Multi-agent coupling control based multi-machine spraying uniformity improvement method

Abstract

The application discloses a multi-agent coupling control-based multi-machine spraying uniformity improvement method, and aims at solving the problem that multi-machine uniformity control cannot be closed loop due to the fact that the online observability and verifiability of the spray deposition amount and the coverage rate in the operation process cannot be achieved. The application realizes the technical effects of the online observability and verifiability of the deposition and coverage, the multi-machine collaborative closed loop control of the physical conservation consistency, and the spraying uniformity and coverage rate improvement through the following steps: multi-source data acquisition and space-time alignment, cross-modal fusion to generate deposition observation and uncertainty, introduction of a physical constraint neural network with global mass conservation constraint and Lagrange duality and joint reconstruction with a graph neural network, short-time prediction of a wind field graph network and risk-sensitive distributed model predictive control, order-preserving calibration and closed loop updating.

Description

Technical Field

[0001] This invention relates to the field of drone spraying, and in particular to a method for improving the uniformity of multi-drone spraying based on multi-agent coupling control. Background Technology

[0002] Agricultural plant protection spraying operations have widely adopted multi-machine collaborative methods, including ground spraying equipment and drone formations.

[0003] To improve coverage and uniformity, existing technologies have made some progress in path planning, formation control, constant speed and distance spraying, and sensor-based adaptive parameter tuning. In terms of environmental modeling, weather stations and airborne anemometers are commonly used to provide wind speed and direction, and simulation evaluation is carried out in combination with convection-diffusion models or empirical drift models. In terms of effect evaluation, it often relies on water-sensitive test strips, tracer sampling and offline laboratory analysis, or uses sensing methods such as images and leaf humidity for indirect estimation.

[0004] In recent years, there have been attempts to use deep learning and graph structure methods for predicting environment and sedimentation, but these have mostly focused on offline inference or single-machine scenarios.

[0005] However, existing technologies generally have the following shortcomings:

[0006] 1. Insufficient online observability and verifiability: Spray deposition and coverage are difficult to obtain and calibrate in real time during operation, mainly relying on offline sampling and post-event evaluation, which has a long feedback cycle, limited spatial representativeness, and difficulty in forming a control closed loop;

[0007] 2. Insufficient handling of environmental disturbances and multi-agent coupling: Wind field spatial distribution and time-varying characteristics are strong. Existing methods mostly use static or simplified models, lacking short-term wind field prediction for the operating area and coupling propagation among multiple agents. Multi-agent collaboration often remains at the path and formation level, lacking coupling optimization and constraints directly for deposition uniformity.

[0008] 3. Insufficient utilization of physical consistency and uncertainty: The estimation of sedimentation fields generally does not explicitly apply mass conservation constraints, the mechanisms of evaporation and drift are not adequately characterized, the prediction uncertainty lacks quantification and risk-sensitive control, and there is a lack of calibration and confidence assessment, which makes it difficult to correct overspray or underspray in a timely manner.

[0009] The aforementioned shortcomings have hindered the continuous improvement and closed-loop guarantee of the uniformity of multi-machine spraying.

[0010] Therefore, a multi-machine spraying method that can overcome the shortcomings of the existing technology is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0011] One objective of this invention is to propose a method for improving the uniformity of multi-machine spraying based on multi-agent coupled control. Addressing the problem in existing technologies where spray deposition and coverage are unobservable and unverifiable online during operation, thus hindering closed-loop control of multi-machine uniformity, this invention proposes a technical solution: acquisition and alignment of multi-source data under unified coordinates and clock; cross-modal fusion to generate deposition observations and uncertainties; joint deposition field reconstruction using a physical constraint neural network and a graph neural network with Lagrange duality for global mass conservation constraints; short-time prediction using a wind field graph network combining deposition gaps and conservation errors; risk-sensitive distributed model predictive control with conservation errors as hard constraints or high-weight penalties; and online verification and triggered closed-loop updates based on order-preserving calibration. This invention achieves the technical effects of online observability and verifiability of deposition and coverage, multi-machine collaborative closed-loop control under disturbed wind fields, significantly improved spraying uniformity and coverage, reduced over-spraying and under-spraying risks, and satisfaction of physical conservation consistency.

[0012] A method for improving the uniformity of multi-machine spraying based on multi-agent coupled control according to an embodiment of the present invention is characterized by comprising:

[0013] S1. Collect and synchronize raw observation data and output them;

[0014] S2. Input the original observation data and perform cross-modal fusion to obtain the sedimentation observation set, observation uncertainty, and operation status feature set;

[0015] S3. Input the sedimentary observation set, observation uncertainty and operation status feature set, execute the joint model of physical constraint neural network and graph neural network to reconstruct the sedimentary field and introduce global mass conservation constraints with Lagrange duality, and output the sedimentary field estimation results, conservation error index and sedimentary gap field and observation uncertainty.

[0016] S4. Input the sedimentation field estimation results, sedimentation gap field, conservation error index, observation uncertainty and operation status characteristic set, perform wind field map network prediction and form control preparation set;

[0017] S5. Input the control preparation set, execute risk-sensitive distributed model predictive control, and output multi-agent control instructions and control prediction sequences;

[0018] S6. Input multi-agent control instructions and control prediction sequences, execute according to multi-agent control instructions and generate job execution observation data and verification pairing data;

[0019] S7. Input verification pairing data, perform order-preserving calibration and verification, generate trigger signals, and output uniformity confidence interval and trigger signals;

[0020] S8. Perform closed-loop update based on the trigger signal and output the updated original observation data.

[0021] Optionally, step S1 specifically includes:

[0022] Each intelligent agent collects data on nozzle flow rate, nozzle pressure, operating speed, attitude, relative canopy height, wind speed and direction, relative positioning, and information on plot boundaries and no-spraying zones.

[0023] The collected data is synchronized in time, a unified clock reference is established and the timestamps are aligned, and data with different sampling frequencies are interpolated or resampled to form a time series with a unified time step.

[0024] Spatial registration is performed on the collected data to convert the relative positioning data and attitude to coordinates and attitude under a unified operating coordinate system, and the land parcel boundary and no-spraying zone information are represented in the unified operating coordinate system;

[0025] Output the raw observation data, which is a time-ordered and spatially labeled dataset with coordinates and timestamps.

[0026] Optionally, step S2 specifically includes:

[0027] Input the raw observation data into the cross-modal fusion model;

[0028] The original observation data is preprocessed, including timestamp alignment, spatial registration correction, noise suppression, scale calibration, missing value imputation and outlier handling, to form a preprocessed dataset with coordinates and timestamps.

[0029] Using the preprocessed dataset as input, spray deposition observations at corresponding coordinates and times are generated and organized into a deposition observation set according to coordinates and timestamps;

[0030] The cross-modal fusion model simultaneously outputs the uncertainty score for each spray deposition observation, and organizes the observation uncertainty by coordinates and timestamps;

[0031] During the fusion process, based on the preprocessed data set, the operation speed, attitude, wind speed and direction, relative canopy height and relative positioning data are extracted and organized into an operation status feature set according to coordinates and timestamps;

[0032] Output the sedimentation observation set and the set of observation uncertainty and operational status characteristics.

[0033] Optionally, step S3 specifically includes:

[0034] The sedimentary observation set is used as the observation input for the graph nodes, and the operation status feature set is used to construct a multi-agent operation topology graph;

[0035] In the loss function of the joint model of physical constraint neural network and graph neural network, mass conservation constraints of ejection, deposition, evaporation, drift and boundary flux are explicitly introduced. Dual optimization is established by Lagrange multipliers to make ejection equal to the sum of deposition, evaporation, drift and boundary flux. At the same time, the convection-diffusion equation and evaporation term are used as physical residuals to participate in the optimization. The solution yields the estimated deposition field of the covered operation area.

[0036] The conservation error indices for the global and regional areas are calculated based on the sedimentation field estimation results, and the sedimentation gap field is obtained by the difference between the target uniform sedimentation benchmark and the sedimentation field estimation results.

[0037] Optionally, step S4 specifically includes:

[0038] The sedimentation field estimation results and sedimentation gap fields are extracted as aerodynamic source features according to coordinates and timestamps. Under a unified operating coordinate system, the wind speed, wind direction, attitude, operating speed and relative positioning data in the operating status feature set are spatially and temporally aligned to form the input feature set of the wind field map network.

[0039] Using the input feature set as input, short-term prediction is performed in the wind field map network to obtain the short-term wind field prediction results within the future rolling window, and the short-term wind field prediction results are organized according to the time step and coordinates.

[0040] The short-term wind field prediction results, sedimentation field estimation results, sedimentation gap field, conservation error index, and observation uncertainty are organized into a control preparation set according to coordinates and timestamps.

[0041] Optionally, step S5 specifically includes:

[0042] Input the control preparation set into the distributed model predictive control problem;

[0043] In the distributed model predictive control problem, the short-term wind field prediction results are organized into a perturbation sequence according to the time step, the sedimentation field estimation results and the sedimentation gap field constitute a coupled control objective, the conservation error index is added to the constraint set as a hard constraint or weighted penalty, and the risk weight is set according to the observation uncertainty.

[0044] Using the multi-agent operation topology graph as the adjacency relationship, each agent establishes a local prediction model and a local optimization problem. The decision variables of the local prediction model are the temporal trajectory of operation speed, heading, lateral spacing and jet volume within the prediction window. The local prediction model updates the state by the temporal evolution of the operation state characteristics under the unified operation coordinate system and superimposes the disturbance sequence.

[0045] The goal of the local optimization problem is to reduce the deposition gap field while taking into account control stability and operational efficiency. Constraints include operational speed, heading change rate, upper and lower limits of lateral spacing and spray volume, block boundary and no-spray zone constraints, lower limit of relative distance between adjacent machines, and conservation consistency constraints where the conservation error index does not exceed a preset threshold or is included in the form of a weighted penalty.

[0046] The multi-agent control commands for each agent, including operating speed, heading, lateral spacing, and spray volume, are obtained by solving under the adjacency coupling term. The predicted values ​​of deposition and uniformity indices within the prediction window are then organized according to the time step and coordinates to form a control prediction sequence.

[0047] Optionally, step S6 specifically includes:

[0048] Multi-agent control commands are issued to each agent and executed under a unified operating coordinate system and a unified clock reference. The operating speed, heading, lateral spacing and spray volume are controlled according to the time step of the multi-agent control commands.

[0049] During the execution process, newly added spray deposition observations were collected and their corresponding coordinates and timestamps were recorded. The operation execution observation data were then organized according to the coordinates and timestamps.

[0050] The operation execution observation data and control prediction sequence are aligned under a unified operation coordinate system and a unified clock reference. They are paired one by one in a way that the coordinates and timestamps are the same or are considered to be consistent within the preset spatial error limit and time error limit, to form verification pairing data. The verification pairing data includes each spray deposition observation value and its corresponding predicted deposition value and the predicted value of the uniformity index of the corresponding spatiotemporal location.

[0051] Optionally, step S7 specifically includes:

[0052] Input the verification pairing data into the sequence-preserving calibration and verification process;

[0053] The calibration score is calculated based on the verification pairing data under a unified operating coordinate system and a unified clock reference. The calibration score includes the error between the predicted value of the uniformity index for each pair and the measured value of the uniformity index calculated from the spray deposition observation value according to the preset uniformity evaluation method, as well as the error between the predicted value of the coverage and the measured value of the coverage obtained by mapping the predicted deposition value and the spray deposition observation value to the coverage state according to the preset coverage determination threshold and summarizing them.

[0054] Under a preset confidence level, construct confidence intervals for uniformity and coverage using the statistical boundaries of the calibration scores, organize the uniformity confidence intervals by coordinates and timestamps, and output the uniformity confidence intervals.

[0055] The uniformity confidence interval is determined based on a preset threshold or a conservation error index, and a trigger signal is generated when the non-compliance condition is met.

[0056] Optionally, step S8 specifically includes:

[0057] The uniformity confidence interval and the trigger signal input closed-loop update process;

[0058] When the trigger signal indication fails to meet the standard, active sampling, model recalibration, or risk weight adjustment are selected and executed based on the out-of-bounds position and out-of-bounds magnitude of the uniformity confidence interval.

[0059] Active sampling involves collecting spray deposition observations and recording coordinates and timestamps at the aforementioned out-of-bounds locations and time periods under a unified operating coordinate system and a unified clock reference, thus forming new sampling data.

[0060] Model recalibration involves recalibrating the parameters of the cross-modal fusion model and the joint model of the physical constraint neural network and the graph neural network, and generating recalibrated data update terms.

[0061] The risk weight adjustment is to update the risk weight parameters in the distributed model predictive control based on the width of the uniformity confidence interval. The update is used in step S5 of the next rolling window and does not change the structure of the original observation data.

[0062] The newly added sampling data and the recalibrated data update items are merged into the original observation data according to coordinates and timestamps under a unified operating coordinate system and a unified clock reference to form the updated original observation data.

[0063] When the trigger signal indicates that the target has been met, the original observation data is kept unchanged and the updated original observation data is directly output.

[0064] The updated original observation data is output as input for step S1 to complete the closed-loop iteration.

[0065] The beneficial effects of this invention are:

[0066] 1. Achieve online observability and verifiability of spray deposition amount and coverage and form closed-loop control: Generate deposition observations and uncertainties through cross-modal fusion, perform order-preserving calibration with verification paired data after control execution, construct confidence intervals for uniformity and coverage and trigger active sampling or model recalibration, shorten the feedback cycle and improve prediction credibility and operational reliability.

[0067] 2. Enhance physical conservation consistency and robust control: The joint model of physical constraint neural network and graph neural network explicitly introduces global mass conservation constraints with Lagrangian duality to ensure that the ejection, deposition, evaporation, drift and boundary flux are conserved. The conservation error is used as a hard constraint or high-weight penalty for model predictive control. Combined with short-term prediction by wind field map network, the risk of over-ejection and under-ejection is reduced and stability is maintained under environmental disturbances.

[0068] 3. Improve multi-agent collaborative efficiency and spray uniformity: Taking the deposition gap field as the coupling target, distributed optimization is carried out by comprehensively considering constraints and adjacency relationships such as operating speed, heading, lateral spacing, spray volume, and boundary and no-spray zone, so as to realize multi-agent collaborative operation, improve deposition uniformity and coverage, reduce repeated spraying and drift, and improve operation efficiency. Attached Figure Description

[0069] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0070] Figure 1 This is a flowchart of a method for improving the uniformity of multi-machine spraying based on multi-agent coupling control proposed in this invention. Detailed Implementation

[0071] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0072] refer to Figure 1 A method for improving the uniformity of multi-machine spraying based on multi-agent coupled control, characterized in that it includes:

[0073] S1. Collect and synchronize raw observation data and output them;

[0074] S2. Input the original observation data and perform cross-modal fusion to obtain the sedimentation observation set, observation uncertainty, and operation status feature set;

[0075] S3. Input the sedimentary observation set, observation uncertainty and operation status feature set, execute the joint model of physical constraint neural network and graph neural network to reconstruct the sedimentary field and introduce global mass conservation constraints with Lagrange duality, and output the sedimentary field estimation results, conservation error index and sedimentary gap field and observation uncertainty.

[0076] S4. Input the sedimentation field estimation results, sedimentation gap field, conservation error index, observation uncertainty and operation status characteristic set, perform wind field map network prediction and form control preparation set;

[0077] S5. Input the control preparation set, execute risk-sensitive distributed model predictive control, and output multi-agent control instructions and control prediction sequences;

[0078] S6. Input multi-agent control instructions and control prediction sequences, execute according to multi-agent control instructions and generate job execution observation data and verification pairing data;

[0079] S7. Input verification pairing data, perform order-preserving calibration and verification, generate trigger signals, and output uniformity confidence interval and trigger signals;

[0080] S8. Perform closed-loop update based on the trigger signal and output the updated original observation data.

[0081] In this specific embodiment, S1 specifically refers to:

[0082] Under a unified operating coordinate system and a unified clock reference, each agent conducts multi-source data acquisition and spatiotemporal alignment. Specifically, each agent collects data on nozzle flow rate, nozzle pressure, operating speed, attitude, relative canopy height, wind speed and direction, and relative positioning, and associates this data with plot boundaries and no-spraying zone information in the same coordinate system. To eliminate clock scaling and zero-point errors between different agents, a linear time correction model is adopted.

[0083] Perform time synchronization;

[0084] in Represents a standard timestamp under a unified clock reference. Indicates the first Clock scaling factor of each agent Indicates the first Clock zero offset of each agent, Indicates the first The first intelligent agent The local timestamp of the second sample, Indicates agent index, Represents the total number of agents and satisfies Indicates the local sampling index;

[0085] By unifying the resampling step size within the rolling job window, a discrete unified time series is constructed:

[0086] ;

[0087] in Indicates the first A unified sampling time, Indicates the start time under a unified clock reference. Indicates a unified time step, Represents a non-negative integer time-series index;

[0088] After time alignment, spatial registration is performed to transform the local coordinates and poses of each agent to global coordinates in a unified operational coordinate system using rigid body transformation.

[0089] ;

[0090] in Indicates the first The global position vector of each agent in a unified operating coordinate system, Indicates by the first The rotation matrix obtained from the pose calculation of each agent Indicates the first The position vector of an agent in its local coordinate system This represents the translation vector determined by the relative positioning;

[0091] After completing the spatiotemporal alignment, the data is organized into a time-ordered and spatially labeled set of original observation data:

[0092] ;

[0093] in Represents the original set of observation data, Represents the number of samples in the set. Indicates the spatially registered unified coordinate position. It represents the sensor feature vector collected at a uniform moment and includes channels such as nozzle flow rate, nozzle pressure, operating speed, attitude, relative canopy height, wind speed and direction, and relative positioning;

[0094] The data items also include information on land parcel boundaries and no-spray zones in the form of identifiers to ensure that subsequent steps can be directly based on this unified spatiotemporal data to carry out cross-modal fusion, physical constraint modeling, and control optimization.

[0095] In this specific embodiment, S2 specifically refers to:

[0096] Under a unified operating coordinate system and a unified clock reference, the raw observation data undergoes cross-modal fusion processing. First, preprocessing steps are performed, including timestamp alignment, spatial registration correction, noise suppression, scale calibration, missing value imputation, and outlier handling, to eliminate sampling inconsistencies between channels and sensor biases, and to establish coordinate-time consistency. This process is formally denoted as... ,in This represents the preprocessed data set. This indicates a preprocessing operator that includes steps such as time alignment, spatial correction, and data cleaning. Represents the original set of observation data;

[0097] Then The sample input is used to create a cross-modal fusion model to generate spray deposition observations and their uncertainty scores at corresponding coordinates and times, denoted as . ,in Indicates the first Spray deposition observations of the sample This indicates the uncertainty score corresponding to the sedimentary observation. Represents cross-modal fusion model, This represents the trainable parameter vector of the model. Indicates the first Pre-processed multi-channel input Indicates sample index, Indicates the total number of samples;

[0098] During the fusion process, job status features are extracted and structured, denoted as... ,in Indicates the first The feature vector of the working status of each sample Indicates feature extraction operators, Denotes the parameters of the operator, and Based on the speed of operation Attitude vector Wind field vector (Including wind speed and direction), relative canopy height With relative positioning vector composition;

[0099] To facilitate subsequent physical constraint reconstruction, wind field prediction, and distributed control optimization, the above results are organized into three output sets based on coordinates and timestamps:

[0100] ;

[0101] in This represents a set of sedimentary observations, with the subscript dep indicating sedimentation. Represents the set of observation uncertainties, Represents the set of job status features, Indicates the coordinate position in a unified working coordinate system. Represents a timestamp under a unified clock reference and is related to Records in pairs.

[0102] In this specific embodiment, S3 specifically refers to:

[0103] sedimentary observation ensemble As the observation input for graph nodes, and based on the set of job status features Constructing a multi-agent operation topology graph To characterize spatial adjacency and multi-machine coupling, a joint model of physical constraint neural network and graph neural network is used to reconstruct the sedimentation field, and a global mass conservation constraint with Lagrangian duality and physical residuals of convection-diffusion including evaporation are explicitly introduced into the loss.

[0104] First, define the global mass conservation residual:

[0105] ;

[0106] in Indicates time Conservation residuals Indicates time Total ejection volume of all agents Spatial domain representing the work area Represents the boundary of the spatial domain, Indicates position With time sediment density, Indicates position With time Evaporation loss density, Indicates position With time Drift loss density, Indicates position With time Boundary flux density, and These represent the measures of the volume integral and the boundary surface integral, respectively.

[0107] To illustrate the mechanisms of convection diffusion and evaporation, physical residuals are used:

[0108] ;

[0109] in Indicates position With time Physical residuals This represents the sedimentary density estimated by the joint model. Represents the wind field vector, Indicates the eddy diffusion coefficient, Indicates the evaporation coefficient, Indicates the spray source item, and These represent the gradient and divergence operators, respectively.

[0110] Joint optimization employs the Lagrange form:

[0111] ;

[0112] in Represents the joint loss function, This represents the data fitting term weighted by observation uncertainty. Lagrange multipliers representing conservation constraints Indicates the physical residual penalty weight, Represents the set of discrete moments in a rolling time window. Represents the L2 norm;

[0113] The sedimentary field estimate is obtained by solving the problem. Then calculate the global conservation error index:

[0114] ;

[0115] in Indicates global conservation error, Represents a set The base number, the partition conservation error can be divided according to the job partition. The same calculation applies when restricting to a subdomain;

[0116] Construct a sedimentary gap field based on a target homogeneous sedimentary baseline:

[0117] ;

[0118] in Indicates sedimentary gaps, Indicates a target uniform deposition benchmark;

[0119] It can be a constant field or a prescription diagram, and the final output is... and and and topology graph The structural information is used in conjunction with subsequent short-term predictions of the wind field map network and predictive control of the risk-sensitive distributed model.

[0120] In this specific embodiment, S4 specifically refers to:

[0121] Under a unified operating coordinate system and a unified clock reference, the sedimentation field estimation, sedimentation gap, conservation error, wind speed and direction, attitude, operating speed and relative positioning are spatially and temporally aligned and then input into the wind field map network for short-term prediction. This data is then compiled into a control preparation set for subsequent distributed model predictive control. Specifically, the key quantities are first compressed into input feature vectors:

[0122] ;

[0123] in Indicates position With time Input feature vector, Indicates sedimentary field estimation, Indicates sedimentary gaps, Represents a wind field vector containing wind speed and direction. Represents attitude vector, Represents the scalar of operation speed, Represents a relative positioning vector;

[0124] Short-term rolling prediction is based on a graph structure constructed from job nodes and spatial adjacency relationships. The mapping relationship is written as follows:

[0125] ;

[0126] in Indicates the location The Wind field prediction vector, Represents a wind field diagram network model with parameters of This represents a graph constructed from nodes and their adjacency relationships within the work area. Indicates short-term prediction step index, Indicates the upper limit of the prediction steps;

[0127] To facilitate further control, the wind field predictions for future steps, along with current sediment estimates, sedimentary gaps, global conservation errors, and observation uncertainties, are organized by coordinates and timestamps into a control preparation set:

[0128] ;

[0129] in Indicates control preparation set, Indicates a unified time step, This represents the global conservation error index calculated within the scrolling window. Indicates the location of sedimentary observations. With time Uncertainty score This represents the set of discrete sampling nodes under a unified operating coordinate system. The set is organized in lexicographical order of coordinates and timestamps to ensure seamless integration with the control solution interface.

[0130] In this specific embodiment, S5 specifically includes:

[0131] Using the control preparation set as input, a risk-sensitive distributed model predictive control problem is constructed under a unified operational coordinate system and a unified clock reference. Under the adjacency constraint of the multi-agent operational topology graph, each agent establishes a local predictive model, and short-term wind field predictions are superimposed on the state evolution as a perturbation sequence. The local decision variables are time-series trajectory vectors.

[0132] ;

[0133] in Indicates the first An agent in the prediction step Decision vector, Indicates work speed, Indicates heading angle, Indicates horizontal spacing, Indicates spray volume, Represents the agent index and satisfies , Represents the total number of agents, Represents the prediction step index and satisfies This indicates the maximum number of prediction steps for the scroll window;

[0134] To reflect the risk sensitivity driven by uncertainty, observation uncertainty is mapped to spatiotemporal risk weights and the penalty for depositional gaps is weighted accordingly.

[0135] ;

[0136] in Indicates position In the prediction step Risk weights, The scaling factor representing the risk weights, Indicates position At any moment Observation uncertainty score Indicates a unified time step, Indicates the start time of the current scroll window;

[0137] Under the above settings, a distributed objective function is constructed to reduce the predicted deposition gap while maintaining control stability, as follows:

[0138] ;

[0139] in Indicates the overall optimization goal, Indicates the first Each agent is responsible for a specific subdomain of tasks. Indicating in the prediction step The predicted sedimentary gap is derived from sedimentary field estimation, short-term wind field disturbances, and current decision-making extrapolation. The penalty weights representing the stationarity of control Represents the L2 norm;

[0140] In a distributed framework, the constraint set simultaneously embodies job boundaries, safety, and physical conservation consistency. The core constraints are written as:

[0141] ;

[0142] in Indicates the upper and lower limits of the working speed. Indicates the upper and lower limits of the spray volume. Indicates the upper and lower limits of the horizontal spacing. Indicates the upper limit of the rate of change of heading, Indicates the first With the An agent in the prediction step relative distance Indicates the lower limit of relative distance, Represents the first in the topological graph The adjacency set of an agent, This represents the global conservation error index obtained from step S3 and updated within the rolling window. The threshold representing the consistency of conservation;

[0143] The optimal control sequence for the multi-agent system is obtained by solving under the above objectives and constraints:

[0144] ;

[0145] in Represents the complete set of optimal solutions for multi-agent control instructions;

[0146] Subsequently, the predicted values ​​of deposition and uniformity indices within the prediction window are organized according to the time step and coordinates to form a control prediction sequence, which is then issued for execution.

[0147] In this specific embodiment, S6 specifically refers to:

[0148] Under a unified operational coordinate system and a unified clock reference, multi-agent control commands are issued sequentially and executed in discrete time steps. The unified scheduling time is written as follows:

[0149] ;

[0150] in Indicates the first A unified execution time, Indicates the start time of the current scroll window. Indicates a unified time step, Time index representing a non-negative integer;

[0151] For the The agent in the th... The control command vector for the step is denoted as:

[0152] ;

[0153] in Represents the control command vector, Indicates work speed, Indicates heading angle, Indicates horizontal spacing, Indicates spray volume, Represents the agent index and satisfies Indicates the total number of agents;

[0154] While controlling the execution, newly added spray deposition observations are collected at each unified moment, and their coordinates and timestamps are recorded, denoted as . ,in Indicates the first The agent in the th... The corresponding unified operation coordinate position is as follows: This represents the sedimentary observation value at that location and time;

[0155] The above-mentioned operational observation data and control prediction sequences are aligned under a unified spatiotemporal reference. The control prediction sequences are represented as follows: ,in Indicates predicted location, Indicates the predicted timestamp, Indicates predicted sedimentary values, The predicted value of the uniformity index corresponding to the spatiotemporal location. Represents the predicted sample index and satisfies Indicates the total number of predicted samples;

[0156] Alignment determination adopts the spatiotemporal tolerance pairing criterion:

[0157] ;

[0158] in Indicates the first Observation and the first Indicator function for predicting whether a match is found. Indicates spatial distance, Indicates time error, Indicates the preset space error limit, Indicates the preset time error limit, Represents the Euclidean second norm, Represents the index of the observation entry and satisfies Indicates the total number of observation entries;

[0159] In satisfying From the candidates, the nearest predicted entry is selected according to the spatial distance priority principle, and the matching mapping is defined as:

[0160] ;

[0161] in Indicates the first The prediction index corresponding to each observation;

[0162] The final result is a set of validation pairings:

[0163] ;

[0164] in Indicates the verification of paired data sets, and They represent the first Unified coordinates and timestamps for each observation Indicates observed sediment values, Indicates the predicted sedimentary value that matches it. This represents the predicted value of the uniformity index at the matching point;

[0165] This ensures that each observation and its corresponding prediction are matched one-to-one within the preset spatiotemporal error limit and are completely preserved for subsequent order-preserving calibration and verification.

[0166] In this specific embodiment, S7 specifically refers to:

[0167] Under a unified operating coordinate system and a unified clock reference, the verification pairing data set is input into the order-preserving calibration and verification process. The overall process involves measuring the error between the uniformity prediction and the actual measurement for each pair and constructing a uniformity confidence interval. Simultaneously, using a coverage determination threshold, the deposition prediction and deposition observation are mapped to a coverage state, and the difference between the predicted and actual coverage is summarized. Then, under a preset confidence level, a coverage confidence interval is constructed using the statistical boundaries of the aforementioned calibration scores, and a trigger signal is generated accordingly. Specifically, for the first pair... The uniformity calibration score for strip pairing is defined as follows:

[0168] ;

[0169] in Indicates the first Absolute error of uniformity of strip pairing This indicates that it is obtained from step S5 and is related to the first... The predicted value of the uniformity index matched by the observation within the preset spatiotemporal error limit. Indicates the first Matching index of prediction entries corresponding to observations Indicates by the first The measured values ​​of uniformity index obtained by calculating the uniformity index of the spray deposition observations according to the preset uniformity evaluation method. Represents the index of paired entries and satisfies Indicates the total number of paired entries;

[0170] Coverage is determined based on the deposition threshold. Mapping sedimentation predictions and sedimentation observations to a binary cover state:

[0171] ;

[0172] in Indicates the first Coverage status prediction values ​​of paired strips Indicates the relationship with the first Predicted sedimentary values ​​matched by observations Indicates the first Measured values ​​of coverage status of paired strips Indicates the first Sedimentary values ​​observed Indicates the coverage threshold, Indicates an indicator function;

[0173] At confidence level The following is a set of scores calibrated for uniformity. Construct the uniformity confidence interval for the upper quantile:

[0174] ;

[0175] in Indicates the first Confidence intervals for uniformity of paired bars This indicates the confidence level on the uniformity calibration score set. The upper quantile bound obtained from statistics, Indicates the significance level;

[0176] Coverage is calculated by summing the sample means to obtain both predicted and measured coverage:

[0177] ;

[0178] in The predicted value representing coverage The measured value representing coverage Indicates the number of paired samples;

[0179] The statistical bound of the above errors is defined by the coverage error set. The upper quantile approximation is used to obtain and construct the coverage confidence interval:

[0180] ;

[0181] in The confidence interval representing the coverage rate Indicates at confidence level The upper quantile of the coverage error Indicates the significance level;

[0182] To trigger closed-loop updates, define an interval width function. The trigger signal is determined based on the interval width of uniformity and coverage, as well as the conservation error.

[0183] ;

[0184] in A binary indicator representing the trigger signal. The preset width threshold representing the uniformity confidence interval; The preset width threshold representing the coverage confidence interval; This indicates the global conservation error index obtained from step S3 and updated within the scrolling window. The threshold representing the conservation consistency is used to finally output the uniformity confidence interval and coverage confidence interval organized by coordinates and timestamps, and generate a trigger signal for the next closed-loop update.

[0185] In this specific embodiment, S8 specifically refers to:

[0186] Under a unified operating coordinate system and a unified clock reference, the uniformity confidence interval, coverage confidence interval, and trigger signal are integrated into the closed-loop update process. The interval width is used to measure out-of-bounds behavior, and the optimal choice is made between active sampling, model recalibration, and risk weight adjustment. At the same time, the new information is incorporated into the original observation data for the next rolling window. First, the difference between the upper and lower bounds of any confidence interval is characterized by the interval width function:

[0187] ;

[0188] in Indicates confidence interval Width and These represent the upper and lower bounds of the interval, respectively.

[0189] Define the severity index for exceeding the boundary:

[0190] ;

[0191] in Indicates the severity of the boundary crossing. Indicates the first Confidence intervals for uniformity of paired bars Indicates the threshold width of the uniformity interval. Indicates the confidence interval for coverage. Indicates the coverage interval width threshold, Indicates the global conservation error index, Indicates the conservation consistency threshold, Indicates a paired index that satisfies Indicates the total number of paired samples;

[0192] When the trigger signal is not up to standard, select the update action according to the severity:

[0193] ;

[0194] in Indicates the selected update action; AS indicates active sampling; MR indicates model recalibration; RW indicates risk weight adjustment. and These represent the severity thresholds for tiered triggering;

[0195] In active sampling scenarios, sedimentary observations were collected at locations and time periods that exceeded the sampling boundaries, and the coordinates and timestamps were recorded. These data were then organized into a newly sampled dataset.

[0196] ;

[0197] in Indicates the newly added sampled data set, Indicates unified operation coordinates, Indicates the time under a unified clock reference. Represents newly sampled sedimentary observations, Represents the set of out-of-bounds locations. Represents the set of time periods that exceed the boundary;

[0198] In the case of model recalibration, the parameters of the cross-modal fusion model and the joint reconstruction model are updated and data update items are generated:

[0199] ;

[0200] in and Represent the original parameter vectors of the cross-modal fusion model and the physical constraint joint model, respectively. and Represents the recalibrated parameter vector, Indicates the recalibration operator, Indicates the verification of paired data sets, Represents the set of data update items after recalibration. Indicates the update term generation operator, Represents the original set of observation data;

[0201] In the case of risk weight adjustment, without changing the data structure, only updating the risk parameters of the distributed model prediction control, the uncertainty is first measured by the average width of the uniformity interval:

[0202] ;

[0203] in The average width of the uniformity interval is then used to update the risk scaling factor and weighting function:

[0204] ;

[0205] in and These represent the risk scaling factors before and after adjustment, respectively. Sensitivity coefficient representing risk scaling Indicates position In the Risk weight of the step Indicates the location of sedimentary observations. With time Uncertainty score Indicates a unified time step, Indicates the start time of the current scroll window. Indicates the short-term prediction step index;

[0206] Finally, under a unified operating coordinate system and a unified clock reference, the newly sampled data and the recalibrated data update items are merged into the original observation data and spatiotemporal alignment is completed. The closed-loop output is defined in segments according to the trigger signal:

[0207] ;

[0208] in This represents the updated set of original observation data. This indicates that the trigger signal generated in step S7 is binary and takes two values. Represents the set union operation, This refers to the spatiotemporal alignment and incorporation operator under unified coordinates and a unified clock. If the target is met, the original observation data remains unchanged; if the target is not met, the incorporation is updated according to the selected action. This serves as the input for step S1 of the next rolling window to complete the closed-loop iteration.

[0209] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0210] This application employs a multi-modal approach, including data acquisition and spatiotemporal alignment, cross-modal fusion to generate sedimentary observations and uncertainties, joint reconstruction using physical constraint neural networks and graph neural networks with the introduction of global mass conservation constraints with Lagrange duality, short-term prediction via wind field map networks, risk-sensitive distributed model predictive control, and order-preserving calibration with triggered closed-loop updates to form an end-to-end closed loop. This combination enables online observability and verifiability of sedimentation amount and coverage during operation, while joint mass conservation and convection-diffusion-evaporation residuals ensure physical consistency. Under wind field disturbances, the distributed model predicts and coordinates the optimization of velocity, heading, lateral spacing, and spray volume with the sedimentation gap field as the coupling target. After execution, adaptive updates are triggered using uniformity confidence intervals and coverage confidence intervals, thereby significantly improving spray uniformity and coverage, reducing the risk of overspraying and underspraying, and maintaining robust stability under complex wind field and multi-machine coupling conditions.

[0211] In terms of algorithm structure, this case has made targeted improvements based on the characteristics of the problem:

[0212] First, the global mass conservation constraint with Lagrange duality is embedded into the sedimentation field reconstruction and carried out throughout the control stage, and the conservation error is used as a hard constraint or a high-weight penalty term to enhance the consistency between modeling and control.

[0213] Second, by replacing path and formation-based indirect indicators with sedimentary gap fields, the environmental reconstruction results are directly transformed into collaborative control objectives, shortening the information link and improving convergence efficiency.

[0214] Third, in sedimentation reconstruction and wind field prediction, a graph structure is uniformly used to express the operational topology and spatial adjacency, and to characterize the mutual influence of multiple machines and the propagation of disturbances.

[0215] Fourth, uncertainty is integrated into modeling, control, verification and updating. Active sampling, model recalibration and weight adjustment are driven by risk weights and order-preserving calibration, so that the closed loop can prioritize correction for high-risk areas.

[0216] The aforementioned structural enhancements enable the system to form a verifiable, triggerable, and adaptive collaborative closed loop within the rolling window, converging more quickly to the operational state that meets the uniformity and coverage requirements.

Claims

1. A method for improving the uniformity of multi-machine spraying based on multi-agent coupled control, characterized in that, include: S1. Collect and synchronize raw observation data and output them; S2. Input the original observation data and perform cross-modal fusion to obtain the sedimentation observation set, observation uncertainty, and operation status feature set; S3. Input the sedimentary observation set, observation uncertainty and operation status feature set, execute the joint model of physical constraint neural network and graph neural network to reconstruct the sedimentary field and introduce global mass conservation constraints with Lagrange duality, and output the sedimentary field estimation results, conservation error index and sedimentary gap field and observation uncertainty. Specifically, the sedimentary observation set is used as the observation input for graph nodes, and a multi-agent operation topology graph is constructed using the operation status feature set. In the loss function of the joint model of physical constraint neural network and graph neural network, mass conservation constraints of ejection, deposition, evaporation, drift and boundary flux are explicitly introduced. Dual optimization is established by Lagrange multipliers to make ejection equal to the sum of deposition, evaporation, drift and boundary flux. At the same time, the convection-diffusion equation and evaporation term are used as physical residuals to participate in the optimization. The solution yields the estimated deposition field of the covered operation area. The conservation error indices for the global and regional areas are calculated based on the sedimentation field estimation results, and the sedimentation gap field is obtained by the difference between the target uniform sedimentation benchmark and the sedimentation field estimation results. S4. Input the sedimentation field estimation results, sedimentation gap field, conservation error index, observation uncertainty and operation status characteristic set, perform wind field map network prediction and form control preparation set; The wind field map network is specifically as follows: Short-term rolling prediction is based on a graph structure constructed from job nodes and spatial adjacency relationships. The mapping relationship is written as follows: ； in Indicates the location The Wind field prediction vector, Represents a wind field diagram network model with parameters of This represents a graph constructed from nodes and their adjacency relationships within the work area. Indicates short-term prediction step index, Indicates the upper limit of the prediction steps, The input feature vector for the operation node corresponding to position x and time t under the unified operation coordinate system includes: the features corresponding to position x and time t in the operation state feature set, the sedimentation estimate corresponding to position x and time t in the sedimentation field estimation results, the gap value corresponding to position x and time t in the sedimentation gap field, the conservation error index, and the observation uncertainty. To facilitate further control, the wind field predictions for future steps, along with current sediment estimates, sedimentary gaps, global conservation errors, and observation uncertainties, are organized by coordinates and timestamps into a control preparation set: ； in Indicates control preparation set, Indicates a unified time step, This represents the global conservation error index calculated within the scrolling window. Indicates the location of sedimentary observations. With time Uncertainty score This represents the set of discrete sampling nodes in a unified operating coordinate system. The set is organized in lexicographical order of coordinates and timestamps to ensure seamless integration with the control solution interface. This indicates the location of the sedimentary field estimation results. ,time The estimated value of the sedimentation, Indicates the location of the sedimentary gap field ,time The gap value; S5. Input control preparation set, execute risk-sensitive distributed model predictive control, and output multi-agent control instructions and control prediction sequence. The risk-sensitive distributed model predictive control refers to mapping observation uncertainty to spatiotemporal risk weight in distributed model predictive control, and weighting the objective function cost term corresponding to the deposition gap field with risk weight, so that the risk weight is higher when the uncertainty is greater, and more conservative and robust multi-agent cooperative control instructions are obtained. S6. Input multi-agent control instructions and control prediction sequences, execute according to multi-agent control instructions and generate job execution observation data and verification pairing data; S7. Input verification pairing data, perform order-preserving calibration and verification and generate trigger signals, output uniformity confidence interval and trigger signals. The order-preserving calibration refers to learning a monotonic mapping relationship based on the verification pairing data, and calibrating the uniformity index prediction values ​​while keeping the relative size order of the predicted values ​​unchanged, so that the calibrated prediction error statistical boundary is consistent with the preset confidence level, which is used to construct the uniformity confidence interval and make a standard-reaching judgment. S8. Perform closed-loop update based on the trigger signal and output the updated original observation data.

2. The method for improving the uniformity of multi-machine spraying based on multi-agent coupling control according to claim 1, characterized in that, S1 specifically refers to: Each intelligent agent collects data on nozzle flow rate, nozzle pressure, operating speed, attitude, relative canopy height, wind speed and direction, relative positioning, and information on plot boundaries and no-spraying zones. Synchronize the collected data by time, establish a unified clock reference and align the timestamps, and form a time series with a unified time step by interpolation or resampling for data with different sampling frequencies. Spatial registration is performed on the collected data to convert the relative positioning data and attitude to coordinates and attitude under a unified operating coordinate system, and the land parcel boundary and no-spraying zone information are represented in the unified operating coordinate system. Output the raw observation data, which is a time-ordered and spatially labeled dataset with coordinates and timestamps.

3. The method for improving the uniformity of multi-machine spraying based on multi-agent coupling control according to claim 1, characterized in that, S2 specifically refers to: Input the raw observation data into the cross-modal fusion model; The original observation data is preprocessed, including timestamp alignment, spatial registration correction, noise suppression, scale calibration, missing value imputation and outlier handling, to form a preprocessed dataset with coordinates and timestamps. Using the preprocessed dataset as input, spray deposition observations at corresponding coordinates and times are generated and organized into a deposition observation set according to coordinates and timestamps; The cross-modal fusion model simultaneously outputs the uncertainty score for each spray deposition observation, and organizes the observation uncertainty by coordinates and timestamps; During the fusion process, based on the preprocessed data set, the operation speed, attitude, wind speed and direction, relative canopy height and relative positioning data are extracted and organized into an operation status feature set according to coordinates and timestamps; Output the sedimentation observation set and the set of observation uncertainty and operational status characteristics.

4. The method for improving the uniformity of multi-machine spraying based on multi-agent coupling control according to claim 1, characterized in that, S4 specifically refers to: The sedimentation field estimation results and sedimentation gap fields are extracted as aerodynamic source features according to coordinates and timestamps. Under a unified operating coordinate system, the wind speed, wind direction, attitude, operating speed and relative positioning data in the operating status feature set are spatially and temporally aligned to form the input feature set of the wind field map network. Using the input feature set as input, short-term prediction is performed in the wind field map network to obtain the short-term wind field prediction results within the future rolling window, and the short-term wind field prediction results are organized according to the time step and coordinates. The short-term wind field prediction results, sedimentation field estimation results, sedimentation gap field, conservation error index, and observation uncertainty are organized into a control preparation set according to coordinates and timestamps.

5. The method for improving the uniformity of multi-machine spraying based on multi-agent coupling control according to claim 1, characterized in that, S5 specifically refers to: Input the control preparation set into the distributed model predictive control problem; In the distributed model predictive control problem, the short-term wind field prediction results are organized into a perturbation sequence according to the time step, the sedimentation field estimation results and the sedimentation gap field constitute a coupled control objective, the conservation error index is added to the constraint set as a hard constraint or weighted penalty, and the risk weight is set according to the observation uncertainty. Using the multi-agent operation topology graph as the adjacency relationship, each agent establishes a local prediction model and a local optimization problem. The decision variables of the local prediction model are the temporal trajectory of operation speed, heading, lateral spacing and jet volume within the prediction window. The local prediction model updates the state by the temporal evolution of the operation state characteristics under the unified operation coordinate system and superimposes the disturbance sequence. The goal of the local optimization problem is to reduce the deposition gap field while taking into account control stability and operational efficiency. Constraints include operational speed, heading change rate, upper and lower limits of lateral spacing and spray volume, block boundary and no-spray zone constraints, lower limit of relative distance between adjacent machines, and conservation consistency constraints where the conservation error index does not exceed a preset threshold or is included in the form of a weighted penalty. The multi-agent control commands for each agent, including operating speed, heading, lateral spacing, and spray volume, are obtained by solving under the adjacency coupling term. The predicted values ​​of deposition and uniformity indices within the prediction window are then organized according to the time step and coordinates to form a control prediction sequence.

6. The method for improving the uniformity of multi-machine spraying based on multi-agent coupled control according to claim 1, characterized in that, S6 specifically refers to: Multi-agent control commands are issued to each agent and executed under a unified operating coordinate system and a unified clock reference. The operating speed, heading, lateral spacing and spray volume are controlled according to the time step of the multi-agent control commands. During the execution process, newly added spray deposition observations were collected and their corresponding coordinates and timestamps were recorded. The operation execution observation data were then organized according to the coordinates and timestamps. The operation execution observation data and control prediction sequence are aligned under a unified operation coordinate system and a unified clock reference. They are paired one by one in a way that the coordinates and timestamps are the same or are considered to be consistent within the preset spatial error limit and time error limit, to form verification pairing data. The verification pairing data includes each spray deposition observation value and its corresponding predicted deposition value and the predicted value of the uniformity index of the corresponding spatiotemporal location.

7. The method for improving the uniformity of multi-machine spraying based on multi-agent coupling control according to claim 1, characterized in that, S7 specifically refers to: Input the verification pairing data into the sequence-preserving calibration and verification process; The calibration score is calculated based on the verification pairing data under a unified operating coordinate system and a unified clock reference. The calibration score includes the error between the predicted value of the uniformity index for each pair and the measured value of the uniformity index calculated from the spray deposition observation value according to the preset uniformity evaluation method, as well as the error between the predicted value of the coverage and the measured value of the coverage obtained by mapping the predicted deposition value and the spray deposition observation value to the coverage state according to the preset coverage determination threshold and summarizing them. Under a preset confidence level, construct confidence intervals for uniformity and coverage using the statistical boundaries of the calibration scores, organize the uniformity confidence intervals by coordinates and timestamps, and output the uniformity confidence intervals. The uniformity confidence interval is determined based on a preset threshold or a conservation error index, and a trigger signal is generated when the non-compliance condition is met.

8. The method for improving the uniformity of multi-machine spraying based on multi-agent coupled control according to claim 1, characterized in that, S8 specifically refers to: The uniformity confidence interval and the trigger signal input closed-loop update process; When the trigger signal indication fails to meet the standard, active sampling, model recalibration, or risk weight adjustment are selected and executed based on the out-of-bounds position and out-of-bounds magnitude of the uniformity confidence interval. Active sampling involves collecting spray deposition observations and recording coordinates and timestamps at the aforementioned out-of-bounds locations and time periods under a unified operating coordinate system and a unified clock reference, thus forming new sampling data. Model recalibration involves recalibrating the parameters of the cross-modal fusion model and the joint model of the physical constraint neural network and the graph neural network, and generating recalibrated data update terms. The risk weight adjustment is to update the risk weight parameters in the distributed model predictive control based on the width of the uniformity confidence interval. The update is used in step S5 of the next rolling window and does not change the structure of the original observation data. The newly added sampling data and the recalibrated data update items are merged into the original observation data according to coordinates and timestamps under a unified operating coordinate system and a unified clock reference to form the updated original observation data. When the trigger signal indicates that the target has been met, the original observation data is kept unchanged and the updated original observation data is directly output. The updated original observation data is output as input for step S1 to complete the closed-loop iteration.

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