A moving track multi-objective optimization method of a powder extraction robot

Abstract

The application discloses a moving track multi-objective optimization method of a powder extraction robot, and solves the problem that the moving track of the powder extraction robot is not accurate enough when the powder extraction robot is extracting, and the technical solution points are as follows: S1: acquiring powder target area information, constructing a feasible area of extraction, and initializing an environment; S2: inputting the information after the initialization in the step S1 into a multi-objective optimization model; S3: solving the multi-objective optimization model in the step S2 by using an improved decomposition multi-objective evolutionary algorithm, optimizing the moving track of the extraction robot, and thus improving the extraction efficiency and accuracy.

Description

Technical Field

[0001] This invention belongs to the technical field of material separation devices, specifically referring to a multi-objective optimization method for the movement trajectory of a powder extraction robot. Background Technology

[0002] Powder extraction is a technique for extracting powdered intermediate products, widely used in petroleum, chemical, pharmaceutical, and biochemical fields. However, due to the interlacing and uneven boundaries of different compound layers, precise extraction of the target analyte is challenging. Manual extraction methods are typically used in laboratory trace component analysis, but these methods are slow and have low raw material utilization.

[0003] While using robots to replace manual labor can improve extraction efficiency, the current robots' movement trajectories are not precisely set during the extraction of powders. This leads to situations where some powder distribution areas are not extracted or some areas are extracted repeatedly. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a multi-objective optimization method for the movement trajectory of a powder extraction robot, solving the problem of unreasonable design of the robot's powder extraction trajectory, enabling it to search and optimize more accurately, thereby improving extraction efficiency and accuracy.

[0005] The objective of this invention is achieved as follows: a multi-objective optimization method for the movement trajectory of a powder extraction robot, comprising the following steps:

[0006] S1: Obtain information about the target area of ​​the powder, construct the extracted feasible area, and initialize the environment;

[0007] S2: Input the information initialized in step S1 into the multi-objective optimization model;

[0008] S3: Using an improved decomposition multi-objective evolutionary algorithm, the multi-objective optimization model in step S2 is solved to optimize and extract the robot's movement trajectory.

[0009] Further, in step S1, obtaining target region information and constructing the extracted feasible region includes the following steps: obtaining an image of the target powder region, performing image processing and analysis on the image; extracting the target powder region from the background region and performing binarization processing; calculating the area A of the target powder region; calculating the area of ​​the extracted feasible region based on the area A of the target powder region; and constructing the extracted feasible region based on the calculated area of ​​the extracted feasible region.

[0010] Further, in step S1, the environment initialization includes the following steps: First, establish a global coordinate system 0-XY, and initialize the range of x and y axis direction constraints in the target powder region to be extracted and the feasible region to be extracted in the coordinate system respectively; then, extract the N node positions of the trajectory, and form the initial node of the first walking trajectory in the target powder region to be extracted; finally, update the initial node of the first walking trajectory formed in the target powder region to be extracted in the feasible region.

[0011] Furthermore, in step S2, the initialized information is input into the multi-objective optimization model, specifically including the following steps:

[0012] First, based on the target area A and the purity requirement η, the area of ​​the feasible extraction region is calculated. Then, the initial environment and the distribution of trajectory nodes N are planned. Based on the area, purity, and trajectory nodes of the feasible region, a multi-objective optimization mathematical model for the powder extraction robot's movement trajectory is established.

[0013] minF(x)=(f1(x), f2(x), f3(x))

[0014] Where: f1(x) is the difference between the actual extraction purity after optimization of the movement trajectory and the target purity requirement η; f2(x) represents the sum of all movement segments; f3(x) represents the sum of the angles between two adjacent segments after the movement trajectory optimization.

[0015] Furthermore, the optimal objective function f1(x) representing the difference between the actual extracted purity and the target purity requirement η after optimization based on the movement trajectory is:

[0016]

[0017] The optimal objective function f2(x) for the sum of all the moving road segments is:

[0018]

[0019] The optimal objective function f3(x) for the sum of the angles between two adjacent segments of the movement trajectory is:

[0020]

[0021] Where: n represents the number of nodes in the updated first movement trajectory optimization, i is the i-th node, ξ is the diameter of the robot's suction nozzle, μ is the number of round trips by the robot in the map area, (x i y i ), (x i+1 y i+1 ) represents the movement trajectory node P i P i+1 Coordinates of |Pi P i+1 |For P i P i+1 The length of the trajectory between; θ i For the trajectory in P i The angle between two adjacent road segments at a point.

[0022] Further, in step S3, the improved multi-objective evolutionary algorithm based on decomposition includes the following steps:

[0023] Step S301: Initialize the positions of the initially extracted movement trajectory nodes; then, update the nodes and optimize the node sequence.

[0024] Step S302: Decompose the target space and set the weight vector of any j-th subproblem as... in The weight of the i-th objective function. For the weight vector of each subproblem, find the T nearest vectors according to the neighborhood size set in step S301, i.e., neighborhood B(j) = {λ j1 ,...,λ jT The Chebyshev function is improved to calculate the composite objective function of node x in the j-th subproblem: then, a normalization operation is performed;

[0025] Step S303: Use a probability model to model each decomposed weight vector in step S302, and randomly sample to obtain a new solution x′;

[0026] Step S304: For each index r∈B(j), calculate the synthesized objective function value of x′ obtained from the sampling in step S303, if g tch (x′|λ r , z * w * )≤g tch (x r |λ r , z * w * Then x r Replaced by x′, F(x) r )=F(x);

[0027] Step S305: Terminate iteration: When the current iteration number g_en = the maximum iteration number g enamx If the value is not found, the calculation stops; otherwise, g... en =g en +1, return to step S303;

[0028] Step S306: Output the target value {F(x)} 1), ..., F(x) N )}, the corresponding optimal solution {x 1 , ..., x N}; Set the number of round trips for extraction, μ.

[0029] Further, in step S301, the node update specifically involves: sampling N more complete initial node sequences in the target powder extraction area, ultimately forming N updated nodes for the initial walking trajectory, denoted as path = {P1, ..., P...} N}, where x = P1, ..., P N A sequence of discrete trajectory points;

[0030] The optimization of the node sequence is represented as: x = x1, x2, ..., x n Initial iteration count g en =0, set the maximum number of iterations g enmax Population size N is the number of subproblems; Population is randomly initialized using pop = (x 1 ,....x N That is, N sequences and a reference point; set a set of weight vectors λ. 1 ,...,λ N The neighborhood size T of the subproblem.

[0031] Further, in step S302, the improved Chebyshev function is:

[0032]

[0033] St x∈Ω

[0034] Where m is the number of objectives, Ω is the decision space, and the function f i Z is the i-th objective function. * = [z1 * ,,,,,z m * ] T w * =[w1 * w m * ] T These serve as the best and worst reference points.

[0035] Further, in step S306, within the feasible region, based on the initial extracted movement trajectory formed by the optimal solution, and using the robot's diameter ξ as a reference, the extraction round trip count μ is set:

[0036] The outstanding and beneficial technical effects of this invention compared to the prior art are as follows: This invention proposes a multi-objective optimization method for the movement trajectory of a powder extraction robot. It adopts an improved decomposition multi-objective evolutionary algorithm to achieve accurate search and optimization of the movement trajectory in the powder region, thereby improving the accuracy and purity of powder extraction. This enables the powder robot to perform fine operations in complex environments, reduces the difficulty of operation for operators, and reduces production costs. Attached Figure Description

[0037] Figure 1 This is a flowchart of the method for optimizing the movement trajectory of the powder extraction robot of the present invention.

[0038] Figure 2 This is a system structure diagram of the multi-objective optimization device for the movement trajectory of the powder extraction robot provided in this embodiment of the invention;

[0039] Figure 3 This is a comparison of the results of solving a powder extraction robot trajectory optimization method (MOEA / D-EDA-MM) and the MOEA / D,NSGA-II method according to an embodiment of the present invention.

[0040] Figure 4 This is a diagram of the reciprocating movement trajectory of a powder extraction robot provided in an embodiment of the present invention;

[0041] Figure 5 This is a schematic diagram of the image processing and path planning section (recognition device) provided in an embodiment of the present invention. Detailed Implementation

[0042] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of this invention.

[0043] This embodiment provides a multi-objective optimization method for the movement trajectory of a powder extraction robot, including the following steps:

[0044] S1: Obtain information about the target area of ​​the powder, construct the extracted feasible area, and initialize the environment;

[0045] The process of acquiring information about the target powder region and constructing a feasible extraction region involves transmitting images captured by a camera on a powder extraction robot to a processor. The processor performs image processing and analysis on the basic information of the target powder region. The processed image is then segmented to extract the target powder region from the background. Binarization is performed to obtain a binary contour edge image of the target powder region. The binary image is then rasterized, retaining the location information of each pixel: pixels in the target region are assigned a value of 1, and pixels in the background region are assigned a value of 0, resulting in a binary black-and-white raster map. The area of ​​the target powder region, A, is calculated by traversing the entire binary raster map using pixel area analysis. Based on purity requirements, the area of ​​the feasible extraction region is calculated by converting the area of ​​the target powder region A to the area in the raster map. Finally, based on the calculated area of ​​the feasible extraction region, the pixel width of the target powder region is expanded. A threshold is set to generate a feasible boundary for robot extraction, thus constructing a feasible extraction region. Regions larger than the threshold are considered infeasible extraction regions.

[0046] The specific steps for environment initialization are as follows:

[0047] Establish a global coordinate system 0-XY: Initialize the range of x-axis constraints in the target powder region to be extracted and the feasible region to be extracted within the coordinate system. min and x max The range of the y-axis direction constraint y min and y max Extract the positions of N nodes of the trajectory. The N node positions of the movement trajectory during environment initialization include:

[0048] P s Start, proceed along the y-axis until the same side of the y-axis is reached. max The optimization of the robot's initial walking trajectory is achieved by adjusting the starting point P. s and the endpoint on the same side, i.e., y max Connect the points with a straight line, and this straight line is the main line segment; first, in the target powder area to be extracted, use (x min y max Starting from the main line segment, the boundary of the target area of ​​the powdery substance is divided into several sub-segments. The intersection of the main line segment and the sub-segment becomes a node. Each sub-segment and the main line segment form the vertex of the sub-segment area, forming the initial node of the first walking trajectory.

[0049] Secondly, within the feasible area, update the initial nodes of the first walking trajectory formed in the target powdery material region to be extracted: sequentially construct sampling regions in the sub-segment regions between two adjacent initial nodes, and randomly sample and update N nodes of the first walking trajectory, represented as: path={P1,...,P N}, where x = P1, ..., P N Let x be a sequence of discrete trajectory points, and let x be the independent variable in the trajectory optimization problem. The goal is to find an optimal sequence of x that optimizes the multi-objective function of the trajectory.

[0050] S2: Input the information initialized in step S1 into the multi-objective optimization model; specifically, this includes the following steps:

[0051] Based on the target area A and the purity requirement η, the area of ​​the feasible extraction region is calculated. Then, the initial environment and distribution of trajectory nodes N for the entire problem are planned again. Based on these areas, purity, and trajectory nodes, the mathematical model function to be established is analyzed. Specifically, the multi-objective optimization mathematical model F(x) for establishing the movement trajectory of the powder extraction robot is:

[0052] minF(x)=(f1(x), f2(x), f3(x))

[0053] Where: f1(x) is the difference between the actual extraction purity after optimization of the movement trajectory and the target purity requirement η, that is, the smaller f1(x) is, the more accurate the actual extraction purity of the robot; f2(x) represents the sum of all movement segments, that is, the smaller f2(x) is, the faster the robot extraction speed; f3(x) represents the sum of the angles between two adjacent segments after the movement trajectory is optimized, that is, the smaller f3(x) is, the larger the angle between two adjacent segments at the node, and the smoother the route;

[0054] The optimal objective function f1(x) for the difference between the actual extracted purity of the movement trajectory and the target purity requirement η is:

[0055]

[0056] The optimal objective function f2(x) for the sum of the movement trajectory segments is:

[0057]

[0058] The optimal objective function f3(x) for the sum of the angles between two adjacent segments of the movement trajectory is:

[0059]

[0060] Where: n represents the number of nodes in the updated first movement trajectory optimization, i represents the i-th node, ξ represents the diameter of the robot nozzle, μ represents the number of round trips to the robot map area, (x i y i ), (x i+1 y i+1 ) represents the movement trajectory node P i P i+1 Coordinates of |Pi P i+1 | indicates that P is one of them. i P i+1 The length of the trajectory between; θ i Indicating the trajectory at point P i The angle between two adjacent road segments at a point.

[0061] S3: Using an improved decomposition multi-objective evolutionary algorithm, the multi-objective optimization model in step S2 is solved to optimize and extract the robot's movement trajectory.

[0062] An improved decomposition-based multi-objective evolutionary algorithm is used to optimize the initial movement trajectory of the extraction robot. This algorithm uses the decomposition-based multi-objective evolutionary algorithm (MOEA / D) as a framework and embeds a distribution estimation algorithm (EDA) to plan the optimal movement trajectory of the extraction robot. This includes: within the feasible area, using the improved decomposition-based multi-objective evolutionary algorithm to optimize the initial movement trajectory of the extraction robot; based on the range of constraints in the x-axis direction and the range of constraints in the y-axis direction, and using the robot's diameter ξ as a basis, setting the number of extraction round trips μ until all the target powder is extracted.

[0063] The improved decomposition-based multi-objective evolutionary algorithm specifically includes the following steps:

[0064] Step S301: First, initialize the updated first extracted movement trajectory node positions obtained in "N node positions of movement trajectory in environment initialization"; the intersection of the main line segment and the sub-road segment becomes a node, and the sub-road segment and the main line segment form the vertices of the sub-road segment region. These form the initial nodes of the first walking trajectory.

[0065] Secondly, based on the initial nodes formed in the previous stage, node updates are performed. A more comprehensive sequence of N initial nodes is obtained by sampling from the target powder extraction area, ultimately forming the updated N nodes for the initial walking trajectory, denoted as path = {P1, ..., P...}. N}, where x = P1, ..., P N The sequence is a discrete trajectory point. Then, using the method described in this application, the node sequence is optimized from the initial sequence obtained after these two stages. This is represented as x = x1, x2, ..., x... n Initial iteration count g en =0, set the maximum number of iterations g enmax Population size N is the number of subproblems; Population is randomly initialized: pop = (x 1 ,....x N That is, N sequences and a reference point; set a set of weight vectors λ. 1 ,...,λ N The neighborhood size T of the subproblem.

[0066] Step S302: Decompose the target space and set the weight vector of any j-th subproblem as... in The weight of the i-th objective function. For the weight vector of each subproblem, find the T nearest vectors according to the neighborhood size set in step S301, i.e., neighborhood B(j) = {λ j1 ,...,λ jT The Chebyshev function is improved to calculate the composite objective function of node x in the j-th subproblem: the composition method of each weight vector is changed so that the weight vectors that are uniformly distributed in the objective space can generate uniformly distributed search directions; normalization is performed to eliminate the influence of differences in the dimensions and orders of magnitude of the objective function on the optimization results.

[0067] The improved Chebyshev function is:

[0068]

[0069] St x∈Ω

[0070] Where m is the number of objectives, Ω is the decision space, and the function f i Z is the i-th objective function. * = [z1 * ,,,,,z m * ] T w * =[w1 * w m * ] T These serve as the best and worst reference points.

[0071] Step S303: Model each weight vector after decomposition in step S302 using a probability model, and randomly sample to obtain a new solution x′.

[0072] Step S304: According to the formula, for each index r∈B(j), calculate the synthesized objective function value of x′ obtained from the sampling in step S303;

[0073] If g tch (x′|λ r , z * w * )≤g tch (x r |λ r , z * w * Then x rReplaced by x′, F(x) r )=F(x).

[0074] Step S305: Terminate iteration: When the current iteration number g_en = maximum iteration number g enamx If the value is not found, then stop the calculation. Otherwise, g en =g en +1, return to step S303;

[0075] Step S306: Output the target value {F(x)} 1 ), ..., F(x) N The corresponding optimal solution {x} 1 , ..., x N};

[0076] The number of round trips μ is set, specifically including:

[0077] Within the feasible region, based on the initial extraction trajectory formed by the aforementioned optimal solution, and using the robot's diameter ξ as a reference, the extraction round trip count μ is set:

[0078]

[0079] The robot extracts coordinates (x) from the nodes. min y min Start extraction along the y-axis. If μ is an integer, extract from the starting point to the endpoint on the same side according to the optimal trajectory of the first movement, then move horizontally by ξ, and continue walking along the initial trajectory. Repeat this process μ times until extraction ends. If μ is not an integer, extract the integer part of μ a few times; then reposition and extract the outermost edge of the robot along the y-axis. max Starting from the initial point, extract the endpoint on this side according to the initial movement trajectory.

[0080] On the other hand, the present invention also includes a multi-objective optimization system for the movement trajectory of a powder extraction robot, the system comprising the following modules:

[0081] 1. Camera and image processing module M1: The extract to be extracted is placed on the extraction plate. The camera 1 collects data from the extraction plate and connects to the host computer 2 via a data cable. The captured image data is transmitted to the computer 2 in real time. The original image is converted to grayscale, then the image is enhanced, and then morphological filtering is performed. A BP neural network edge detection algorithm is established, which combines momentum method and adaptive learning rate to complete edge detection on the powder extraction plate 3 and obtain a binary contour edge image of the target area.

[0082] 2. The trajectory optimization module M2 extracts the edge feature points of the powder, rasterizes the binary image, establishes a multi-objective optimization function, and determines the optimal trajectory for the first extraction based on the improved decomposition multi-objective evolutionary algorithm. Then, based on the robot's diameter and the extraction area, it determines the number of round trips for the extraction robot. This module includes an initialization unit, a modeling unit, and a trajectory optimization unit. The initialization unit acquires basic information about the target powder area, constructs the feasible extraction area, and performs environmental initialization. The modeling unit uses the feasible area in the initialization unit to establish a multi-objective optimization mathematical model. The trajectory optimization unit uses the improved decomposition multi-objective evolutionary algorithm to solve the multi-objective optimization model established by the modeling unit and plans the optimal trajectory for the extraction robot.

[0083] 3. Milling module M3 that adapts to the height of the powder surface: The powder extraction robot moves along the trajectory obtained by module M2 and uses a milling device that adapts to the height of the powder surface to extract the extract. The robot can be controlled to move by the X, Y, and Z three-axis transmission mechanism.

[0084] 4. Judgment module M4 is used to determine whether the maximum number of extractions is met after taking the optimal movement trajectory obtained by module M2 as the execution path of the powder extraction robot. Then, it determines whether the optimal movement trajectory has completely extracted all the target powder. If so, it triggers the stop working module M5.

[0085] The following describes the specific implementation steps of the powder extraction robot, based on the multi-objective optimization method and system for its movement trajectory.

[0086] Step 1: Determine the feasible area for the powder extraction robot to extract:

[0087] Step 2: The solid material is placed on the powder extraction plate 3, and the image is captured using the camera 1;

[0088] Step 3: Camera 1 is connected to computer 2 via a data cable to transmit the captured image data to the computer in real time. The original image is converted to grayscale, then enhanced, and then morphological filtering is performed. The original image after image processing is segmented, the target region is extracted from the background region, and binarized to obtain the binarized contour edge image of the target region.

[0089] Step 4: Rasterize the area to be extracted, convert the binarized image into a raster map. After conversion, the location information of each pixel is still retained: assign the pixel of the target area in the image to 1 and the pixel of the background area to 0, and obtain a binary black and white raster map.

[0090] Step 5: Using the pixel-based area method, traverse the entire binary raster map to count the total number, perimeter, and edge dimensions of the target pixels in the image. After converting the number of target pixels according to the actual pixel representation, calculate the area A. The area of ​​the target color can then be obtained using the following formula:

[0091]

[0092] Where: f(x,y) is the pixel value of the target pixel;

[0093] Step 6: Based on the purity requirement η, calculate the area of ​​the feasible extraction region by converting the area A of the target powder region to the area in the grid map. Based on the calculated area of ​​the feasible extraction region, expand the target powder region by pixel width, set a threshold, generate the feasible boundary for robot extraction, and construct the feasible extraction region. Regions larger than the threshold are considered infeasible extraction regions.

[0094] Step 7: Initialize the N child nodes of the movement trajectory:

[0095] First, in the target powder area to be extracted, point (x min y min (P is the starting point) s Start, proceed along the y-axis until the same side of the y-axis is reached. max The optimization of the robot's initial movement trajectory is achieved by adjusting point P. s and the endpoint on the same side, i.e., y max The points are connected by a straight line, which is the main line segment. Then the boundary of the target powdery area is divided into several sub-segments. The intersection of the main line segment and the sub-segment becomes a node. Each sub-segment and the main line segment form the vertex of the sub-segment area, forming the initial node of the first extracted movement trajectory.

[0096] Secondly, within the feasible area, a sampling region is constructed, and N random sampling points are updated. Specifically, the sampling region is constructed using the sub-segment region between two adjacent initial nodes. During sampling, the parameter ∈ is the magnification factor of the random sampling region width. When the search operator searches between the two sub-nodes, according to the requirement of η, Δ∈ is the range of sampling region transformation. If the initially constructed sampling region cannot find a solution, the region will be magnified or shrunk according to ∈, extending to both sides to construct a new sampling region.

[0097] ∈ new =∈±Δ∈

[0098] When ∈ is very small, the random points generated by full-image sampling have a high probability of being distributed near the edge lines between child nodes. Assume that two of these child nodes are P. i and P jUsing these two nodes as reference points, the line connecting the two child nodes is used as the principal axis to construct the rectangular sampling region. Random sampling regions are constructed in both directions perpendicular to the principal axis. The four vertices P of the sampling region are obtained using the coordinate system relationship. il ,P ir ,P jl ,P jr Uniform sampling is performed on the constructed region.

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] l is P i and P j The Euclidean distance between them, l r It is a random selection of the length of l, ∈ new.r It is a random selection ∈ new The length of P, θ is the length of P i and P j The angle between them. It generates random sampling points;

[0105] l = ||P i -P j ||2

[0106] l r =l·rand,l r ∈[0,l]

[0107] ∈ new.r =∈ new ·rand,∈ new.r ∈[0,∈ new ]

[0108]

[0109] (Collect path nodes on the left side of the main axis)

[0110] (Collect path nodes on the right side of the main axis),

[0111] Random sampling updates and optimizations of movement trajectory nodes can be represented as path = {P} s ,P1,...,P N ,P t,}, where x=P1,...,P N Let x be a sequence of discrete path points, and let x be the independent variable in the trajectory optimization problem. The goal is to find an optimal sequence of x that makes the multi-objective function for extracting the trajectory optimal.

[0112] Reference Appendix Figure 4 As an embodiment of the present invention, the initialization of the movement trajectory can be expressed as starting from the starting point P. s To the target point P t A series of discrete points. Specifically, first, starting from the movement starting point P... s Centered on the target direction, nodes P are randomly generated within the sampling area selection window. i1 P i2 In step 7, a new node P1 is generated in a free grid. Then, with P1 as the center, moving towards the target point, node P2 is randomly generated based on step 7, and other nodes on the trajectory are generated sequentially until the target point P is reached. t ;

[0113] Step 8: Optimize the movement trajectory based on the improved decomposition multi-objective evolutionary algorithm, including the following steps:

[0114] 1. First, initialize P in the coordinate system. s P t And the positions of N nodes. The positions of all nodes are represented as x = x1, x2, ..., xn. n Randomly generate N sequences to initialize the population Pop = (x 1 ,....x N );

[0115] 2. Calculate the corresponding objective function F(x) 1 )...F(x N The objective function for extracting the robot's optimal trajectory is constructed as follows:

[0116] minF(x)=(f1(x),f2(x),f3(x))

[0117]

[0118]

[0119]

[0120] Where: n represents the number of nodes in the initial movement trajectory, i represents the i-th node, ξ represents the robot's diameter, and μ represents the number of round trips extracted by the robot; (x i ,y i ), (x i+1 ,y i+1 ) represents the movement trajectory node Pi ,P i+1 Coordinates of |P i ,P i+1 | indicates that P is one of them. i ,P i+1 The length of the trajectory between; θ i Indicates the trajectory at P i The angle between two adjacent road segments at a point.

[0121] f1(x) represents the difference between the actual extraction purity after trajectory optimization and the target purity requirement η. That is, the smaller f1(x) is, the more accurate the actual extraction purity of the robot. f2(x) represents the sum of all road segments after trajectory optimization. That is, the smaller f2(x) is, the faster the robot extraction speed. f3(x) represents the sum of the angles between two adjacent road segments in trajectory optimization. That is, the smaller f3(x) is, the larger the angle between two adjacent road segments at the node, and the smoother the route.

[0122] 3. Initialize the best and worst reference points Z * =[z1 * ,,,,,z m * ] T ,w * =[w1 * ,,,,,w m * ] T The parameters of the multi-objective evolutionary algorithm based on decomposition are as follows: The target space is decomposed based on the nodes of the updated movement trajectory. The algorithm sets the number of iterations, the population size N (i.e., the number of subproblems), and a set of weight vectors λ. 1 ,...,λ N The neighborhood size T of the subproblem; the initial number of iterations g. en =0, maximum number of iterations g enmax ;

[0123] 4. The weight vector for any given j-th subproblem is: in The weight of the i-th objective function. For each subproblem's weight vector, find the T nearest vectors to it, i.e., the neighborhood B(j) = {λ j1 ,...,λ jT The improved Chebyshev algorithm is used to compute the composite objective function of node x in the j-th subproblem, which is:

[0124]

[0125] St x∈Ω

[0126] Where z*=[z1 * z2* z3 * ] T It is a reference point. w*=[w1 * w2 * w3 * ] T It's the worst point. m is the number of objectives, Ω is the decision space, and the function f i It is the objective function of the i-th objective;

[0127] 5. Update the probability model and perform random sampling. Model each decomposed subproblem using a mixed Mallows probability model, and perform random sampling: First, set the current initial path x... K Set as center path According to the probability model Sampling is performed to obtain a new solution x′ and F(x′) is calculated;

[0128]

[0129] Where θ i To extend the parameters, D(x, x0) represents the distance function between x and x0, and ψ(θ) i The representation depends on the distance metric D and θ. i The normalization constant;

[0130] 6. F(x′) is used to update the reference point, and Pop is updated with x′. According to equation (1-12), for each index r∈B(j), if g tch (x′|λ r ,z * ,w * )≤g tch (x r |λ r ,z * ,w * ). So x r Replaced by x′, F(x) r )=F(x′);

[0131] 7. Terminate iteration: When the current iteration number g is satisfied. en = Maximum number of iterations g enmax If the value is not found, then stop the calculation. Otherwise, g en =g en +1, return to reselect the probability model;

[0132] 8. Output target value {F(x)} 1 ),...,F(x N )}, the corresponding optimal solution {x1 ,...,x N}

[0133] Step 9: Determine the number of round trips μ for robot extraction, specifically:

[0134] Within the feasible region, based on the optimal solution obtained above, the initial extraction trajectory is used to determine the number of extraction round trips μ, using the robot's diameter ξ as a reference.

[0135]

[0136] Extracting the coordinates (x) of the robot from the nodes of its initial movement trajectory. min y min Start extraction along the y-axis. If μ is an integer, extract from the starting point to the endpoint on the same side according to the optimal trajectory, then move horizontally by ξ, and continue walking along the optimal trajectory. Repeat this process μ times until extraction ends. If μ is not an integer, extract the integer part of μ a few times; then reposition and extract the outermost edge of the robot along the y-axis. max Starting from the optimal trajectory, extract the endpoint on this side.

[0137] To further verify the effectiveness of the method of the present invention, a simulation experiment was conducted in detail: Powdered material with irregular edge points was distributed within a 1600mm × 150mm working environment, such as... Figure 4 As shown. Given the irregularity of the simulation scene, the diverse distribution of the path's starting and ending points needs to be considered. The coordinate configuration of the starting and ending points of the test path is given, where the origin is located at the lower left corner of the map, the coordinate unit is mm, and the starting point is P. s (102, 203), same side y max Point P is the endpoint of the initial movement trajectory. t (1232, 132).

[0138] The table below shows the initial parameter settings of the multi-objective optimization algorithm. Each update expands the parameter θ = 6.480. At the same time, the algorithm is compared with the classic non-dominated sorting genetic algorithm (NGSA-II) and the decomposition-based multi-objective evolutionary algorithm (MOEA / D) to optimize three indicators: the accuracy of extraction purity f1(x), the sum of road segments f2(x), and the smoothness of the movement trajectory f3(x).

[0139]

[0140] Algorithm parameter configuration table

[0141] To intuitively illustrate the merits of the obtained Pareto non-dominated optimal solutions, Figure 3 It gives the following: Figure 4In a certain test of the path, the spatial distribution of the Pareto non-dominated solution set obtained by the method (MOEA / D-EDA-MM) and NGSA-II and MOEA / D methods described in this invention is the distribution of the solution set in the three-dimensional coordinate system of the extraction purity accuracy f1, the sum of road segments f2(x) and the smoothness of the movement trajectory f3(x).

[0142] In summary, this invention employs an improved decomposition-based multi-objective evolutionary algorithm to achieve precise search and optimized extraction trajectory for powdery material regions, thereby improving the accuracy and purity of powdery material extraction and reducing the workload for operators.

Claims

1. A multi-objective optimization method for the movement trajectory of a powder extraction robot, characterized in that, Includes the following steps: S1: Obtain information about the target area of ​​the powder, construct the extracted feasible area, and initialize the environment; S2: Input the information initialized in step S1 into the multi-objective optimization model; S3: Using an improved decomposition multi-objective evolutionary algorithm, the multi-objective optimization model in step S2 is solved to optimize and extract the robot's movement trajectory; In step S2, the initialized information is input into the multi-objective optimization model, which specifically includes the following steps: First, based on the target powder area A and purity requirements... The area of ​​the feasible extraction region is calculated; then, the initial environment and trajectory distribution nodes are planned again; based on the area, purity, and trajectory nodes of the feasible region, a multi-objective optimization mathematical model for the movement trajectory of the powder extraction robot is established: in: To determine the actual extracted purity and target purity requirements after optimization based on the movement trajectory. difference, This represents the sum of all the segments of the journey. This represents the sum of the angles between two adjacent road segments after the trajectory optimization; The actual extracted purity after optimization based on the movement trajectory and the target purity requirement The optimal objective function of the difference for: The optimal objective function for the sum of all the moving segments. for: The optimal objective function is the sum of the angles between two adjacent segments of the movement trajectory. for: in: This indicates the number of nodes optimized for the first movement trajectory after the update. For the first 1 node Robotic nozzle diameter This represents the number of round trips the robot makes in the map area. Movement trajectory node The coordinates; For one of them The length of the trajectory between them; For the trajectory in The angle between two adjacent road segments at a point.

2. The multi-objective optimization method for the movement trajectory of the powder extraction robot according to claim 1, characterized in that, In step S1, obtaining target region information and constructing the extracted feasible region includes the following steps: obtaining an image of the target powder region, performing image processing and analysis on the image; extracting the target powder region from the background region and performing binarization processing; and calculating the area A of the target powder region. Calculate the area of ​​the feasible extraction region based on the area A of the target powder region; Based on the calculated area of ​​the feasible region, construct the feasible region for extraction.

3. The multi-objective optimization method for the movement trajectory of the powder extraction robot according to claim 1, characterized in that, In step S1, the environment initialization includes the following steps: First, establish a global coordinate system 0-XY, and initialize the range of X and Y axis direction constraints in the target powder region to be extracted and the feasible region to be extracted in the coordinate system respectively; then, extract the N node positions of the trajectory, and form the initial node of the first walking trajectory in the target powder region to be extracted; finally, update the initial node of the first walking trajectory formed in the target powder region to be extracted in the feasible region.

4. The multi-objective optimization method for the movement trajectory of the powder extraction robot according to claim 1, characterized in that, In step S3, the improved decomposition-based multi-objective evolutionary algorithm includes the following steps: Step S301: Initialize the positions of the initially extracted movement trajectory nodes; then, update the nodes and optimize the node sequence. Step S302: Decompose the target space and set any first... The weight vector of each sub-problem is ,in For the first The weights of each objective function For each subproblem, the weight vector is determined based on the neighborhood size set in step S301. T The nearest vector, i.e., the neighborhood The Chebyshev function is improved to compute nodes. In the The objective function for the synthesis of the subproblems is then normalized. Step S303: Model each decomposed weight vector from step S302 using a probabilistic model, and obtain a new solution through random sampling. ; Step S304: For each indicator Calculate the samples obtained in step S303 The value of the synthesized objective function, if So quilt replace, ; = As the optimal reference point vector, = Let be the worst-case reference point vector; where, It is the number of targets; Step S305: Terminate iteration: When the current iteration count is satisfied. =Maximum number of iterations If the calculation stops, then stop; otherwise... Return to step S303; Step S306: Output target value The corresponding optimal solution N represents N sequences and a reference point, and the number of round trips for extraction is set. .

5. The multi-objective optimization method for the movement trajectory of the powder extraction robot according to claim 4, characterized in that, In step S301, the node update specifically involves: sampling N more complete initial node sequences in the target powder extraction area to ultimately form N updated nodes for the initial walking trajectory, denoted as... ,in A sequence of discrete trajectory points; Initial iteration count Set the maximum number of iterations. The group size N is the number of subproblems. Randomly initialize the population pop = ( That is, N sequences and a reference point; set a set of weight vectors. The neighborhood size of the subproblem.

6. The multi-objective optimization method for the movement trajectory of the powder extraction robot according to claim 4, characterized in that, In step S302, the improved Chebyshev function is: st Where Ω is the decision space, and the function is... It is the first One objective function.

7. The multi-objective optimization method for the movement trajectory of the powder extraction robot according to claim 4, characterized in that, In step S306, within the feasible region, based on the initially extracted movement trajectory formed by the optimal solution, the diameter of the robot nozzle is used as the reference. Based on: , and This defines the range of constraints along the x-axis.

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