Spraying trajectory optimization method based on digital twinning and multi-target genetic algorithm

Abstract

The invention relates to a spraying track optimization method based on a digital twinning and multi-target genetic algorithm. The method comprises the steps that a spraying scene needing to be optimized is determined; obtaining a target three-dimensional model and a current spraying track; a spraying scene is initialized and calibrated; simulation spraying is conducted on the target three-dimensional model and the current spraying track, and current spraying evaluation is obtained; predicting the spraying effect by using a neural network; a genetic algorithm is used for optimizing the current spraying track, and an optimized spraying track is obtained; simulation spraying is conducted on the target three-dimensional model and the optimized spraying track, and optimized spraying evaluation is obtained; the current spraying evaluation and the optimized spraying evaluation are compared, and the spraying track corresponding to the spraying evaluation with the good spraying effect is selected as the current optimal spraying track. According to the digital twin spraying effect, high-precision simulation can be carried out, the original spraying track and the optimized spraying track effect can be visually compared through the evaluation system, and meanwhile paint does not need to be wasted.

Description

Technical Field

[0001] This invention relates to the technical field of spraying optimization, and in particular to a spraying trajectory optimization method based on digital twins and multi-objective genetic algorithms. Background Technology

[0002] The development of industrial robots has brought about significant changes to industrial production. For example, traditional painting techniques were based on manual teaching, but with technological advancements, more and more scenarios now support automated painting by industrial robots, leading to increasingly higher requirements for painting quality.

[0003] Traditional manual teaching spraying technology relies on highly skilled workers to teach and determine the optimal spraying trajectory. The actual spraying effect is closely related to the teaching sample, which not only wastes manpower and resources, but also results in poor versatility of spraying effect and inability to maintain a consistent quality level. In addition, it is time-consuming, poses safety hazards, and makes it difficult to train a universal spraying trajectory and spraying quality model. Summary of the Invention

[0004] The purpose of this invention is to provide a spraying trajectory optimization method based on digital twins and multi-objective genetic algorithms, which aims to solve the technical problems of inconsistent spraying quality, poor spraying efficiency, and material waste caused by existing spraying equipment.

[0005] To address the aforementioned technical problems, a spraying trajectory optimization method based on digital twins and multi-objective genetic algorithms is provided, comprising:

[0006] S1, Identify the painting scenarios that need optimization;

[0007] S2, acquire the target 3D model and the current spraying trajectory;

[0008] S3, Initialize and calibrate the spraying scene;

[0009] S4, simulate spraying on the target 3D model and the current spraying trajectory respectively, obtain the current spraying evaluation, and use a neural network to fit the spraying process parameters and spraying effect;

[0010] S5, use a genetic algorithm to optimize the current spraying trajectory and obtain an optimized spraying trajectory;

[0011] S6, Simulate spraying on the target 3D model and the optimized spraying trajectory respectively to obtain an optimized spraying evaluation;

[0012] S7. Compare the current spraying evaluation and the optimized spraying evaluation, and select the spraying trajectory corresponding to the spraying evaluation with good spraying effect as the current optimal spraying trajectory.

[0013] Furthermore, the spraying evaluation includes spraying quality evaluation and spraying trajectory evaluation; the parameters of the spraying quality evaluation include spraying thickness, coating uniformity, paint adhesion rate and paint utilization rate, and the parameters of the spraying trajectory evaluation include the robot's speed, acceleration and total spraying time during the robot's movement.

[0014] Furthermore, after step S7, the following steps are also included: S8, preset the target spraying effect, divide the spraying area into grids, and if the spraying effect corresponding to the current optimal spraying trajectory does not reach the target spraying effect, perform step S7 again to optimize the area with poor spraying effect until the spraying effect corresponding to the current optimal spraying trajectory reaches the target spraying effect.

[0015] Further, step S8 includes:

[0016] S81 uses the spraying parameters of the triangular mesh in the digital twin system, treats each triangular mesh as a point, calculates the variance of the thickness of all triangular meshes on the workpiece, and judges whether the variance difference meets the set standard.

[0017] S82 collects the paint utilization rate of the workpiece surface after digital twin spraying. Through algorithms and spray gun models, it compares the statistical paint utilization rate with the utilization rate before optimization to see if the paint utilization rate is better than the former.

[0018] S83 calculates the spraying time required for a single process and determines whether the spraying efficiency meets the preset time standard.

[0019] Further, step S5 includes: using a neural network combined with a genetic algorithm, with the decision variables of the trajectory points as the optimization objective, to optimize and solve the trajectory of the painting robot arm, as follows:

[0020] S51, based on the input parameter range of the neural network, randomly initializes a population of size N to generate the initial parent population of the trajectory point decision variables, and adopts a random initialization strategy to make the solution cover the entire search space.

[0021] S52, construct a fitness function, take minimizing the error of the target spraying quality Y1 and optimizing the spraying efficiency Y2 as the optimization objectives, calculate the fitness value, and select high-quality individuals according to the fitness ranking;

[0022] S53 employs Tournament Selection, selecting individuals with the best fitness as the next generation parent population based on spraying accuracy and energy consumption constraints.

[0023] S54 uses simulated binary crossover (SBX Crossover) and polynomial mutation to perform genetic operations, generating new offspring populations to enhance search capabilities and avoid local optima;

[0024] S55, repeat S52 to S54 until the preset maximum number of iterations is reached. Finally, the optimal trajectory parameter variables are substituted into the neural network model to calculate the optimal spraying trajectory, and the trajectory is smoothed using methods such as B-spline interpolation, thereby generating an optimized spraying path and robotic arm motion trajectory, improving spraying quality and efficiency.

[0025] Furthermore, the spraying equipment sprays the workpiece according to the spraying trajectory. During the spraying process, the data acquisition system collects real-time processing data and feeds it back to the controller. The controller adjusts the digital twin model based on the feedback real-time data, and the digital twin model monitors and predicts the spraying process in real time.

[0026] Furthermore, the spraying efficiency satisfies the following formula:

[0027]

[0028] Where Q is the actual paint flow rate of the spray gun, representing the total amount of paint sprayed per unit time;

[0029] D represents the distance between the spray gun and the surface to be sprayed;

[0030] θ represents the opening and closing angle of the spray gun nozzle.

[0031] Furthermore, the method also includes:

[0032] Establish a distribution model for the coating thickness;

[0033] Minimize the non-uniformity of the thickness distribution model and paint waste;

[0034] Establish a mapping between robot trajectory and process parameters and processing results;

[0035] Adjust the control parameters of the thickness distribution model;

[0036] The thickness distribution model is optimized by combining genetic algorithms.

[0037] Furthermore, the establishment of the coating thickness prediction model includes: establishing a model based on a neural network. After collecting relationship pairs based on digital twin simulation or physical experiments, a prediction model is established through a neural network. With X as the input parameter, the corresponding Y is obtained by analyzing and measuring the simulation results. The relationship pair between X and Y is obtained by using digital twin simulation. The relationship between X and Y is fitted using a neural network, and the result of Y can be predicted through X.

[0038] Furthermore, the steps for importing the model include:

[0039] 3D models of the robot and spray gun used for spraying are constructed.

[0040] Import the constructed 3D model and the current spraying trajectory into the digital twin software to construct a digital twin of the robot;

[0041] The digital twin includes: a model of the spray gun used by the robot for spraying, the robot's kinematic parameters, and the corresponding information of the object being sprayed.

[0042] Implementing the embodiments of the present invention will have the following beneficial effects:

[0043] This embodiment presents a spraying trajectory optimization method based on digital twins and multi-objective genetic algorithms. It utilizes neural networks to predict spraying effects and employs genetic algorithms to optimize the spraying trajectory. Firstly, by simulating natural selection and genetic mechanisms to search for the optimal solution, the accuracy of the spraying trajectory is improved, thereby enhancing spraying quality. Secondly, as an automated optimization technique, genetic algorithms reduce reliance on highly skilled workers and mitigate the impact of human factors on spraying results. Thirdly, optimizing the spraying trajectory reduces unnecessary spraying actions, shortens spraying time, and improves overall spraying efficiency. High-precision simulations can be performed based on the digital twin spraying effect. This evaluation system allows for a direct comparison of the original and optimized spraying trajectories, while eliminating paint waste. The optimized trajectory curve can be quickly converted into the corresponding spraying endpoint using digital twin software and then imported into the corresponding robot program. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 The flowchart of the spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm described in this embodiment of the invention is as follows. Figure 1 ;

[0046] Figure 2 This is a flowchart illustrating step S5 as described in an embodiment of the present invention.

[0047] Figure 3 This is a flowchart illustrating step S8 in an embodiment of the present invention. Detailed Implementation

[0048] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0049] It should be noted that when a component is said to be "fixed to" another component, it can be directly attached to the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0050] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0051] Please refer to Figures 1-3 This invention provides a method for optimizing spraying trajectories based on digital twins and multi-objective genetic algorithms, including:

[0052] S1, Identify the painting scenarios that need optimization;

[0053] S2, acquire the target 3D model and the current spraying trajectory;

[0054] S3 initializes and calibrates the spraying scene;

[0055] S4, simulate spraying on the target 3D model and the current spraying trajectory respectively, obtain the current spraying evaluation, and use a neural network to fit the spraying process parameters and spraying effect;

[0056] S5, use a genetic algorithm to optimize the current spraying trajectory and obtain an optimized spraying trajectory;

[0057] S6, simulate spraying on the target 3D model and the optimized spraying trajectory respectively, and obtain the optimized spraying evaluation;

[0058] S7. Compare the current spraying evaluation and the optimized spraying evaluation, and select the spraying trajectory corresponding to the spraying evaluation with good spraying effect as the current optimal spraying trajectory.

[0059] Compared to existing technologies, the trajectory optimization method used in this application employs digital twin technology. This technology offers several advantages over traditional offline programming: First, it allows for quantitative statistical analysis of simulated spraying effects; second, it enables trajectory optimization; third, with a well-developed model, it allows for the exploration of optimal trajectory design and kinematic parameters by considering various factors affecting the spraying effect, such as spraying distance, spray gun speed, and spray gun angle; and fourth, it allows for comparison before and after optimization. The trajectory can be generated and simulated in a virtual environment before being imported into the robot for actual spraying, significantly reducing the workload of personnel and the use of materials, improving production efficiency, and simplifying the original operating procedures. Simultaneously, a multi-objective improved genetic algorithm is used to optimize the trajectory. The spraying parameters are optimized through individual encoding, selection, crossover, and mutation operations, improving the accuracy and quality of spraying and providing a universal spraying model. Compared to existing technologies that require manual teaching, it eliminates the need to generate trajectories for each sprayed object, thus improving applicability.

[0060] The spraying trajectory optimization method based on digital twins and multi-objective genetic algorithms in this embodiment utilizes genetic algorithms to optimize the spraying trajectory. Firstly, it can search for the optimal solution by simulating natural selection and genetic mechanisms, thereby improving the accuracy of the spraying trajectory and thus enhancing spraying quality. Secondly, as an automated optimization technique, genetic algorithms can reduce reliance on highly skilled workers and mitigate the impact of human factors on the spraying effect. Thirdly, by optimizing the spraying trajectory, unnecessary spraying actions can be reduced, spraying time shortened, and overall spraying efficiency improved. Based on the effect of digital twin spraying, high-precision simulations can be performed. This evaluation system allows for a direct comparison of the original and optimized spraying trajectories, while avoiding paint waste. The optimized trajectory curve can be quickly converted into the corresponding spraying endpoint using digital twin software and then imported into the corresponding robot program. After optimization, the corresponding robot program is converted.

[0061] In this embodiment, the corresponding program import input function can import the optimized trajectory points from the optimization program into the digital twin software, and can also convert the simulation in the digital twin into the corresponding robot control program, which can be directly called, increasing efficiency.

[0062] In one possible implementation, the spraying evaluation includes spraying quality evaluation and spraying trajectory evaluation; the parameters for spraying quality evaluation include spraying thickness, coating uniformity, paint adhesion rate and paint utilization rate, and the parameters for spraying trajectory evaluation include the robot's speed, acceleration and total spraying time during the robot's movement.

[0063] In one possible implementation, after step S7, the following steps are also included: S8, presetting the target spraying effect, dividing the spraying area into a mesh, and if the spraying effect corresponding to the current optimal spraying trajectory does not reach the target spraying effect, step S7 is executed again for the area with poor spraying effect to optimize it individually until the spraying effect corresponding to the current optimal spraying trajectory reaches the target spraying effect. For example, after the spraying trajectory is optimized to the optimal solution, the program is imported into the application scenario. A high-precision workpiece triangular mesh model is created. The spraying thickness is represented by a color table corresponding to the thickness table, for example, 0-1000, which means there are 1000 colors representing different thicknesses; that is, color equals thickness. During spraying coloring, the three vertices of the triangular mesh are calculated using the previous mathematical model to obtain the values ​​corresponding to the three vertices. Then, these values ​​are used to color the mesh. When the thickness needs to be calculated, the vertex color data of the triangular mesh is obtained. Within the triangular mesh, the thickness value is obtained by interpolation using the color data of the three vertices. Each triangular mesh uses the average thickness value of its vertices as a reference, and the variance of all meshes is used as an evaluation index for coating uniformity. For more precise results, simply generate a higher density mesh. Mesh with poor uniformity can also be identified and locally optimized to improve the coating effect.

[0064] Please refer to Figure 3 In one possible implementation, step S8 includes:

[0065] S81 uses the spraying parameters of the triangular mesh in the digital twin system, treats each triangular mesh as a point, calculates the variance of the thickness of all triangular meshes on the workpiece, and judges whether the variance difference meets the set standard.

[0066] S82 collects the paint utilization rate of the workpiece surface after digital twin spraying. Through algorithms and spray gun models, it compares the statistical paint utilization rate with the utilization rate before optimization to see if the paint utilization rate is better than the former.

[0067] S83 calculates the spraying time required for a single process and determines whether the spraying efficiency meets the preset time standard.

[0068] Please refer to Figure 2 In one possible implementation, step S5 includes: using a neural network combined with a genetic algorithm, with the decision variables of the trajectory points as the optimization objective, to optimize the trajectory of the painting robot arm, as follows:

[0069] S51, based on the input parameter range of the neural network, randomly initializes a population of size N to generate the initial parent population of the trajectory point decision variables, and adopts a random initialization strategy to make the solution cover the entire search space.

[0070] S52, construct a fitness function, take minimizing the error of the target spraying quality Y1 and optimizing the spraying efficiency Y2 as the optimization objectives, calculate the fitness value, and select high-quality individuals according to the fitness ranking;

[0071] S53 employs Tournament Selection, selecting individuals with the best fitness as the next generation parent population based on spraying accuracy and energy consumption constraints.

[0072] S54 uses simulated binary crossover (SBX Crossover) and polynomial mutation to perform genetic operations, generating new offspring populations to enhance search capabilities and avoid local optima;

[0073] S55, repeat S52 to S54 until the preset maximum number of iterations is reached. Finally, the optimal trajectory parameter variables are substituted into the neural network model to calculate the optimal spraying trajectory, and the trajectory is smoothed using methods such as B-spline interpolation, thereby generating an optimized spraying path and robotic arm motion trajectory, improving spraying quality and efficiency.

[0074] In one possible implementation, the spraying equipment sprays the workpiece according to the spraying trajectory. During the spraying process, the data acquisition system collects real-time processing data and feeds it back to the controller. The controller adjusts the digital twin model based on the feedback real-time data. The digital twin model monitors and predicts the spraying process in real time.

[0075] In one possible implementation, the spraying efficiency satisfies the following formula:

[0076]

[0077] Where Q is the actual paint flow rate of the spray gun, representing the total amount of paint sprayed per unit time; Q is a measure of the total amount of paint sprayed by the spray gun during the painting process, expressed as the volume of paint per unit time. The paint utilization rate is calculated using a spray gun mathematical model and a loss model: If the paint sprayed within Δt time is initially fully adhered to the workpiece without considering losses, the paint utilization rate is affected by the spraying distance (the farther the spraying distance, the less paint adheres to the surface) and the size of the spraying angle (for the same spraying distance, the larger the spraying angle, the more dispersed the paint adhered to the workpiece surface). Therefore, establishing a relationship between the paint sprayed within Δt time, the spraying distance, and the spraying angle yields the paint utilization rate on the workpiece surface after considering losses.

[0078] D represents the distance between the spray gun and the surface to be sprayed; the spraying distance D affects the amount of paint adhered, the greater the distance, the less paint adhered.

[0079] θ represents the opening angle of the spray gun nozzle. θ affects the distribution range of the paint; the larger the opening angle, the wider the paint distribution and the less paint adheres.

[0080] The above formula describes the amount of paint actually adhering to the workpiece surface per unit time, considering the spraying distance and opening angle. (D+1) in the formula... 2 This indicates that the effect of spraying distance on paint adhesion is a square relationship; that is, as the distance increases, the rate of decrease in adhesion is quadratic. This indicates that the effect of the opening angle on the amount of coating adhesion is linear; that is, as the opening angle increases, the rate at which the amount of coating adhesion decreases is linear.

[0081] In one possible implementation, the method further includes:

[0082] Establish a thickness distribution model;

[0083] Minimize the non-uniformity of the thickness distribution model and paint waste;

[0084] Establish a mapping between robot trajectory and process parameters and processing results;

[0085] Adjust the control parameters of the thickness distribution model;

[0086] The thickness distribution model is optimized by combining genetic algorithms.

[0087] In one possible implementation, establishing a coating thickness prediction model includes: establishing a model to a neural network; after collecting relationship pairs based on digital twin simulation or physical experiments, establishing a prediction model through a neural network; using X as the input parameter; obtaining the corresponding Y by analyzing and measuring the simulation results; obtaining the relationship pair between X and Y using digital twin simulation; fitting the relationship between X and Y using a neural network; and predicting the result of Y using X.

[0088] In one possible implementation, the model import step includes:

[0089] 3D models of the robot and spray gun used for spraying are constructed.

[0090] Import the constructed 3D model and the current spraying trajectory into the digital twin software to construct a digital twin of the robot;

[0091] The digital twin includes: a model of the spray gun used by the robot, the robot's kinematic parameters, and the corresponding information of the object being sprayed.

[0092] Based on the aforementioned genetic algorithm-based digital twin method for coating thickness, a spray gun model is established, including: robot trajectory (distance, angle), speed, real-time spray gun parameters (opening, fan shape, atomization), and material supply system parameters (viscosity, instantaneous flow rate). The spraying process is expressed using a parameterized method, with control parameters including spray trajectory, flow rate, and pressure. Specific spraying process control parameters are expressed as parameter vectors. Given a set of spraying control parameters, a definite spraying result is obtained, which includes at least the coating thickness or area at key points.

[0093] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for optimizing spraying trajectories based on digital twins and multi-objective genetic algorithms, characterized in that, include: S1, Identify the painting scenarios that need optimization; S2, acquire the target 3D model and the current spraying trajectory; S3, Initialize and calibrate the spraying scene; S4, simulate spraying on the target 3D model and the current spraying trajectory respectively, obtain the current spraying evaluation, and use a neural network to fit the spraying process parameters and spraying effect; S5, use a genetic algorithm to optimize the current spraying trajectory and obtain an optimized spraying trajectory; S6, Simulate spraying on the target 3D model and the optimized spraying trajectory respectively to obtain an optimized spraying evaluation; S7. Compare the current spraying evaluation and the optimized spraying evaluation, and select the spraying trajectory corresponding to the spraying evaluation with good spraying effect as the current optimal spraying trajectory.

2. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 1, characterized in that, The spraying evaluation includes spraying quality evaluation and spraying trajectory evaluation; the parameters of the spraying quality evaluation include spraying thickness, coating uniformity, paint adhesion rate and paint utilization rate, and the parameters of the spraying trajectory evaluation include the robot's speed, acceleration and total spraying time during the robot's movement.

3. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 1, characterized in that, After step S7, also Includes the following steps: S8, preset the target spraying effect, divide the spraying area into grids, if the spraying effect corresponding to the current optimal spraying trajectory does not reach the target spraying effect, execute step S7 again to optimize the area with poor spraying effect until the spraying effect corresponding to the current optimal spraying trajectory reaches the target spraying effect.

4. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 3, characterized in that, Step S8 includes: S81 uses the spraying parameters of the triangular mesh in the digital twin system, treats each triangular mesh as a point, calculates the variance of the thickness of all triangular meshes on the workpiece, and judges whether the variance difference meets the set standard. S82 collects the paint utilization rate of the workpiece surface after digital twin spraying. Through algorithms and spray gun models, it compares the statistical paint utilization rate with the utilization rate before optimization to see if the paint utilization rate is better than the former. S83 calculates the spraying time required for a single process and determines whether the spraying efficiency meets the preset time standard.

5. The robot spraying trajectory optimization method based on digital twin and neural network genetic algorithm according to claim 1, characterized in that, Step S5 includes: using a neural network combined with a genetic algorithm, with the decision variables of the trajectory points as the optimization objective, to optimize the trajectory of the painting robot arm, as follows: S51, based on the input parameter range of the neural network, randomly initializes a population of size N to generate the initial parent population of the trajectory point decision variables, and adopts a random initialization strategy to make the solution cover the entire search space. S52, construct a fitness function, take minimizing the error of the target spraying quality Y1 and optimizing the spraying efficiency Y2 as the optimization objectives, calculate the fitness value, and select high-quality individuals according to the fitness ranking; S53 employs Tournament Selection, selecting individuals with the best fitness as the next generation parent population based on spraying accuracy and energy consumption constraints. S54 uses simulated binary crossover (SBX Crossover) and polynomial mutation to perform genetic operations, generating new offspring populations to enhance search capabilities and avoid local optima; S55, repeat S52 to S54 until the preset maximum number of iterations is reached. Finally, the optimal trajectory parameter variables are substituted into the neural network model to calculate the optimal spraying trajectory, and the trajectory is smoothed using methods such as B-spline interpolation, thereby generating an optimized spraying path and robotic arm motion trajectory, improving spraying quality and efficiency.

6. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 1, characterized in that, The spraying equipment sprays the workpiece according to the spraying trajectory. During the spraying process, the data acquisition system collects real-time processing data and feeds it back to the controller. The controller adjusts the digital twin model based on the real-time feedback data. The digital twin model monitors and predicts the spraying process in real time.

7. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 1, characterized in that, Spraying efficiency satisfies the following formula: Where Q is the actual paint flow rate of the spray gun, representing the total amount of paint sprayed per unit time; D represents the distance between the spray gun and the surface to be sprayed; θ represents the opening and closing angle of the spray gun nozzle.

8. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 1, characterized in that, The method further includes: Establish a distribution model for the coating thickness; Minimize the non-uniformity of the thickness distribution model and paint waste; Establish a mapping between robot trajectory and process parameters and processing results; Adjust the control parameters of the thickness distribution model; The thickness distribution model is optimized by combining genetic algorithms.

9. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 8, characterized in that, The establishment of the coating thickness prediction model includes: establishing a model based on a neural network. After collecting relationship pairs based on digital twin simulation or physical experiments, a prediction model is established through a neural network. With X as the input parameter, the corresponding Y is obtained by analyzing and measuring the simulation results. The relationship pair between X and Y is obtained by using digital twin simulation. The relationship between X and Y is fitted by a neural network, and the result of Y can be predicted by X.

10. The spraying trajectory optimization method based on digital twin and multi-objective genetic algorithm according to claim 8, characterized in that, The steps for importing a model include: 3D models of the robot and spray gun used for spraying are constructed. Import the constructed 3D model and the current spraying trajectory into the digital twin software to construct a digital twin of the robot; The digital twin includes: a model of the spray gun used by the robot for spraying, the robot's kinematic parameters, and the corresponding information of the object being sprayed.

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