Robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm

Abstract

The invention discloses a robot path planning method based on an adaptive fuzzy aggregation strategy and an improved decentralized search algorithm, and belongs to the technical field of robot path planning. The method comprises the following steps: (1) generating an initial path solution by using a diversified initialization method; (2) improving a decentralized search algorithm by adopting a self-adaptive fuzzy aggregation strategy, guiding local search to aggregate towards a potential optimal solution, and realizing the balance of global exploration and local search in combination with the global search capability of the decentralized search algorithm; (3) updating the reference set by adopting a Cauchy variation method, and selecting the reference set from the optimized path solution; (4) performing pairwise non-repeated combination on the path solutions in the reference set by utilizing a binary subset generation method to generate a binary subset; (5) introducing a linear weighting rule, and generating a plurality of new path solutions by using the binary subset; and iterating according to the steps (2) to (5) until stopping, and outputting an optimal path solution. The method has the advantages that the number of fuzzy clustering is dynamically determined, and local search is effectively guided to gather towards a potential optimal solution.

Description

Technical Field

[0001] The present invention relates to the technical field of robot path planning, and specifically provides a robot path planning method based on an adaptive fuzzy clustering strategy and an improved scatter search algorithm. Background Technique

[0002] With the rapid development of control technology and artificial intelligence, robots are increasingly widely used in industries, military, and daily life. As the core part of robot autonomous navigation, path planning performance directly depends on the design and optimization of algorithms. Path planning algorithms not only affect the movement efficiency and safety of robots, but also are crucial for their overall performance.

[0003] Heuristic intelligent search algorithms are an important research direction in path planning. Existing research has achieved certain results in search ability and fitness function design, but there are still problems such as insufficient search stability and imbalance between global and local searches. In addition, existing fitness functions mostly focus on path length, ignoring the balance of multiple factors and dimensional differences, resulting in the weakening of some factors in different scenarios or scales, which affects the algorithm effect. The scatter search algorithm (SS) is a novel heuristic algorithm mainly used for combinatorial optimization problems. It constructs new solutions through a systematic method, taking into account both search concentration and diversity, and performs well in fields such as production scheduling, but there is less research on its application in robot path planning.

[0004] To solve the above problems, the present invention proposes a robot path planning method based on an adaptive fuzzy clustering strategy and an improved scatter search algorithm. Summary of the Invention

[0005] The purpose of the present invention is to provide a robot path planning method based on an adaptive fuzzy clustering strategy and an improved scatter search algorithm to solve problems such as balancing global search and local search and improper design of fitness functions, which leads to the inability to find a better path solution.

[0006] To achieve the above purpose, the present invention provides the following technical solution: A robot path planning method based on an adaptive fuzzy clustering strategy and an improved scatter search algorithm, including the following steps:

[0007] S1. Diversified initialization method: used to generate an initial path solution;

[0008] S2. Add the adaptive fuzzy clustering strategy to the scatter search algorithm, and the specific steps are as follows:

[0009] a. Perform adaptive fuzzy clustering on the path solutions;

[0010] The steps of performing adaptive fuzzy clustering on the path solutions are:

[0011] (1) Determine the range of the number of clusters; (2) Initialize a membership degree U; (3) Calculate the cluster center C according to the membership degree U; (4) Calculate the objective function J; (5) Calculate the membership degree U again according to the cluster center C, and return to step 3, and keep looping until the end; (6) Calculate the silhouette coefficient value under this number of clusters; (7) Wait for the loop to end, and dynamically determine the number of clusters according to the silhouette coefficient value;

[0012] b. Path solution sorting

[0013] Sort the path solutions according to the designed new fitness function, and the designed fitness function is as follows:

[0014]

[0015] Where α, β, and γ are the weight coefficients of three evaluation indicators, n is the number of path nodes, Norm((·)) represents the normalization function, f(dis) represents the shortest path deviation, f(bra) represents the branch deviation, and f(len) represents the path length;

[0016] The first 50% gather towards the optimal path solution, and the remaining path solutions randomly update their positions;

[0017] The adaptive fuzzy clustering strategy balances the global and local search capabilities of the algorithm and further optimizes the existing path solutions;

[0018] S3. Update the reference set using the Cauchy mutation method

[0019] Use the Cauchy mutation operator to enhance the ability to jump out of the local optimum;

[0020] S4. Generate binary subsets

[0021] Use the binary subset generation method to combine the path solutions in the reference set pairwise without repetition to generate binary subsets for use in the solution combination method;

[0022] S5. Generate multiple different path solutions

[0023] Introduce a linear weighting rule in the solution combination method, and generate multiple different path solutions according to whether the two elements in the binary subset belong to the high-quality path solutions in the reference set;

[0024] Iterate according to the steps S2 to S5 until stopping, and output the optimal path solution.

[0025] Preferably, the step S1 is specifically:

[0026] Diversified initialization method: The initial path population is generated by the controlled frequency method. On the basis of randomly generating the necessary path nodes, a counting rule is introduced. When generating the necessary path nodes, counting is performed, and the probability of the appearance of the path nodes is inversely proportional to the counting frequency. Finally, on the premise of avoiding obstacles, the necessary nodes are connected to form a feasible path.

[0027] Preferably, the specific steps of step S2 are as follows:

[0028] S21. Randomly generate the membership degree U of the path solution;

[0029] S22. Calculate the clustering center C, and the calculation method is shown in formula (1):

[0030]

[0031] In the formula: x i represents the path solution, j represents the number of clusters, and i represents the number of path solutions;

[0032] S23. Calculate the objective function J, and the calculation method is shown in formula (2):

[0033]

[0034] In the formula: represents the membership degree of the current path solution, and d ij represents the distance between the current path solution i and the clustering center;

[0035] S24. Update the membership degree U, and the update method is shown in formula (3):

[0036]

[0037] In the formula: d ij represents the distance between the current path solution i and the clustering center j, and d ik represents the distance between the current path solution i and k clustering centers;

[0038] S25. Calculate the silhouette coefficient of the number of clusters: In the adaptive fuzzy clustering strategy, the silhouette coefficient is used as an index for evaluating the clustering effect. In the case of different numbers or scales of path solutions, the optimal number of clustering centers is also different. By calculating the average silhouette coefficient under different numbers of clusters, dynamically determining the optimal number of clustering centers can improve the clustering effect and thus improve the search efficiency; the calculation method of the silhouette coefficient is shown in formula (4):

[0039] S = max(S2…S k )

[0040]

[0041] where: k represents the range of the number of clusters, k > 1, n represents the number of path solutions, and the calculation method of S(i) is shown in formula (5):

[0042]

[0043] coh(i) represents the cohesion degree. For each path solution i, calculate its average distance from all other path solutions in the same cluster. The calculation method is shown in formula (6):

[0044]

[0045] where: n represents the number of path solutions in the same cluster;

[0046] sep(i) represents the separation degree. For each path solution i, find its nearest non-self cluster, and calculate the average distance between path solution i and all path solutions in that cluster. The calculation method is shown in formula (7):

[0047]

[0048] where: n represents the number of path solutions in its nearest non-self cluster;

[0049] S26. The adaptive fuzzy clustering strategy sorts the fitness values of path solutions, and the path solutions with the top 50% of the fitness function values are updated using formula (8):

[0050]

[0051] where: represents the optimal path solution in the solution set in the current iteration, represents the membership degree of the current path solution, and its value is the maximum value in the membership degrees, represents the current path solution to be updated, A + = A T (AA T ) -1 A is a 1×d-dimensional vector with values of randomly assigned 1 or -1, and L is a 1×d-dimensional vector all of 1, represents the updated path solution;

[0052] S27. The solutions with the bottom 50% of the fitness values are updated using formula (9):

[0053]

[0054] where: Q is a random number following a normal distribution, represents the worst path solution in the population in the current iteration, represents the current path solution to be updated, and i represents the sequence number of this path solution in the population, Indicates the updated path solution;

[0055] S28. Subsequently, perform solution optimization on the path solution, optimizing the path length from the starting point to the ending point found by the algorithm. By randomly replacing the necessary nodes in the path and retaining the connections of the necessary nodes close to the line connecting the starting point and the ending point to form a path solution.

[0056] Preferably, the specific steps of step S3 are as follows:

[0057] Refset represents the reference set, and its size is represented by b = b1 + b2 = |RefSet|; the Refset contains b1 high-quality solutions and b2 diverse solutions; select the best b1 solutions from the path solution population to construct the initial Refset, and add the best b1 solutions to the Refset and delete them from the path solution population; calculate the minimum Euclidean distance dmin(x) between each remaining solution x and the solutions y currently in the RefSet, select the individual with the maximum value among these minimum distances, add it to the Refset, and delete it from the path solution population, and then update the minimum distance; the calculation method of dmin(x) is as shown in formula (10):

[0058] d min (x) = min{d(x,y)}

[0059]

[0060] where d(x,y) is the Euclidean distance between x and y; perform mutation on the path solutions in the reference set through the Cauchy algorithm to enhance the ability of the algorithm to jump out of the local optimum; the calculation method is as shown in formula (11):

[0061] Mutation X(t) = X(t)(1 + tan(π(r - 0.5))) (11)

[0062] where: mutation X(t) is the position of the individual after Cauchy mutation, X(t) is the original position of the individual, and r is a random number within the interval [0,1].

[0063] Preferably, the specific steps of step S4 are as follows:

[0064] Use the binary subset generation method to combine the path solutions in the reference set pairwise, fully exploiting the potential of the reference set and laying a foundation for the subsequent improvement and global search of the path solution; binary combination is more efficient in calculation and can maintain sufficient diversity at the same time; high-dimensional combination may lead to a sharp increase in computational complexity, while binary has already generated potential new path solutions.

[0065] Preferably, the specific steps of step S5 are as follows:

[0066] In the decomposition method, a linear weighting rule is introduced to generate multiple different path solutions according to whether the two elements in the binary subset belong to the high-quality path solutions in the reference set;

[0067] For each binary subset, check whether both solutions belong to the high-quality path solutions, or one of them is high-quality and the other is a diverse solution; secondly, apply different linear weighting rules to generate multiple different path solutions; the specific method is as shown in formula (12)

[0068]

[0069] In the formula, r is a random number between 0 and 1. If x' and x" in the binary subset belong to the solutions in the high-quality ones, then apply C1 and C3 once and C2 twice to generate 4 solutions; if one of x' and x" belongs to the solutions in the high-quality ones, then apply C1, C2, and C3 once respectively to generate 3 solutions; if neither x' nor x" belongs to the solutions in the high-quality ones, then apply C2 once and randomly select C1 or C3 to generate two solutions.

[0070] Preferably, the shortest path deviation: The proposed shortest path deviation refers to the perpendicular distance between each node in the path and the line connecting the starting point and the ending point, which reflects the degree of difference between the actually selected path and the theoretically shortest path, and it reflects whether the path selection is close to the shortest path;

[0071] The calculation method of the shortest path deviation is shown in formula (14):

[0072]

[0073] In the formula: y i represents the ordinate, x i represents the abscissa, A = y n - y0, B = x n - x0, (x0, y0) represents the starting point, (x n , y n ) represents the ending point;

[0074] The branch deviation: It refers to the angular difference between the slope of the line connecting each node in the path to the starting point and the slope of the line connecting the starting point and the ending point. The main purpose of proposing the branch deviation is to measure the degree of deviation of the path from the straight line distance between the starting point and the ending point;

[0075] The calculation method of the branch deviation is shown in formula (15):

[0076]

[0077] In the formula: y i represents the ordinate, x i represents the abscissa, represents the slope of the line connecting the starting point and the ending point;

[0078] The path length is calculated using the Euclidean distance, which calculates the distances between all path nodes from the starting point to the ending point;

[0079] The calculation method of the shortest path deviation degree is shown in formula (16):

[0080]

[0081] In the formula: y i represents the ordinate, and x i represents the abscissa;

[0082] The calculation method of the normalization function is shown in formula (17):

[0083]

[0084] In the formula: f i represents the data to be normalized.

[0085] Compared with the prior art, the beneficial effects of the present invention are:

[0086] ① The present invention proposes a robot path planning method of an adaptive fuzzy aggregation strategy and an improved scatter search algorithm, and proposes an adaptive fuzzy aggregation strategy to be added to the scatter search algorithm, improving the traditional scatter search algorithm. By calculating the silhouette coefficient in different categories, the number of fuzzy clusters is dynamically determined, effectively guiding the local search to converge to the potential optimal solution, and at the same time combining the global search ability of the SS algorithm to balance the global search and local search abilities of the algorithm. This method can also be used in other optimization fields.

[0087] ② The present invention designs a new fitness function, proposes the concepts of the shortest path deviation degree and the branch deviation, and combines various factors such as the path length and smoothness. In addition, a normalization method is added to eliminate the differences between different dimensions among multiple factors and balance the contribution degrees among multiple factors, effectively accelerating the convergence speed of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 is a schematic framework diagram of the adaptive fuzzy aggregation strategy and the improved scatter search algorithm in the embodiment of the present invention.

[0089] Figure 2 is a comparison diagram of the optimal paths planned by the adaptive fuzzy aggregation strategy and the improved scatter search algorithm in the embodiment of the present invention and other algorithms. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0090] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. The experimental methods described in the following embodiments are all conventional methods unless otherwise specified.

[0091] Based on the problems mentioned in the background technology, a robot path planning method combining an adaptive fuzzy aggregation strategy and an improved scatter search algorithm is proposed. An adaptive fuzzy aggregation strategy is added to the scatter search algorithm to improve the traditional scatter search algorithm, which can effectively guide the local search to converge to the potential optimal solution. Combining the global search ability of the scatter search algorithm, the balance between global exploration and local search is achieved. A new fitness function is also designed, and the concepts of shortest path deviation and branch deviation are proposed. A normalization method is comprehensively added considering multiple factors to balance the contribution degrees between multiple factors, making the path shorter and smoother.

[0092] The technical solution of the present invention is as follows:

[0093] Step 1, Diversified initialization method: It is used to generate the initial path solutions, and its function is to provide a high-quality and diverse initial solution set for the algorithm, thus laying a foundation for the subsequent search and optimization process.

[0094] Step 2, An adaptive fuzzy aggregation strategy is added to the scatter search algorithm to improve the traditional scatter search algorithm. Specifically, based on the newly designed fitness function, the path solutions are evaluated and sorted. Among them, the top 50% of the path solutions will converge towards the current optimal solution direction to enhance the local search ability; while the remaining path solutions maintain the diversity of the population by randomly updating their positions. This adaptive fuzzy aggregation strategy effectively balances the global exploration and local exploitation capabilities of the algorithm.

[0095] Sort the path solutions according to the newly designed fitness function, and the designed fitness function is as follows:

[0096]

[0097] Where α, β, and γ are the weight coefficients of three evaluation indicators, n is the number of path nodes, Norm((·)) represents the normalization function, f(dis) represents the shortest path deviation, f(bra) represents the branch deviation, and f(len) represents the path length;

[0098] Step 3, Use the Cauchy mutation method to update the reference set. To further avoid the solutions in the reference set falling into the local optimum, the Cauchy mutation operator is used to enhance the ability to jump out of the local optimum.

[0099] Step 4: Use the binary subset generation method to construct subsets. The generation mechanism of binary subsets provides a diverse source of path solutions for the disassembly combination method, laying a solid foundation for the generation of new path solutions.

[0100] Step 5: Introduce a linear weighting rule for each binary subset solution in the disassembly combination method, and generate different path solutions according to the relationship between the elements in the binary subset and the high-quality solutions in the reference set, further increasing the diversity of path solutions and avoiding the generation of the same path solutions.

[0101] Iterate according to Steps 2 - 5 until stopping, and output the optimal path solution.

[0102] Among them, the specific content of the above steps is as follows:

[0103] The overall framework of the adaptive fuzzy aggregation strategy and the improved scatter search algorithm is as Figure 1 shown. It mainly includes five parts: diverse initialization method, adaptive fuzzy aggregation strategy, Cauchy mutation reference set update method, binary subset generation method, and disassembly combination method.

[0104] First, use the diverse initialization method. On the basis of randomly generating the necessary path nodes, introduce a counting rule to count when generating the necessary path nodes. The probability of the path node appearance is inversely proportional to the counting frequency. Finally, connect the necessary nodes to form a feasible path on the premise of avoiding obstacles.

[0105] Secondly, propose an adaptive fuzzy aggregation strategy and add it to the scatter search algorithm to improve the traditional scatter search algorithm and further optimize the initial path population.

[0106] The steps of the adaptive fuzzy clustering for path solutions are: (1) Determine the range of the number of clusters; (2) Initialize a membership degree U; (3) Calculate the cluster center C according to the membership degree U; (4) Calculate the objective function J; (5) Calculate the membership degree U again according to the cluster center C, and return to Step 3, and keep looping until the end; (6) Calculate the silhouette coefficient value under this number of clusters; (7) After the loop ends, dynamically determine the number of clusters according to the silhouette coefficient value;

[0107] The specific steps of the adaptive fuzzy aggregation strategy are:

[0108] 1. Randomly generate the membership degree U of path solutions

[0109] 2. Calculate the cluster center C, and the calculation method is shown in formula (1):

[0110]

[0111] In the formula: x iLet \(x\) represent the path solution, \(j\) represent the number of clusters, and \(i\) represent the number of path solutions.

[0112] 3. Calculate the objective function \(J\), and the calculation method is shown in formula (2):

[0113]

[0114] In the formula: \(u_{ij}\) represents the membership degree of the current path solution, and \(d_{ij}\) ij represents the distance between the current path solution \(i\) and the cluster center.

[0115] 4. Update the membership degree \(U\), and the update method is shown in formula (3):

[0116]

[0117] In the formula: \(d_{ij}\) ij represents the distance between the current path solution \(i\) and the cluster center \(j\), and \(d_{ik}\) ik represents the distance between the current path solution \(i\) and \(k\) cluster centers.

[0118] 5. Calculate the silhouette coefficient of the number of clusters: In the adaptive fuzzy clustering strategy, the silhouette coefficient is used as an index to evaluate the clustering effect. When the number or scale of path solutions is different, the optimal number of cluster centers is also different. By calculating the average silhouette coefficient under different numbers of clusters, dynamically determining the optimal number of cluster centers can improve the clustering effect and thus improve the search efficiency. The calculation method of the silhouette coefficient is shown in formula (4):

[0119] \(S=\max(S_2,\cdots,S_k)\) k )

[0120]

[0121] In the formula: \(k\) represents the range of the number of clusters, \(k > 1\), \(n\) represents the number of path solutions, and the calculation method of \(S(i)\) is shown in formula (5):

[0122]

[0123] \(coh(i)\) represents the cohesion. For each path solution \(i\), calculate the average distance between it and all other path solutions in the same cluster, and the calculation method is shown in formula (6):

[0124]

[0125] In the formula: \(n\) represents the number of path solutions in the same cluster.

[0126] \(sep(i)\) represents the separation. For each path solution \(i\), find the nearest non-self cluster, and calculate the average distance between the path solution \(i\) and all path solutions in that cluster, and the calculation method is shown in formula (7):

[0127]

[0128] In the formula: n represents the number of path solutions in its nearest non-self cluster.

[0129] 6. The adaptive fuzzy clustering strategy sorts the fitness values of the path solutions, and the path solutions with the top 50% of the fitness function values are updated using formula (8):

[0130]

[0131] In the formula: represents the optimal path solution in the solution set in the current iteration, represents the membership degree of the current path solution, and its value is the maximum value in the membership degrees, represents the path solution to be updated currently, A + = A T (AA T ) -1 A is a 1×d-dimensional vector with values of randomly assigned 1 or -1, and L is a 1×d-dimensional vector all of 1, represents the updated path solution.

[0132] 7. The solutions with the bottom 50% of the fitness values are updated using formula (9):

[0133]

[0134] In the formula: Q is a random number following a normal distribution, represents the worst path solution in the population in the current iteration, represents the path solution to be updated currently, and i represents the sequence number of this path solution in the population, represents the updated path solution.

[0135] 8. Subsequently, solution optimization is performed on the path solutions, which optimizes the path length from the starting point to the ending point found by the algorithm. By randomly replacing the necessary nodes in the path and retaining the connections of the necessary nodes close to the line connecting the starting point and the ending point, path solutions are formed.

[0136] Subsequently, solution optimization is performed on the path solutions, which optimizes the path length from the starting point to the ending point found by the algorithm. By randomly replacing the necessary nodes in the path and retaining the connections of the necessary nodes close to the line connecting the starting point and the ending point, path solutions are formed.

[0137] Next, the reference set is updated: The Cauchy mutation method is used to update the reference set. A part of high-quality path solutions and diverse path solutions are selected to jointly form the reference set. Refset represents the reference set, and its size is represented by b = b1 + b2 = |RefSet|. Refset contains b1 high-quality solutions and b2 diverse solutions. The best b1 solutions are selected from the path solution population to construct the initial Refset. These solutions are added to Refset and removed from the path solution population. Then, the minimum Euclidean distance dmin(x) between each remaining solution x and the solutions y currently in RefSet is calculated. The individual with the maximum value among these minimum distances is selected, added to Refset, and removed from the path solution population, and then the minimum distance is updated. The calculation method of dmin(x) is as shown in formula (10)

[0138] d min (x) = min{d(x, y)}

[0139]

[0140] where d(x, y) is the Euclidean distance between x and y. The path solutions in the reference set are mutated by the Cauchy algorithm to enhance the ability of the algorithm to jump out of the local optimum. The calculation method is as shown in formula (11)

[0141] Mutation X(t) = X(t)(1 + tan(π(r - 0.5))) (11)

[0142] where: mutation X(t) is the position of the individual after Cauchy mutation, X(t) is the original position of the individual, and r is a random number within the interval [0, 1].

[0143] Next, the pairwise non-repeating combinations of the path solutions in the reference set are generated using the binary subset generation method to generate binary subsets for use in the solution combination method. This binary subset generation mechanism provides a diverse source of path solutions for the solution combination method, thus laying a solid foundation for the generation of new path solutions. By introducing the binary subset generation strategy, the potential high-quality solution combinations in the reference set can be effectively mined. Finally, multiple new path solutions are generated using the solution combination method. A linear weighting rule is introduced in the solution combination method, and multiple different path solutions are generated according to whether the two elements in the binary subset belong to the high-quality path solutions in the reference set. The calculation method is as shown in formula (12)

[0144]

[0145] Where r is a random number between 0 and 1. If x' and x" in the binary subset belong to the solutions in high quality, then apply C1 and C3 once and C2 twice to generate 4 solutions; if one of x' and x" belongs to the solutions in high quality, then apply C1, C2, and C3 once respectively to generate 3 solutions; if neither x' nor x" belongs to the solutions in high quality, then apply C2 once and randomly select C1 or C3 to generate 2 solutions.

[0146] In addition, the shortest path deviation: The proposed shortest path deviation refers to the perpendicular distance between each node in the path and the line connecting the starting point and the ending point, which reflects the degree of difference between the actually selected path and the theoretically shortest path, and it reflects whether the path selection is close to the shortest path.

[0147] The calculation method of the shortest path deviation is shown in formula (14):

[0148]

[0149] In the formula: y i represents the ordinate, x i represents the abscissa, A = y n - y0, B = x n - x0, (x0, y0) represents the starting point, (x n , y n ) represents the ending point;

[0150] The branch deviation: It refers to the angular difference between the slope of the line connecting each node in the path to the starting point and the slope of the line connecting the starting point and the ending point. The main purpose of proposing the branch deviation is to measure the degree of deviation of the path from the straight line distance between the starting point and the ending point;

[0151] The calculation method of the branch deviation is shown in formula (15):

[0152]

[0153] In the formula: y i represents the ordinate, x i represents the abscissa, represents the slope of the line connecting the starting point and the ending point;

[0154] The path length adopts the Euclidean distance to calculate the distance between all path nodes from the starting point to the ending point;

[0155] The calculation method of the shortest path deviation is shown in formula (16):

[0156]

[0157] In the formula: y i represents the ordinate, x i represents the abscissa;

[0158] The calculation method of the normalization function is shown in Equation (17):

[0159]

[0160] In the formula: f i represents the data to be normalized.

[0161] The shortest path deviation: The proposed shortest path deviation refers to the perpendicular distance between each node in the path and the line connecting the starting point and the ending point, which reflects the degree of difference between the actually selected path and the theoretically shortest path, and it reflects whether the path selection is close to the shortest path;

[0162] The calculation method of the shortest path deviation is shown in Equation (14):

[0163]

[0164] In the formula: y i represents the ordinate, x i represents the abscissa, A = y n - y0, B = x n - x0, (x0, y0) represents the starting point, (x n , y n ) represents the ending point;

[0165] The branch deviation: It refers to the angular difference between the slope of the line connecting each node in the path to the starting point and the slope of the line connecting the starting point and the ending point. The main purpose of proposing the branch deviation is to measure the degree of deviation of the path from the straight line distance between the starting point and the ending point;

[0166] The calculation method of the branch deviation is shown in Equation (15):

[0167]

[0168] In the formula: y i represents the ordinate, x i represents the abscissa, represents the slope of the line connecting the starting point and the ending point;

[0169] The path length is calculated using the Euclidean distance to calculate the distance between all path nodes from the starting point to the ending point;

[0170] The calculation method of the shortest path deviation is shown in Equation (16):

[0171]

[0172] In the formula: y i represents the ordinate, x i represents the abscissa;

[0173] The calculation method of the normalization function is shown in Formula (17):

[0174]

[0175] In the formula: f i represents the data to be normalized.

[0176] To better illustrate the solution and actual effects of the present invention, the implementation of the present invention is described through specific examples. The algorithm is implemented using Matlab R2023b and compared with existing SSA algorithm, PSO algorithm, GA algorithm, PSO-GA algorithm, and Lis-PSO algorithm. Each algorithm runs 30 times and the average value is taken. The relevant parameter settings are as follows: the population size is 100, the inertia weight is 0.9, the learning factors c1 = c2 = 2, the proportion of discoverers is 0.1, the proportion of joiners is 0.9, the proportion of scouts is 0.2, the crossover probability is 0.9, and the mutation probability is 0.2.

[0177] The experimental results on a map scale of 100×100 are shown in Table 1. The experimental results show that the present invention achieves the best results in terms of indicators such as the shortest path, the longest path, and the average path length, which effectively proves the effectiveness of the algorithm. Among the average running times of each algorithm, the PSO-GA algorithm obtains the optimal result, and the GA algorithm is the worst. Compared with the SSA algorithm, PSO algorithm, GA algorithm, PSO-GA algorithm, Lis-PSO algorithm, and traditional SS algorithm, the average path of the present invention is improved by 16.75%, 16.69%, 10.58%, 19.09%, 17.54%, and 14.88% respectively.

[0178] Table 1 Path planning data of different algorithms for 100×100

[0179]

[0180] Figure 2 The best paths of each algorithm on a scale of 100×100 are given. It can be seen from this that, compared with the paths planned by other algorithms, the path planned by the present invention is smoother, has fewer inflection points, and is more in line with the connection line between the starting point and the ending point, which further verifies the effectiveness and robustness of the present invention.

[0181] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A robot path planning method based on an adaptive fuzzy aggregation strategy and an improved decentralized search algorithm, characterized in that: The following steps are involved: S1, Diversified initialization method: used to generate initial path solutions; S2, the adaptive fuzzy clustering strategy is added to the decentralized search algorithm. The specific steps are as follows: a. Perform adaptive fuzzy clustering on the path solution; The steps of performing adaptive fuzzy clustering of the path solution are: (1) Determine the number range of clusters; (2) Initialize a membership degree U; (3) Calculate the cluster center C based on the membership degree U; (4) Calculate the objective function J; (5) Return to calculate the membership degree U based on the cluster center C, return to step 3, and loop until the end; (6) Calculate the silhouette coefficient value under this number of clusters; (7) After the loop ends, dynamically determine the number of clusters based on the silhouette coefficient value; b. Path solution sorting The path solutions are sorted according to the designed new fitness function, and the designed fitness function is as follows: Among them, α, β, and γ are the weight coefficients of the three evaluation indicators, n is the number of path nodes, Norm((·)) represents the normalization function, f(dis) represents the shortest path deviation, f(bra) represents the branch deviation, and f(len) represents the path length; The first 50% are aggregated towards the optimal path solution, and the remaining path solutions randomly update their positions; The adaptive fuzzy clustering strategy balances the global and local search capabilities of the algorithm and further optimizes the existing path solutions; S3. Update the reference set using the Cauchy mutation method The Cauchy mutation operator is used to enhance the ability to escape from local optimality; S4. Generate binary subsets The path solutions in the reference set are combined pairwise without duplication using a binary subset generation method to generate binary subsets for use in the solution combination method; S5. Generate multiple different path solutions A linear weighting rule is introduced into the solution combination method to generate multiple different path solutions according to whether the two elements in the binary subset belong to the high-quality path solutions in the reference set. Iterate according to steps S2 to S5 until stopping, and output the optimal path solution.

2. The robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm according to claim 1, characterized in that: The step S1 specifically comprises: Diversified initialization method: The controlled frequency method is used to generate the initial path population. On the basis of randomly generating the necessary path nodes, a counting rule is introduced to count the necessary path nodes when they are generated. The probability of the path node appearing is inversely proportional to the counting frequency. Finally, the necessary nodes are connected to form a feasible path while ensuring that obstacles are avoided.

3. The robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm according to claim 1, characterized in that: The step S2 specifically comprises: S21, randomly generate the membership degree U of the path solution; S22. Calculate the cluster center C. The calculation method is shown in formula (1): Where: x i represents the path solution, j represents the number of clusters, and i represents the number of path solutions; S23. Calculate the objective function J. The calculation method is shown in formula (2): Where: Indicates the membership degree of the current path solution, d ij Indicates the distance between the current path solution i and the cluster center; S24, update the membership degree U, the updating method is shown in formula (3): Where: d ij Indicates the distance between the current path solution i and the cluster center j, d ik Indicates the distance between the current path solution i and the k cluster centers; S25. Calculate the silhouette coefficient of the number of clusters: In the adaptive fuzzy clustering strategy, the silhouette coefficient is used as an indicator for evaluating the clustering effect. When the number or size of path solutions is different, the number of optimal cluster centers is also different. By calculating the average silhouette coefficient under different numbers of clusters, dynamically determining the optimal number of cluster centers can improve the clustering effect and thus improve the search efficiency. The silhouette coefficient calculation method is shown in formula (4): Where: k represents the number range of clusters, k>1, n represents the number of path solutions, and the calculation method of S(i) is shown in formula (5): coh(i) represents cohesion. For each path solution i, the average distance between it and all other path solutions in the same cluster is calculated. The calculation method is shown in formula (6): Where: n represents the number of path solutions within the same cluster; sep(i) represents the separation degree. For each path solution i, find its nearest non-self cluster and calculate the average distance between path solution i and all path solutions in the cluster. The calculation method is shown in formula (7): Where: n represents the number of path solutions in the nearest non-self cluster; S26, the adaptive fuzzy aggregation strategy sorts the fitness values ​​of the path solutions, and the path solutions with the top 50% fitness function values ​​are updated using formula (8): Where: represents the optimal path solution in the solution set in the current iteration, Indicates the membership of the current path solution, and its value is the maximum value among the memberships. Indicates the path solution to be updated, A + =A T (AA T ) -1 A is a 1×d dimensional vector whose values ​​are randomly assigned 1 or -1, and L is a 1×d dimensional vector whose values ​​are all 1. represents the updated path solution; S27, the last 50% of the solutions of the fitness value are updated using formula (9): Where: Q is a random number that obeys the normal distribution, represents the worst path solution of the population in the current iteration, represents the current path solution to be updated, i represents the sequence number of the path solution in the population, represents the updated path solution; S28. Then, the path solution is optimized and the algorithm is optimized to find the path length from the starting point to the end point. The path solution is formed by randomly replacing the necessary nodes in the path and retaining the necessary nodes close to the line connecting the starting point and the end point.

4. The robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm according to claim 1, characterized in that: The step S3 specifically comprises: Refset represents a reference set, and its size is represented by b=b1+b2=|RefSet|; the Refset contains b1 high-quality solutions and b2 diverse solutions; the best b1 solutions are selected from the path solution population to construct the initial Refset, and the best b1 solutions are added to the Refset and deleted from the path solution population; the minimum Euclidean distance dmin(x) between each remaining solution x and the solution y currently in RefSet is calculated, the largest individual among these minimum distances is selected, added to Refset, deleted from the path solution population, and then the minimum distance is updated; the calculation method of dmin(x) is as shown in formula (10): Where d(x,y) is the Euclidean distance between x and y. The path solutions in the reference set are mutated by the Cauchy algorithm to enhance the ability of the algorithm to escape from the local optimum. The calculation method is as shown in formula (11): Mutation X(t)=X(t)(1+tan(π(r-0.5))) (11) Among them: mutation X(t) is the position of the individual after Cauchy mutation, X(t) is the original position of the individual, and r is a random number in the interval [0,1].

5. The robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm according to claim 1, characterized in that: The step S4 specifically comprises: The binary subset generation method is used to combine the path solutions in the reference set in pairs, fully exploring the potential of the reference set and laying the foundation for subsequent improvement of path solutions and global search; binary combination is more efficient in computation while maintaining sufficient diversity; high-dimensional combination may lead to a sharp increase in computational complexity, while binary has generated potential new path solutions.

6. The robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm according to claim 1, characterized in that: The step S5 specifically comprises: A linear weighting rule is introduced into the solution combination method to generate multiple different path solutions according to whether the two elements in the binary subset belong to the high-quality path solutions in the reference set; For each binary subset, check whether both solutions belong to high-quality path solutions, or whether one of them is high-quality and the other is a diversity solution; secondly, apply different linear weighting rules to generate multiple different path solutions; the specific method is as shown in formula (12) Where r is a random number between 0 and 1. If x' and x" are high-quality solutions in the binary subset, C1 and C3 are applied once and C2 is applied twice to generate 4 solutions. If one of x' and x" is a high-quality solution, C1, C2 and C3 are applied once respectively to generate 3 solutions. If neither x' nor x" is a high-quality solution, C2 is applied once and C1 or C3 is randomly selected to generate two solutions.

7. The robot path planning method based on adaptive fuzzy aggregation strategy and improved decentralized search algorithm according to claim 1, characterized in that: The shortest path deviation: The shortest path deviation proposed refers to the vertical distance between each node in the path and the line connecting the starting point to the end point, which reflects the difference between the actual selected path and the theoretical shortest path, and reflects whether the path selection is close to the shortest path; The shortest path deviation calculation method is shown in formula (14): Where: y i Indicates the vertical coordinate, x i Represents the horizontal axis, A = y n -y0,B=x n -x0, (x0, y0) indicates the starting point, (x n ,y n ) indicates the end point; The branch deviation refers to the angle difference between the slope of the line connecting each node to the starting point in the path and the slope of the line connecting the starting point to the end point. The purpose of proposing the branch deviation is mainly to measure the degree of deviation between the path and the straight line distance from the starting point to the end point. The branch deviation calculation method is shown in formula (15): Where: y i Indicates the vertical coordinate, x i represents the horizontal axis, Indicates the slope of the line connecting the starting point and the end point; The path length is calculated by using the Euclidean distance to calculate the distance between all path nodes from the starting point to the end point; The shortest path deviation calculation method is shown in formula (16): Where: y i Indicates the vertical coordinate, x i represents the horizontal axis; The normalization function calculation method is shown in formula (17): Where: f i Indicates data that needs to be normalized.

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