Multi-target spraying robot trajectory planning method based on lens imaging reverse learning

Abstract

The application relates to the field of robot trajectory planning, and aims to realize efficient, accurate and smooth collaborative spraying of a large and complex polyhedral workpiece, and provides a multi-target spraying robot trajectory planning method based on lens imaging reverse learning, which takes the spraying gun moving speed and the adjacent path overlap rate as the core decision variables of a multi-target optimization algorithm to synchronously solve, and calculates the real scanning path interval according to the dynamically generated overlap rate, thereby realizing joint and collaborative control of the operation beat and the spraying path topology; in the iterative optimization process, the non-dominated elite solution in the external Pareto archive is extracted as a benchmark, high-quality reverse candidate solutions are generated on the symmetrical side of the search space through the dynamic nonlinear optical mapping principle and are supplemented to the population, the algorithm is forced to jump out of the local extreme value trap and expand the mining of the potential feasible region, and through a closed-loop optimization mechanism of the bivariate dynamic optimization and the lens reverse learning, the collaborative spraying effect is realized.

Description

Technical Field

[0001] This invention relates to the field of robot trajectory planning, specifically a multi-objective spraying robot trajectory planning method based on lens imaging back learning. Background Technology

[0002] In current research on industrial robot spraying trajectory optimization, the most mainstream approach is parameter optimization based on fixed topology paths. Researchers typically pre-define the geometric path of the spray gun and then use metaheuristic algorithms to optimize process or kinematic parameters. For example, some studies use improved particle swarm optimization algorithms to optimize the joint motion trajectories of redundant robots on fixed paths, or use improved sparrow search algorithms to optimize the row spacing and spraying distance of a zigzag path; other studies have also explored joint optimization of multi-objective process parameters based on hybrid algorithms. The essence of these methods is to perform parameter optimization on a pre-set fixed path.

[0003] Despite the progress made in the aforementioned research, existing technologies still have some shortcomings when dealing with the spraying of large polyhedra. First, existing optimization algorithms are prone to getting trapped in local optima and lack sufficient accuracy under complex high-dimensional constraints. Existing technologies often employ traditional particle swarm optimization, genetic algorithms, or sparrow algorithms. When handling high-dimensional multi-objective optimization problems involving constraints on industrial robot joints, maximum speed, and acceleration, the population diversity tends to decrease sharply in the later stages of iteration, making it difficult to find a uniformly distributed true Pareto front solution. Second, whether using slice projection to generate trajectories for complex surfaces or conventional spraying trajectories, existing technologies often employ a single optimization parameter. Since the geometric areas, normal vectors, and required spatial poses of different faces of large, complex workpieces vary significantly, this fixed parameter strategy creates severe mutual constraints between the total spraying time, coating thickness, and the smoothness of the robot arm's end effector motion. For example, fixing the global overlap rate too low will result in excessively thin edges of the sprayed area, while fixing it too high will exponentially increase invalid path inflection points and exacerbate joint impacts on the robot. Similarly, a single operating speed cannot simultaneously ensure efficiency in large straight sections and smooth transitions at corners. Summary of the Invention

[0004] To achieve efficient, precise, and smooth collaborative spraying of large, complex, and polyhedral workpieces, this application provides a multi-objective spraying robot trajectory planning method based on lens imaging back learning.

[0005] The technical solution adopted by the present invention to solve the above problems is:

[0006] A multi-objective spraying robot trajectory planning method based on lens imaging back learning includes:

[0007] Step 1: Initialization of the spraying operation environment and dual-station polyhedron parameters: Establish the geometric three-dimensional model of the target spraying workpiece and perform mesh generation; set the physical constraints of the spraying robot, including the maximum allowable speed and maximum allowable acceleration of the end effector; set the base transformation matrix of station one and station two.

[0008] Step 2: Trajectory topology generation based on bivariate dynamic coding: Set the decision variables of the optimization algorithm as two-dimensional vectors. ,in This represents the target's movement speed, Represents the overlap rate of adjacent spray paths; based on the current overlap rate. Dynamically calculate the actual distance D between adjacent scanning paths, and generate continuous spatial waypoints covering the workpiece surface based on the distance D;

[0009] Step 3: Generation of end effector execution parameters and construction of multi-objective evaluation function: Based on spatial waypoints and target movement speed, the position, velocity and acceleration time series of the end effector are generated, and a three-dimensional multi-objective evaluation function for measuring the quality of the trajectory is constructed, including total spraying time, coating thickness optimization index and robotic arm motion smoothness evaluation index.

[0010] Step 4: Perform multi-objective optimization based on lens back learning to determine the optimal frontier solution set;

[0011] Step 5: Based on the actual production workshop's preferences for total spraying time, coating thickness optimization index, and robotic arm motion smoothness evaluation index, normalize the objective function values ​​and then sum them by weight. Select the best bivariate combination scheme based on the weighted score, and use the selected scheme to generate a spatial trajectory sequence and normal vector sequence with timestamps.

[0012] Furthermore, ,in This refers to the effective spray width of the spray gun.

[0013] Furthermore, the target sprayed workpiece is a five-sided box; in step 2, when generating spatial waypoints, a dual-station stage separation strategy is adopted: in the first stage, the robot at station one is responsible for generating the paths for the front, left and top half of the workpiece; in the second stage, the control slide rail is switched to station two, which is responsible for generating the paths for the back, right and top half of the workpiece.

[0014] Furthermore, in step 2, when generating spatial waypoints, the normal vectors corresponding to the waypoints are corrected so that they are perpendicular to the target machining surface and always point outward from the workpiece.

[0015] Furthermore, the generation of the position, velocity, and acceleration time series of the end effector based on spatial waypoints and target movement speed specifically includes: determining the spraying section and the cross-surface transition section; for the spraying section, allocating the motion time interval according to the Euclidean distance and velocity between two adjacent waypoints; for the cross-surface transition section, allocating a fixed safe transition time; and using a fifth-order polynomial to smoothly interpolate the path to generate the position, velocity, and acceleration time series of the end effector.

[0016] Furthermore, the total spraying time ,in The total running time for the robot to execute the spraying and transition trajectory. The fixed time for the slide rail to switch between two workstations;

[0017] Coating thickness optimization index ,in, The total number of valid grid points with a surface coating thickness greater than zero. For the first The final paint film thickness for each effective grid point;

[0018] Evaluation index of robotic arm motion smoothness ,in, This represents the total number of discrete sampling points in the trajectory time series. For the first The three-dimensional impact vector of the end effector at each time step.

[0019] Furthermore, the paint film thickness is calculated based on the flat-top Gaussian distribution model: , Indicates the radius of the distance from the center of the spray pattern as The cumulative thickness of the coating at that location Indicates the maximum coating thickness at the center of the spray gun. Let Euclidean distance be the distance from the target point to the projection point of the spray gun's axis center. To characterize the variance parameter of the spray width, This is the flat-top index.

[0020] Furthermore, step 4 specifically involves:

[0021] Step 41: Generate an initial population using Latin hypercube sampling, substitute it into the evaluation function to calculate the target fitness vector, perform fast non-dominated sorting and crowding distance calculation, and extract the initial non-dominated solution set and store it in the Pareto archive.

[0022] Step 42: Enter the main loop iteration. For each individual, select guiding prey from the archive based on roulette, calculate the olfactory intensity by combining the dynamic density factor and Euclidean distance, and perform position updates for the digging or honey-gathering stage according to random probability, and then perform symbiotic mutation.

[0023] Step 43: At the end of each iteration, use probability... Triggering dynamic lens imaging reverse learning mutation, where the dynamic scaling factor For the first in the archives One solution Generate an inverted real image using the following formula: The generated inverse elite solutions are merged with the regular population, sorted using a non-dominated algorithm, and then inferior solutions are removed. The Pareto archive is then updated. In the formula, t represents the current iteration number. The maximum number of iterations, These are the upper and lower limits of the decision variable, respectively;

[0024] Step 44: Perform early stopping detection. When the early stopping condition is met, terminate the loop and output the Pareto optimal frontier solution set.

[0025] Furthermore, in step 44, early stopping detection employs a dual standard based on the normalized norm, specifically including:

[0026] Calculate the normalized relative rate of change of the average fitness vector between two adjacent generations of archive sets;

[0027] If the lens back-learning mechanism is not triggered in the previous generation, the stall counter is cleared when the normalized relative rate of change is greater than the conventional progress threshold.

[0028] If the lens back learning mechanism is triggered by the previous generation, the stall counter is cleared when the normalized relative rate of change is greater than the stringent progress threshold.

[0029] Otherwise, increment the stall counter;

[0030] The loop terminates when the stall counter exceeds the preset upper limit or the number of iterations reaches the maximum set value; among them, the stringent progress threshold is greater than the normal progress threshold.

[0031] Furthermore, it also includes step 6, calling the kinematic model of the selected painting robot for inverse kinematic verification.

[0032] The advantages of this invention compared to the prior art are:

[0033] By simultaneously solving the spray gun movement speed and the overlap rate of adjacent paths as the core decision variables of the multi-objective optimization algorithm, and adaptively calculating the actual scanning path spacing based on the dynamically generated overlap rate, the joint and coordinated control of the running cycle and the topology of the spraying path is realized, thereby improving the comprehensive optimization level of multiple core process indicators.

[0034] During the iterative optimization process, non-dominated elite solutions from the external Pareto archive are extracted as benchmarks. Through the principle of dynamic nonlinear optical mapping, high-quality reverse candidate solutions are generated on the symmetric side of the search space and added to the population. This forces the algorithm to escape local extremum traps and expands the exploration of potential feasible regions. It significantly enhances the algorithm's ability to escape local optimum traps under high-dimensional complex physical constraints, and also ensures that the obtained real Pareto front solution set has higher quality and a more uniform distribution.

[0035] Through a closed-loop optimization mechanism that integrates bivariate dynamic optimization and lens back learning, the system can perfectly adapt to the physical constraints of real robots, maximizing paint film thickness and minimizing motion impact without sagging. It has extremely high engineering feasibility and ultimately achieves efficient, precise, and smooth automated collaborative spraying in large, complex, multifaceted workpieces. Attached Figure Description

[0036] Figure 1 The flowchart shows a multi-objective spraying robot trajectory planning method based on lens imaging reverse learning.

[0037] Figure 2 This is a schematic diagram of the lens imaging principle.

[0038] Figure 3 Optimize flowcharts for multiple objectives;

[0039] Figure 4 This is a distribution map of the Pareto front for multiple objectives. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] This invention uses the spray gun moving speed and the overlap rate of adjacent paths as dual decision variables for dynamic optimization, breaking the limitation of fixed parameters in traditional spraying trajectory planning. For large polyhedral workpieces, it combines dual-station sliding rail collaboration with a flat-top Gaussian coating accumulation model, and introduces a lens back learning mechanism and a dual-standard early stopping strategy in the multi-objective optimization iteration, ultimately outputting realistic robot control commands that balance optimal time, maximize anti-sagging thickness, and ensure the smoothest movement of the robotic arm.

[0042] like Figure 1 As shown, the trajectory planning method for a multi-objective spraying robot based on lens imaging back learning includes:

[0043] Step 1: Initialization of the spraying operation environment and dual-station polyhedron parameters: Establish the geometric three-dimensional model of the target spraying workpiece and perform mesh generation; set the physical constraints of the spraying robot, including the maximum allowable speed and maximum allowable acceleration of the end effector; set the base transformation matrix of station one and station two.

[0044] First, a geometric 3D model of the target workpiece is established in the control system, extracting the workpiece's length, width, and height dimensions, and setting the physical constraints of the painting robot, including the maximum allowable speed and maximum allowable acceleration of the end effector. Then, addressing the issue of insufficient workspace for a single-base robot on large polyhedrons (such as a five-sided box), a dual-station collaborative operation environment with "robot plus slide rail" is initialized, setting the base transformation matrices for station one and station two.

[0045] In order to achieve accurate cumulative calculation of subsequent coating thickness, the control system performs mesh discretization on the five surfaces to be processed of the target workpiece: each surface is divided at equal intervals along the length and width directions with a preset mesh resolution, generating a regular mesh matrix covering the entire workpiece surface.

[0046] To accurately simulate the coating effect of real industrial spray guns and overcome the errors of traditional ideal Gaussian models, this invention introduces a flat-top Gaussian distribution model to characterize the cumulative coating thickness characteristics of the spray gun. The cross-sectional thickness distribution formula of the flat-top Gaussian distribution model is defined as follows: In this formula, Indicates the radius of the distance from the center of the spray pattern as The cumulative thickness of the coating at that location Indicates the maximum coating thickness at the center of the spray gun. Let Euclidean distance be the distance from the target point to the projection point of the spray gun's axis center. To characterize the variance parameter of the spray width, The flat-top index is used. This coating accumulation model effectively overcomes the edge attenuation error of the traditional ideal Gaussian distribution, providing a high-precision mathematical basis for subsequent thickness statistics of large-scale grid points.

[0047] Step 2: Trajectory topology generation based on bivariate dynamic coding: Set the decision variables of the optimization algorithm as two-dimensional vectors. ,in This represents the target's movement speed, Represents the overlap rate of adjacent spray paths; based on the current overlap rate. The actual distance D between adjacent scanning paths is dynamically calculated, and continuous spatial waypoints covering the workpiece surface are generated based on the distance D.

[0048] After setting up the basic environment, this invention breaks away from the limitations of fixed parameters in traditional trajectory planning and sets the decision variables of the optimization algorithm as two-dimensional vectors. ,in This represents the target's movement speed, This represents the overlap rate between adjacent spray paths. The control system determines the overlap rate based on the current overlap rate. The actual spacing between adjacent scan paths is dynamically calculated. ,in This represents the effective spray width of the spray gun. Based on this dynamic spacing, the system generates continuous spatial waypoints covering the workpiece surface.

[0049] When generating waypoints, the system employs a dual-station stage separation strategy: in the first stage, the robot at station one is responsible for generating paths for the front, left, and top half of the workpiece; in the second stage, the control rail switches to station two, which is responsible for generating paths for the rear, right, and top half of the workpiece. While generating each spatial waypoint, the system rigorously corrects the corresponding normal vector, ensuring it is perpendicular to the target machining surface and always points outwards from the workpiece. This guarantees the correct rotation of the spray gun and avoids collisions between the robotic arm and the workpiece during subsequent inverse kinematics calculations.

[0050] Step 3: Generation of end effector execution parameters and construction of multi-objective evaluation function: Based on spatial waypoints and target movement speed, the position, velocity and acceleration time series of the end effector are generated, and a three-dimensional multi-objective evaluation function for measuring the quality of the trajectory is constructed, including total spraying time, coating thickness optimization index and robotic arm motion smoothness evaluation index.

[0051] Based on the spatial waypoints and target movement speed generated in step 2, the control system first distinguishes between the spraying section and the transition section. For the spraying section where the normal vector is effective, the movement time interval is allocated according to the Euclidean distance and speed between adjacent waypoints; for the jump transition section that crosses surfaces, a fixed safe transition time is allocated. Subsequently, a fifth-order polynomial is used to smoothly interpolate the path, generating the position, velocity, and acceleration time series of the end effector, and simultaneously generating the trigger signal to control the spray gun switch. On this basis, a three-dimensional multi-objective evaluation function is constructed to measure the quality of the trajectory.

[0052] First objective function The total spraying time is calculated using the following formula: ,in The total running time for the robot to execute the spraying and transition trajectory. The fixed time for the slide rail to switch between two workstations.

[0053] Second objective function To optimize coating thickness and guide the algorithm in finding the solution that achieves the thickest possible coating without sagging, this invention sets the system to extract the cumulative thickness of all effective grid points on the five surfaces of the workpiece and minimize the negative of its average thickness. The calculation formula is as follows: ,in, The total number of valid grid points with a surface coating thickness greater than zero. The first result obtained after cumulative calculation using the flat-top Gaussian model The final paint film thickness at each effective grid point; the optimizer optimizes by making... Minimizing the thickness essentially maximizes the overall average thickness.

[0054] Third objective function The smoothness of robotic arm motion is evaluated by calculating the root mean square of the end effector jerk (i.e., the impact Jerk). ,in, This represents the total number of discrete sampling points in the trajectory time series. For the first The three-dimensional impact vector of the end effector at each time step; the smaller the value, the less vibration and flexible impact during the operation of the robotic arm.

[0055] Step 4: Perform multi-objective optimization based on lens back learning to determine the optimal frontier solution set.

[0056] To simultaneously optimize the three objective functions in a complex nonlinear space, this invention employs a multi-objective honey badger algorithm based on lens back-learning to perform global iterative optimization on a bivariate population containing velocity and overlap rate. The lens imaging principle diagram is shown below. Figure 2 As shown. The complete algorithm flow includes three core stages: population initialization, core position update and co-mutation, and dynamic lens back-learning, as follows. Figure 3 As shown, it specifically includes:

[0057] The first step is population initialization and evaluation. The control system sets the population size and maximum number of iterations. The upper and lower bounds of the physical constraints corresponding to the two variables Within the system, Latin Hypercube Sampling (LHS) is used to generate the initial population matrix. LHS ensures that the initial population uniformly and broadly covers the entire two-dimensional search space by equally dividing and independently arranging the decision variable space. The initial population is then substituted into the evaluation function in step 3 to calculate the target fitness vector, while simultaneously initializing the historical best position matrix for each individual. Subsequently, the system performs fast non-dominated sorting and crowding distance calculation: if an individual's performance on all objective functions is no worse than another compared individual, and it is strictly better on at least one objective, then the former is considered to dominate the latter. Based on this relationship, the system divides the population into multiple non-dominated levels, with the first level containing all currently non-dominated best individuals. To maintain the diversity of the solution set distribution in the target space and avoid solutions clustering in local areas, the system further calculates the crowding distance for individuals within the same level. For each objective function, individuals within the level are sorted in ascending order of fitness value. Then, the crowding distance for boundary individuals is set to infinity, and for individuals in the middle positions... The formula for summing the crowding distance is: In this formula, and They respectively represent the target Next to each other after sorting The second and first objective function values, and These represent the maximum and minimum fitness values ​​of the set at that level on the target, respectively.

[0058] After summing all target dimensions, the larger the distance value of an individual, the sparser the target space region it belongs to. Finally, based on the comprehensive selection principle of "the earlier the non-dominated level, the better, and the larger the crowding distance within the same level, the better", the initial non-dominated solution set is extracted and stored in the external Pareto archive.

[0059] After entering the main loop iteration phase, for each individual in the population, the system uses the roulette wheel algorithm to select the sparsest non-dominated solution from the current database based on crowding distance as the guiding prey target. The system incorporates a density factor that dynamically decays with the current iteration number. And the Euclidean distance between the individual and the guiding goal in the decision space. Calculate the intensity of smell The system then uses a preset random probability. Determine whether the current individual will perform the mining or honey-gathering phase:

[0060] when During the mining phase, the formula for updating the individual position is:

[0061] ;

[0062] when During the honey-collecting phase, the location update formula is: ;

[0063] In the above formula, This is the updated individual position vector. This is the mining capacity coefficient. Random positive and negative flags are used to control the search direction. All Random numbers within.

[0064] After the core update is completed, the system uses the historical best position of the current individual and another random individual in the population to perform cross-mutation with a certain probability to generate a co-existing candidate solution. If the fitness of the candidate solution is better than the original solution, it is replaced, and boundary pull-back correction is performed on all out-of-bounds solutions.

[0065] This is followed by the Lens-imaging Learning (LIL) mutation phase. To prevent high-dimensional constraints from causing the database solution set to get trapped in local optima, the system performs a probability-based check at the end of each update. Triggering the LIL mechanism. Unlike conventional algorithms that target mutations across the entire population, the LIL mechanism of this invention precisely targets elite solutions in the Pareto archive, and the lens focal length dynamically scales non-linearly with the number of iterations. The system defines a dynamic scaling factor. and the first in the archive One solution An object on one side of a convex lens generates a reversed real image on the symmetrical side through optical refraction: This formula shows that in the early stages of iteration Smaller size, wider refraction range for better global exploration; later iterations The size is increased so that the real image is closer to the origin to facilitate local convergence. The generated inverse elite solution is merged with the regular population, sorted by non-dominated order, and inferior solutions are removed, thus completing the update of the Pareto archive.

[0066] Finally, the system enters the dual-criteria early stopping detection stage based on the normalized norm. Since the reverse solution introduced by the LIL mechanism can cause a drastic jump in the average fitness of the archive set, thus deceiving the conventional stagnation detector, this invention implements a dual detection criterion based on the LIL trigger state. The system calculates the normalized relative change rate of the average fitness vector of the archive set between adjacent generations. After each generation's evaluation: if the LIL mechanism is not triggered in this generation, the system uses a conventional progress threshold for judgment. When the relative change rate is greater than this conventional threshold, it is considered to have achieved effective progress, and the stagnation counter is reset to zero. If the LIL mechanism is triggered in this generation, the system automatically switches to a stringent criterion. In this case, the relative change rate must be greater than a stringent progress threshold that is much higher than the conventional threshold before the stagnation counter is reset to zero. If no effective progress is achieved, the stagnation counter is incremented. Once the number of stagnant generations exceeds a preset upper limit or the number of iterations reaches a maximum set value, the loop terminates, and the final Pareto optimal frontier solution set is output, such as... Figure 4 As shown.

[0067] Step 5: Based on the actual production workshop's preferences for total spraying time, coating thickness optimization index, and robotic arm motion smoothness evaluation index, normalize the objective function values ​​and then sum them by weight. Select the best bivariate combination scheme based on the weighted score, and use the selected scheme to generate a spatial trajectory sequence and normal vector sequence with timestamps.

[0068] After obtaining the Pareto optimal solution set, the control system automatically selects the best bivariate combination scheme with the lowest score using a normalized weighted scoring method, based on the actual production workshop's preferences for efficiency, quality, and machine wear. Subsequently, the selected scheme is used to regenerate a spatial trajectory sequence and a normal vector sequence with precise timestamps.

[0069] Furthermore, to ensure the feasibility of this theoretical trajectory in the real physical world, the system calls the kinematic model of the selected painting robot (such as ABB IRB52) to perform inverse kinematics solutions. During the solution process, strict physical limit constraints are injected into each joint of the robotic arm, and the reference coordinate system is dynamically switched according to the workstation base transformation matrix set in step 1. If a singular point is encountered in the calculation, random joint perturbation is initiated or the robot returns to a safe starting posture for retry. Ultimately, it is ensured that all spatial waypoints are mapped to a continuous, smooth, and limit-free sequence of robot six-axis joint angle control commands, thereby seamlessly sending the optimization results to the industrial robot's underlying controller for execution.

[0070] This invention introduces a bivariate dynamic joint optimization strategy involving spray gun movement speed and adjacent path overlap rate, achieving adaptive and coordinated control of tool spacing and cycle time. This enables the control system to accurately reflect and dynamically resolve the contradiction between production efficiency and coating quality under complex polyhedral conditions, thereby improving the comprehensive optimization level of multiple core process indicators. Simultaneously, this invention employs a lens imaging back-learning mechanism in the multi-objective algorithm: during iterative optimization, dynamic nonlinear optical mapping is performed on elite solutions in the external Pareto archive, generating inverse real images on the symmetrical side of the search space, forcing the algorithm to expand the search range and fully explore unknown potential feasible regions; during the solution set update phase, high-quality inverse solutions are added to the population, achieving iterative evolution through survival of the fittest. This design not only significantly enhances the algorithm's ability to escape local optima traps under high-dimensional complex physical constraints but also ensures that the obtained true Pareto front solution set has higher quality and a more uniform distribution. Through a closed-loop optimization mechanism that integrates bivariate dynamic optimization and lens back learning, the system can perfectly adapt to the physical constraints of real robots, maximizing paint film thickness and minimizing motion impact without sagging. It has extremely high engineering feasibility and ultimately achieves efficient, precise, and smooth automated collaborative spraying in large, complex, multifaceted workpieces.

Claims

1. A trajectory planning method for a multi-objective spraying robot based on lens imaging reverse learning, characterized in that, include: Step 1: Initialization of the spraying operation environment and dual-station polyhedron parameters: Establish the geometric three-dimensional model of the target spraying workpiece and perform mesh generation; set the physical constraints of the spraying robot, including the maximum allowable speed and maximum allowable acceleration of the end effector; set the base transformation matrix of station one and station two. Step 2: Trajectory topology generation based on bivariate dynamic coding: Set the decision variables of the optimization algorithm as two-dimensional vectors. ,in This represents the target's movement speed, Represents the overlap rate of adjacent spray paths; based on the current overlap rate. Dynamically calculate the actual distance D between adjacent scanning paths, and generate continuous spatial waypoints covering the workpiece surface based on the distance D; Step 3: Generation of end effector execution parameters and construction of multi-objective evaluation function: Based on spatial waypoints and target movement speed, the position, velocity and acceleration time series of the end effector are generated, and a three-dimensional multi-objective evaluation function for measuring the quality of the trajectory is constructed, including total spraying time, coating thickness optimization index and robotic arm motion smoothness evaluation index. Step 4: Perform multi-objective optimization based on lens back learning to determine the optimal frontier solution set; Step 5: Based on the actual production workshop's preferences for total spraying time, coating thickness optimization index, and robotic arm motion smoothness evaluation index, normalize the objective function values ​​and then sum them by weight. Select the best bivariate combination scheme based on the weighted score, and use the selected scheme to generate a spatial trajectory sequence and normal vector sequence with timestamps.

2. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 1, characterized in that, ,in This refers to the effective spray width of the spray gun.

3. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 1, characterized in that, The target workpiece to be sprayed is a five-sided box; in step 2, when generating spatial waypoints, a dual-station stage separation strategy is adopted: in the first stage, the robot at station one is responsible for generating the paths for the front, left and top half of the workpiece. In the second stage, the control slide rail is switched to station two, which is responsible for generating the paths for the back, right, and top half of the workpiece.

4. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 3, characterized in that, Step 2 involves generating spatial waypoints by correcting the normal vectors corresponding to the waypoints, ensuring they are perpendicular to the target machining surface and always point outwards from the workpiece.

5. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 1, characterized in that, The specific steps for generating the position, velocity, and acceleration time series of the end effector based on spatial waypoints and target movement speed include: determining the spraying section and the cross-surface transition section; for the spraying section, allocating the motion time interval according to the Euclidean distance and velocity between two adjacent waypoints; for the cross-surface transition section, allocating a fixed safe transition time; and using a fifth-order polynomial to smoothly interpolate the path to generate the position, velocity, and acceleration time series of the end effector.

6. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 5, characterized in that, Total spraying time ,in The total running time for the robot to execute the spraying and transition trajectory. The fixed time for the slide rail to switch between two workstations; Coating thickness optimization index ,in, The total number of valid grid points with a surface coating thickness greater than zero. For the first The final paint film thickness for each effective grid point; Evaluation index of robotic arm motion smoothness ,in, This represents the total number of discrete sampling points in the trajectory time series. For the first The three-dimensional impact vector of the end effector at each time step.

7. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 6, characterized in that, Calculation of paint film thickness based on flat-top Gaussian distribution model: , Indicates the radius of the distance from the center of the spray pattern as The cumulative thickness of the coating at that location Indicates the maximum coating thickness at the center of the spray gun. Let Euclidean distance be the distance from the target point to the projection point of the spray gun's axis center. To characterize the variance parameter of the spray width, This is the flat-top index.

8. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 1, characterized in that, Step 4 is as follows: Step 41: Generate an initial population using Latin hypercube sampling, substitute it into the evaluation function to calculate the target fitness vector, perform fast non-dominated sorting and crowding distance calculation, and extract the initial non-dominated solution set and store it in the Pareto archive. Step 42: Enter the main loop iteration. For each individual, select guiding prey from the archive based on roulette, calculate the olfactory intensity by combining the dynamic density factor and Euclidean distance, and perform position updates for the digging or honey-gathering stage according to random probability, and then perform symbiotic mutation. Step 43: At the end of each iteration, use probability... Triggering dynamic lens imaging reverse learning mutation, where the dynamic scaling factor For the first in the archives One solution Generate an inverted real image using the following formula: The generated inverse elite solutions are merged with the regular population, sorted using a non-dominated algorithm, and then inferior solutions are removed. The Pareto archive is then updated. In the formula, t represents the current iteration number. The maximum number of iterations, These are the upper and lower limits of the decision variable, respectively; Step 44: Perform early stopping detection. When the early stopping condition is met, terminate the loop and output the Pareto optimal frontier solution set.

9. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 8, characterized in that, In step 44, early stopping detection employs a dual standard based on the normalized norm, specifically including: Calculate the normalized relative rate of change of the average fitness vector between two adjacent generations of archive sets; If the lens back-learning mechanism is not triggered in the previous generation, the stall counter is cleared when the normalized relative rate of change is greater than the conventional progress threshold. If the lens back learning mechanism is triggered by the previous generation, the stall counter is cleared when the normalized relative rate of change is greater than the stringent progress threshold. Otherwise, increment the stall counter; The loop terminates when the stall counter exceeds the preset upper limit or the number of iterations reaches the maximum set value; among them, the stringent progress threshold is greater than the normal progress threshold.

10. The multi-objective spraying robot trajectory planning method based on lens imaging reverse learning according to claim 1, characterized in that, It also includes step 6, calling the kinematic model of the selected painting robot for inverse kinematic verification.

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