Multi-robot task area distribution method based on regular hexagon grid map

Abstract

The invention discloses a multi-robot task area distribution method based on a regular hexagon grid map, and the method comprises the following steps: 1, carrying out the rasterization of a task area based on a regular hexagon, taking a regular hexagon cell as a unit, and carrying out the modeling of the whole task area into the regular hexagon grid map; 2, based on the wavefront distance principle, calculating an initial wavefront distance matrix, and according to the initial positions of robot members, calculating a wavefront distance matrix from the orthohexagonal grid map to other unoccupied grids; according to the scheme, three requirements of multi-robot task area distribution in a two-dimensional environment can be met, namely, proportional distribution, full communication in sub-areas and full coverage, in addition, the map coverage rate and the task distribution efficiency can be remarkably improved, and the task distribution efficiency is improved. The reasonable task area allocation method not only can improve the overall efficiency of task execution of the robot, but also facilitates optimization of resource utilization, thereby better meeting the demand of full-coverage tasks.

Description

Technical Field

[0001] The invention belongs to the technical field of robot application, and in particular relates to a multi-robot task area allocation method based on a regular hexagonal grid map. Background Art

[0002] In recent years, with the development of robotics technology, robots have gradually entered many fields of human production and life, such as search and rescue, indoor cleaning and regional disinfection. In order to ensure full coverage of the area, the full coverage path planning problem of robots has become a hot issue. Reasonable task area allocation is the basis for robot clusters to achieve full coverage tasks, which also provides key support for cluster path planning. The task area allocation of robot clusters is intended to serve full coverage path planning, which is significantly challenging, especially when multiple robots share the same working space. The characteristics of shared space increase the risk of path conflicts in path planning, which may lead to adverse situations such as collisions and deadlocks. Therefore, it is particularly necessary to study how to reasonably allocate full coverage task areas. In other words, reasonable task allocation (i.e., effective regional division of known space) is the prerequisite for ensuring that robot clusters can collaboratively complete regional coverage tasks.

[0003] The common approach to the research on the full coverage path planning problem of multi-robots at home and abroad is to first allocate the task area, then plan the full coverage path for the allocated sub-areas, and finally achieve full coverage of the task area. The allocation of multi-robot task areas for known environments needs to meet the following three conditions: (i) the allocation can be made according to the initial positions of multiple robot members, the number of robots, and the task execution capabilities of each member, so as to make full use of the capabilities of each robot, that is, to allocate in proportion to the robot's task capabilities; (ii) the sub-areas allocated to each robot must be completely connected, because disconnected areas will increase the robot's movement cost and may cause collisions between robots; (iii) the union of the sub-areas allocated to all robots is equal to the entire task area, that is, full coverage of the task area.

[0004] For the problem of multi-robot task area allocation, existing methods can be divided into clustering methods and unit decomposition methods. Clustering-based methods mainly include multi-path spectral clustering algorithm, Lloyd's algorithm and K-means algorithm. These methods often fail to consider the initial position of the robot, easily generate disconnected areas or generate irregular areas with narrow shapes and gradually narrowed ends, which brings challenges to subsequent path planning. Unit decomposition methods generally include precise unit decomposition and approximate unit decomposition. Precise unit decomposition methods include ox-plow decomposition, trapezoidal decomposition and rectangular decomposition. These methods can achieve more effective space segmentation and task allocation for a single simple obstacle environment, but in areas with complex obstacles, this method often only divides the task area into a large number of sub-areas of different sizes, which cannot meet the requirements of proportional allocation according to the robot's task capabilities. The approximate unit decomposition method divides the free space by representing it as a fine grid of the same size. For example, building a square grid map. However, the square grid map-based approach is prone to blind spots and repeated coverage areas, resulting in reduced coverage efficiency. In addition, since each unit of the square grid is only directly connected to four adjacent units, its connectivity is limited, which may lead to poor path planning of the robot during task execution, thereby increasing the cost of movement and may also increase the risk of collision due to path complexity.

[0005] Based on this, the present invention designs a multi-robot task area allocation method based on a regular hexagonal grid map to solve the above problems. Summary of the invention

[0006] The purpose of the present invention is to meet the needs of reasonably allocating task areas according to the number of multiple robots, the initial positions of robot members and the task execution capabilities, and to overcome the shortcomings of traditional square grids in coverage efficiency and connectivity. Ultimately, the task area can be divided into sub-areas equal to the number of robot members according to the proportion of task execution capabilities, and each sub-area is guaranteed to be completely connected. A multi-robot task area allocation method based on a regular hexagonal grid map is proposed.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions: The multi-robot task area allocation method based on a regular hexagonal grid map includes the following steps: Step 1: Rasterize the mission area based on regular hexagons. Take regular hexagonal cells as units and model the entire mission area as a regular hexagonal grid map. Step 2: Based on the wavefront distance principle, calculate the initial wavefront distance matrix. According to the initial position of the robot member, calculate the wavefront distance matrix to other unoccupied grids on the regular hexagonal grid map; Step 3: Initial allocation of task areas, according to the decision matrix corresponding to the multi-robot members, the initial allocation results are obtained; Step 4: Error correction. Based on the task area and the initial allocation result of the previous step, the error matrix is ​​calculated and the corresponding decision matrix of each robot is adjusted, so that the task allocation area finally meets the requirements of proportionality, full connectivity and full coverage in the sub-area.

[0008] As a further description of the above technical solution: In the step 1, the regular hexagonal grid map cannot use the traditional Cartesian coordinate system. At present, the regular hexagonal grid is mainly established by using the offset coordinate system (Offset coordinates) and the longitudinal coordinate system (Axial coordinates). The longitudinal coordinate system can calculate the distance between two units through a simple mathematical formula without considering the parity of rows and columns. Compared with the offset coordinate system, it is more concise and efficient. In addition, the longitudinal coordinate system only needs to use two coordinate values, which can more conveniently determine adjacent points. The maintainability and execution efficiency of the code are also improved, which is more suitable for application scenarios that require frequent calculations; Therefore, the present invention uses the longitudinal coordinate to establish a regular hexagonal grid map, such as Figure 2 As shown, assuming that the diameter of the robot is , the side length of the regular hexagon , the entire task allocation area is rasterized into regular hexagons, and the position of each regular hexagonal grid is determined by the vertical coordinate (column coordinate) and the horizontal coordinate (row coordinate) Each grid can be indexed by the coordinates of the center position of a regular hexagon express: (1); For each regular hexagonal unit from 0 to The vertex coordinates are calculated at equally spaced angles, which can be obtained by calculating the sine and cosine values ​​of each angle, where each angle corresponds to a vertex of the regular hexagon: (2); According to the center position and vertices of each regular hexagon, the mission area is initialized to the entire regular hexagonal grid map. The number of rows and columns of the grid map are and , the entire mission area for: (3); The distribution of adjacent cells of each cell in the established regular hexagonal grid is regular, such as Figure 3 As shown. For coordinates The six adjacent grids are , , , , , ; The grids not occupied by obstacles will be used for further allocation, denoted as P: (4); in Represents all grids, Represents the grid occupied by obstacles; Based on the task execution capability of each robot, the allocation ratio can be calculated ( ); The expected number of grids assigned to each robot ( )yes: (5); in is the number of robots, and the sum of the allocation ratios is 1, that is, .

[0009] As a further description of the above technical solution: In step 2, the wavefront distance algorithm is used to calculate the distance of each robot from its initial position to other unoccupied grids. This method uses the initial position of each robot as a "seed" and then uses a wave-like propagation method to assign a numerical distance value to each unoccupied grid. This process is similar to pseudo-gradient descent of the digital potential energy function defined by the robot's starting position. The wavefront distance algorithm intuitively grasps the spatial relationship between each grid and the robot's initial position, and effectively simulates how obstacles affect spatial accessibility.

[0010] Using the Decision Matrix It represents the wavefront distance of each robot from the initial position to other unoccupied cells. First, expand from the initial position of the robot in six directions to examine all its unvisited adjacent grids. If they are not occupied, their distances are updated to the distance of the current grid plus one. This update process ensures that the distance value is correct and takes into account the influence of obstacles. The shortest distance from the seed point to each grid is obtained. This process continues until the entire task space is traversed and all reachable grids are assigned a distance value, reflecting the distance from the initial position. The shortest distance to the grid, forming the corresponding decision matrix : (6); in is the initial position of the ith robot, Indicates the robot's initial position grid All unoccupied grids except From the initial position To other free grids The initial decision matrix only contains the wavefront distances from each robot to other free grids.

[0011] As a further description of the above technical solution: In step 3, when assigning tasks, the algorithm evaluates each cell and selects the robot that is closest to the task to perform, so as to optimize the efficiency of the robot and reduce the travel time. The input is the decision matrix , Contains the shortest wavefront distance from each robot to each cell, and the output is the allocation matrix : (7); Among them, A represents the entire area There are a total of sub-regions, initial decision matrix It only contains the wavefront distance from the robot's initial position to the cell, and takes into account the influence of obstacles. According to the allocation strategy, each cell will be assigned to the robot with the smallest wavefront distance. Therefore, the initial allocation matrix ensures that each sub-area is fully connected. The assigned area of ​​the i-th robot : (8); The actual number of cells assigned to the i-th robot Is the area assigned to this robot A collection of: (9).

[0012] As a further description of the above technical solution: In step 4, by calculating the correction factor Implementation, correction factor Used to adjust the corresponding decision matrix The adjustment process ensures that each unit is uniquely assigned to the robot and meets the ratio requirements until all conditions are met, and finally the sub-area of ​​each robot is determined. ,This method ensures fair distribution among multiple robots and improves their efficiency in a shared environment (10); in is the correction factor of the ith robot; In addition, in order to evaluate the effectiveness of space allocation between different robots, an allocation error metric is introduced to compare the size of the area allocated to each robot, which is defined as follows: (11); in represents the total distribution error, is the actual grid number of the ith robot, is the total number of robots; To minimize the actual allocation With expected distribution To ensure fairness, we use the cyclic coordinate descent method, which is a non-gradient optimization method that searches and adjusts sequentially along the coordinate direction until the minimum value of the objective function is found; When the global minimum of the objective function is always between the upper and lower thresholds, The lower threshold and The upper threshold is expressed as: (12); Accordingly, the correction factors are updated as follows: (13); During the allocation optimization process, and The relationship between may be negative. If the robot allocation exceeds its expected number, that is, the objective function exceeds the upper limit, the corresponding correction factor needs to be calculated to increase the distance from each grid to the initial position until the expected allocation is met; To ensure the continuity of robot task allocation, a continuity correction factor is introduced, and a depth-first search (DFS) is used to determine whether the allocation area is connected. DFS is an algorithm that starts from the starting node and traverses the adjacent nodes in sequence until all connected nodes are found; In addition, a regular hexagonal grid is constructed using a column coordinate system. The adjacent cells of each cell are determined (upper, lower, left, right, upper left, lower right). When DFS determines the connection, it will start from an unmarked cell and visit all its adjacent unvisited cells until the entire connected area is identified, forming an assigned continuity set. ; (14); matrix Represents the number of connected parts in each robot's assigned area. 0 means the assigned area is not connected, and 1 means it is connected. To solve the problem of disassociated areas, the matrix Force robots to prioritize adjacent areas and promote coherent spatial allocation; In order to ensure the continuity of task assignment, a method for calculating and managing the number of connected areas of robot assignment is adopted. When the robot assignment spans two or more disconnected areas, this method ensures the connectivity of its assignment. If the number of connected areas exceeds 2 (i.e. ), there is a disconnected area. To avoid this problem, use the matrix ,encourages the robot to prioritize the allocation of areas close to the initial position, forming a coherent and unified allocation; Here It is expressed as: (15); in Indicates direct connection to the robot's initial position The grid set of , as the main continuous area of ​​the allocation, Includes all other mesh sets assigned to the robot but not directly connected to , indicating that these are dispersed allocations; By calculating the matrix Then, the decision matrix Revised to reflect the prioritization of connectivity: (16); Correction using element-by-element multiplication Adjustment , making the allocation more connected, by repeatedly adjusting the decision matrix ,The algorithm achieves a balanced task allocation that not only meets the ,proportion requirement but also ensures the coherence and connectivity of each robot’s ,assigned area.

[0013] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: In the present invention, by using the invention, it is only necessary to obtain the boundary of the task area, the obstacle area, the initial positions of the multi-robot members and their respective execution capabilities (i.e., the allocation ratio) to automatically calculate the allocation plan of the task area. This plan can meet the three requirements of multi-robot task area allocation in a two-dimensional environment, namely, proportional allocation, full connectivity within sub-areas, and full coverage. In addition, this method can significantly improve the map coverage rate and task allocation efficiency. Such a reasonable task area allocation method can not only improve the overall effectiveness of the robot in executing tasks, but also help to optimize resource utilization, thereby better meeting the needs of full coverage tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A coordinate system diagram established by a regular hexagonal grid of a multi-robot task area allocation method based on a regular hexagonal grid map proposed in the present invention, wherein a is an offset coordinate system diagram and b is a longitudinal coordinate system diagram; Figure 2 A regular hexagonal cell size diagram of the multi-robot task area allocation method based on a regular hexagonal grid map proposed by the present invention; Figure 3A regular hexagonal adjacent grid map of the multi-robot task area allocation method based on a regular hexagonal grid map proposed by the present invention; Figure 4 A 6*6 regular hexagonal grid map including obstacle areas and initial positions of robots in the multi-robot task area allocation method based on regular hexagonal grid maps proposed by the present invention; Figure 5 The multi-robot task area allocation method based on the regular hexagonal grid map proposed by the present invention calculates the wavefront distance map of two robots on the 6*6 regular hexagonal grid map respectively; Figure 6 This is a schematic diagram of the task area allocation results of three robots in the multi-robot task area allocation method based on the regular hexagonal grid map proposed in the present invention. DETAILED DESCRIPTION

[0015] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] Please see attached Figure 1 -Attached Figure 6 The present invention provides a technical solution: a multi-robot task area allocation method based on a regular hexagonal grid map, comprising the following steps: Step 1: Rasterize the mission area based on regular hexagons. Take regular hexagonal cells as units and model the entire mission area as a regular hexagonal grid map. Step 2: Based on the wavefront distance principle, calculate the initial wavefront distance matrix. According to the initial position of the robot member, calculate the wavefront distance matrix to other unoccupied grids on the regular hexagonal grid map; Step 3: Initial allocation of task areas, according to the decision matrix corresponding to the multi-robot members, the initial allocation results are obtained; Step 4: Error correction. Based on the task area and the initial allocation result of the previous step, the error matrix is ​​calculated and the corresponding decision matrix of each robot is adjusted, so that the task allocation area finally meets the requirements of proportionality, full connectivity and full coverage in the sub-area.

[0017] Step 1. Regular hexagonal grid maps cannot use the traditional Cartesian coordinate system. At present, the offset coordinate system and the axial coordinate system are mainly used to establish regular hexagonal grids. The axial coordinate system can calculate the distance between two units through a simple mathematical formula without considering the parity of rows and columns. It is simpler and more efficient than the offset coordinate system. In addition, the axial coordinate system only needs two coordinate values, which can more conveniently determine adjacent points. The maintainability and execution efficiency of the code are also improved, which is more suitable for application scenarios that require frequent calculations. Therefore, the present invention uses the longitudinal coordinate to establish a regular hexagonal grid map, such as Figure 2 As shown, assuming that the diameter of the robot is , the side length of the regular hexagon , the entire task allocation area is rasterized into regular hexagons, and the position of each regular hexagonal grid is determined by the vertical coordinate (column coordinate) and the horizontal coordinate (row coordinate) Each grid can be indexed by the coordinates of the center position of a regular hexagon express: (1); For each regular hexagonal unit from 0 to The vertex coordinates are calculated at equally spaced angles, which can be obtained by calculating the sine and cosine values ​​of each angle, where each angle corresponds to a vertex of the regular hexagon: (2); According to the center position and vertices of each regular hexagon, the mission area is initialized to the entire regular hexagonal grid map. The number of rows and columns of the grid map are and , the entire mission area for: (3); The distribution of adjacent cells of each cell in the established regular hexagonal grid is regular, such as Figure 3 As shown. For coordinates The six adjacent grids are , , , , , ; The grids not occupied by obstacles will be used for further allocation, denoted as P: (4); in Represents all grids, Represents the grid occupied by obstacles; Based on the task execution capability of each robot, the allocation ratio can be calculated ( ); The expected number of grids assigned to each robot ( )yes: (5); in is the number of robots, and the sum of the allocation ratios is 1, that is, .

[0018] In step 2, the wavefront distance algorithm is used to calculate the distance from each robot's initial position to other unoccupied grids. This method uses the initial position of each robot as a "seed" and then uses a wave-like propagation method to assign a numerical distance value to each unoccupied grid. This process is similar to pseudo-gradient descent of the digital potential energy function defined by the robot's starting position. The wavefront distance algorithm intuitively grasps the spatial relationship between each grid and the robot's initial position, effectively simulating how obstacles affect spatial accessibility.

[0019] Using the Decision Matrix It represents the wavefront distance of each robot from the initial position to other unoccupied cells. First, expand from the initial position of the robot in six directions to examine all its unvisited adjacent grids. If they are not occupied, their distances are updated to the distance of the current grid plus one. This update process ensures that the distance value is correct and takes into account the influence of obstacles. The shortest distance from the seed point to each grid is obtained. This process continues until the entire task space is traversed and all reachable grids are assigned a distance value, reflecting the distance from the initial position. The shortest distance to the grid, forming the corresponding decision matrix : (6); in is the initial position of the ith robot, Indicates the robot's initial position grid All unoccupied grids except From the initial position To other free grids The initial decision matrix only contains the wavefront distances from each robot to other free grids.

[0020] In step 3, when assigning tasks, the algorithm evaluates each cell and selects the robot that is closest to the task to perform in order to optimize the efficiency of the robot and reduce the travel time. The input is the decision matrix , Contains the shortest wavefront distance from each robot to each cell, and the output is the allocation matrix : (7); Among them, A represents the entire area There are a total of sub-regions, initial decision matrix It only contains the wavefront distance from the robot's initial position to the cell, and takes into account the influence of obstacles. According to the allocation strategy, each cell will be assigned to the robot with the smallest wavefront distance. Therefore, the initial allocation matrix ensures that each sub-area is fully connected. The assigned area of ​​the i-th robot : (8); The actual number of cells assigned to the i-th robot Is the area assigned to this robot A collection of: (9).

[0021] In step 4, the correction factor is calculated by Implementation, correction factor Used to adjust the corresponding decision matrix The adjustment process ensures that each unit is uniquely assigned to the robot and meets the ratio requirements until all conditions are met, and finally the sub-area of ​​each robot is determined. ,This method ensures fair distribution among multiple robots and improves their efficiency in a shared environment (10); in is the correction factor of the ith robot; In addition, in order to evaluate the effectiveness of space allocation between different robots, an allocation error metric is introduced to compare the size of the area allocated to each robot, which is defined as follows: (11); in represents the total distribution error, is the actual grid number of the ith robot, is the total number of robots; To minimize the actual allocation With expected distribution To ensure fairness, we use the cyclic coordinate descent method, which is a non-gradient optimization method that searches and adjusts sequentially along the coordinate direction until the minimum value of the objective function is found; When the global minimum of the objective function is always between the upper and lower thresholds, The lower threshold and The upper threshold is expressed as: (12); Accordingly, the correction factors are updated as follows: (13); During the allocation optimization process, and The relationship between may be negative. If the robot allocation exceeds its expected number, that is, the objective function exceeds the upper limit, the corresponding correction factor needs to be calculated to increase the distance from each grid to the initial position until the expected allocation is met; To ensure the continuity of robot task allocation, a continuity correction factor is introduced, and a depth-first search (DFS) is used to determine whether the allocation area is connected. DFS is an algorithm that starts from the starting node and traverses the adjacent nodes in sequence until all connected nodes are found; In addition, a regular hexagonal grid is constructed using a column coordinate system. The adjacent cells of each cell are determined (upper, lower, left, right, upper left, lower right). When DFS determines the connection, it will start from an unmarked cell and visit all its adjacent unvisited cells until the entire connected area is identified, forming an assigned continuity set. ; (14); matrix Represents the number of connected parts in each robot's assigned area. 0 means the assigned area is not connected, and 1 means it is connected. To solve the problem of disassociated areas, the matrix Force robots to prioritize adjacent areas and promote coherent spatial allocation; In order to ensure the continuity of task assignment, a method for calculating and managing the number of connected areas of robot assignment is adopted. When the robot assignment spans two or more disconnected areas, this method ensures the connectivity of its assignment. If the number of connected areas exceeds 2 (i.e. ), there is a disconnected area. To avoid this problem, use the matrix ,encourages the robot to prioritize the allocation of areas close to the initial position, forming a coherent and unified allocation; Here It is expressed as: (15); in Indicates direct connection to the robot's initial position The grid set of , as the main continuous area of ​​the allocation, Includes all other mesh sets assigned to the robot but not directly connected to , indicating that these are dispersed allocations; By calculating the matrix Then, the decision matrix Revised to reflect the prioritization of connectivity: (16); Correction using element-by-element multiplication Adjustment , making the allocation more connected, by repeatedly adjusting the decision matrix ,The algorithm achieves a balanced task allocation that not only meets the ,proportion requirement but also ensures the coherence and connectivity of each robot’s ,assigned area.

[0022] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A multi-robot task area allocation method based on a regular hexagonal grid map, characterized in that: The following steps are involved: Step 1: Rasterize the mission area based on regular hexagons. Take regular hexagonal cells as units and model the entire mission area as a regular hexagonal grid map. Step 2: Based on the wavefront distance principle, calculate the initial wavefront distance matrix. According to the initial position of the robot member, calculate the wavefront distance matrix to other unoccupied grids on the regular hexagonal grid map; Step 3: Initial allocation of task areas, according to the decision matrix corresponding to the multi-robot members, the initial allocation results are obtained; Step 4: Error correction. Based on the task area and the initial allocation result of the previous step, the error matrix is ​​calculated and the corresponding decision matrix of each robot is adjusted, so that the task allocation area finally meets the requirements of proportionality, full connectivity and full coverage in the sub-area.

2. The multi-robot task area allocation method based on a regular hexagonal grid map according to claim 1 is characterized in that: In the step 1, the regular hexagonal grid map cannot use the traditional Cartesian coordinate system. At present, the regular hexagonal grid is mainly established by using the offset coordinate system and the longitudinal coordinate system. The longitudinal coordinate system can calculate the distance between two units by a simple mathematical formula without considering the parity of rows and columns. Compared with the offset coordinate system, it is more concise and efficient. In addition, the longitudinal coordinate system only needs to use two coordinate values, which can more conveniently determine adjacent points, and the maintainability and execution efficiency of the code are also improved, which is more suitable for application scenarios that require frequent calculations. Assume that the diameter of the robot is , the side length of the regular hexagon , the entire task allocation area is rasterized into regular hexagons, and the position of each regular hexagonal grid is determined by the vertical coordinate (column coordinate) and the horizontal coordinate (row coordinate) Each grid can be indexed by the coordinates of the center position of a regular hexagon express: (1) For each regular hexagonal unit from 0 to The vertex coordinates are calculated at equally spaced angles, which can be obtained by calculating the sine and cosine values ​​of each angle, where each angle corresponds to a vertex of the regular hexagon: (2) According to the center position and vertices of each regular hexagon, the mission area is initialized to the entire regular hexagonal grid map. The number of rows and columns of the grid map are and , the entire mission area for: (3) The distribution of adjacent cells of each unit in the established regular hexagonal grid is regular. The six adjacent grids are , , , , , ; The grids not occupied by obstacles will be used for further allocation, denoted as P: (4) in Represents all grids, Represents the grid occupied by obstacles; Based on the task execution capability of each robot, the allocation ratio can be calculated ( ); The expected number of grids assigned to each robot ( )yes: (5) in is the number of robots, and the sum of the distribution ratios is 1, that is, .

3. The multi-robot task area allocation method based on regular hexagonal grid map according to claim 1 is characterized in that: In step 2, the wavefront distance algorithm is used to calculate the distance from each robot's initial position to other unoccupied grids. This method uses the initial position of each robot as a "seed" and then uses a wave-like propagation method to assign a numerical distance value to each unoccupied grid. This process is similar to pseudo-gradient descent of a digital potential energy function defined by the robot's starting position. The wavefront distance algorithm intuitively grasps the spatial relationship between each grid and the robot's initial position, and effectively simulates how obstacles affect spatial accessibility. Using the Decision Matrix It represents the wavefront distance of each robot from the initial position to other unoccupied cells. First, expand from the initial position of the robot in six directions to examine all its unvisited adjacent grids. If they are not occupied, their distances are updated to the distance of the current grid plus one. This update process ensures that the distance value is correct and takes into account the influence of obstacles. The shortest distance from the seed point to each grid is obtained. This process continues until the entire task space is traversed and all reachable grids are assigned a distance value, reflecting the distance from the initial position. The shortest distance to the grid, forming the corresponding decision matrix : (6) in is the initial position of the ith robot, Indicates the grid except the robot's initial position All unoccupied grids except From the initial position To other free grids The initial decision matrix only contains the wavefront distances from each robot to other free grids.

4. The multi-robot task area allocation method based on regular hexagonal grid map according to claim 1 is characterized in that: In step 3, when assigning tasks, the algorithm evaluates each cell and selects the robot that is closest to the task to perform in order to optimize the efficiency of the robot and reduce the travel time. The input is the decision matrix , Contains the shortest wavefront distance from each robot to each cell, and the output is the allocation matrix : (7) Among them, A represents the entire area There are a total of sub-regions, initial decision matrix It only contains the wavefront distance from the robot's initial position to the cell, and takes into account the influence of obstacles. According to the allocation strategy, each cell will be assigned to the robot with the smallest wavefront distance. Therefore, the initial allocation matrix ensures that each sub-area is fully connected. The assigned area of ​​the i-th robot : (8) The actual number of cells assigned to the i-th robot Is the area assigned to this robot A collection of: (9)。 5. The multi-robot task area allocation method based on regular hexagonal grid map according to claim 1 is characterized in that: In step 4, the correction factor is calculated Implementation, correction factor Used to adjust the corresponding decision matrix The adjustment process ensures that each unit is uniquely assigned to the robot and meets the ratio requirements until all conditions are met, and finally the sub-area of ​​each robot is determined. ,This method ensures fair distribution among multiple robots and improves their efficiency in a shared environment (10) in is the correction factor of the ith robot; In addition, in order to evaluate the effectiveness of space allocation between different robots, an allocation error metric is introduced to compare the size of the area allocated to each robot, which is defined as follows: (11) in represents the total distribution error, is the actual grid number of the ith robot, is the total number of robots; To minimize the actual allocation With expected distribution To ensure fairness, we use the cyclic coordinate descent method, which is a non-gradient optimization method that searches and adjusts sequentially along the coordinate direction until the minimum value of the objective function is found; When the global minimum of the objective function is always between the upper and lower thresholds, The lower threshold and The upper threshold is expressed as: (12) Accordingly, the correction factors are updated as follows: (13) During the allocation optimization process, and The relationship between may be negative. If the robot allocation exceeds its expected number, that is, the objective function exceeds the upper limit, the corresponding correction factor needs to be calculated to increase the distance from each grid to the initial position until the expected allocation is met; To ensure the continuity of robot task allocation, a continuity correction factor is introduced, and depth-first search is used to determine whether the allocation area is connected. DFS is an algorithm that starts from the starting node and traverses the adjacent nodes in sequence until all connected nodes are found; In addition, a regular hexagonal grid is constructed using a column coordinate system. The adjacent cells of each cell are determined (upper, lower, left, right, upper left, lower right). When DFS determines the connection, it will start from an unmarked cell and visit all its adjacent unvisited cells until the entire connected area is identified, forming an assigned continuity set. ; (14) matrix Represents the number of connected parts in each robot's assigned area. 0 means the assigned area is not connected, and 1 means it is connected. To solve the problem of disassociated areas, the matrix Force robots to prioritize adjacent areas and promote coherent spatial allocation; In order to ensure the continuity of task allocation, a method for calculating and managing the number of connections in the robot allocation area is adopted. When the robot allocation spans two or more disconnected areas, this method ensures the connectivity of its allocation. If the number of connections exceeds 2 (i.e. ), there is a disconnected area. To avoid this problem, use the matrix ,encourages the robot to prioritize the allocation of areas close to the initial position, forming a coherent and unified allocation; Here It is expressed as: (15) in Indicates direct connection to the robot's initial position The grid set of , as the main continuous area of ​​the allocation, Includes all other mesh sets assigned to the robot but not directly connected to , indicating that these are dispersed allocations; By calculating the matrix Then, the decision matrix Revised to reflect the prioritization of connectivity: (16) Correction using element-by-element multiplication Adjustment , making the allocation more connected, by repeatedly adjusting the decision matrix ,The algorithm achieves a balanced task allocation that not only meets the ,proportion requirement but also ensures the coherence and connectivity of each robot’s ,assigned area.

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