Full-coverage path planning method

Abstract

The invention discloses a full-coverage path planning method. The method comprises the following steps: determining a grid map of an area to be subjected to path planning, and determining a transition probability matrix corresponding to the grid map; an initial population corresponding to the grid map is determined according to the transition probability matrix and preset selection strategies, and the preset selection strategies comprise a greedy selection strategy and a fuzzy selection strategy; determining a local distance contribution value of a target path in the initial population, executing a multi-modal disturbance operation on the target path according to the local distance contribution value, and generating a filial generation population corresponding to the initial population; and performing iterative optimization according to the initial population and the offspring population until an optimal path corresponding to the grid map is determined. According to the invention, technical problems of path redundancy, slow convergence speed and poor adaptability to a complex environment existing in a path planning algorithm in a complex obstacle scene in the prior art are solved.

Description

Technical Field

[0001] This application relates to the field of robot navigation and control technology, and more specifically, to a full-coverage path planning method. Background Technology

[0002] Grid-based full-coverage path planning is a key task in the field of robot navigation, aiming to ensure that mobile robots can efficiently and comprehensively traverse all traversable areas within a given environment, while avoiding obstacles and minimizing repetitive paths. This technology plays a crucial role in applications ranging from household cleaning to complex industrial and emergency situations, including robotic vacuum cleaners, agricultural spraying equipment, industrial inspection robots, and disaster relief robots.

[0003] Traditional path planning methods, such as zigzag, spiral, and grid decomposition, perform well in regular environments, but their efficiency and robustness face challenges when facing complex obstacles, unstructured terrain, or dynamic environments, such as path redundancy, inability to effectively handle disconnected areas, or insufficient real-time obstacle avoidance capabilities.

[0004] With the development of machine learning and intelligent optimization algorithms, methods such as evolutionary algorithms, ant colony optimization, genetic algorithms, and reinforcement learning have been introduced into path planning problems. Intelligent optimization algorithms, due to their global search capabilities and adaptive characteristics, demonstrate significant advantages in solving nonlinear, multi-peak, high-dimensional, and combinatorial optimization problems, effectively addressing the complexity and uncertainty in path planning. However, when dealing with large-scale, highly dynamic grid environments, they still suffer from high computational complexity, slow convergence speed, and insufficient adaptability to complex obstacles, especially in scenarios requiring a balance between shortest path, complete coverage, and energy efficiency.

[0005] In recent years, scholars and engineers have proposed various path planning algorithms, including integer linear programming, multi-objective evolutionary algorithms (such as MOEA / D), biologically motivated neural networks, ox-plowing movement patterns, minimum spanning tree algorithms, and hybrid strategies combining evolutionary algorithms and graph search techniques. These methods perform well in specific scenarios, but generally suffer from the following limitations: First, while integer linear programming algorithms can find optimal solutions, their computational cost is high, making them difficult to apply in real-time to large-scale raster maps. Second, fixed-pattern path planning methods struggle to handle dynamically changing environments, exhibiting low efficiency in path adjustment when encountering new obstacles. Third, some algorithms heavily rely on the regular structure of the map, performing poorly in handling irregular or dense obstacles, and are prone to getting trapped in local optima. Fourth, in areas such as multi-objective optimization and adaptation to complex terrain, some algorithms lack sufficient experimental validation, raising questions about their convergence and engineering practicality.

[0006] In related technologies, there are some full-coverage path planning methods for specific scenarios, such as full-coverage path planning for robotic vacuum cleaners in dynamic environments, efficient coverage flight paths for drones on electronic nautical charts, and cleaning path planning for specific aquaculture environments. While these methods provide solutions for specific application environments, they still need improvement in terms of algorithm efficiency, scenario adaptability, and handling of complex obstacles. For example, algorithms that rely on large-scale computing resources may be difficult to deploy on resource-constrained devices, and reliance on specific sensors (such as ultrasonic sensors) limits the reliability of the methods in high-dust and humid environments. In addition, the lack of consideration for multi-robot collaborative coverage mechanisms and the absence of dynamic obstacle response mechanisms are also significant shortcomings of path planning methods in related technologies.

[0007] Although the above-mentioned raster map full-coverage path planning method has made some progress, it still has problems such as low efficiency, insufficient adaptability and practical limitations when dealing with large-scale, highly dynamic and complex obstacle environments.

[0008] There is currently no effective solution to the above problems. Summary of the Invention

[0009] This application provides a full-coverage path planning method to at least solve the technical problems of path redundancy, slow convergence speed, and poor adaptability to complex environments in path planning algorithms in related technologies under complex obstacle scenarios.

[0010] According to one aspect of the embodiments of this application, a full-coverage path planning method is provided, comprising: determining a grid map of the area to be planned, and determining a transition probability matrix corresponding to the grid map, wherein the transition probability matrix is ​​used to reflect the movement probability between any two grids in the grid map; determining an initial population corresponding to the grid map based on the transition probability matrix and a preset selection strategy, wherein the preset selection strategy includes a greedy selection strategy and a fuzzy selection strategy, the greedy selection strategy constructs a path by selecting the locally optimal neighboring grid, and the fuzzy selection strategy constructs a path by randomly selecting grids based on the probability distribution in the transition probability matrix, and the initial population is used to represent the initial path set corresponding to the grid map; determining the local distance contribution value of the target path in the initial population, performing a multimodal perturbation operation on the target path based on the local distance contribution value, and generating a offspring population corresponding to the initial population, wherein the target path is any path in the initial population, and the local distance contribution value is used to reflect the degree of contribution of each node in the target path to the overall path length; and performing iterative optimization based on the initial population and the offspring population until the optimal path corresponding to the grid map is determined.

[0011] Optionally, determining the transition probability matrix corresponding to the grid map includes: determining the state matrix corresponding to the grid map, wherein the state matrix is ​​used to reflect the traffic status of each grid in the grid map; determining the shortest distance matrix between any two grids in the grid map based on the state matrix; and determining the transition probability matrix based on the shortest distance matrix.

[0012] Optionally, determining the shortest distance matrix between any two grids in the raster map based on the state matrix includes: converting the two-dimensional coordinates in the state matrix into a one-dimensional linear index to obtain the linear index result; determining the adjacency matrix corresponding to the raster map based on the state matrix and the linear index result, wherein the adjacency matrix is ​​used to reflect the connectivity between any two grids in the raster map; determining the shortest path length between any two grids after sequentially introducing intermediate grids based on the adjacency matrix; and determining the shortest distance matrix based on the shortest path length.

[0013] Optionally, determining the transition probability matrix based on the shortest distance matrix includes: determining a weight matrix between any two grids based on the shortest distance matrix and a first control parameter, wherein the first control parameter is used to control the degree of influence of the distance between any two grids on the transition probability; determining the sum of the weights of each row in the weight matrix to obtain the column vector of the weight matrix; and normalizing the weight matrix based on the column vector to obtain the transition probability matrix.

[0014] Optionally, the greedy selection strategy includes: determining a set of walkable graticles in the raster map; initializing a path sequence containing a first graticle and removing the first graticle from the set of walkable graticles to obtain a set of graticles to be visited, wherein the first graticle is any graticle in the set of walkable graticles; determining a third graticle from the set of graticles to be visited that has the highest transition probability with the second graticle based on the transition probability matrix, wherein the second graticle is the last graticle in the path sequence; adding the third graticle to the end of the path sequence and removing the third graticle from the set of graticles to be visited; repeating the graticle selection and path sequence optimization operations until all graticles in the set of graticles to be visited have been added to the path sequence to obtain an initial path corresponding to the raster map.

[0015] Optionally, the fuzzy selection strategy includes: randomly selecting a fourth grid corresponding to the second grid from the set of grids to be visited based on the probability distribution of the transition probability matrix; adding the fourth grid to the end of the path sequence and deleting the fourth grid from the set of grids to be visited; repeating the grid selection and path sequence optimization operations until all grids in the set of grids to be visited have been added to the path sequence to obtain the initial path corresponding to the grid map.

[0016] Optionally, the method further includes: determining a start grid and an end grid in the target path, and determining a preset start grid and a preset end grid corresponding to the target path; and fixing the start grid to the preset start grid and the end grid to the preset end grid when the start grid is different from the preset start grid and the end grid is different from the preset end grid.

[0017] Optionally, performing a multimodal perturbation operation on the target path based on the local distance contribution value includes: determining a target distance matrix corresponding to the target path, wherein the target distance matrix is ​​used to reflect the shortest path distance between any two grids in the target path; determining the local distance contribution value of the target grid based on the target distance matrix, wherein the target grid is any grid in the target path; determining a local distance contribution array corresponding to the target path based on the local distance contribution value; and performing a multimodal perturbation operation on the target path based on the local distance contribution array.

[0018] Optionally, a multimodal perturbation operation is performed on the target path based on the local distance contribution value to generate a sub-population corresponding to the initial population. This includes: determining the perturbation point and perturbation position index corresponding to the target path based on the local distance contribution array; performing a swap operation, a reversal operation, and an insertion operation on the target path based on the perturbation point, the perturbation position index, and a second control parameter, respectively, to obtain a first path, a second path, and a third path, wherein the second control parameter is used to adjust the focusing degree of the target path during the perturbation process; determining the first fitness value of the first path, the second path, and the third path through a fitness function, and determining the path sequence with the highest first fitness value as the sub-path corresponding to the target path in the initial population; and generating a sub-population corresponding to the initial population based on the sub-path.

[0019] Optionally, iterative optimization is performed based on the initial population and the offspring population, including: determining the first number of individuals in the initial population and determining the second number of individuals in the offspring population; determining the second fitness value of all individuals in the initial population and the offspring population through a fitness function, and determining the third number of individuals with the highest second fitness value as the next generation population, wherein the third number of individuals is half the number of the first and second individuals.

[0020] Optionally, the method further includes: determining a predecessor matrix based on the shortest distance matrix of the raster map, wherein the predecessor matrix is ​​used to reflect the node access order between any two rasters in the raster map; updating the optimal path based on the predecessor matrix and the path reconstruction function to obtain the reconstructed path.

[0021] In this embodiment, a grid map of the area to be planned is determined, and a transition probability matrix corresponding to the grid map is determined. The transition probability matrix reflects the movement probability between any two grid cells in the grid map. An initial population corresponding to the grid map is determined based on the transition probability matrix and a preset selection strategy. The preset selection strategy includes a greedy selection strategy and a fuzzy selection strategy. The greedy selection strategy constructs a path by selecting the locally optimal neighboring grid cells, while the fuzzy selection strategy randomly selects grid cells based on the probability distribution in the transition probability matrix. The initial population represents the initial set of paths corresponding to the grid map. The local distance contribution value of the target path in the initial population is determined, and a multimodal perturbation operation is performed on the target path based on the local distance contribution value. A progeny population corresponding to the initial population is generated, where the target path is any path in the initial population. The local distance contribution value is used to reflect the contribution of each node in the target path to the overall path length. Iterative optimization is performed based on the initial population and the progeny population until the optimal path corresponding to the grid map is determined. This achieves the goal of intelligently and efficiently solving the full-coverage path planning problem in complex grid environments. Thus, while ensuring the integrity and optimization of path coverage, it significantly improves the algorithm's convergence speed, reduces path redundancy, and enhances its adaptability to dynamic obstacles and irregular terrain. This solves the technical problems of path planning algorithms in related technologies, such as path redundancy, slow convergence speed, and poor adaptability to complex environments in complex obstacle scenarios. Attached Figure Description

[0022] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0023] Figure 1 It is a schematic diagram of a 4×5 grid map and its corresponding full-coverage path planning scheme;

[0024] Figure 2 This is a flowchart of a full-coverage path planning method according to an embodiment of this application;

[0025] Figure 3 This is a flowchart illustrating the algorithm implementation of full-coverage path planning according to an embodiment of this application;

[0026] Figure 4 This is a schematic diagram of map rasterization according to an embodiment of this application;

[0027] Figure 5 This is a schematic diagram of a two-dimensional coordinate to linear index conversion according to an embodiment of this application;

[0028] Figure 6This is a schematic diagram of an adjacency matrix according to an embodiment of this application;

[0029] Figure 7 This is a schematic diagram of a shortest distance matrix and its corresponding predecessor matrix according to an embodiment of this application;

[0030] Figure 8 This is a schematic diagram of a transition probability matrix according to an embodiment of this application;

[0031] Figure 9 This is a schematic diagram of an experimental setup for multiple grid maps according to an embodiment of this application;

[0032] Figure 10 This is a schematic diagram of the population evolution curve of a multi-grid map according to an embodiment of this application;

[0033] Figure 11 This is a schematic diagram of the full coverage path of a raster map according to an embodiment of this application;

[0034] Figure 12 This is a schematic diagram of the full coverage path of another raster map according to an embodiment of this application;

[0035] Figure 13 This is a schematic diagram of the full coverage path of a grid map according to an embodiment of this application;

[0036] Figure 14 This is a schematic diagram of a full-coverage path of a raster map according to an embodiment of this application. Detailed Implementation

[0037] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0038] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0039] First, some nouns or terms that appear in the explanation of the embodiments of this application shall be interpreted as follows:

[0040] Complete Coverage Path Planning (CCPP) refers to a planning technique that ensures a mobile robot can traverse all accessible areas within its work zone while avoiding obstacles and minimizing path repetition. It is applicable to scenarios such as cleaning robots, agricultural automation equipment, and area inspection.

[0041] Raster map: A two-dimensional representation of the physical environment divided into a series of square or rectangular grids, with each grid recording its corresponding terrain state (such as obstacles or open space).

[0042] Evolutionary Algorithm (EA): Global optimization algorithms inspired by biological evolution, including Genetic Algorithm (GA) and Ant Colony Optimization (ACO). They iteratively generate better solutions through operations such as selection, crossover, and mutation, and are suitable for solving complex optimization problems, such as robot path planning.

[0043] Floyd-Warshall Algorithm: A dynamic programming algorithm for calculating the shortest path between all pairs of nodes. It is applicable to weighted graphs and can be used even if the graph contains negative weight edges (but not negative weight cycles).

[0044] Roulette wheel selection: a selection mechanism in evolutionary algorithms that determines the probability of selection based on each individual's fitness value. Individuals with higher fitness values ​​have a higher probability of being selected, similar to spinning a roulette wheel on a gambling table.

[0045] Full-coverage path planning for a raster map refers to finding the shortest path that traverses all areas except obstacles in an N×M raster map where 0 represents empty space and 1 represents obstacles, given a specified start and end point. For example... Figure 1 As shown, (a) is a 4×5 grid map, where white grids represent open areas and gray grids represent obstacles; (b) is a full-coverage path planning scheme for the grid map, where "●" points are the starting points, "★" points are the ending points, and "→" lines are the shortest planned routes; usually, there is more than one shortest full-coverage path planning scheme for the same grid map, as shown in (c), which is another full-coverage path planning scheme for the grid map.

[0046] The full-coverage path planning problem on a raster map is essentially an extension of the generalized Traveling Salesman Problem (TSP). It requires traversing all reachable nodes and optimizing the total path length, with computational complexity increasing exponentially with map size. This is a typical NP-hard combinatorial optimization problem, its core challenge being to simultaneously satisfy full-area coverage, shortest path, and obstacle avoidance constraints. The mathematical model is as follows:

[0047] 1. Symbol definition.

[0048] 1) Raster map:

[0049] Raster map size: ;

[0050] Raster set: ;

[0051] Obstacle set: ;

[0052] Set of passable areas: There are a total of A passable grid.

[0053] 2) Path parameters:

[0054] starting point: ;

[0055] end: ;

[0056] Path sequence: ,in, Indicates the first The grid cell where the step is located.

[0057] 2. Decision variables.

[0058] 1) Path variables:

[0059] If and only if the robot's first Steps are located in the grid The value is 1 if it is true, and 0 otherwise.

[0060] if and only if the grid The value is 1 if the page has been visited, and 0 otherwise.

[0061] 2) Moving variables:

[0062] If and only if the robot moves from the grid Move to The The step time is 1.

[0063] 3. Objective function.

[0064] Minimize the total path length (i.e., the number of steps):

[0065]

[0066] in, express The set of adjacent passable grid cells (up, down, left, right), where T represents the total number of steps (path length).

[0067] 4. Constraints.

[0068] 1) Path start and end points:

[0069]

[0070]

[0071] in, This means the first step of the path must be located at the starting point. , This indicates that the last step of the path must be located at the endpoint. The variable representing the position of the first step of the path at the starting point is set to 1. This indicates that the first step of the path cannot be in any other grid. The variable representing the position of the last step in the path at the destination is set to 1. This indicates that the last step of the path cannot be in any other grid.

[0072] 2) Full area coverage:

[0073] Each passable grid is visited at least once, and the following conditions are met:

[0074]

[0075] in, This indicates that each accessible grid cell has been visited at least once; it also indicates that if a grid cell has been visited, there is at least one path variable at time t. The value is 1.

[0076] 3) Path continuity:

[0077] Each step can only move to one adjacent grid cell:

[0078]

[0079] The next position is determined by the current move:

[0080]

[0081] 4) Obstacle avoidance constraints:

[0082] The path does not pass through obstacles:

[0083]

[0084] 5) Eliminate sub-loops:

[0085] Introducing auxiliary variables Indicates the order of visits, preventing loops in the path that do not include the start / end point:

[0086]

[0087] Figure 2 This is a flowchart of a full-coverage path planning method according to an embodiment of this application, such as... Figure 2 As shown, the method includes the following steps:

[0088] Step S202: Determine the grid map of the area to be planned and determine the transition probability matrix corresponding to the grid map. The transition probability matrix is ​​used to reflect the movement probability between any two grids in the grid map.

[0089] Step S204: Determine the initial population corresponding to the grid map based on the transition probability matrix and the preset selection strategy. The preset selection strategy includes a greedy selection strategy and a fuzzy selection strategy. The greedy selection strategy constructs a path by selecting the locally optimal neighboring grid, while the fuzzy selection strategy constructs a path by randomly selecting grids based on the probability distribution in the transition probability matrix. The initial population is used to represent the initial path set corresponding to the grid map.

[0090] Step S206: Determine the local distance contribution value of the target path in the initial population, perform multimodal perturbation operation on the target path based on the local distance contribution value, and generate a offspring population corresponding to the initial population. The target path is any path in the initial population, and the local distance contribution value is used to reflect the degree of contribution of each node in the target path to the overall path length.

[0091] Step S208: Iterative optimization is performed based on the initial population and offspring population until the optimal path corresponding to the grid map is determined.

[0092] Through the above steps S202 to S208, the goal of intelligently and efficiently solving the full-coverage path planning problem in complex grid environments is achieved. This results in significantly improving the algorithm's convergence speed, reducing path redundancy, and enhancing its adaptability to dynamic obstacles and irregular terrain while ensuring the integrity and optimization of path coverage. In turn, it solves the technical problems of path redundancy, slow convergence speed, and poor adaptability to complex environments in path planning algorithms in related technologies under complex obstacle scenarios.

[0093] Figure 3 This is a flowchart illustrating an algorithm implementation for full-coverage path planning according to an embodiment of this application, as shown below. Figure 3 As shown, the process first loads data to initialize the model and constructs an adjacency matrix. The shortest distance matrix and predecessor matrix are then calculated using the Floyd algorithm. Next, the transition probability matrix is ​​calculated. Based on this matrix, an initial population is generated using a "greedy + roulette wheel" dual-mode strategy. Individuals in the population undergo start-end point repair and are evaluated using an objective function. Then, a loop is entered, selecting the highest-cost node based on local distance contribution. Three perturbation operations—exchange, reversal, and insertion—are performed to generate a child population. The child population is then repaired, and the objective function is evaluated. Further, after merging the parent and child populations, an elitist strategy is used to retain the optimal group. This process is iteratively updated until a termination condition is met, at which point the optimal individual (optimal path) is output. Finally, the optimal path is reconstructed based on the predecessor matrix, restoring it to a practically communicable grid sequence, resulting in a fully covered path that covers all reachable areas and has the shortest total steps. The following section combines... Figure 3 The algorithm implementation logic described above provides a detailed explanation of steps S202 to S208.

[0094] In step S202 above, the main task is to convert the physical environment into a mathematical model through gridding to form a grid map. Then, the transition probability matrix is ​​calculated based on the shortest distance between each grid, which reflects the tendency to move from any grid to another. This matrix is ​​used to guide the robot to prioritize grids that are closer when planning a path, while also considering the connectivity of the entire map and the distribution of obstacles, thereby providing a probabilistic search guide for subsequent path planning.

[0095] In this embodiment, determining the transition probability matrix corresponding to the raster map includes: determining the state matrix corresponding to the raster map, wherein the state matrix reflects the traffic status of each raster in the raster map; determining the shortest distance matrix between any two raster maps based on the state matrix; and determining the transition probability matrix based on the shortest distance matrix. Specifically, determining the shortest distance matrix between any two raster maps based on the state matrix includes: converting the two-dimensional coordinates in the state matrix into a one-dimensional linear index to obtain a linear index result; determining the adjacency matrix corresponding to the raster map based on the state matrix and the linear index result, wherein the adjacency matrix reflects the connectivity between any two raster maps; determining the shortest path length between any two raster maps after sequentially introducing intermediate raster maps based on the adjacency matrix; and determining the shortest distance matrix based on the shortest path length. That is, this implementation process includes key operations such as map rasterization, linear index conversion, constructing the adjacency matrix, calculating the shortest distance matrix, and generating the transition probability matrix. The specific process analysis is as follows:

[0096] 1. Map rasterization.

[0097] Map rasterization (0 or 1) is the process of discretizing a continuous environment into a uniform grid. Each grid cell is binary (0 represents a passable area, 1 represents an obstacle) to represent the spatial state, suitable for scenarios such as robot navigation and game AI. By dividing the physical space into equal-sized units and combining sensor data or preset information to mark obstacle positions, a structured two-dimensional matrix is ​​generated. This method simplifies the calculation of path planning and obstacle avoidance algorithms, but a trade-off must be made between grid resolution (accuracy and computational cost) and the efficiency of dynamic environment updates. It is a general basic model for solving problems such as full coverage traversal and shortest path search for mobile robots.

[0098] Resolution selection: Set the physical size of each grid according to application requirements. The higher the resolution, the more detailed the map, but the greater the computational load.

[0099] Map size calculation: If the actual area is W×H meters, then the raster map dimensions are:

[0100]

[0101] like Figure 4 As shown, (a) is a 4×5 grid map. The state matrix of the grid map is constructed based on whether there are obstacles in the grid. As shown in (b), the specific expression is as follows:

[0102]

[0103] in, Representation matrix The Line number Column elements, , .

[0104] Based on the above formula, the state matrix of the raster map is calculated as follows:

[0105]

[0106] 2. Linear index conversion.

[0107] like Figure 5 As shown, in the raster map, the two-dimensional subscripts (rows) in the state matrix (as shown in (a)) are... and column Convert to linear index (one-dimensional numbering) The purpose of (b) is to map two-dimensional coordinates to a one-dimensional array or list for storage and access, as shown in (b).

[0108] 1) For forward transformation (two-dimensional subscript to linear index):

[0109] Assuming the size of the raster map is (common OK, (column), row and column indices start from 1 (i.e.) , Then the linear index The calculation method is as follows:

[0110] Row priority:

[0111]

[0112] For example, in In the grid, coordinates The linear index is: .

[0113] Column-major order (all subsequent experimental calculations in this application embodiment will be performed using column-major order as an example):

[0114]

[0115] For example, in In the grid, coordinates The linear index is: .

[0116] 2) For reverse conversion (linear index to two-dimensional subscript):

[0117] Row priority:

[0118]

[0119] For example, when , hour: .

[0120] Column-first:

[0121]

[0122] For example, when , hour: .

[0123] 3. Construct the adjacency matrix.

[0124] For a A raster map, with two-dimensional subscripts for each grid cell. Convert to linear index ,in , The corresponding adjacency matrix is , used to represent the connectivity between grid cells (four-neighborhood), whose elements satisfy:

[0125]

[0126] in, Indicates by index Decoded row and column numbers:

[0127]

[0128] Figure 4 middle The state matrix (b) of the raster map can be obtained from the above calculation. The adjacency matrix, such as Figure 6 As shown, where for .

[0129] 4. Calculate the shortest distance matrix between any two grid cells using the Floyd algorithm.

[0130] The Floyd algorithm is used to find the shortest path between all pairs of nodes in a weighted graph. It supports both directed and undirected graphs containing negative weight edges (but no negative weight cycles). Its core objective is to find the shortest path between every pair of nodes in a raster map. Find the shortest path length; the core idea is based on dynamic programming, gradually introducing intermediate nodes (intermediate grids) to optimize the path. Assume the node set is... ,definition Indicates from node arrive The path is allowed to pass through intermediate nodes. The shortest path length is updated recursively. Finally, the global shortest path is obtained.

[0131] Assume the adjacency matrix of the raster map is ,in:

[0132]

[0133] Applying the recurrence relation of dynamic programming:

[0134]

[0135] in, Indicates no grid. The shortest path, Indicates passing through a grid The path, i.e. .

[0136] Iterative updates, until Termination time, updated distance matrix The shortest path length including all grid pairs, where Indicates from grid arrive The shortest path length.

[0137] At the same time, determine the predecessor matrix corresponding to the shortest distance matrix. Used to record the predecessor raster of each raster in the path sequence. Indicates from arrive On the shortest path The predecessor grid. Its update rule is: if Through the middle grid Update, then .

[0138] Finally, the shortest distance matrix D and the corresponding predecessor matrix are calculated using the Floyd algorithm. like Figure 7 As shown, the expression for the shortest distance matrix D is as follows:

[0139]

[0140] 5. Determine the transition probability matrix.

[0141] In this embodiment, determining the transition probability matrix based on the shortest distance matrix includes: determining a weight matrix between any two grid cells based on the shortest distance matrix and a first control parameter, wherein the first control parameter is used to control the degree of influence of the distance between any two grid cells on the transition probability; determining the sum of the weights of each row in the weight matrix to obtain the column vector of the weight matrix; and normalizing the weight matrix based on the column vector to obtain the transition probability matrix. The specific process analysis is as follows:

[0142] 1) Determine the weight matrix:

[0143]

[0144] Wherein, the distance matrix , Point arrive Distance; First control parameter A real number greater than 0 is used to control the weight of the distance on the probability; the larger the value, the greater the influence of the distance on the weight. This represents the calculated weight matrix, where K represents the total number of elements in the matrix. Indicates the first The next grid cell moves to the [number]th grid cell. The weighting coefficient of a grid cell increases as the distance between two grid cells decreases. ,but .

[0145] 2) Determine the column vector:

[0146]

[0147] Among them, it means Represents the weight matrix The Middle The sum of all elements in the row.

[0148] 3) Determine the probability transition matrix:

[0149] Based on column vectors Weight for each row Normalize and calculate the transition probability matrix between grid cells. :

[0150]

[0151] in, Indicates the first When selecting the grid cell, move to the first grid cell. The probability of grid number 1. The larger the value, the higher the value. The higher the probability of a grid cell being selected, the more likely each row will be selected. The sum is 1.

[0152] It should be noted that the first control parameter The larger the value, the stronger the sensitivity of the probability to distance. This can be adjusted... The algorithm can find a balance between balancing and utilizing the value of , specifically:

[0153] : The influence of distance on probability weakens, the probability distribution tends to be uniform, and the path planning strategy tends to be randomly generated;

[0154] The influence of distance on probability is enhanced, and the probability is highly concentrated on the nearest neighbor. The path planning strategy is close to the classic nearest neighbor algorithm, that is, starting from the current point, the nearest unvisited point is always selected as the next station.

[0155] The probability transition matrix of the final raster map is as follows Figure 8 As shown.

[0156] In step S204 above, during the population initialization phase, based on the transition probability matrix, one of two preset strategies (greedy selection or fuzzy selection) can be used to construct the initial path. The greedy strategy advances the path based on the grid with the highest transition probability at each step, while the fuzzy strategy randomly selects the next grid based on the probability distribution between grids using a roulette wheel selection mechanism.

[0157] In a raster map, the set of walkable raster cells is: There are a total of A passable grid, starting point ,end The set of accessible grid cells. Transforming a two-dimensional subscript set into a linear index set, denoted as , is the set of points to be traversed (fully covered), containing the linear index of the starting point. Endpoint linear index Each full coverage path is based on Beginning, with Finish.

[0158] Each generation of the population contains a number of individuals, each individual Contains point set All elements in, i.e. The order in which the elements are arranged determines the actual full-coverage path. The initialization of the population individuals is based on the point set. Transition probability matrix The process of generating feasible solution sets through a preset selection strategy is analyzed in detail below:

[0159] 1. Greedy selection of individual paths generation.

[0160] In this embodiment, the greedy selection strategy includes: determining a set of walkable grid cells in the grid map; initializing a path sequence containing a first grid cell, and deleting the first grid cell from the set of walkable grid cells to obtain a set of grid cells to be visited, wherein the first grid cell is any grid cell in the set of walkable grid cells; determining a third grid cell from the set of grid cells to be visited that has the highest transition probability with a second grid cell, based on the transition probability matrix, wherein the second grid cell is the last grid cell in the path sequence; adding the third grid cell to the end of the path sequence, and deleting the third grid cell from the set of grid cells to be visited; repeating the grid selection and path sequence optimization operations until all grid cells in the set of grid cells to be visited have been added to the path sequence to obtain an initial path corresponding to the grid map. The specific operations are as follows:

[0161] 1) Initialization: Randomly select a starting point, such as the first grid cell. Initialize path sequence Then the set of remaining unvisited points ;

[0162] 2) Iterative selection: For Select the last point in the path sequence, such as the second grid. ;

[0163] And from Select a point, such as the third grid. Satisfying: Maximum transition probability ;

[0164] 3) Update path: Update the remaining set: ;

[0165] 4) Mathematical representation:

[0166]

[0167] in, ,initial .

[0168] 2. Generation of individual paths through fuzzy selection.

[0169] In this embodiment, the fuzzy selection strategy includes: randomly selecting a fourth grid corresponding to the second grid from the set of grids to be visited based on the probability distribution of the transition probability matrix; adding the fourth grid to the end of the path sequence and deleting the fourth grid from the set of grids to be visited; repeating the grid selection and path sequence optimization operations until all grids in the set of grids to be visited have been added to the path sequence, thus obtaining an initial path corresponding to the grid map. The specific operations are as follows:

[0170] 1) Initialization: Similarly, randomly select a starting point, such as the first grid cell. Initialize path sequence Then the set of remaining unvisited points ;

[0171] 2) Iterative selection: For Select the last point in the path sequence, such as the second grid. ;

[0172] And from Select a point, such as the fourth grid. Its probability is ;

[0173] According to probability distribution Make a roulette wheel selection and get ;

[0174] 3) Update path: Update the remaining set: ;

[0175] 4) Mathematical representation:

[0176]

[0177] in, ,initial .

[0178] Both of the above individual path generation strategies are selected with equal probability during population initialization. That is, an individual Select point That is, elements in a point set .

[0179] Repeat the above individual initialization strategy operation. Next, the initial population corresponding to the grid map is obtained:

[0180]

[0181] in, , indicating population The first in Individual, Indicates the first The full coverage path represented by each individual The grid points visited step by step.

[0182] The population initialization strategy based on the transition probability matrix described above can easily and efficiently construct a high-quality initial population. The creation process of each individual takes into account the adjacency characteristics of the grid and the requirement of the shortest path distance, thus ensuring that each individual is an approximately optimal solution.

[0183] In the embodiments of this application, to address the problem that the path generated by the evolutionary algorithm may not start or end with a preset start and end grid, a population repair operation is also introduced, including: determining the start grid and end grid in the target path, and determining the preset start grid and preset end grid corresponding to the target path; when the start grid is different from the preset start grid and the end grid is different from the preset end grid, fixing the start grid to the preset start grid and fixing the end grid to the preset end grid.

[0184] Specifically, for any path sequence (target path) , which includes the starting point and the end point The goal of the repair operation is to swap the data. Fixed to the beginning and end of the path, i.e., the preset starting grid. and will Fixed to the end of the path, i.e., the preset endpoint grid. Ensure that the constraints are met:

[0185]

[0186] More specifically, the target path sequence is defined as a vector. Its elements are node numbers. Let the original sequence have: starting point The position is ,Right now ;end The position is ,Right now ,and Each location is unique; repair is achieved through two swap operations:

[0187] 1) Fix the starting point by swapping the first element. and starting point :

[0188]

[0189] in, This represents the target path sequence after repairing the starting point.

[0190] 2) End point repair: Swap the last element. and the end point :

[0191]

[0192] in, This represents the target path sequence after repairing the start and end points.

[0193] Combining the two swap operations, the repaired path is:

[0194]

[0195] For example, the input target path is ,in , ,but:

[0196] Start point repair: ,exchange and : ;

[0197] Endpoint Repair: ,exchange and : .

[0198] In step S206 above, the aim is to calculate the local distance contribution value of each grid node in each path, which reflects the connection cost of the node in the path. Subsequently, multimodal perturbation operations are performed on the nodes with the highest local distance contribution values, including node swapping, subpath reversal, and node insertion, thereby optimizing the path structure and reducing path length and repetition rate.

[0199] In this embodiment, based on the characteristics of the grid map full-coverage path planning problem, a progeny population generation strategy based on local distance contribution is introduced. This strategy involves performing multimodal perturbation on the target path based on the local distance contribution value, including: determining a target distance matrix corresponding to the target path, where the target distance matrix reflects the shortest path distance between any two grids in the target path; determining the local distance contribution value of the target grid based on the target distance matrix, where the target grid is any grid in the target path; determining a local distance contribution array corresponding to the target path based on the local distance contribution value; and performing multimodal perturbation on the target path based on the local distance contribution array.

[0200] For example, for the initial population A new population, namely the offspring population, can be obtained through multimodal perturbation operations. , among which each individual New individuals can be generated through the following steps. :

[0201] First, given a sequence of target paths ,in Indicates the first in the path The node numbers; and their corresponding distance matrices. , is used to define the distance between nodes, where Represents a node arrive The distance is calculated; the local distance contribution of each node in the path is calculated to generate a local distance contribution array. .

[0202] For each node in the path (Location Index) ), its local distance contribution value The definition is as follows:

[0203]

[0204] Among them, the first node ( Only the distance to the next node is calculated; the tail node ( ), only calculate the distance from its preceding node to it; intermediate nodes ( ), calculate the average of the distances between the two segments.

[0205] Therefore, individuals Local distance contribution array Each element can be represented as:

[0206]

[0207] In a raster map, since the shortest distance between two grid cells is 1, the array... The minimum contribution of local distance is 1.

[0208] Assuming the path is The partial values ​​of the distance matrix are: Then the local distance contribution array is:

[0209] Further, a multimodal perturbation operation is performed on the target path based on the local distance contribution value to generate a child population corresponding to the initial population. This includes: determining the perturbation point and perturbation position index corresponding to the target path based on the local distance contribution array; performing a swap operation, a reverse operation, and an insertion operation on the target path based on the perturbation point, the perturbation position index, and a second control parameter, respectively, to obtain a first path, a second path, and a third path, wherein the second control parameter is used to adjust the focusing degree of the target path during the perturbation process; determining the first fitness value of the first path, the second path, and the third path through a fitness function, and determining the path sequence with the highest first fitness value as the child path corresponding to the target path in the initial population; and generating a child population corresponding to the initial population based on the child paths.

[0210] Specifically, based on the local distance contribution array Select two perturbation points and the corresponding position index At the same time, set the second control parameter. This is used to control the weight of the local distance contribution on the probability. The smaller the value, the more uniform the probability distribution. The specific operation is as follows:

[0211] Weight vector 1: The reason This is because the shortest distance between grid cells is 1, and nodes with a local distance contribution of 1 can be considered to be in ideal positions and do not need to be changed; This is a minimum value quantity used to prevent the denominator from being 0 during normalization;

[0212] Weight vector 2: ;

[0213] Normalized probability: ;

[0214] Selecting the perturbation point through roulette: ,in The location index is ;

[0215] Subsequently, three perturbation operations (swap, reverse, insertion) were applied to obtain three candidate individuals:

[0216] 1) Swap operation:

[0217] Swap positions and Elements:

[0218]

[0219] Right now:

[0220]

[0221] in, Indicates the target path. This represents the first path obtained after the swap operation. This represents the permutation function used in the exchange operation. This represents the minimum and maximum values ​​of the two indices, and represents the path length.

[0222] 2) Reverse order operation:

[0223] For interval Reverse subsequence:

[0224]

[0225] at this time, This represents the second path obtained after reversing the order.

[0226] 3) Insertion operation:

[0227] Position Insert the element at position nearby: ;

[0228] Randomly select the insertion direction (forward or backward): ;

[0229] The path after insertion is: ;

[0230] at this time, This represents the third path obtained after the insertion operation. Indicates the target insertion point.

[0231] Finally, the fitness of the three candidate paths generated by the multimodal perturbation operation is calculated using the fitness function, and the optimal solution is selected as the offspring path corresponding to the target path, thus obtaining the offspring population.

[0232] The fitness function, also known as the population objective function, measures the quality of each individual in the population. The algorithm selects the best-performing individuals for the next generation based on the objective function value, thereby gradually improving the overall fitness of the population during the optimization process. The specific function expression is as follows:

[0233]

[0234] in, This represents the fitness vector, with a length equal to the population size. , Indicates the first in the population The fitness value of an individual, which is the negative of the total distance of the route:

[0235]

[0236] in, Indicates the first in the path The grid to the first The shortest distance between each grid cell; the shorter the distance, the higher the fitness value, which aligns with the optimization objective of minimizing path length.

[0237] In step S208 above, during the iterative optimization process, each generation of individuals (i.e., paths) repeatedly performs evolutionary operations such as fitness evaluation, selection, and perturbation. Through continuous iteration, individuals in the population gradually evolve towards the optimal solution, and finally, when the termination condition is met, the optimal path corresponding to the grid map is determined.

[0238] In this embodiment of the application, iterative optimization is performed based on the initial population and the offspring population, including: determining the first number of individuals in the initial population and determining the second number of individuals in the offspring population; determining the second fitness value of all individuals in the initial population and the offspring population through a fitness function, and determining the third number of individuals with the highest second fitness value as the next generation population, wherein the third number of individuals is half the number of the first and second individuals.

[0239] In evolutionary algorithms, the parent population generates the offspring population through an evolutionary strategy. The offspring population is highly likely to be superior to the parent population, but this is not absolute. If the offspring population is directly used to replace the parent population for subsequent evolution, it may lead to the loss of the best individuals in the current population, specifically manifested as local oscillations in the evolutionary curve and difficulty in population convergence. Therefore, this application's embodiments introduce an elite strategy. In each generation of the evolutionary algorithm, the parent and offspring populations are merged and sorted according to fitness. The top half of the best individuals in the merged population are selected as the new generation.

[0240] For example, suppose the parent population (taking the initial population as an example) is fitness is The offspring population is fitness is Merge parent and child generations, retaining the previous generation. The operation process for finding the optimal individual can be as follows:

[0241] 1) Merging populations:

[0242]

[0243] in, This represents the merged population. This represents the fitness vector after merging.

[0244] 2) Fitness ranking:

[0245]

[0246]

[0247] in, This represents the fitness vector sorted in ascending order of fitness. express An array of indices returned by the function.

[0248] 3) Before selection The optimal individual:

[0249]

[0250]

[0251] in, Indicating a new generation of population, This represents the fitness vector of the new generation population.

[0252] Through the aforementioned elitist strategy, evolutionary algorithms can preserve information about excellent solutions in the search space and pass it on to their offspring. This selective preservation helps avoid solution degradation and propels the algorithm towards better solutions during evolution. Furthermore, the elitist strategy can accelerate the convergence speed of the algorithm, especially when the search space contains many local optima.

[0253] In this embodiment of the application, a path reconstruction strategy is also introduced, including: determining the predecessor matrix based on the shortest distance matrix of the raster map, wherein the predecessor matrix is ​​used to reflect the node access order between any two rasters in the raster map; updating the optimal path based on the predecessor matrix and the path reconstruction function to obtain the reconstructed path.

[0254] Specifically, the population is continuously evolved through repeated iterations of offspring generation, population repair, fitness calculation, and elite retention operations, ultimately yielding the optimal individual. (i.e., full coverage path). However, two adjacent nodes are not guaranteed to be physically adjacent in terms of the map grid (distance > 1), so it is still necessary to use the predecessor matrix obtained by the Floyd algorithm to reconstruct the path of the obtained optimal individual.

[0255] Given the predecessor matrix is ,in, Indicates from node arrive In the shortest path The direct predecessor node. Reconstruction from arrive The shortest path sequence operation is as follows:

[0256] Define path reconstruction function From arrive The shortest path sequence, with the following recursive rules:

[0257]

[0258] in, Indicates path join operation, for example ; Represents a node The predecessor node, i.e., in the shortest path The previous node.

[0259] For example, suppose The definitions are as follows (node ​​numbers start from 1):

[0260]

[0261] Then the path The unfolding process is as follows:

[0262]

[0263] In the above process, the global search capability of the evolutionary algorithm and the local optima of the Floyd algorithm are combined to achieve dual optimization in path planning. The evolutionary algorithm focuses on finding the optimal grid access sequence, while the predecessor matrix ensures that the movement path in actual physical space is the shortest. The two complement each other and work together to optimize path planning. Compared to using only the evolutionary algorithm, this strategy can significantly reduce path length and movement distance, thereby saving energy consumption and improving task execution efficiency.

[0264] In this embodiment, to comprehensively evaluate the performance of the above algorithm under different environments, four grid maps of different sizes and complexities were designed, and the complexity of the maps was described from three aspects: map size, walkable area ratio, and number of obstacles. The walkable area ratio refers to the ratio of the number of empty grid cells to the total number of grid cells in the map. Specific grid map environmental parameters are shown in Table 1, and each grid map is as follows: Figure 9 As shown.

[0265] Table 1. Raster Map Environmental Parameters

[0266]

[0267] This experiment used four sets of raster maps (as shown in Table 1), with sizes ranging from 20×20 to 40×40. The proportion of obstacles increased from 10.5% to 21.5%, showing a significant gradient in map complexity. Specifically:

[0268] Grid Figure 1 ( Figure 9 Medium (a): Simple open environment with sparse obstacles (42), walkable area accounts for 89.50%, used to verify basic performance;

[0269] Grid Figure 2-3 ( Figure 9Medium (b) and (c): Medium complexity, containing local maze structure (90-162 obstacles), walkable area 87.50%-90.00%, used to test the algorithm's adaptability to winding paths;

[0270] Grid Figure 4 ( Figure 9 Medium (d): A highly complex scenario with dense obstacles (344) and dead zones, where only 78.5% of the area is walkable. This scenario is used to test robustness in extreme environments.

[0271] The experimental results are shown in Table 2, and the population evolution / convergence curves for each grid map are as follows: Figure 10 As shown, the full coverage path is as follows Figures 11-14 As shown.

[0272] Table 2 Experimental parameters and results

[0273]

[0274] The experimental results in Table 2 show that, based on a population size of 100 in the experiments on the four raster maps, the number of iterations gradually increases with the map complexity (2000~50000 generations), verifying the scalability of the algorithm.

[0275] 1. The path convergence analysis is as follows:

[0276] Simple environment: such as Figure 10 As shown in (a), the grid Figure 1 The fast convergence within 200 generations is attributed to the generation of high-quality initial solutions through dual-mode initialization.

[0277] Medium environment: such as Figure 10 As shown in (b) and (c), the grid Figure 2-3 The step-like decrease indicates that the multimodal perturbation operations (swapping / reversal / insertion) effectively broke through the local optimum;

[0278] Complex environments: such as Figure 10 As shown in (d), the grid Figure 4 The convergence exhibits two stages. In the early stage (0-20% iterations), the path length drops sharply, indicating that the directed evolution strategy can quickly optimize high-cost bottleneck nodes. In the later stage (80% iterations), it shows that fine-tuning can eliminate redundancy and finally converge to the target, demonstrating the advantages of parameter adaptation.

[0279] 2. Path compactness analysis is as follows:

[0280] Grid Figure 1 The middle path length is 358 steps, repeating only 1 step, which almost achieves the theoretically optimal coverage, such as Figure 11 As shown;

[0281] Grid Figure 4 The intermediate path length is 1300 steps, repeated 45 times, indicating that the algorithm still approaches its efficiency limit in complex environments. Figure 14 As shown.

[0282] 3. The duplicate coverage analysis is as follows:

[0283] like Figures 11-14 As shown, the repetition rate of the four raster maps is only 0.28% to 3.46%, significantly lower than that of traditional methods. Specifically, the raster maps... Figure 4 Repeated points are concentrated in the U-shaped dead zone ( Figure 14 The yellow areas represent localized path overlaps caused by detouring around obstacles. Overall, no grid cells were missed in any of the route maps, validating the algorithm's 100% area coverage capability.

[0284] This application proposes an evolutionary algorithm combining probabilistic distance modeling, dual-mode population initialization, and multimodal perturbation operations driven by local distance contributions for full-coverage path planning in complex grid environments. By converting the grid map into a probabilistic model and initializing the population using the transition probability matrix, the efficiency and diversity of path generation are ensured. The introduction of a directed evolutionary strategy based on local distance contributions intelligently identifies path bottlenecks and optimizes them using swap, reverse, and insertion operations, significantly improving the efficiency and quality of path planning, especially when handling high obstacle density and irregular terrain. Furthermore, by retaining high-quality solutions through an elite strategy and combining the predecessor matrix for path reconstruction, global optimization of path planning is achieved.

[0285] Overall, this application not only solves the path redundancy problem of traditional methods in complex environments, but also optimizes path length and reduces repetition rate, providing an efficient solution for full-coverage path planning of intelligent robots, drones and other devices in complex grid environments.

[0286] In the above operating environment, this application provides an embodiment of a full-coverage path planning method. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Also, although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than that shown here.

[0287] In the above embodiments of this application, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0288] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for full-coverage path planning, characterized in that, include: A grid map of the area to be planned is determined, and a transition probability matrix corresponding to the grid map is determined, wherein the transition probability matrix is ​​used to reflect the movement probability between any two grids in the grid map; An initial population corresponding to the grid map is determined based on the transition probability matrix and a preset selection strategy. The preset selection strategy includes a greedy selection strategy and a fuzzy selection strategy. The greedy selection strategy constructs a path by selecting the locally optimal neighboring grid. The fuzzy selection strategy constructs a path by randomly selecting grids based on the probability distribution in the transition probability matrix. The initial population is used to represent the initial path set corresponding to the grid map. Determine the local distance contribution value of the target path in the initial population, perform a multimodal perturbation operation on the target path based on the local distance contribution value, and generate a sub-population corresponding to the initial population. The target path is any path in the initial population, and the local distance contribution value is used to reflect the degree of contribution of each node in the target path to the overall path length. The initial population and the offspring population are used for iterative optimization until the optimal path corresponding to the grid map is determined.

2. The method according to claim 1, characterized in that, Determining the transition probability matrix corresponding to the raster map includes: Determine a state matrix corresponding to the grid map, wherein the state matrix is ​​used to reflect the passage status of each grid in the grid map; Based on the state matrix, determine the shortest distance matrix between any two grid cells in the grid map; The transition probability matrix is ​​determined based on the shortest distance matrix.

3. The method according to claim 2, characterized in that, Determining the shortest distance matrix between any two grid cells in the grid map based on the state matrix includes: The two-dimensional coordinates in the state matrix are converted into one-dimensional linear indices to obtain the linear index results. Based on the state matrix and the linear index result, an adjacency matrix corresponding to the raster map is determined, wherein the adjacency matrix is ​​used to reflect the connectivity between any two rasters in the raster map; The shortest path length between any two grid cells after introducing intermediate grid cells is determined based on the adjacency matrix. The shortest distance matrix is ​​determined based on the shortest path length.

4. The method according to claim 2, characterized in that, Determining the transition probability matrix based on the shortest distance matrix includes: The weight matrix between any two grid cells is determined based on the shortest distance matrix and the first control parameter, wherein the first control parameter is used to control the degree of influence of the distance between any two grid cells on the transition probability; Determine the sum of the weights in each row of the weight matrix to obtain the column vector of the weight matrix; The weight matrix is ​​normalized based on the column vectors to obtain the transition probability matrix.

5. The method according to claim 1, characterized in that, The greedy selection strategy includes: Determine the set of walkable grid cells in the grid map; Initialize a path sequence containing the first grid cell, and remove the first grid cell from the set of accessible grid cells to obtain a set of grid cells to be accessed, wherein the first grid cell is any one of the grid cells in the set of accessible grid cells; Based on the transition probability matrix, a third grid with the highest transition probability to the second grid is determined from the set of grids to be visited, wherein the second grid is the last grid in the path sequence; The third grid is added to the end of the path sequence and then removed from the set of grids to be visited. Repeat the grid selection and path sequence optimization operations until all grids in the set of grids to be visited have been added to the path sequence to obtain the initial path corresponding to the grid map.

6. The method according to claim 5, characterized in that, The fuzzy selection strategy includes: Based on the probability distribution of the transition probability matrix, a fourth grid corresponding to the second grid is randomly selected from the set of grids to be accessed; The fourth grid is added to the end of the path sequence and then removed from the set of grids to be visited. Repeat the grid selection and path sequence optimization operations until all grids in the set of grids to be visited have been added to the path sequence to obtain the initial path corresponding to the grid map.

7. The method according to claim 1, characterized in that, The method further includes: Determine the starting grid and ending grid in the target path, and determine the preset starting grid and preset ending grid corresponding to the target path; If the starting grid is different from the preset starting grid and the ending grid is different from the preset ending grid, the starting grid is fixed to the preset starting grid and the ending grid is fixed to the preset ending grid.

8. The method according to claim 1, characterized in that, Perform a multimodal perturbation operation on the target path based on the local distance contribution value, including: Determine the target distance matrix corresponding to the target path, wherein the target distance matrix is ​​used to reflect the shortest path distance between any two grids in the target path; The local distance contribution value of the target grid is determined based on the target distance matrix, wherein the target grid is any grid in the target path; Based on the local distance contribution values, a local distance contribution array corresponding to the target path is determined; A multimodal perturbation operation is performed on the target path based on the local distance contribution array.

9. The method according to claim 8, characterized in that, Based on the local distance contribution value, a multimodal perturbation operation is performed on the target path to generate a offspring population corresponding to the initial population, including: Based on the local distance contribution array, determine the disturbance point and disturbance location index corresponding to the target path; Based on the disturbance point, the disturbance position index, and the second control parameter, the target path is subjected to a swap operation, a reverse operation, and an insertion operation, respectively, to obtain a first path, a second path, and a third path. The second control parameter is used to adjust the focus of the target path during the disturbance process. The fitness function determines the first fitness value of the first path, the second path, and the third path, and the path sequence with the highest first fitness value is determined as the offspring path corresponding to the target path in the initial population; A subpopulation corresponding to the initial population is generated based on the subpopulation path.

10. The method according to claim 9, characterized in that, Iterative optimization is performed based on the initial population and the offspring population, including: Determine the first number of individuals in the initial population, and determine the second number of individuals in the offspring population; The fitness function is used to determine the second fitness value of all individuals in the initial population and the offspring population, and the third number of individuals with the highest second fitness value is determined as the next generation population, wherein the third number of individuals is half the number of the first individuals and the number of the second individuals.

11. The method according to claim 1, characterized in that, The method further includes: The predecessor matrix is ​​determined based on the shortest distance matrix of the grid map, wherein the predecessor matrix is ​​used to reflect the node access order between any two grids in the grid map; The optimal path is updated based on the predecessor matrix and the path reconstruction function to obtain the reconstructed path.

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