive value (PS, 0.05); if If it is PB, then Take zero (ZO, 0), Take the positive value (PB, 0.1).

[0062] When lateral offset error Positive small (PS, i.e.) When the reference path curvature is (meters), If it is negative (NB), then Take the smallest positive value (PS, 0.1). Take the positive value (PB, 0.1); if If the value is negative (NS), then Take the smallest positive value (PS, 0.1). Take the smallest positive value (PS, 0.05); if If it is zero (ZO), then Take the smallest positive value (PS, 0.1). Take zero (ZO, 0); if If it is positive small (PS), then Take the smallest positive value (PS, 0.1). Take the smallest positive value (PS, 0.05); if If it is PB, then Take the smallest positive value (PS, 0.1). Take the positive value (PB, 0.1).

[0063] When lateral offset error For PB (i.e.) When the reference path curvature is (meters), If it is negative (NB), then Take the positive value (PB, 0.2). Take the positive value (PB, 0.1); if If the value is negative (NS), then Take the positive value (PB, 0.2). Take the smallest positive value (PS, 0.05); if If it is zero (ZO), then Take the positive value (PB, 0.2). Take zero (ZO, 0); if If it is positive small (PS), then Take the positive value (PB, 0.2). Take the smallest positive value (PS, 0.05); if If it is PB, then Take the positive value (PB, 0.2). Take the right and the great .

[0064] Control system setting MPC prediction time domain Control Time Domain Calculate the future based on discrete prediction models The offset trend sequence for each control period is calculated as follows:

[0065] in, for Predict the offset at any time. and To predict coordinates, and The coordinates are for the safety passage.

[0066] Next, the offset trend growth rate is calculated as follows:

[0067] in, The offset trend growth rate, for Predict the offset at any time. This is the offset at the current moment. The minimum value for engineering protection (taken as) =0.001 meters), used to avoid calculation anomalies where the denominator is zero.

[0068] When the offset trend growth rate Furthermore, if the offset continues to increase within three consecutive control cycles (cumulative 0.3 seconds), it is determined to be a persistent offset; Based on the predicted offset trend and the updated weight matrix, the optimal control quantity is solved using the rolling optimization objective function, which is calculated as follows:

[0069] in, To optimize the overall objective function in a rolling manner, a smaller value indicates better control performance. j represents the discrete time index within the prediction and control time domains, and its value is a positive integer. To predict the time domain length (the value is 30, which means predicting the state for the next 30 control cycles). The predicted state vector of the tractor at time k+j. Let k+j be the reference state vector of the safe passage. The weighted L2 norm of the state tracking error is calculated using the state weight matrix. In this configuration, the subscript Q is used to identify the weighted calculation of the state tracking error dimension corresponding to this norm. To control the time domain length (the value is 15, which represents the length of the control sequence for rolling optimization). The control increment vector at time k+j includes the steering angle increment and the driving torque difference increment. To control the incremental weighted L2 norm, its weighting coefficients are determined by the control weight matrix. The subscript R is used to identify the weighted calculation of the control increment dimension corresponding to this norm.

[0070] It should be noted that the predicted offset has been incorporated into the prediction model through coordinate state, and the state error in the objective function... The predicted offset has been fully included. The core information is that the two have the same physical meaning, and they participate in the rolling optimization calculation in the form of state vectors.

[0071] The control system solves for the optimal control quantity based on the objective function. The constraints are divided into two categories: path planning constraints and tracking control constraints. The path planning layer inherited constraint is that the real-time heading angle deviation does not exceed the allowable offset angle of the section. The tracking control layer execution constraint is that the steering angle adjustment step size is ≤0.5° / cycle and the left and right track drive torque adjustment range is ≤10% of the rated torque. The tracking control layer state constraint is that the heading angle change rate is ≤2° / cycle (i.e., 20° / second, which is greater than the steering angle change rate of the planning layer in step S3, and reserves margin for control action. The two are not conflicting.

[0072] The final control system outputs a stable control command. ,in, To achieve the optimal steering angle, As the optimal driving torque difference, this vector is stored in binary data frames refreshed at 10Hz and directly transmitted to the vehicle drive and steering actuators to achieve early suppression of offset trends and active path stabilization.

[0073] Furthermore, the onboard intelligent navigation control system of the unmanned tractor performs adaptive path maintenance based on positioning reliability and adaptive update of the segment path model driven by the operation result, as follows: The control system first inputs four types of quantitative data, including the unmanned tractor's operating baseline path model, the real-time positioning coordinates output by the onboard RTK module, and the satellite signal carrier-to-noise ratio. The system collects operational status and path correction data throughout the entire process, as well as real-time attitude and motion data from the inertial measurement unit (IMU) of the unmanned tractor. The satellite signal carrier-to-noise ratio measurement range is 0~60dB-Hz, the sampling frequency is 10Hz, the IMU data sampling frequency is 100Hz, the angle measurement accuracy is ±0.1°, and the effective judgment period for positioning data is 0.1 seconds / time.

[0074] The control system first performs a quantitative assessment of positioning reliability, sets three levels of positioning reliability thresholds, and establishes a high-reliability state. ≥35dB-Hz, medium reliability is 25dB-Hz <35dB-Hz, low reliability / lost-lock status is If there is no valid positioning data for dB-Hz or for 5 consecutive sampling cycles (cumulative 0.5 seconds), the threshold is determined according to the national standard for the reliability of RTK positioning signals in farmland.

[0075] Simultaneously, the location fusion weights are calculated, specifically as follows: ,in, Weighting of RTK location data fusion 60 represents the real-time satellite signal carrier-to-noise ratio, and 60 is the maximum range setting for the carrier-to-noise ratio, used to normalize the positioning quality.

[0076] The control system performs adaptive path-keeping control based on positioning reliability. In the high-reliability state, RTK positioning data is used directly, with a path tracking deviation constraint of ±1.5 cm. In the medium-reliability state, fused positioning data is used, as calculated below:

[0077] in, To fuse the positioning state vector (including planar coordinates, heading angle, and speed), Locate the state vector for RTK. The recursive localization state vector is used for the IMU.

[0078] In low reliability / lockout states, the system switches to historical trajectory and kinematic recursive positioning, forcibly restricting the tractor's travel range to within ±7 cm laterally along the S3 safety passage path, thus preventing sudden corrections and trajectory oscillations caused by positioning fluctuations.

[0079] After the control system completes a single operation, it calculates the quantitative operation indicators for each section, including the number of times the offset per unit length exceeds the self-correction sensitivity threshold of the current section. (times / 10 meters), total number of path corrections (times), success rate of crop safe avoidance (Percentage), Cumulative Duration of Positioning Fluctuations (seconds / 10 meters), with a statistical resolution of 0.1 meters for all indicators.

[0080] The control system adaptively updates the segment path model based on statistical indicators, introduces an adaptive step-size learning mechanism based on operational indicator deviations, and sets quantitative update rules, including the number of times the unit length deviation exceeds the limit. When the deviation exceeds the standard by 10 meters, the sensitivity threshold is updated and corrected according to the proportion of deviation exceeding the standard. The reduction amount is positively correlated with the deviation exceeding the standard rate, and the lower limit of the threshold is locked at 1 centimeter. When the crop safety avoidance success rate is... When the positioning fluctuation accumulates, the safe avoidance distance is adaptively increased according to the deviation ratio of the avoidance failure. When the speed is 1 second / 10 meters, the lower limit of the positioning fusion weight is adaptively adjusted according to the proportion of positioning fluctuation time. The minimum value of the lower limit of the weight is 0.3. The segment parameters are iterated through adaptive step size and boundary constraints.

[0081] It should be noted that the process of updating the sensitivity threshold according to the proportion of deviation exceeding the standard is as follows: First, calculate the deviation exceeding the standard rate: ,in, The deviation exceeding the standard rate, This represents the number of times the offset per unit length exceeded the limit. The maximum number of times per unit length is allowed to exceed the limit (calibrated value is) (times / 10 meters), then calculate the corrected sensitivity threshold: ,in, To adjust the sensitivity threshold for the updated i-th segment, To correct the sensitivity threshold of the i-th segment before the update, The adaptive adjustment coefficient (calibrated to 0.1) was determined through field testing. To correct the lower limit of the sensitivity threshold.

[0082] After the update, a new version of the unmanned tractor operation baseline path model is generated. The model dimensions and storage format are completely consistent with the operation baseline path model in step S1. Finally, the control system overwrites the original model with the updated model as a binary serialized file. The file is arranged in ascending order by segment ID, and all quantitative parameters and coordinate sequences are retained simultaneously. This realizes the iterative optimization of the plot-specific path model and provides a continuously adaptable structured path reference for subsequent unmanned tractor precision operations.

[0083] It should be noted that, in this document, 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, the phrase "comprising an element defined as..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0084] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for precise operation path correction of an unmanned tractor, characterized in that: Includes the following steps: Step S1: Collect the field operation data of the unmanned tractor and construct the operation benchmark path model of the unmanned tractor based on the field operation data; Step S2: Based on the unmanned tractor operation baseline path model, collect real-time operation data of the unmanned tractor and calculate the risk assessment value. Determine the operation status of the unmanned tractor based on the risk assessment value to obtain the risk quantification result. Step S3: Based on the risk quantification results, the unmanned tractor is used to plan a safe passage path by improving the ARA* algorithm; Step S4: Based on the safe passage path, the unmanned tractor is predicted and controlled by the fuzzy adaptive model predictive control algorithm to obtain stable control commands, thereby realizing the accurate correction of the unmanned tractor's working path.

2. The method for precise operation path correction of an unmanned tractor according to claim 1, characterized in that: The process of collecting field operation data from unmanned tractors and constructing a baseline path model for unmanned tractor operations based on this data includes the following specific steps: Collect land operation data of unmanned tractors, including land boundary plane coordinate data, terrain distribution elevation raster data and historical operation trajectory data; The land parcels are divided into grid cells and clustered to obtain continuous operating sections; A segment digital identifier is assigned to a continuous operation segment and path control attributes are configured. The path control attributes include at least the allowed offset direction, the correction sensitivity threshold, and the safe avoidance distance. Establish a local plane coordinate system for the land parcel, and construct a reference path model for unmanned tractor operation based on the local plane coordinate system of the land parcel. The operational baseline path model consists of segment digital identifiers, plane coordinate vectors of the baseline path, and path control attributes.

3. The method for precise operation path correction of an unmanned tractor according to claim 2, characterized in that: The steps of collecting real-time operation data of unmanned tractors and calculating risk assessment values ​​based on the unmanned tractor operation baseline path model include: Based on the unmanned tractor's operating baseline path model, real-time operating data is collected. The real-time operating data includes at least the tractor's real-time planar coordinates, body attitude angle, track vertical force, ground undulation elevation difference, crop height, and crop spacing. The collected real-time coordinates are compared with the baseline path coordinates to calculate the position offset. The position offset and real-time operation data are normalized and combined with the preset risk coupling weight coefficient to calculate the risk assessment value.

4. The method for precise operation path correction of an unmanned tractor according to claim 3, characterized in that: The process of determining the operational status of the unmanned tractor based on the risk assessment value to obtain a risk quantification result includes the following steps: The operational risk level is determined based on the preset threshold range in which the risk assessment value falls; Based on the trend of position offset change within a continuous control cycle, a persistent offset risk flag is obtained. The real-time operation data is compared with the corresponding safety threshold to obtain the crop damage risk flag. The risk quantification results include the risk level, the persistent offset risk marker, and the crop damage risk marker.

5. The method for precise operation path correction of an unmanned tractor according to claim 4, characterized in that: Based on the risk quantification results, a safe passage path is obtained by improving the ARA* algorithm for unmanned tractor path planning, as detailed below: When the risk level is high, the improved ARA* algorithm is used to plan the path for the unmanned tractor to obtain a safe passage path. When the risk level is medium and the crop damage risk flag is valid, the improved ARA* algorithm is used to plan the path for the unmanned tractor to obtain a safe passage path. Using the real-time positioning coordinates of the tractor as the starting point of the path and the nearest regression point of the current work section's benchmark path as the ending point of the path, a path search is performed within the passable area and the sparse crop safety area, and an initial correction path is generated based on the node cost function. The initial correction path is smoothly reconstructed using a third-order B-spline curve to obtain the safe passage path.

6. The method for precise operation path correction of an unmanned tractor according to claim 5, characterized in that: The improved ARA* algorithm specifically includes: An adaptive initial expansion factor is calculated based on the vertical and horizontal scales of the plot and the crop density. The adaptive initial expansion factor is constrained to be no less than a preset minimum threshold. The formula for calculating the adaptive initial expansion factor is: ; in, The longitudinal length of the plot. The horizontal width of the plot. For crop density, For floor operations, This is the adaptive initial expansion factor.

7. The method for precise operation path correction of an unmanned tractor according to claim 6, characterized in that: The node cost function is specifically as follows: The node cost function includes path length normalized cost, heuristic distance normalized cost, and crop sparsity incentive term; The formula for calculating the node cost function is: ; Among them, key For nodes Total driving cost The cost of path length normalization. To inspire the cost of distance normalization, The inflation factor for the current iteration round. This represents the crop sparsity incentive weighting coefficient. This represents the normalized value of crop plant spacing.

8. The method for precise operation path correction of an unmanned tractor according to claim 7, characterized in that: The method of predicting and controlling path deviation of the unmanned tractor based on a safe passage path and using a fuzzy adaptive model predictive control algorithm includes the following steps: Based on the safe passage path, a fuzzy adaptive model predictive control algorithm is used to predict and control the path deviation of the unmanned tractor. The fuzzy adaptive model predictive control algorithm takes the safe passage path vector, real-time operation data and fixed kinematic parameters of the unmanned tractor as inputs, and sets up a fuzzy adaptive module; The fuzzy adaptive module takes the lateral offset error and the reference path curvature as inputs and outputs the state weight adaptive correction coefficient and the control weight adaptive correction coefficient. The weight matrix is ​​updated based on the adaptive correction coefficients of the state weights and the adaptive correction coefficients of the control weights, resulting in the updated weight matrix.

9. The method for precise operation path correction of an unmanned tractor according to claim 8, characterized in that: The step of predicting and controlling path deviation of the unmanned tractor using the fuzzy adaptive model predictive control algorithm further includes: Calculate the predicted offset and the offset trend growth rate based on the discrete prediction model; Determine and predict the offset trend based on the offset trend growth rate; Based on the predicted offset trend and the updated weight matrix, the optimal control quantity is solved according to the rolling optimization objective function, and a stable control command is output, which includes the optimal steering angle and the optimal driving torque difference.

10. The method for precise operation path correction of an unmanned tractor according to claim 9, characterized in that: The specific objective function for the rolling optimization is as follows: ; in, To perform rolling optimization of the overall objective function, j is the index of the discrete time in the prediction and control time domain, and k represents the current time. To predict the length of the time domain, The predicted state vector of the tractor at time k+j. Let k+j be the reference state vector of the safe passage. Let Q be the weighted L2 norm of the state tracking error, and Q represent the weighting dimension of the corresponding state tracking error. To control the length of the time domain, The control increment vector at time k+j To control the increment weighted L2 norm, R represents the weighted dimension of the corresponding control increment.