Multi-Robot Task Area Allocation Method Based on Regular Hexagon Grid Map

Abstract

The present invention discloses a method for multi-robot task area allocation based on a regular hexagon grid map, comprising the following steps: Step 1: Based on regular hexagon grid division of the task area, taking regular hexagon cells as units, the entire task area is modeled as a regular hexagon grid map; Step 2: Based on the wavefront distance principle, an initial wavefront distance matrix is calculated, and according to the initial positions of the robot members, the wavefront distance matrix to other unoccupied grids on the regular hexagon grid map is calculated; In the present invention, this solution can meet the three requirements for multi-robot task area allocation in a two-dimensional environment, namely proportional allocation, full connectivity within sub-regions, 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 enhance the overall efficiency of robots in performing tasks, but also help optimize resource utilization, thus better meeting the requirements of full coverage tasks.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot applications, and particularly relates to a method for multi-robot task area allocation based on a regular hexagon grid map. Background Art

[0002] In recent years, with the development of robot technology, robots have gradually entered multiple fields of human production and life, such as search and rescue, indoor cleaning, and area disinfection. To ensure complete coverage of an area, the problem of full coverage path planning for robots has become a hot issue. Reasonable task area allocation is the basis for a robot cluster to achieve full coverage tasks, which also provides key support for cluster path planning. The task area allocation of a robot cluster aims to serve full coverage path planning, and this path planning is significantly challenging, especially when multiple robots share the same working space. The characteristics of the 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 deeply study how to reasonably allocate the full coverage task area. In other words, reasonable task allocation (i.e., effective area division of the known space) is a prerequisite for ensuring that a robot cluster collaboratively completes the area coverage task.

[0003] Regarding the research on the multi-robot full coverage path planning problem at home and abroad, the common approach is to first allocate the task area, then separately perform full coverage path planning for the allocated sub-areas, and finally achieve full coverage of the task area. The multi-robot task area allocation for a known environment needs to meet the following three conditions: (i) It can be allocated 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, proportional allocation according to the task capabilities of the robots; (ii) The sub-areas allocated to each robot must be completely connected internally, because unconnected areas will increase the movement cost of the robots and may lead to 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:

[0008] The multi-robot task area allocation method based on a regular hexagonal grid map includes the following steps:

[0009] 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.

[0010] Step 2: Based on the wavefront distance principle, calculate the initial wavefront distance matrix. According to the initial positions of the robot members, calculate the wavefront distance matrix from the occupied grid on the regular hexagon grid map to other unoccupied grids.

[0011] Step 3: Initial allocation of the task area. According to the decision matrix corresponding to multiple robot members, obtain the initial allocation result.

[0012] Step 4: Error correction. Based on the task area and the initial allocation result of the previous step, calculate the error matrix, and adjust the corresponding decision matrix of each robot, so that the task allocation area finally meets the requirements of proportionality, full connectivity and full coverage within the sub-region.

[0013] As a further description of the above technical solution: In step 1, the regular hexagon grid map cannot adopt the Cartesian coordinate system in the traditional sense. At present, the establishment of regular hexagon grids mainly adopts the offset coordinate system (Offset coordinates) and the axial coordinate system (Axial coordinates). The axial coordinate system can calculate the distance between two units through a simple mathematical formula without considering the parity of rows and columns, which is more concise and efficient than the offset coordinate system. In addition, the axial 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, making it more suitable for application scenarios that require frequent calculations.

[0014] Therefore, the present invention uses axial coordinates to establish a regular hexagon grid map. As Figure 2 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. The position of each regular hexagon grid is determined by the axial coordinate (column coordinate) and the transverse coordinate (row coordinate) . Each grid can be indexed by the coordinates of the center position of the regular hexagon as follows:

[0015] (1);

[0016] For each regular hexagon unit, calculate the vertex coordinates at equal intervals from 0 to . This can be obtained by calculating the sine and cosine values of each angle. Each angle corresponds to a vertex of the regular hexagon:

[0017] (2);

[0018] According to the center position and vertices of each regular hexagon, the task area is initially set as the entire regular hexagon grid map. The number of rows and columns of the grid map are respectively and the entire task area is as follows:

[0019] (3);

[0020] The distribution of adjacent cells of each cell in the established regular hexagonal grid has regularity, as Figure 3 shown. For the grid with coordinates , the six adjacent grids are respectively , , , , , ;

[0021] The grids not occupied by obstacles will be used for further allocation, denoted as P:

[0022] (4);

[0023] wherein represents all grids, represents the grids occupied by obstacles;

[0024] According to the task execution ability of each robot, the allocation ratio ( ) can be calculated; the number of grids expected to be allocated to each robot ( ) is:

[0025] (5);

[0026] wherein is the number of robots, and the sum of the allocation ratios is 1, that is .

[0027] As a further description of the above technical solution: in step 2, the wavefront distance algorithm is used to calculate the distance from the initial position of each robot to other unoccupied grids. This method takes the initial position of each robot as the "seed", and then uses a wave-like propagation method to assign numerical distance values to each unoccupied grid. This process is similar to performing a pseudo-gradient descent on the digital potential 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.

[0028] Use the decision matrix Indicates the wavefront distance from the initial position of each robot to other unoccupied cells. First, expand from the initial position of the robot in six directions and examine all its unvisited adjacent grids. If it is not occupied, update its distance to the distance of the current grid plus one. This update process ensures the correctness of the distance value, taking into account the influence of obstacles, and obtains the shortest distance from the seed point to each grid. This process continues until the entire task space is traversed, and all reachable grids are assigned a distance value, reflecting the shortest distance from the initial position to this grid, forming the corresponding decision matrix :

[0029] (6);

[0030] where is the initial position of the i-th robot, represents all unoccupied grids except the grid at the initial position of the robot outside, represents the wavefront distance from the initial position to other free grids . The initial decision matrix only contains the wavefront distances from each robot to other free grids.

[0031] As a further description of the above technical solution: in step 3, when assigning tasks, the algorithm evaluates each cell and selects the robot closest to the task to execute, in order to optimize the efficiency of the robot and reduce the travel time. The input is the decision matrix , which contains the shortest wavefront distances from each robot to each cell, and the output is the assignment matrix :

[0032] (7);

[0033] where A represents the assignment of sub-regions in the entire area. There are a total of sub-regions. The initial decision matrix only contains the wavefront distances from the initial position of the robot to the cells, taking into account the influence of obstacles. According to the assignment strategy, each cell will be assigned to the robot with the smallest wavefront distance to it. Therefore, the initial assignment matrix ensures that each sub-region is completely connected internally;

[0034] The assignment area of the i-th robot :

[0035] (8);

[0036] The actual number of cells assigned to the i-th robot is assigned to the robot area is the set of:

[0037] (9).

[0038] As a further description of the above technical solution: in step 4, by calculating the correction factor to achieve, the correction factor is used to adjust the corresponding decision matrix , and the adjustment process ensures that each cell is uniquely assigned to a robot and meets the proportional requirements until all conditions are satisfied, and finally determines the sub - area of each robot , this method guarantees fair distribution among multiple robots and improves their efficiency in a shared environment

[0039] (10);

[0040] where is the correction factor of the i - th robot;

[0041] In addition, to evaluate the effectiveness of the spatial allocation among different robots, an allocation error metric is introduced to compare the sizes of the areas assigned to each robot, and this metric is defined as follows:

[0042] (11);

[0043] where represents the total allocation error, is the actual number of grids of the i - th robot, is the total number of robots;

[0044] is to minimize the difference between the actual allocation and the expected allocation to ensure fairness, the cyclic coordinate descent method is adopted, which is a non - gradient optimization method that searches and adjusts sequentially along the coordinate directions until the minimum value of the objective function is found;

[0045] When the global minimum of the objective function is always between the lower and upper threshold values, the lower threshold and the upper threshold are expressed as:

[0046] (12);

[0047] Accordingly, the correction factor is updated as follows:

[0048] (13);

[0049] During the allocation optimization process, and The relationship may be negative. If the allocation of a robot exceeds its expected quantity, i.e., the objective function exceeds the upper limit, a corresponding correction factor needs to be calculated to increase the distance of each grid to the initial position until the expected allocation is satisfied.

[0050] To ensure the continuity of robot task allocation, a continuity correction factor is introduced. Depth-First Search (DFS) is used to determine whether the allocated areas are connected. DFS is an algorithm that starts from the starting node and traverses adjacent nodes in sequence until all connected nodes are found.

[0051] In addition, a column coordinate system is used to construct a regular hexagonal grid. The adjacent cells of each cell are determined (up, down, left, right, upper left, lower right). When DFS determines connectivity, it starts from an unmarked cell and visits all its adjacent unvisited cells until the entire connected area is identified, forming a continuous set of allocations. ;

[0052] (14);

[0053] matrix represents the number of connected parts within the allocated area of each robot. 0 indicates that the allocated area is not connected, and 1 indicates connectivity. To solve the problem of disconnected allocated areas, the matrix is introduced to force the robot to preferentially allocate adjacent areas and promote coherent space allocation.

[0054] To ensure the continuity of task allocation, a method for calculating and managing the connectivity number of the robot's allocated area is adopted. When the robot's allocation spans two or more disconnected areas, this method ensures its allocation connectivity. If the connectivity number exceeds 2 (i.e., ), it indicates that there are disconnected areas. To avoid this problem, the matrix is used to encourage the robot to preferentially allocate areas close to the initial position to form a coherent and unified allocation.

[0055] Here, is expressed as:

[0056] (15);

[0057] where represents the set of grids directly connected to the robot's initial position as the main continuous area of allocation, includes all other sets of grids allocated to the robot, but these sets of grids are not directly connected to , indicating that these are scattered allocations.

[0058] After obtaining the matrix through calculation After that, the decision matrix is corrected to reflect the prioritization of connectivity:

[0059] (16);

[0060] The correction is performed using element-wise multiplication Adjust , making the assignment more connected. By repeatedly adjusting the decision matrix , the algorithm achieves a balanced task assignment that meets the proportional requirements and ensures the coherence and connectivity of the assigned areas for each robot.

[0061] In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are as follows:

[0062] In the present invention, by using this invention, only the boundaries of the task area, the obstacle area, the initial positions of multiple robot members, and their respective execution capabilities (i.e., the allocation ratio) need to be obtained, and then the allocation scheme of the task area can be automatically calculated. This scheme can meet the three requirements for 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 efficiency of robots performing tasks but also help optimize resource utilization, thus better meeting the requirements of full-coverage tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 FIG. is a coordinate system diagram established for the hexagonal grid of the multi-robot task area allocation method based on a hexagonal grid map proposed by the present invention, where a is the offset coordinate system diagram and b is the longitudinal coordinate system diagram;

[0064] Figure 2 FIG. is a diagram of the hexagonal cell size of the multi-robot task area allocation method based on a hexagonal grid map proposed by the present invention;

[0065] Figure 3 FIG. is a diagram of adjacent hexagonal grids of the multi-robot task area allocation method based on a hexagonal grid map proposed by the present invention;

[0066] Figure 4 FIG. is a 6×6 hexagonal grid map containing the obstacle area and the initial positions of robots for the multi-robot task area allocation method based on a hexagonal grid map proposed by the present invention;

[0067] Figure 5 FIG. is a wavefront distance map calculated for two robots respectively on a 6×6 hexagonal grid map for the multi-robot task area allocation method based on a hexagonal grid map proposed by the present invention;

[0068] Figure 6 This is a schematic diagram of the task area allocation results of three robots for the multi-robot task area allocation method based on a regular hexagon grid map proposed by the present invention. Detailed implementation manners

[0069] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0070] Please refer to the attached Figure 1 - attached Figure 6 , the present invention provides a technical solution: a multi-robot task area allocation method based on a regular hexagon grid map, including the following steps:

[0071] Step 1: Based on the regular hexagon grid task area, taking the regular hexagon cell as a unit, model the entire task area as a regular hexagon grid map;

[0072] Step 2: Based on the wavefront distance principle, calculate the initial wavefront distance matrix, and according to the initial positions of the robot members, calculate the wavefront distance matrix to other unoccupied grids on the regular hexagon grid map;

[0073] Step 3: Initial allocation of the task area, and obtain the initial allocation result according to the decision matrix corresponding to the multi-robot members;

[0074] Step 4: Error correction, based on the task area and the initial allocation result of the previous step, calculate the error matrix, adjust the decision matrix of each robot accordingly, and finally make the task allocation area meet the requirements of proportionality, full connectivity and full coverage within the sub-area.

[0075] In step 1, the regular hexagon grid map cannot adopt the Cartesian coordinate system in the traditional sense. At present, the establishment of regular hexagon grids mainly adopts the offset coordinate system (Offset coordinates) and the axial coordinate system (Axialcoordinates). The axial coordinate system can calculate the distance between two units through simple mathematical formulas without considering the parity of rows and columns, which is more concise and efficient than the offset coordinate system. In addition, the axial 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 accordingly, making it more suitable for application scenarios that require frequent calculations;

[0076] Therefore, the present invention uses the axial coordinates to establish a regular hexagon grid map, asFigure 2 As shown, assume the diameter of the robot is , and the side length of the regular hexagon is . The entire task assignment area is rasterized into regular hexagons. The position of each regular hexagon grid is determined by the longitudinal coordinate (column coordinate) and the transverse coordinate (row coordinate) . Each grid can be indexed by the coordinates of the center position of the regular hexagon: It is expressed as:

[0077] (1);

[0078] For each regular hexagon cell, calculate the vertex coordinates at equal - interval angles from 0 to . It can be obtained by calculating the sine and cosine values of each angle. Each angle corresponds to a vertex of the regular hexagon:

[0079] (2);

[0080] According to the center position of each regular hexagon and the vertices of the regular hexagon, the task area is initialized as the entire regular hexagon grid map. The number of rows and columns of the grid map are and respectively. The entire task area is:

[0081] (3);

[0082] The distribution of adjacent cells in each cell of the established regular hexagon grid has regularity, as shown in Figure 3 . For the grid with coordinates , the six adjacent grids are respectively , , , , , ;

[0083] The grids not occupied by obstacles will be used for further assignment, denoted as P:

[0084] (4);

[0085] Among them, represents all grids, and represents the grids occupied by obstacles;

[0086] According to the task - execution ability of each robot, the assignment ratio ( ) can be calculated; the number of grids expected to be assigned to each robot ( ) is:

[0087] (5);

[0088] where is the number of robots, and the sum of the allocation ratios is 1, i.e., .

[0089] In step 2, the wavefront distance algorithm is used to calculate the distance from the initial position of each robot to other unoccupied grids. This method takes the initial position of each robot as a "seed", and then uses a wave propagation - like method to assign numerical distance values to each unoccupied grid. This process is similar to performing a pseudo - gradient descent on the digital potential function defined by the starting positions of the robots. The wavefront distance algorithm intuitively grasps the spatial relationship between each grid and the initial position of the robot, and effectively simulates how obstacles affect spatial accessibility.

[0090] Using the decision matrix to represent the wavefront distance from the initial position of each robot to other unoccupied cells. First, expand in six directions from the initial position of the robot, examine all its unvisited adjacent grids. If unoccupied, update its distance to the distance of the current grid plus one. This update process ensures the correctness of the distance value, takes into account the influence of obstacles, and obtains the shortest distance from the seed point to each grid. This process continues until the entire task space is traversed, and all reachable grids are assigned a distance value, reflecting the shortest distance from the initial position to this grid, forming the corresponding decision matrix

[0091] (6);

[0092] where is the initial position of the i - th robot, represents all unoccupied grids except the grid of the initial position of the robot , represents the wavefront distance from the initial position to other free grids . The initial decision matrix only contains the wavefront distances from each robot to other free grids.

[0093] In step 3, when assigning tasks, the algorithm evaluates each cell and selects the robot closest to the task to execute, in order to optimize the efficiency of the robot and reduce the travel time. The input is the decision matrix , which contains the shortest wavefront distances from each robot to each cell, and the output is the allocation matrix :

[0094] (7);

[0095] Among them, A represents the allocation of sub-regions in the entire area, with a total of sub-regions. The initial decision matrix only contains the wavefront distance from the initial position of the robot to the cells, taking into account the influence of obstacles. According to the allocation strategy, each cell will be assigned to the robot with the smallest wavefront distance to it. Therefore, the initial allocation matrix ensures that each sub-region is fully connected internally;

[0096] The allocation area of the i-th robot :

[0097] (8);

[0098] The actual number of cells assigned to the i-th robot is the set of the area assigned to this robot :

[0099] (9).

[0100] In step 4, it is achieved by calculating the correction factor . The correction factor is used to adjust the corresponding decision matrix . The adjustment process ensures that each cell is uniquely assigned to a robot and meets the proportional requirements until all conditions are satisfied, and finally determines the sub-regions of each robot . This method guarantees fair allocation among multiple robots and improves their efficiency in the shared environment

[0101] (10);

[0102] Where is the correction factor of the i-th robot;

[0103] In addition, in order to evaluate the effectiveness of the spatial allocation among different robots, an allocation error metric is introduced to compare the sizes of the areas assigned to each robot. This metric is defined as follows:

[0104] (11);

[0105] Where represents the total allocation error, is the actual number of grids of the i-th robot, is the total number of robots;

[0106] is to minimize the actual allocation and the expected allocation To ensure fairness, the cyclic coordinate descent method is adopted. This is a non-gradient optimization method that searches and adjusts sequentially along the coordinate directions until the minimum value of the objective function is found;

[0107] When the global minimum of the objective function is always between the lower and upper threshold values, The lower threshold and The upper threshold are expressed as:

[0108] (12);

[0109] Accordingly, the correction factor is updated as follows:

[0110] (13);

[0111] During the allocation optimization process, and The relationship between them may be negative. If the allocation of the robot exceeds its expected quantity, 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 satisfied;

[0112] To ensure the continuity of robot task allocation, a continuity correction factor is introduced. The depth-first search (DFS) is used to determine whether the allocation areas are connected. DFS is an algorithm that starts from the starting node and traverses adjacent nodes in turn until all connected nodes are found;

[0113] In addition, a column coordinate system is used to construct a regular hexagonal grid. The adjacent cells of each cell are determined (up, down, left, right, upper left, lower right). When DFS determines connectivity, it starts from an unmarked cell and visits all its unvisited adjacent cells until the entire connected area is identified, forming a continuous set of allocations ;

[0114] (14);

[0115] The matrix represents the number of connected parts within the allocation area of each robot. 0 indicates that the allocation area is not connected, and 1 indicates connectivity. To solve the disconnected allocation areas, the matrix is introduced to force the robot to preferentially allocate adjacent areas and promote coherent space allocation;

[0116] To ensure the continuity of task allocation, a method for calculating and managing the number of connected areas of robot allocations is adopted. When the robot allocation spans two or more disconnected areas, this method ensures its allocation connectivity. If the number of connected areas exceeds 2 (i.e., ), it indicates that there is a disconnected area. To avoid this problem, a matrix is used to encourage the robot to preferentially allocate areas close to the initial position to form a coherent and unified allocation;

[0117] Here, is represented as:

[0118] (15);

[0119] Among them, represents the grid set directly connected to the robot's initial position as the main continuous area for allocation, including all other grid sets allocated to the robot, but these grid sets are not directly connected to , indicating that these are scattered allocations;

[0120] After obtaining the matrix through calculation, the decision matrix is corrected to reflect the prioritization of connectivity:

[0121] (16);

[0122] The correction adopts element-by-element multiplication to adjust , making the allocation more connected. By repeatedly adjusting the decision matrix , the algorithm achieves a balanced task allocation that not only meets the proportional requirements but also ensures the coherence and connectivity of the areas allocated to each robot.

[0123] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. A multi-robot task area allocation method based on a regular hexagon grid map, characterized in that, Including the following steps: Step 1: Based on the regular hexagon rasterization of the task area, with regular hexagon cells as units, the entire task area is modeled as a regular hexagon raster map; Step 2: Based on the wavefront distance principle, calculate the initial wavefront distance matrix. According to the initial positions of the robot members, calculate the wavefront distance matrix from the initial positions of the robot members to other unoccupied grids on the regular hexagon raster map; Step 3: Initial allocation of the task area. According to the decision matrix corresponding to multiple robot members, obtain the initial allocation result; Step 4: Error correction. Based on the task area and the initial allocation result of the previous step, calculate the error matrix, and adjust the decision matrix of each robot. Finally, make the task allocation area meet the requirements of proportional allocation, full connectivity and full coverage within the sub-region; In the said Step 1, the regular hexagon grid is established using a longitudinal coordinate system, and the longitudinal coordinate system can calculate the distance between two units through a simple mathematical formula; Assume that the diameter of the robot is d and the side length of the regular hexagon The entire task assignment area is rasterized into regular hexagons. The position of each regular hexagon grid is determined by the longitudinal coordinate q and the transverse coordinate r. Each grid can be represented by the coordinates (x, y) of the center position of the regular hexagon: For each regular hexagon cell, at the center position of the regular hexagon, equally spaced angular divisions are made from 0 to 2π, and the vertex coordinates are calculated. It can be obtained by calculating the sine and cosine values of each angle. Each angle corresponds to a vertex of the regular hexagon: hex_coords=(size×cos(angle),size×sin(angle)) (2) According to the center position of each regular hexagon and the vertices of the regular hexagon, the task area is initially set as the entire regular hexagon grid map. The number of rows and columns of the raster map are rows and cols respectively. The entire task area L is: The distribution of adjacent cells of each cell in the established regular hexagon grid is regular. For the raster with coordinates (x,y), the six adjacent rasters are A(x,y + 1), B(x - 1,y), C(x - 1,y - 1), D(x,y - 1), E(x + 1,y), F(x + 1,y + 1); The grids not occupied by obstacles will be used for further allocation, denoted as P; Among them, Grid all represents all grids, and Grid obs represents the grids occupied by obstacles; Based on the task execution capabilities of each robot, the allocation ratio can be calculated The expected number of grids allocated to each robot is: where n r is the number of robots, and Ci represents the allocation ratio of the i-th robot when the total task volume is allocated to each robot according to the task execution ability of the robot. The sum of the allocation ratios is 1, that is 2. The multi-robot task area allocation method based on a regular hexagon grid map according to claim 1, characterized in that, In the said Step 2, the wavefront distance algorithm is used to calculate the distance from the initial position of each robot to other unoccupied grids. This method uses the initial position of each robot as the "seed"; Use the decision matrix D to represent the wavefront distance from the initial position of each robot to other unoccupied cells. First, expand in six directions from the initial position of the robot, examine all its unvisited adjacent grids. If not occupied, update its distance to the distance of the current grid plus one. This update process ensures the correct distance value, taking into account the influence of obstacles, and obtains the shortest distance from the seed point to each grid. This process continues until the entire task space is traversed, and all reachable grids are assigned a distance value, reflecting the shortest distance from the initial position (x i , y i ) to that grid, forming the corresponding decision matrix D i : where (x i , y i ) is the initial position of the i-th robot, χ represents all unoccupied grids except the grid (x i , y i ) of the initial position of the robot, ω represents the wavefront distance from the initial position (x i , y i ) to other free grids χ, and the initial decision matrix only contains the wavefront distances from each robot to other free grids.

3. The multi-robot task area allocation method based on a regular hexagon grid map according to claim 1, wherein In step 3, when allocating tasks, the algorithm evaluates each cell and selects the robot closest to the task to execute, so as to optimize the efficiency of the robot and reduce the travel time. The input is the decision matrix D i , D i which contains the shortest wavefront distance from each robot to each cell, and the output is the allocation matrix A: Among them, A represents the allocation of n r sub-regions in the entire area, and there are n r sub-regions. The initial decision matrix D only contains the wavefront distance from the initial position of the robot to the cell, taking into account the influence of obstacles. According to the allocation strategy, each cell will be assigned to the robot with the smallest wavefront distance to it. Therefore, the initial allocation matrix ensures that each sub-region is completely connected internally; Allocation area L of the i-th robot i : The actual number of allocated cells of the i-th robot is the set of areas L allocated to the robot i :

4. The multi-robot task area allocation method based on a regular hexagon grid map according to claim 1, wherein In step 4, the correction factor e is calculated i to achieve this. The correction factor e i is used to adjust the corresponding decision matrix D i , and the adjustment process ensures that each cell is uniquely assigned to a robot and meets the proportional requirements until all conditions are met, and finally the sub-region L of each robot is determined i . This method ensures fair distribution among multiple robots and improves their efficiency in a shared environment D i = e i × D i (10) where e i is the correction factor of the i-th robot; In addition, to evaluate the effectiveness of the spatial allocation among different robots, an allocation error metric is introduced to compare the sizes of the regions assigned to each robot, which is defined as follows: where J represents the total allocation error, is the actual number of grids of the i-th robot, and n r is the number of robots; To minimize the actual allocation and the expected allocation To ensure fairness, the cyclic coordinate descent method, a non-gradient optimization method, is adopted. This method searches and adjusts sequentially along the coordinate directions until the minimum value of the objective function is found; When the global minimum value of the objective function is always between the lower limit threshold and the upper limit threshold, the lower limit threshold down and the upper limit threshold upper are expressed as: Accordingly, the correction factor is updated as follows: During the allocation optimization process, and e i The relationship between them may be negative. If the allocation of the robot exceeds its expected quantity, that is, the objective function exceeds the upper limit, the corresponding correction factor needs to be calculated to increase the distance of 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. The depth-first search is used to judge whether the allocation area is connected. DFS is an algorithm that starts from the starting node and traverses adjacent nodes in turn until all connected nodes are found; In addition, a longitudinal coordinate system is used to construct the regular hexagon grid, and the six adjacent cells of each cell are determined. When DFS judges connectivity, it will start from an unmarked cell and visit all its adjacent unvisited cells until the entire connected area is identified, forming the continuity set S of the allocation; The matrix S represents the number of connected parts within the allocation area of each robot. 0 means the allocation area is not connected, and 1 means it is connected; To ensure the continuity of task allocation, a method is adopted to calculate and manage the number of connected regions for robot allocation. When a robot's allocation spans two or more disconnected regions, this method ensures its allocation connectivity. If the number of connected regions exceeds 2, it indicates the existence of disconnected regions. To avoid this problem, matrix Z is used i , encouraging the robot to preferentially allocate regions close to the initial position to form a coherent and unified allocation; Z here i is expressed as: where R i represents a set of grids directly connected to the initial position (x i , y i ) of the robot, serving as the main continuous area for allocation, and Q i includes all other sets of grids assigned to the robot, but these sets of grids are not directly connected to R i , indicating that these are scattered allocations; After obtaining matrix Z through calculation i then, the decision matrix D i is corrected to reflect the prioritization of connectivity: Correction using element-wise multiplication Adjust D i , making the allocation more connected, by repeatedly adjusting the decision matrix D i , the algorithm achieves a balanced task allocation that not only meets the proportional requirements but also ensures the coherence and connectivity of the assigned areas for each robot.

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