Multi-robot cooperative measurement path planning method based on reinforcement learning

Abstract

The invention belongs to the technical field of path planning, and particularly relates to a multi-robot collaborative measurement path planning method based on reinforcement learning, which comprises the following steps: acquiring a model and point cloud data of a large complex component, and preprocessing; constructing a three-dimensional environment model based on the preprocessed point cloud data, and defining a state space of a reinforcement learning environment, an executable action space and a reward function of a reinforcement learning process; on the basis of the constructed three-dimensional environment model, measuring tasks are distributed to the multiple robots, an initial path covering the surface of the large complex component is generated, the initial path is optimized through a reinforcement learning method, and an optimized path is generated; and sharing the optimized paths and states of the plurality of robots in real time, performing future potential conflict prediction, dynamically and cooperatively adjusting the paths and states of the plurality of robots based on a prediction result, and generating a final path and a control instruction so as to realize multi-robot cooperative measurement path planning.

Description

Technical Field

[0001] The present invention belongs to the technical field of path planning, and in particular relates to a multi-robot collaborative measurement path planning method based on reinforcement learning. Background Art

[0002] Amid the rapid development of high-end equipment manufacturing industries such as aerospace, shipbuilding, and new energy, high-precision three-dimensional measurement of large, complex components, such as aircraft fuselages, wind turbine blades, and ship sections, has become a core requirement in intelligent manufacturing. These components are characterized by complex geometric surfaces (high curvature and multi-feature fusion), large spatial scales (often reaching tens to hundreds of meters in length), and demanding measurement accuracy requirements (submillimeter error tolerance). To overcome the efficiency bottlenecks, coverage blind spots, and lack of adaptability to dynamic environments inherent in traditional single-machine measurement methods, multi-machine collaborative measurement technology is currently being adopted to achieve global optimization of multi-agent path planning, while simultaneously ensuring measurement accuracy and motion safety under complex surface constraints. Existing measurement path planning methods for large components include offline planning based on geometric decomposition, random sampling algorithms (such as RRT*), and swarm intelligence optimization (such as the ant colony algorithm). Among them, the offline planning method based on geometric decomposition manually divides the measurement area and presets the scanning trajectory, which is difficult to adapt to surface mutations and dynamic obstacles, and can easily lead to a repeated measurement rate of more than 30%; the random sampling algorithm can ensure probabilistic completeness, but the generated path is highly tortuous and requires additional smoothing processing, which can easily lead to path conflicts in multi-machine collaboration scenarios; the swarm intelligence optimization method can rely on heuristic rules, but the computational complexity will increase exponentially with the increase in component scale, and cannot meet real-time requirements.

[0003] The introduction of reinforcement learning (RL) methods has shown certain potential in robot path planning, but it still has certain limitations in large-scale component measurement scenarios, which are manifested in: insufficient integration of component geometric features and multi-machine collaborative constraints, resulting in insufficient state space modeling; traditional Q-learning and other methods have difficulty in handling continuous control problems, resulting in low path fit and discretization of the action space; and existing research lacks a multi-agent competition-cooperation balance strategy, resulting in an imbalance in the allocation of measurement resources and a lack of a collaborative mechanism. Summary of the Invention

[0004] The present invention provides a multi-robot collaborative measurement path planning method based on reinforcement learning. By constructing a three-layer collaborative architecture of global task allocation, local path optimization, and real-time conflict resolution, it can realize efficient collaborative operation of multiple robots; at the same time, the path and state of each robot are detected and dynamically adjusted in real time, so that each robot can work together without conflict and with high precision during the measurement process, thereby ensuring the measurement accuracy of complex surfaces while efficiently covering the surface of large and complex components, reducing the repeated measurement rate, and realizing global optimization of multi-agent path planning.

[0005] A multi-robot collaborative measurement path planning method based on reinforcement learning, comprising: Obtain models and point cloud data of large and complex components and perform pre-processing; Build a 3D environment model based on preprocessed point cloud data and define the state space of the reinforcement learning environment, the executable action space, and the reward function of the reinforcement learning process; Based on the constructed 3D environment model, the measurement tasks are assigned to multiple robots to generate an initial path covering the surface of large and complex components. The initial path is then optimized using reinforcement learning methods to generate an optimized path. Share the optimized paths and states of multiple robots in real time, predict potential future conflicts, and dynamically and collaboratively adjust the paths and states of multiple robots based on the prediction results to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning.

[0006] By building a three-layer collaborative architecture of global task allocation, local path optimization, and real-time conflict resolution, efficient collaborative operation of multiple robots can be achieved. At the same time, the path and status of each robot are detected and dynamically adjusted in real time, so that each robot can work together without conflict and with high precision during the measurement process, thereby ensuring the measurement accuracy of complex surfaces while efficiently covering the surfaces of large and complex components, reducing the rate of repeated measurements, and achieving global optimization of multi-agent path planning.

[0007] Furthermore, the acquisition of the model and point cloud data of the large and complex component and pre-processing thereof include: Directly obtain the CAD model of large and complex components and convert it into the first triangle mesh model; Use a laser scanner to scan large and complex components to obtain point cloud data on the surface of large and complex components, perform denoising and downsampling processing, and generate downsampled point cloud data; Based on the first triangular mesh model and downsampled point cloud data, the iterative closest point algorithm is used for alignment.

[0008] Furthermore, the method of constructing a three-dimensional environment model based on the pre-processed point cloud data and defining the state space of the reinforcement learning environment, the executable action space, and the reward function of the reinforcement learning process includes: Based on the downsampled point cloud data, a Poisson surface reconstruction algorithm is used to generate a second triangular mesh model, which is combined with the first triangular mesh model to obtain the surface information of large and complex components. Based on the surface information of large and complex components, the surface of large and complex components is divided into multiple manageable sub-areas using surface geometric feature information and spatial position information to construct a three-dimensional environmental model; Based on the 3D environment model, the geometric representation of large and complex components is sampled and combined with multiple robot states and environment states to define the state space of the reinforcement learning environment. Define the executable action space based on the stand-alone action of a single robot and the coordinated action of multiple robots; Define the reward function for the reinforcement learning process based on coverage, efficiency, conflict avoidance, and quality measurements of large complex components.

[0009] By embedding the geometric representation of large and complex components into the state space of reinforcement learning and using surface geometric feature information and spatial position information to perform spatial physical feasibility constraints, the problem of traditional path planning methods being prone to deviation and difficult to converge on complex surfaces can be solved, thereby improving the fit and accuracy of the measurement path.

[0010] Furthermore, based on the surface information of large and complex components, the surface of large and complex components is divided into multiple manageable sub-areas using surface geometric feature information and spatial position information to construct a three-dimensional environment model, including: Based on the surface information of large and complex components, the surface of large and complex components is divided into multiple initial sub-regions using surface geometric feature information and spatial feature information; The multiple initial sub-regions are clustered using the similarity matrix and the Laplace matrix to form multiple manageable sub-regions and construct a three-dimensional environment model.

[0011] Furthermore, when defining the executable action space, the coordinated actions of multiple robots include task reallocation and a robot priority matrix, which are used to prioritize the allocation of high curvature sub-areas and to actively avoid conflicts with low-priority robots.

[0012] Furthermore, based on the constructed three-dimensional environment model, the measurement tasks are assigned to multiple robots to generate an initial path covering the surface of a large and complex component, and the initial path is optimized using a reinforcement learning method to generate an optimized path, including: Based on the division of large and complex components into multiple sub-areas, the complexity of each sub-area is quantified; Evaluate each robot's measurement performance based on its maximum speed, measurement accuracy, endurance, and field of view. Based on the measurement performance of each robot, a particle swarm optimization algorithm is used to assign a sub-area of ​​measurement to each robot; Based on the sub-area assigned to each robot, a UV parameterized function is used to map the 2D zigzag path to a 3D surface. The 3D coordinates and path directions of the path points are calculated, and the path points are globally connected. Combined with real-time collision detection between the path points, the measurement path and corresponding time-velocity sequence of each robot are adjusted and generated to form an initial path covering the surface of large and complex components. Based on the initial path, the trained policy network and evaluation network are used to predict the actions of each robot, calculate the continuous path points, and combine the real-time detection of path conflicts between path points of robots to adjust and generate the optimized path covering the surface of large and complex components.

[0013] By building a three-layer collaborative architecture of global task allocation, local path optimization, and real-time conflict resolution, it combines the collective intelligence of particle swarm optimization with the autonomous decision-making advantages of multi-agent reinforcement learning, breaking through the limitations of a single algorithm in terms of scalability and dynamic adaptability, and thus achieving efficient collaborative operation of multiple robots.

[0014] Furthermore, based on the sub-area assigned to each robot, a UV parameterized function is used to map the 2D zigzag path to a 3D surface. The 3D coordinates and path directions of the path points are calculated, and the path points are globally connected. Combined with real-time collision detection between the path points, the measurement path and corresponding time-velocity sequence of each robot are adjusted and generated to form an initial path covering the surface of large and complex components, including: Based on the sub-area assigned to each robot, the UV parameterization function is used to map the two-dimensional Z-shaped path to a three-dimensional surface to obtain a three-dimensional path, and the three-dimensional coordinates of each path point and the path direction are determined; Based on the path point sequence, a piecewise cubic spline interpolation algorithm is used to smooth the path segments formed by connecting the path points, and to perform global connection of each path point. The global connection of each path point includes assigning weights to the path segments and corresponding sub-regions, and using an optimization algorithm to solve the optimal path segment connection sequence. Real-time collision detection is performed based on the distance between the path points of each robot, and path correction is performed based on the real-time collision detection results. The initial path point set and its corresponding time-speed sequence for each robot are generated to form an initial path covering the surface of large and complex components. The initial path point set of each robot is expressed as: ; Where, Indicates the The initial path point set of each robot; Indicates the The first robot waypoints; The time-velocity sequence of each robot is expressed as: ; Where, Indicates the Time-velocity sequence of each robot; Indicates the The first robot The collection of times and speeds of the waypoints.

[0015] Furthermore, based on the initial path, the trained policy network and evaluation network are used to predict the actions of each robot, calculate continuous path points, and combine the real-time detection of path conflicts between path points of the robots to adjust and generate an optimized path covering the surface of large and complex components, including: Taking the initial path as the starting point, we design a policy network and an evaluation network to output the actions that each robot should perform in its current state, and to evaluate the expected cumulative rewards for a given state and all actions performed by the robots. Based on a triangular mesh model, a priority replay strategy is used to focus on key sub-areas, surface constraints are added to limit the robot's range of motion, and the evaluation network is updated by minimizing the temporal difference error and the policy network parameters are updated by maximizing the reward value, resulting in a trained policy network. Based on the trained policy network, the robot predicts the actions it should perform and generates continuous path points. It then combines the continuity constraints between adjacent path points and the surface fit constraints between path points and large, complex components to construct a spatiotemporal joint optimization objective function, eliminate path jitter, and obtain an optimized continuous path. Based on the distance between the path points of the robots, the robot can detect the path conflicts in real time and make directional adjustments based on the results of the path conflicts to generate an optimized path covering the surface of large and complex components. The optimized path for covering the surface of a large complex component is expressed as: ; Where, Represents the optimized path covering the surface of a large and complex component; After optimization The three-dimensional coordinates of the path point at that moment; After optimization the speed of the moment; After optimization The surface direction vector at the moment; , Indicates the total number of moments.

[0016] Furthermore, the real-time sharing of optimized paths and states of multiple robots, prediction of future potential conflicts, and dynamic collaborative adjustment of the paths and states of multiple robots based on the prediction results to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning include: Share the optimized paths and states of multiple robots in real time; the robot states include current position, speed, posture, remaining energy, and measurement status; Based on the optimized path and speed of each robot, the future position of the robot is predicted, and future position conflict determination between the robots is performed; the future position conflict determination between the robots includes triggering conflict adjustment when the distance between the path points of the two robots at a future time is lower than a preset distance threshold; Based on the future position conflict judgment results, the paths and states of each robot are dynamically and collaboratively adjusted to generate the final path and control instructions to realize multi-robot collaborative measurement path planning.

[0017] Furthermore, based on the future position conflict judgment results, the paths and states of each robot are dynamically and collaboratively adjusted to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning, including: When a conflict between the future positions of two robots is predicted, the robot priority matrix is ​​used to adjust the conflict weight, giving priority to adjusting the path of the robot with the lower priority, and the adjusted robot path is used as the final path; The conflict weight adjustment is expressed as: ; Where, Indicates the adjusted The robot is relative to the The priority of each robot; Indicates the unadjusted The robot is relative to the The priority of each robot; Indicates the A robot in The location of the waypoint at the moment; Indicates the A robot in The location of the waypoint at the moment; The path adjustment of the robot is expressed as: ; Where, Indicates the A robot in The position of the path point is adjusted at all times, and the adjusted path point position fits the triangular mesh model, that is, , Represents a point in a triangular mesh model, represents a triangular mesh model, A function that represents the value of the independent variable that minimizes the objective function; , that is, The robot has higher priority than the A robot; When it is predicted that the measurement progress of two robots is different, the speed of the robot with the lagging measurement progress is adjusted first; The speed adjustment of the robot is expressed as: ; Where, Indicates the The robot accelerates to the adjusted speed; Indicates the The unadjusted speed of each robot; Indicates the The percentage of coverage points of each robot relative to the number of points in the divided sub-areas; Indicates the The percentage of coverage points of each robot relative to the number of points in the divided sub-areas; , which means the The robot lags behind A robot measures progress; Combined with the robot's measurement accuracy, the robot's posture is dynamically adjusted; The robot posture adjustment is expressed as: ; Where, Indicates the The posture of each robot after acceleration adjustment; Indicates the The unadjusted posture of the robot; Indicates the Sensor field of view and surface normal vector of each robot Angle The robot priority matrix, as well as the adjusted robot speed and robot posture, are combined as control instructions and combined with the final path to achieve multi-robot collaborative measurement path planning.

[0018] The beneficial effects of the present invention are: The present invention can realize the efficient collaborative operation of multiple robots by constructing a three-layer collaborative architecture of global task allocation, local path optimization, and real-time conflict resolution; at the same time, the path and status of each robot are detected and dynamically adjusted in real time, so that each robot can work together without conflict and with high precision during the measurement process, thereby ensuring the measurement accuracy of complex surfaces while efficiently covering the surfaces of large and complex components, reducing the repeated measurement rate, and realizing global optimization of multi-agent path planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flow chart of the present invention; Figure 2 Schematic diagram of the system structure of the present invention; Figure 3 A schematic diagram of the structure of a computer device. DETAILED DESCRIPTION

[0020] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0021] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0022] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood in specific situations.

[0023] Example 1 Figure 1The figure shows a multi-robot collaborative measurement path planning method based on reinforcement learning. By building a three-layer collaborative architecture of global task allocation, local path optimization, and real-time conflict resolution, it can achieve efficient collaborative operation of multiple robots. At the same time, the path and state of each robot are detected and dynamically adjusted in real time, so that each robot can work together without conflict and with high precision during the measurement process, thereby ensuring the measurement accuracy of complex surfaces while efficiently covering the surface of large and complex components, reducing the rate of repeated measurements, and achieving global optimization of multi-agent path planning. The specific steps include the following: S1: Obtain the model and point cloud data of large and complex components and perform preprocessing; S11: directly obtain the CAD model of a large and complex component and convert it into a first triangular mesh model; In this embodiment, the large complex component model in STL and STEP format is converted into the first triangular mesh model. , which is expressed as: ; Where, Represents the first triangular mesh model ; Represents the vertex set of the first triangle mesh; A set of faces representing the first triangular mesh; S12: Use a laser scanner to scan large and complex components to obtain point cloud data on the surface of the large and complex components, perform denoising and downsampling processing, and generate downsampled point cloud data; In this embodiment, a laser scanner is used to scan point cloud data on the surface of a large and complex component, and the point cloud data obtained is in PCD and PLY formats.

[0024] Among them, denoising and downsampling processing are performed to generate downsampled point cloud data, including: S121: Based on the point cloud data, the statistical outlier removal algorithm is used to perform denoising to obtain denoised point cloud data. ; In this embodiment, the statistical outlier removal algorithm is to perform a statistical analysis on each point in the point cloud data. , calculate the average distance of its k nearest neighbors , when the average distance When the elimination conditions are met, the current point cloud data is eliminated as an abnormal point.

[0025] Among them, the average distance The expression is: ; Where, Indicates the The average distance of the k nearest neighbors of a point, ; Indicates the Point cloud data; Indicates a point 's nearest neighbors; Indicates a point and neighboring points The Euclidean distance of Among them, the exclusion conditions are: ; Where, represents the average of the average distances of the k nearest neighbors of all points, that is, ; represents the standard deviation of the average distance of the k nearest neighbors of all points, that is ; ; S122: Based on denoised point cloud , use voxel grid filtering method to perform downsampling processing to generate downsampled point cloud data ; In this embodiment, the voxel grid size is set to 0.01m.

[0026] S13: Based on the first triangular mesh model and the downsampled point cloud data, an iterative closest point algorithm is used to perform alignment operations; Among them, the objective function of the alignment operation using the iterative closest point algorithm is: ; Where, represents the objective function of the iterative closest point algorithm; The rotation matrix representing the first triangular mesh model or downsampled point cloud data; Represents the translation vector of the triangular mesh model or downsampled point cloud data; Indicates the first triangular mesh model With downsampled point cloud data Points in corresponding points; S2: Build a 3D environment model based on the preprocessed point cloud data and define the state space of the reinforcement learning environment, the executable action space, and the reward function of the reinforcement learning process; S21: Based on the downsampled point cloud data, a Poisson surface reconstruction algorithm is used to generate a second triangular mesh model, which is combined with the first triangular mesh model to obtain the surface information of large and complex components; In this embodiment, the downsampled point cloud data Each point in , set the search radius to 0.05m, and calculate the covariance matrix based on the k-nearest neighbor method to estimate the normal vector.

[0027] Among them, the covariance matrix is ​​expressed as: ; Where, represents the covariance matrix; represents the number of neighboring points, ; Indicates a point The centroid of the k nearest neighbors; Indicates a point 's nearest neighbors; represents the transposed matrix; The expression of the normal vector is: ; Where, Indicates a point The normal vector at point The orientation of the local surface; Indicates a point The three-dimensional coordinates of the normal vector; Use the Poisson reconstruction method to construct the equation and solve the equation to generate the second triangular mesh model . The constructed equation is expressed as: ; Where, represents the Laplace operator; represents a scalar function; represents the divergence operator; Represents all downsampled point cloud data The normal vector field of In this embodiment, the second triangular mesh model The depth is 8 and the smoothing factor is 0.5.

[0028] Combined with the first triangular mesh model and the second triangular mesh model , forming a triangular mesh model , obtain surface information of large and complex components.

[0029] S22: Based on the surface information of large and complex components, the surface is divided into multiple manageable sub-areas using surface geometric feature information and spatial position information to construct a three-dimensional environment model; S221: Based on the surface information of the large complex component, the surface of the large complex component is divided into multiple initial sub-regions using the surface geometric feature information and spatial feature information; Among them, the surface geometric feature information is curvature, and its calculation expression is: ; ; Where, Indicates a point curvature; Represents the determinant value of the first-order matrix; Represents the determinant value of the second-order matrix; Represents the normalized point curvature; represents the minimum value among all curvatures; represents the maximum value among all curvatures; S222: clustering the multiple initial sub-regions using a similarity matrix and a Laplace matrix to form multiple manageable sub-regions, and constructing a three-dimensional environment model; S221: Construct a similarity matrix based on the curvature of each point ; Among them, the similarity matrix Each element in is represented as: ; Where, Represents the similarity matrix midpoint and point Elements used to represent points and point Similarity in spatial position and curvature, that is, the larger the value, the higher the similarity between the two points; Indicates a point The spatial position vector of Indicates a point The spatial position vector of represents the spatial position weight; Indicates a point curvature; Indicates a point curvature; represents the curvature weight; S222: Based on similarity matrix ,The Laplace matrix is ​​used to cluster the initial sub-regions into multiple manageable sub-regions and construct a 3D environment model; Among them, the Laplace matrix expression is: ; Where, represents the Laplace matrix; represents a diagonal matrix; In this embodiment, the sub-region set formed by clustering is expressed as: ; Where, represents a set of sub-regions; represents the number of cluster sets, that is, in this embodiment, ; S223: Combined triangular mesh model , sub-region set , and obstacle boundaries , construct a three-dimensional space model; Among them, the three-dimensional environment model is expressed as: ; Where, Represents a three-dimensional environment model; Represents a triangular mesh model; represents the sub-region after clustering; Indicates the obstacle boundary.

[0030] S23: Based on the 3D environment model, sample the geometric representation of large and complex components and combine multiple robot states and environment states to define the state space of the reinforcement learning environment; Among them, the state space of the reinforcement learning environment is defined as: ; Where, Represent the state space of the reinforcement learning environment; Represents the geometric representation of large and complex components, which is derived from triangular mesh models Sampling is performed in Status Expressed as: , 、 、 Indicates a point The three-dimensional coordinates of An identifier representing the robot; Represents the robot, that is, each robot state Expressed as: , 、 、 Indicates the The three-dimensional coordinates of the robot, 、 、 Indicates the The three posture angles of the robot, Indicates the robot's moving speed; Indicates environmental parameters; Indicates the robot's field of view; Represents the robot's motion parameters; Indicates the environmental state, which is expressed as: , 、 、 represents the coordinates of obstacles in the environment, represents the width of the obstacle, represents the length of the obstacle, Indicates the specific coordinates of the obstacle; The variational autoencoder is used for dimensionality reduction. The loss function of the variational autoencoder is: ; Where, represents the loss function of the variational autoencoder; Indicates the current state; Indicates the next state; represents the hyperparameter, i.e. ; represents the Kullback-Leibler divergence function; represents the variational posterior distribution; represents the prior distribution; represents a distribution variable; In this embodiment, the state space is normalized and updated at a frequency of 10 Hz using robot sensor data and communication (ROS2, MQTT).

[0031] S24: Define the executable action space based on the stand-alone action of a single robot and the coordinated action of multiple robots; Among them, the executable action space is defined as: ; Where, represents the executable action space; Indicates the The single action of a robot, that is, The stand-alone state of a robot is expressed as: , 、 、 Indicates the The displacement of a robot in three-dimensional space is , Represents the arc information in the robot's posture, that is ; represents the moving speed of the robot, that is , Indicates whether the robot starts measuring. ,Right now When the measurement is not started, When it is on, it indicates that the measurement has started; Represents the coordinated action of multiple robots, that is , Indicates task redistribution, i.e. , represents the priority matrix, i.e. ; , Indicates the total number of robots; Among them, when allocating tasks, high curvature sub-regions are allocated first, which is expressed as: ; Where, Indicates that the sub-area will be measured The task is assigned to the A robot; Indicates the robot number that minimizes the value being evaluated ; Indicates the The endurance of each robot; Indicates the measurement sub-area The weight of the task; At the same time, in order to ensure that the robot's movement always fits the surface of the triangular mesh model and avoids deviation from the surface of large and complex components, the executable action constraints are as follows: ; Where, Indicates the The position of the robot after it moves; Indicates the The current position of the robot; Represents a point in a triangular mesh model; S25: Define reward functions for reinforcement learning processes based on coverage, efficiency, conflict avoidance, and quality measurements of large, complex components. Among them, the reward function Leverage the current state , perform actions and the next state To optimize the coverage, efficiency, conflict avoidance and quality of large and complex component measurements, it is defined as: ; ; ; ; ; ; Where, represents the reward function; represents the coverage bonus, which is used to measure new measurement points; represents the efficiency reward and penalty time and energy consumption, which is used to evaluate the time and energy consumption of the measurement path; represents the conflict avoidance reward, which is used to evaluate the collision risk and field of view overlap between multiple robots; represents the quality reward, which is used to evaluate the accuracy of the measurement data and the uniformity of the point cloud distribution; represents the coverage weight coefficient, that is ; represents the efficiency weight coefficient, that is ; represents the conflict weight coefficient, i.e. ; represents the quality weight coefficient, i.e. ; represents the increment of the previously uncovered sub-area covered by the new measurement point; Indicates the total area of ​​large and complex components; represents the indicator function; Represents the parameters, that is ; Represents the parameters, that is ; Represents the parameters, that is ; Represents the parameters, that is ; Indicates the The robot and The position difference of the measurement points of the robots; Indicates the The robot and A robot measures the intersection area of ​​the sub-areas; Indicates the A robot measures the area of ​​the sub-region; Represents the parameters, that is ; Represents the parameters, that is ; Indicates the total number of measurement points; Indicates the measurement point To triangular mesh model distance; Indicates whether the robot has started measuring; Indicates the The measurement accuracy of each robot; Indicates the measurement point To a point in a triangular mesh model distance; S3: Based on the constructed 3D environment model, the measurement tasks are assigned to multiple robots to generate an initial path covering the surface of large and complex components. The initial path is then optimized using reinforcement learning methods to generate an optimized path. S31: Based on the division of large and complex components into multiple sub-areas, quantify the complexity of each sub-area; Each sub-region The complexity is expressed as: ; Where, Indicates the The complexity of each sub-region; Indicates sub-area area; Indicates the Sub-region triangle mesh vertices; Indicates the curvature value of the sub-region vertex; S32: Evaluate the measurement performance of each robot based on its maximum moving speed, measurement accuracy, endurance, and field of view. Among them, the measured performance of each robot Expressed as: ; Where, Indicates the Measuring performance of each robot; No. The maximum movement speed of a robot; Indicates the The measurement accuracy of each robot; Indicates the The endurance of each robot; Indicates the The robot's field of view; S33: Based on the measurement performance of each robot, a particle swarm optimization algorithm is used to assign a measurement sub-area to each robot; Among them, the particle swarm optimization algorithm is used for sub-area allocation, and the objective function is constructed by minimizing the load variance and total time, which is expressed as: ; Where, It means that the objective function is constructed by minimizing the load variance and the total time; represents the variance function; Indicates that the The sub-areas are assigned to A robot; Update particle position is expressed as: ; Where, Indicates that the particles the speed of the moment; Indicates that the particles the speed of the moment; 、 Represents a random number, which is used to adjust the degree to which the particle learns from its own historical optimal position and the global optimal position; Represents the historical optimal position of the particle itself; Indicates that the particles Position at the moment; Represents the global optimal position of the entire particle swarm; In this embodiment, the high curvature sub-region ( ) are given priority to high measurement accuracy ( ) robot.

[0032] S34: Based on the sub-area assigned to each robot, a UV parameterized function is used to map the 2D zigzag path to a 3D surface. The 3D coordinates and path directions of the path points are calculated, and the path points are globally connected. Combined with real-time collision detection between the path points, the measurement path and corresponding time-velocity sequence of each robot are adjusted and generated to form an initial path covering the surface of large and complex components. S341: Based on the sub-area assigned to each robot, a UV parameterization function is used to map the two-dimensional zigzag path to a three-dimensional surface to obtain a three-dimensional path, and the three-dimensional coordinates of each path point and the path direction are determined; In this embodiment, the spacing of the two-dimensional zigzag path is 0.01m. When mapped to a three-dimensional curved surface, the coordinates of the path points are: ; Where, Represents the coordinates of the path point on the three-dimensional surface; Represents UV parameterized function; Represents the two-dimensional glyph path coordinates, ; Among them, the main curvature direction field determines the path direction, and the eigenvalue of the surface Hessian matrix is ​​obtained by solving it, that is, the path direction is expressed as: ; Where, Indicates the path direction; Indicates the parameter that makes the function reach its maximum value; represents the Hessian matrix eigenvalue; represents the transposed matrix; S342: Based on the path point sequence, a piecewise cubic spline interpolation algorithm is used to smooth the path segments formed by connecting the path points, and to perform global connection of each path point. Among them, the path smoothing transition curve obtained by path smoothing is expressed as: ; Where, Represents a smooth transition curve between path points, ; 、 、 、 、 、 、 、 、 、 、 、 Respectively represent the coefficients of the piecewise cubic spline interpolation curve; the boundary conditions are: , ; The continuity constraints are: ; When performing global connection of path points, the problem is transformed into a weighted optimal access sequence problem. That is, weights are assigned to the path connection segments and the corresponding sub-regions, and an optimization algorithm is used to solve the optimal path connection sequence. The cost function in the optimal access sequence method is expressed as: ; Where, represents the cost function; Represents the approximate geodesic distance function calculated by the A* algorithm; They represent the sub-region ranges of the surface of large and complex components respectively; represents the regional mean curvature; S343: Perform real-time collision detection based on the distance between the path points of each robot, and perform path correction based on the real-time collision detection results to generate an initial path point set for each robot and its corresponding time-velocity sequence, thereby forming an initial path covering the surface of the large and complex component; Among them, real-time collision detection is achieved through distance field. When any two path points meet When , the offset correction is performed, which is expressed as: ; Where, Indicates the corrected path point; Indicates the path point before correction; Indicates a waypoint The normal vector at , Functional expression representing a two-dimensional path; Representation of normal vector The model; Among them, the initial path point set of each robot is expressed as: ; Where, Indicates the The initial path point set of each robot; Indicates the The first robot waypoints; Among them, the time-velocity sequence of each robot is expressed as: ; Where, Indicates the Time-velocity sequence of each robot; Indicates the The first robot The collection of times and speeds of the waypoints.

[0033] S351: Based on the initial path, the trained policy network and evaluation network are used to predict the movements of each robot, calculate the continuity path points, and combine the real-time detection of path conflicts between path points of robots to adjust and generate the optimized path covering the surface of large and complex components.

[0034] S3511: Using the initial path as a starting point, design a policy network and an evaluation network to output the actions that each robot should perform in the current state, and to evaluate the expected cumulative rewards for a given state and all actions performed by the robots. Among them, a strategy network is designed for each robot, namely , to output the action that each robot should perform in the current state. The policy network consists of a 4-layer network structure, where the number of neurons in the hidden layer is 256, 128, and 64, respectively. Residual connections are introduced to enhance gradient propagation. The hidden layer is represented as: ; Where, Indicates the Hidden layer state at all times; Indicates the Hidden layer state at all times; Indicates the Hidden layer state at all times; represents the activation function; Indicates The weight matrix at the moment; Indicates Bias vector at time instant; Among them, an evaluation network is designed for each robot, namely , to evaluate the expected cumulative reward under a given state and all actions performed by the robot. The evaluation network integrates global and local features, where the number of neurons in the hidden layer is 512, 256, 128, and 64, respectively, and a self-attention mechanism is added to the last layer. The self-attention mechanism is expressed as: ; Where, Represents the weight of the self-attention mechanism; represents the activation function; 、 represents the weight factor; represents the scaling factor; S3512: Based on the triangular mesh model, a priority replay strategy is used to focus on key sub-regions. Surface constraints are added to limit the robot's range of motion. The evaluation network is updated using the temporal difference error minimization method, and the policy network parameters are updated by maximizing the reward value, resulting in a trained policy network. Load a large and complex component model in the simulation environment and train the model. The loss function of the evaluation network update process using the method of minimizing the temporal difference error is expressed as: ; Where, Represents the loss function of the evaluation network; Represents the expectation operator; express Instant rewards from Moment Robot; Indicates that the evaluation network is in state Predict the reward value of subsequent actions based on the strategy; Indicates that the status Take action The reward value prediction of ; By maximizing the reward U value, the policy function is updated. That is, by adjusting the parameters of the policy function, the robot chooses actions that can obtain higher cumulative rewards in the current state. The policy function update process is: ; Where, Represents the gradient of the objective function of the policy network, which is used to update the parameters of the policy network; Indicates that the status Take action The gradient of the reward value prediction; Represents the gradient of the policy function with respect to the policy network parameters; the learning rate of the policy function is .

[0035] Due to the natural non-uniformity of measurement data of large and complex components, priority playback based on temporal differential error is used to automatically focus on key sub-areas to compensate for the distribution deviation of measurement data, which can be expressed as: ; Where, Indicates the Sampling priority of each sampling point; Indicates the The timing difference error of each sampling point; At the same time, during the training process, the robot's movements should be strictly restricted within the surface space of large and complex components to ensure that the generated measurement path meets physical feasibility. Constraints are imposed by adding regularized movements with surface constraints, which can be expressed as: ; Where, Regularized loss function representing surface constraints; Indicates that the status Next, using the policy network Generated motion and triangular mesh models The distance between them.

[0036] S3513: Based on the trained policy network, the robot predicts the actions it should perform and generates continuous path points. It then combines the continuity constraints between adjacent path points and the surface fit constraints between path points and large, complex components to construct a spatiotemporal joint optimization objective function, eliminate path jitter, and obtain an optimized continuous path. When performing path jitter elimination, a spatiotemporal joint optimization objective function is constructed to smooth the path sequence. The constructed objective function is expressed as: ; Where, represents the objective function of spatiotemporal joint optimization; Represents a continuity constraint, which is used to minimize the Euclidean distance between adjacent path points to ensure smooth motion of the robot arm; Represents a surface fit constraint, which is used to penalize the deviation of path points from the surface of large and complex components; Solve the objective function through the Gauss-Grund algorithm and output a sequence of path points that meets the continuity condition .

[0037] S3514: Performs real-time path conflict detection based on the distance between path points between robots, and makes directional adjustments based on the path conflict detection results to generate an optimized path that covers the surface of large and complex components; In the multi-robot collaborative scenario, real-time path conflict detection is performed. When the path points of any two robots meet When , the repulsive force adjustment mechanism is triggered, which is expressed as: ; ; Where, Indicates the The corrected path points of the robot; Indicates the The path points of the robot before correction; Indicates the Normal direction of each robot at the corresponding point on the surface of a large complex component; Representation of normal vector The model; Indicates the The corrected path points of the robot; Indicates the The path points of the robot before correction; Indicates the Normal direction of each robot at the corresponding point on the surface of a large complex component; Representation of normal vector The model; By adjusting the normal offset, the corrected path is ensured to remain on the large and complex component surface, that is, the triangular mesh model, and conflicts can be quickly eliminated through directional adjustment.

[0038] The generated optimized path covering the surface of a large and complex component is expressed as: ; Where, Represents the optimized path covering the surface of a large and complex component; After optimization The three-dimensional coordinates of the path point at that moment; After optimization the speed of the moment; After optimization The surface direction vector at the moment; , Indicates the total number of moments.

[0039] S4: Share the optimized paths and states of multiple robots in real time, predict potential future conflicts, and dynamically and collaboratively adjust the paths and states of multiple robots based on the prediction results to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning; S41: Share optimized paths and states of multiple robots in real time; In this embodiment, each robot shares its optimized path in real time through the communication network and status, the robot's status includes the current position ,speed ,attitude , residual energy and measurement status Shared data is updated at a 10Hz frequency, with communication latency kept to under 10ms, ensuring real-time multi-machine collaboration. During actual processing, robot state information is smoothed using a Kalman filter to ensure data reliability and provide accurate input for conflict prediction and progress synchronization.

[0040] S42: Based on the optimized path and speed of each robot, predict the future position of the robot and perform future position conflict determination between the robots; the future position conflict determination between the robots includes triggering conflict adjustment when the distance between the path points of the two robots at a future moment is lower than a preset distance threshold; In this embodiment, based on the current path of each robot and speed , and make position predictions for the next 10 steps Specifically, when any two robots meet in the future At any time, adjustments are triggered.

[0041] S43: Based on the future position conflict judgment results, the paths and states of each robot are dynamically and collaboratively adjusted to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning; S431: When a conflict in the future positions of two robots is predicted, the conflict weight is adjusted using the robot priority matrix, the path of the robot with the lower priority is adjusted first, and the adjusted robot path is used as the final path; Due to the overlap of robot fields of view, the priority matrix Adjusting the conflict weights can ensure that high-priority robots retain their paths and low-priority robots actively avoid collisions. The conflict weight adjustment is expressed as: ; Where, Indicates the adjusted The robot is relative to the The priority of each robot, that is, the closer the distance, the greater the priority adjustment; Indicates the unadjusted The robot is relative to the The priority of each robot; Indicates the A robot in The location of the waypoint at the moment; Indicates the A robot in The location of the waypoint at the moment; Among them, the path adjustment of the robot is expressed as: ; Where, Indicates the A robot in The position of the path point is adjusted at all times, and the adjusted path point position fits the triangular mesh model, that is, , Represents a point in a triangular mesh model, represents a triangular mesh model, A function that represents the value of the independent variable that minimizes the objective function; , that is, The robot has higher priority than the A robot; S432: When it is predicted that the measurement progress of the two robots is different, the speed of the robot with the lagging measurement progress is adjusted first; Among them, the speed adjustment of the robot is expressed as: ; Where, Indicates the The robot accelerates to the adjusted speed; Indicates the The unadjusted speed of each robot; Indicates the The percentage of coverage points of each robot relative to the number of points in the divided sub-areas; Indicates the The percentage of coverage points of each robot relative to the number of points in the divided sub-areas; , which means the The robot lags behind A robot measures progress; S433: Dynamically adjust the robot posture based on the robot's measurement accuracy; Among them, the robot posture adjustment is expressed as: ; Where, Indicates the The posture of each robot after acceleration adjustment; Indicates the The unadjusted posture of the robot; Indicates the Sensor field of view and surface normal vector of each robot Angle S434: Combining the robot priority matrix, the adjusted robot speed and the robot posture as control instructions, and combining them with the final path to achieve multi-robot collaborative measurement path planning.

[0042] Example 2 Based on the same technical concept, such as Figure 2 As shown, this embodiment also provides a multi-robot collaborative measurement path planning based on reinforcement learning, including a data acquisition and preprocessing module, a model building module, a path generation module, a path adjustment module, and a control module.

[0043] Specifically, the data acquisition and preprocessing module is used to acquire the model and point cloud data of large and complex components and perform preprocessing; Specifically, the model building module is used to build a three-dimensional environment model based on the preprocessed point cloud data and define the state space of the reinforcement learning environment, the executable action space, and the reward function of the reinforcement learning process; Specifically, the path generation module is used to assign measurement tasks to multiple robots based on the constructed 3D environment model, generate an initial path covering the surface of large and complex components, and optimize the initial path using reinforcement learning methods to generate an optimized path; Specifically, the path adjustment module is used to share the optimized paths and states of multiple robots in real time, predict potential future conflicts, and dynamically and collaboratively adjust the paths and states of multiple robots based on the prediction results to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning; Specifically, the control module is used to input control instructions into the system to execute high-precision collaborative measurement operations of multiple robots.

[0044] Example 3 Based on the same technical concept, the embodiment of the present application also provides a computer device, including a memory 1 and a processor 2, such as Figure 3 As shown, the memory 1 stores a computer program, and the processor 2 implements any of the above methods when executing the computer program.

[0045] Memory 1 includes at least one type of readable storage medium, including flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory), a magnetic storage device, a magnetic disk, an optical disk, etc. In some embodiments, memory 1 can be an internal storage unit for reinforcement learning-based multi-robot collaborative measurement path planning, such as a hard disk. In other embodiments, memory 1 can also be an external storage device for reinforcement learning-based multi-robot collaborative measurement path planning, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash memory card, etc. Furthermore, memory 1 can include both an internal storage unit and an external storage device for reinforcement learning-based multi-robot collaborative measurement path planning. Memory 1 can be used not only to store application software and various data installed in reinforcement learning-based multi-robot collaborative measurement path planning, such as the code of the reinforcement learning-based multi-robot collaborative measurement path planning program, but can also be used to temporarily store data that has been output or is about to be output.

[0046] In some embodiments, the processor 2 can be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip, used to run the program code stored in the memory 1 or process data, such as executing a multi-robot collaborative measurement path planning program based on reinforcement learning.

[0047] The disclosed embodiments of the present invention further provide a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to perform the steps of the method described in the above method embodiments. The storage medium may be a volatile or non-volatile computer-readable storage medium.

[0048] The computer program product of the reinforcement learning-based multi-robot collaborative measurement path planning method provided in the disclosed embodiment of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the steps of the method described in the above method embodiment. For details, please refer to the above method embodiment and will not be repeated here.

[0049] The disclosed embodiments of the present invention further provide a computer program that, when executed by a processor, implements any of the methods of the aforementioned embodiments. This computer program product can be implemented in hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is embodied as a computer storage medium. In another alternative embodiment, the computer program product is embodied as a software product, such as a software development kit (SDK).

[0050] It can be understood that the same or similar parts of the above embodiments can be referenced to each other, and the contents not described in detail in some embodiments can refer to the same or similar contents in other embodiments.

[0051] It should be noted that, in the description of the present invention, the terms "first", "second", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance. In addition, in the description of the present invention, unless otherwise specified, the meaning of "plurality" is at least two.

[0052] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a specific logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0053] It should be understood that various components of the present invention may be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods may be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof may be used: a discrete logic circuit having logic gate circuits for implementing logic functions on data signals, an application-specific integrated circuit having suitable combinational logic gate circuits, a programmable gate array (PGA), a field-programmable gate array (FPGA), etc.

[0054] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0055] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing module, or each unit may exist physically separately, or two or more units may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or in the form of software functional modules. If the integrated modules are implemented in the form of software functional modules and sold or used as independent products, they may also be stored in a computer-readable storage medium.

[0056] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0057] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0058] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A multi-robot collaborative measurement path planning method based on reinforcement learning, characterized in that: include: Obtain models and point cloud data of large and complex components and perform pre-processing; Build a 3D environment model based on preprocessed point cloud data and define the state space of the reinforcement learning environment, the executable action space, and the reward function of the reinforcement learning process; Based on the constructed 3D environment model, the measurement tasks are assigned to multiple robots to generate an initial path covering the surface of large and complex components. The initial path is then optimized using reinforcement learning methods to generate an optimized path. Share the optimized paths and states of multiple robots in real time, predict potential future conflicts, and dynamically and collaboratively adjust the paths and states of multiple robots based on the prediction results to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning.

2. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 1 is characterized in that: The acquisition of the model and point cloud data of the large and complex component and pre-processing thereof include: Directly obtain the CAD model of large and complex components and convert it into the first triangle mesh model; Use a laser scanner to scan large and complex components to obtain point cloud data on the surface of large and complex components, perform denoising and downsampling processing, and generate downsampled point cloud data; Based on the first triangular mesh model and downsampled point cloud data, the iterative closest point algorithm is used for alignment.

3. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 2 is characterized in that: The method of constructing a three-dimensional environment model based on the pre-processed point cloud data and defining the state space of the reinforcement learning environment, the executable action space, and the reward function of the reinforcement learning process includes: Based on the downsampled point cloud data, a Poisson surface reconstruction algorithm is used to generate a second triangular mesh model, which is combined with the first triangular mesh model to obtain the surface information of large and complex components. Based on the surface information of large and complex components, the surface of large and complex components is divided into multiple manageable sub-areas using surface geometric feature information and spatial position information to construct a three-dimensional environmental model; Based on the 3D environment model, the geometric representation of large and complex components is sampled and combined with multiple robot states and environment states to define the state space of the reinforcement learning environment. Define the executable action space based on the stand-alone action of a single robot and the coordinated action of multiple robots; Define the reward function for the reinforcement learning process based on coverage, efficiency, conflict avoidance, and quality measurements of large complex components.

4. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 3 is characterized in that: Based on the surface information of large and complex components, the surface is divided into multiple manageable sub-areas using surface geometric feature information and spatial position information to construct a 3D environment model, including: Based on the surface information of large and complex components, the surface of large and complex components is divided into multiple initial sub-regions using surface geometric feature information and spatial feature information; The multiple initial sub-regions are clustered using the similarity matrix and the Laplace matrix to form multiple manageable sub-regions and construct a three-dimensional environment model.

5. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 3 is characterized in that: When defining the executable action space, the coordinated actions of multiple robots include task reallocation and a robot priority matrix, which is used to prioritize the allocation of high curvature sub-areas and to actively avoid conflicts with low-priority robots.

6. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 1 is characterized in that: The method allocates measurement tasks to multiple robots based on the constructed three-dimensional environment model, generates an initial path covering the surface of a large and complex component, and optimizes the initial path using a reinforcement learning method to generate an optimized path, including: Based on the division of large and complex components into multiple sub-areas, the complexity of each sub-area is quantified; Evaluate each robot's measurement performance based on its maximum speed, measurement accuracy, endurance, and field of view. Based on the measurement performance of each robot, a particle swarm optimization algorithm is used to assign a sub-area of ​​measurement to each robot; Based on the sub-area assigned to each robot, a UV parameterized function is used to map the 2D zigzag path to a 3D surface. The 3D coordinates and path directions of the path points are calculated, and the path points are globally connected. Combined with real-time collision detection between the path points, the measurement path and corresponding time-velocity sequence of each robot are adjusted and generated to form an initial path covering the surface of large and complex components. Based on the initial path, the trained policy network and evaluation network are used to predict the actions of each robot, calculate the continuous path points, and combine the real-time detection of path conflicts between path points of robots to adjust and generate the optimized path covering the surface of large and complex components.

7. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 6 is characterized in that: Based on the sub-area assigned to each robot, a UV parameterized function is used to map the 2D zigzag path to a 3D surface. The 3D coordinates and path directions of the path points are calculated, and the path points are globally connected. Combined with real-time collision detection between the path points, the measurement path and corresponding time-velocity sequence of each robot are adjusted and generated to form an initial path covering the surface of large and complex components, including: Based on the sub-area assigned to each robot, the UV parameterization function is used to map the two-dimensional Z-shaped path to a three-dimensional surface to obtain a three-dimensional path, and the three-dimensional coordinates of each path point and the path direction are determined; Based on the path point sequence, a piecewise cubic spline interpolation algorithm is used to smooth the path segments formed by connecting the path points, and to perform global connection of each path point. The global connection of each path point includes assigning weights to the path segments and corresponding sub-regions, and using an optimization algorithm to solve the optimal path segment connection sequence. Real-time collision detection is performed based on the distance between the path points of each robot, and path correction is performed based on the real-time collision detection results. The initial path point set and its corresponding time-speed sequence for each robot are generated to form an initial path covering the surface of large and complex components. The initial path point set of each robot is expressed as: ； Where, Indicates the The initial path point set of each robot; Indicates the The first robot waypoints; The time-velocity sequence of each robot is expressed as: ； Where, Indicates the Time-velocity sequence of each robot; Indicates the The first robot The collection of times and speeds of the waypoints.

8. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 6 is characterized in that: Based on the initial path, the trained policy network and evaluation network are used to predict the actions of each robot, calculate continuous path points, and combine the real-time detection of path conflicts between path points of robots to adjust and generate an optimized path covering the surface of large and complex components, including: Taking the initial path as the starting point, we design a policy network and an evaluation network to output the actions that each robot should perform in its current state, and to evaluate the expected cumulative rewards for a given state and all actions performed by the robots. Based on a triangular mesh model, a priority replay strategy is used to focus on key sub-areas, surface constraints are added to limit the robot's range of motion, and the evaluation network is updated by minimizing the temporal difference error and the policy network parameters are updated by maximizing the reward value, resulting in a trained policy network. Based on the trained policy network, the robot predicts the actions it should perform and generates continuous path points. It then combines the continuity constraints between adjacent path points and the surface fit constraints between path points and large, complex components to construct a spatiotemporal joint optimization objective function, eliminate path jitter, and obtain an optimized continuous path. Based on the distance between the path points of the robots, the robot can detect the path conflicts in real time and make directional adjustments based on the results of the path conflicts to generate an optimized path covering the surface of large and complex components. The optimized path for covering the surface of a large complex component is expressed as: ； Where, Represents the optimized path covering the surface of a large and complex component; After optimization The three-dimensional coordinates of the path point at that moment; After optimization the speed of the moment; After optimization The surface direction vector at the moment; , Indicates the total number of moments.

9. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 1 is characterized in that: The system shares the optimized paths and states of multiple robots in real time, predicts potential future conflicts, and dynamically and collaboratively adjusts the paths and states of multiple robots based on the prediction results to generate the final path and control instructions to achieve multi-robot collaborative measurement path planning, including: Share the optimized paths and states of multiple robots in real time; the robot states include current position, speed, posture, remaining energy, and measurement status; Based on the optimized path and speed of each robot, the future position of the robot is predicted, and future position conflict determination between the robots is performed; the future position conflict determination between the robots includes triggering conflict adjustment when the distance between the path points of the two robots at a future time is lower than a preset distance threshold; Based on the future position conflict judgment results, the paths and states of each robot are dynamically and collaboratively adjusted to generate the final path and control instructions to realize multi-robot collaborative measurement path planning.

10. The multi-robot collaborative measurement path planning method based on reinforcement learning according to claim 9, characterized in that: The method of dynamically and collaboratively adjusting the paths and states of each robot based on the future position conflict judgment results and generating the final path and control instructions to realize multi-robot collaborative measurement path planning includes: When a conflict between the future positions of two robots is predicted, the robot priority matrix is ​​used to adjust the conflict weight, giving priority to adjusting the path of the robot with the lower priority, and the adjusted robot path is used as the final path; The conflict weight adjustment is expressed as: ； Where, Indicates the adjusted The robot is relative to the The priority of each robot; Indicates the unadjusted The robot is relative to the The priority of each robot; Indicates the A robot in The location of the waypoint at the moment; Indicates the A robot in The location of the waypoint at the moment; The path adjustment of the robot is expressed as: ； Where, Indicates the A robot in The position of the path point is adjusted at all times, and the adjusted path point position fits the triangular mesh model, that is, , Represents a point in a triangular mesh model, represents a triangular mesh model, A function that represents the value of the independent variable that minimizes the objective function; , that is, The robot has higher priority than the A robot; When it is predicted that the measurement progress of two robots is different, the speed of the robot with the lagging measurement progress is adjusted first; The speed adjustment of the robot is expressed as: ； Where, Indicates the The robot accelerates to the adjusted speed; Indicates the The unadjusted speed of each robot; Indicates the The percentage of coverage points of each robot relative to the number of points in the divided sub-areas; Indicates the The percentage of coverage points of each robot relative to the number of points in the divided sub-areas; , which means the The robot lags behind A robot measures progress; Combined with the robot's measurement accuracy, the robot's posture is dynamically adjusted; The robot posture adjustment is expressed as: ； Where, Indicates the The posture of each robot after acceleration adjustment; Indicates the The unadjusted posture of the robot; Indicates the Sensor field of view and surface normal vector of each robot Angle The robot priority matrix, as well as the adjusted robot speed and robot posture, are combined as control instructions and combined with the final path to achieve multi-robot collaborative measurement path planning.

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