A mobile robot two-dimensional full coverage path planning method and related equipment

Abstract

The application discloses a two-dimensional full coverage path planning method for a mobile robot and related equipment, and belongs to the technical field of robot full coverage path planning. In a complex two-dimensional environment model, for example, a two-dimensional map in which irregular obstacles and concave-convex polygon obstacles exist, firstly, Maklink lines generated by Maklink graph theory can effectively divide the map into multiple sub-regions, which is helpful to simplify the path search problem and improve the search efficiency; then, the order in which the robot visits each sub-region is calculated, and the optimal path for the robot to switch between each sub-region is calculated; finally, the Boustrophedon path is used for "bow" shape traversal, which can ensure that the robot efficiently covers the entire sub-region, reduces the possibility of omission and repeated cleaning, and moves between sub-regions according to the optimal switching path and the visiting order, which is helpful to reduce the repeated path and invalid movement of the robot when traversing the sub-region.

Description

Technical Field

[0001] This invention belongs to the field of robot full-coverage path planning technology, specifically a two-dimensional full-coverage path planning method and related equipment for mobile robots. Background Technology

[0002] In recent years, research on artificial intelligence algorithms and applications has flourished, and mobile robots, as one of the representative carriers of artificial intelligence technology, have become an important frontier area of ​​exploration for the global scientific community. This has led to the increasing application of mobile robots in various scenarios, particularly in home indoor services. They can not only assist or independently complete tasks but also greatly facilitate people's household activities, such as robotic vacuum cleaners. However, due to the lack of reliable global navigation satellite system signals for indoor navigation and the challenges posed by complex and ever-changing real-world environments, effective, reasonable, and accurate path planning algorithms have become an important aspect of mobile robot research.

[0003] There are two main models for mobile robot path planning. The first is the optimal path designed autonomously by the mobile robot from the starting point to the destination, which is the shortest in distance, time, and collision-free. The second is the optimal path designed autonomously by the mobile robot in a two-dimensional space, which minimizes repetition, maximizes efficiency, and effectively avoids obstacles. To date, scholars both domestically and internationally have conducted extensive research on mobile robot path planning, proposing or improving numerous algorithms, including traditional algorithms such as A* algorithm, Dijstra's algorithm, Rapid Expanding Random Tree (RRT) algorithm, Randomized Roadmap (PRM) algorithm, and Artificial Potential Field (APF) method, as well as intelligent optimization algorithms such as Genetic Algorithm (GA), Artificial Fish Swarm Algorithm (AFS), Particle Swarm Optimization (POS) algorithm, Neural Network Algorithm (NN) algorithm, and Ant Colony Algorithm (ACO). Among these algorithms, the Ant Colony Algorithm, as a heuristic search algorithm, has advantages such as strong robustness, excellent distributed computing capabilities, and ease of integration with other algorithms, making it a hot topic in distributed artificial intelligence research. Many algorithms derived from the ant colony model are increasingly being applied in various fields, especially in the field of mobile robot path planning, where they have been widely applied and developed.

[0004] However, in mobile robot path planning, the lack of a defined order for visiting sub-regions leads to numerous duplicate paths in the full coverage path; grid maps are commonly used, resulting in wasted computing resources and numerous duplicate paths. Summary of the Invention

[0005] This invention provides a two-dimensional full-coverage path planning method and related equipment for mobile robots, which solves the problem of high full-coverage path coverage caused by the lack of setting of sub-region access order and the common practice of traversing and planning in grid maps.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A two-dimensional full-coverage path planning method for a mobile robot, characterized by comprising:

[0008] On a map containing obstacles, Maklink graph theory is used to generate Maklink lines to divide the traversed sub-regions and construct a two-dimensional path planning feasible space.

[0009] The optimal access order for traversing sub-regions is obtained using a one-dimensional ant colony algorithm. Then, based on the feasible space of two-dimensional path planning, the optimal path for the robot to switch between sub-regions is obtained using an ant colony algorithm that finds the minimum function value.

[0010] Using the Boustrophedon path, a bow-shaped traversal is performed within each subregion in the best access order and the optimal path for subregion transformation.

[0011] Preferably, the steps of generating the sub-regions to be traversed by Maklink lines and constructing the feasible space for two-dimensional path planning using Maklink graph theory are as follows:

[0012] First, the obstacles and environment of the experimental space are represented. Then, convex and concave polygons are used to represent the obstacles in the environment. Maklink links are used to connect the vertices of different obstacles. The links do not pass through the obstacles, and the external angle formed by the links and the boundary of the obstacles is no greater than 1 / 3. Furthermore, the connecting lines do not intersect each other. By using the connecting lines, the boundary lines of obstacles, and the boundary of the two-dimensional map, the working space is divided into multiple convex polygons to construct the traversable sub-regions of the mobile robot.

[0013] Preferably, the steps for determining the optimal access order for traversing sub-regions using the one-dimensional ant colony algorithm are as follows:

[0014] First, identify the sub-regions with adjacent edges. Set the connection weight of any two sub-regions with connecting edges to 1. Treat each sub-region as a node and give the adjacency matrix corresponding to each sub-region. Based on the adjacency matrix, give the path between any two sub-regions. Use the one-dimensional ant colony algorithm for solving the "Traveling Salesman Problem" to obtain the order in which the robot visits the sub-regions.

[0015] Preferably, the steps for obtaining the optimal path for the robot to transition between sub-regions using the ant colony algorithm to find the minimum function value based on the feasible space of two-dimensional path planning are as follows:

[0016] The objective function is the path length from the starting point to the destination along a point on a Maklink link. The independent variable is a point on the Maklink link. The Maklink links are normalized. Each calculation is performed to back-normalize the specific position on the Maklink link based on the normalization result. The optimal path for the mobile robot to switch between regions is obtained through multiple iterations.

[0017] Preferably, the optimal path for the mobile robot to switch between regions is further optimized through triangulation. Specifically, if multiple consecutive nodes in the path... This forms a multi-segment broken line. and If the direct connection path does not pass through any obstacles, then use and Replace the straight line segments between arrive Multiple bends in the line segment.

[0018] Preferably, the final step of using the Boustrophedon path to perform a "bow"-shaped traversal within the sub-regions according to the optimal access order and the optimal path for sub-region transformation is as follows:

[0019] The mobile robot moves to the sub-region that needs to be traversed according to the optimal path of sub-region transformation in the best access order of sub-regions. It moves back and forth along the longest edge of the sub-region in a "bow" shape to the other vertex of that edge. When it reaches the other vertex of this edge, it moves back and forth along the longest edge again, thus realizing the path planning of full coverage of the mobile robot.

[0020] A two-dimensional full-coverage path planning system for mobile robots includes:

[0021] Partitioning and Construction Module: Used to generate Maklink lines to partition traversed sub-regions and construct a two-dimensional path planning feasible space on a map with obstacles, using Maklink graph theory.

[0022] The calculation module is used to determine the optimal access order for traversing sub-regions using a one-dimensional ant colony algorithm, and then to obtain the optimal path for the robot to switch between sub-regions using an ant colony algorithm that finds the minimum function value based on the feasible space of two-dimensional path planning.

[0023] Traversal module: Used to perform a bow-shaped traversal within subregions using Boustrophedon paths, following the optimal access order and the optimal path for subregion transformation.

[0024] Preferably, in the calculation module, the step of obtaining the optimal path for the robot to transition between sub-regions using the ant colony algorithm to find the minimum function value based on the feasible space of two-dimensional path planning is as follows:

[0025] The objective function is the path length from the starting point, through some points on the Maklink links, to the destination. The independent variables are the points on the Maklink links traversed. These Maklink links are normalized. In each calculation, the specific positions on these Maklink links are back-normalized based on the normalization result. Through multiple iterations, the optimal path for the mobile robot to transition between regions is obtained. Then, the optimal path for the mobile robot to transition between regions is further optimized using triangulation pruning. Specifically, if there are multiple consecutive nodes in the path... This forms a multi-segment broken line. and If the direct connection path does not pass through any obstacles, then it can be used and Replace the straight line segments between arrive Multiple bends in the line segment.

[0026] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a two-dimensional full-coverage path planning method for a mobile robot.

[0027] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a two-dimensional full-coverage path planning method for a mobile robot.

[0028] Compared with existing technologies, this invention has the following advantages: This invention provides a two-dimensional full-coverage path planning method for mobile robots. In complex two-dimensional environment models, such as two-dimensional maps with irregular obstacles or concave-convex polygonal obstacles, the Maklink lines generated by Maklink graph theory can effectively divide the map into multiple sub-regions, which helps simplify the path search problem and improve search efficiency. Then, the order in which the robot visits each sub-region is calculated, and the optimal transition path between each sub-region is calculated. This ensures that the robot efficiently covers the entire sub-region, reduces the possibility of omissions and repeated cleaning, and moves between sub-regions according to the optimal transition path and visiting order, helping to reduce repeated paths and invalid movements when traversing sub-regions.

[0029] Furthermore, the transition paths between sub-regions also employ geometric optimization using triangular pruning, which optimizes the better transition paths calculated by the ant colony algorithm into the optimal paths. Attached Figure Description

[0030] Figure 1 This is a flowchart of a two-dimensional full-coverage path planning method for a mobile robot according to the present invention;

[0031] Figure 2 This invention provides an embodiment of Maklink graph theory for dividing planar regions.

[0032] Figure 3 This is the original sub-region access order after the Maklink graph is divided into sub-regions according to an embodiment of the present invention;

[0033] Figure 4 This represents the optimal access order for sub-regions in this embodiment of the invention.

[0034] Figure 5 This is the traversal path of the mobile robot in the first sub-region according to an embodiment of the present invention;

[0035] Figure 6 This is a simplified transition path for the mobile robot from the first sub-region to the second sub-region in an embodiment of the present invention;

[0036] Figure 7 This describes the complex transition path of the mobile robot from the third sub-region to the fourth sub-region in an embodiment of the present invention.

[0037] Figure 8 This is the global traversal path of the mobile robot in a two-dimensional map containing concave and convex polygonal obstacles according to an embodiment of the present invention;

[0038] Figure 9 This is a schematic diagram of triangular pruning (geometric optimization) in an embodiment of the present invention;

[0039] Figure 10 This is a block diagram of a two-dimensional full-coverage path planning system for a mobile robot according to the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0041] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0042] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0043] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0044] like Figure 1 As shown, this invention provides a two-dimensional full-coverage path planning method for mobile robots, comprising:

[0045] On a map containing obstacles, Maklink graph theory is used to generate Maklink lines to divide the traversed sub-regions and construct a two-dimensional path planning feasible space.

[0046] The optimal access order for traversing sub-regions is obtained using a one-dimensional ant colony algorithm. Then, based on the feasible space of two-dimensional path planning, the optimal path for the robot to switch between sub-regions is obtained using an ant colony algorithm that finds the minimum function value.

[0047] Using the Boustrophedon path, a bow-shaped traversal is performed within each subregion in the best access order and the optimal path for subregion transformation.

[0048] The detailed steps are as follows:

[0049] The method uses Maklink graphs based on the free space method to build an environment model;

[0050] The free-space method represents obstacles by their vertices and makes the following assumptions about the experimental environment: Obstacles exist in the experimental environment. The first obstacle, the second One obstacle have ( If there are 10 vertices, then the obstacles and the environment are represented as follows:

[0051]

[0052]

[0053] in: Indicates the first The first obstacle The coordinates of each vertex.

[0054] Then, the Maklink graph is constructed using the principles and basic requirements of free link lines in Maklink graph theory:

[0055] ① Combine the vertices of all concave and convex polygonal obstacles into a set.

[0056] ,

[0057] Draw perpendicular lines from each vertex to the boundary, connect all pairs of points, and arrange them in ascending order of length, storing them in a set. middle.

[0058] ② Select set The first line segment in the diagram.

[0059] ③ Determine if the selected line segment intersects with the concave-convex polygon obstacle. If it intersects, the line segment cannot be used as a Maklink line, discard the line segment, and check the set. The next line segment is checked until the checked line segment does not intersect with the concave-convex polygon obstacle, then proceed to step ④.

[0060] ④ Check the two exterior angles formed by the line segment and the vertex of the concave-convex polygon obstacle. If both exterior angles are... If the vertex is the optimal connecting line, delete all other connecting lines to that vertex and proceed to step ⑦; if a certain exterior angle If so, then the connecting line is added to the candidate connecting lines of that vertex.

[0061] ⑤ Check if there is an exterior angle among all candidate connecting lines to this vertex. If it exists, then select the set. Find the next line segment in the sequence and return to step 3); if it does not exist, proceed to step 6.

[0062] ⑥ Delete any other redundant connecting lines to this vertex.

[0063] ⑦ Repeat steps ① to ⑥ until all vertices are completed. This completes the construction of the Maklink graph.

[0064] Furthermore, the principle of sub-region division in the method is as follows:

[0065] On the Maklink map, multiple convex polygons bounded by Maklink links, obstacle boundaries, and 2D map boundaries constitute the traversable sub-regions for the mobile robot, such as... Figure 2 As shown.

[0066] Then, the order in which the mobile robot visits the sub-regions (generalized Hamiltonian path) is determined using the one-dimensional ant colony algorithm, and the sub-region numbers are given.

[0067] In the original access sequence diagram (such as...) Figure 3 As shown in the diagram, when there are adjacent edges between two sub-regions, the two sub-regions are considered connected, and the connection weight is set to 1. Each sub-region is a node, and the corresponding adjacency matrix is ​​obtained:

[0068]

[0069] Given the adjacency matrix A, the path between any two subregions is given.

[0070]

[0071] The specific one-dimensional ant colony algorithm is as follows:

[0072] Let the number of ants in the entire ant colony be . The number of sub-regions is subregion sub-region The distance between them is , Time sub-region sub-region The pheromone concentration along the connection path is Initially, the pheromone concentrations on the connection paths between each sub-region are the same; let's assume they are 100%. .

[0073] Ant The next sub-region to be visited is determined by the pheromone concentration along the connection paths between sub-regions. Let... express Time Ant From sub-region Transfer to sub-region The probability of is calculated using the following formula:

[0074]

[0075] in, For heuristic functions, This indicates that the ant is moving from the sub-region. Transfer to sub-region The level of expectation; For ants The set of sub-regions visited, initially, There is Each element includes, except for ants. As time progresses, all other subregions of the starting subregion... The number of elements in the array decreases continuously until it is empty, which means that all sub-regions have been visited.

[0076] This is a pheromone importance factor; the higher the value, the greater the role of pheromone concentration in the transfer process. This is the importance factor of the heuristic function. The larger the value, the greater the role of the heuristic function in the transition, meaning that ants will have a higher probability of moving to the shorter sub-region.

[0077] Ant colony optimization uses pheromones to attract ants to search. The setting and updating of pheromone locations are of great importance to the successful search of ant colony optimization. The pheromone at each point is updated after the ants pass by.

[0078] The updating of pheromones consists of two parts: local updating and global updating. Local updating refers to the reduction of pheromones at a point when an ant passes through it. The purpose of local updating is to increase the probability of the ant searching for points it has not yet visited, thus achieving the goal of global searching. Local pheromone updating continues as the ant searches, and the pheromone update formula is:

[0079]

[0080] in, sub-region sub-region The pheromone value carried along the connection path; The decay coefficient of pheromones.

[0081] As ants release pheromones, the pheromone concentration along the connecting paths between different sub-regions gradually disappears. Let parameters... This indicates the degree of pheromone volatilization. Therefore, after all ants complete one cycle, the pheromone concentration along the connecting paths between sub-regions needs to be updated in real time.

[0082]

[0083] in, Indicates the first Only ants in the sub-region sub-region The concentration of pheromones released along the connection path; This indicates that all ants are in the sub-region. sub-region The sum of pheromone concentrations released along the connection path.

[0084] Ants on shorter paths release more pheromones. As time progresses, the pheromone concentration on shorter paths gradually increases, and more and more ants choose these paths. Eventually, the entire ant population will converge on the optimal path under positive feedback, which corresponds to the optimal solution to the problem.

[0085] Then, the ant colony algorithm, which minimizes the function value, is used to obtain the optimal path for the robot to switch between sub-regions.

[0086]

[0087]

[0088] in: The nodes that the path passes through in sequence, and the corresponding free link lines are: S and T represent the starting point and the ending point, respectively.

[0089] set up and They are respectively The two endpoints of the link are then represented as follows: Within the movable space corresponding to one side of the obstacle, other points on the link are:

[0090]

[0091] in: For proportional parameters, Then a group Corresponding to a set of paths, This is the solution optimized using the minimum function ant colony algorithm.

[0092] Minimum function value is one method for finding the minimum path between two points. The following example uses a three-segment path minimum function value algorithm to illustrate the algorithm principle.

[0093] Let the starting coordinates be The endpoint coordinates are The first path in the three-segment path has the following start and end points: The vector representation of this path segment is as follows ,in ; Then there is ;

[0094] The start and end points of the second segment are respectively The start and end points of the third path are respectively Similarly, the following can be concluded:

[0095] ;

[0096] ;

[0097]

[0098] Therefore, the path length from the starting point to the ending point can be expressed as:

[0099]

[0100] The ant colony algorithm is used to iteratively solve the expression for the path length to find the optimal value. The optimal value includes the minimum value of the function obtained in each iteration and the value of its corresponding independent variable.

[0101] For each iteration, get The solution and its corresponding path length value Let the maximum value among them be The minimum value is Then, pheromones are defined as:

[0102]

[0103] In the iterative process using the ant colony algorithm, the expression for its heuristic function is:

[0104]

[0105] The state transition probability expression for this ant is:

[0106]

[0107] The probability values ​​for local search and global search are median value The smaller the function value, the greater the corresponding transition probability, and the more necessary a local search should be; the larger the function value, the smaller the corresponding transition probability, and the more necessary a global search should be.

[0108] During the iterative optimization process of the ant colony, if the state transition probability is greater than... The ant colony then performs a local search, and during the local process... The search scope is ,in The iteration number is given; if the state transition probability is less than... Then the ant colony performs a global search, during which it searches for... The search scope is until obtained Each corresponds to a certain value, such that the path length Minimum.

[0109] If during the iterative solution process, Then let If it appears Then let Then, substitute it into the next iteration calculation. Continue until the number of iterations is exhausted or the optimal value in the iteration process remains unchanged for several consecutive generations, and the minimum function value based on the ant colony algorithm can be obtained.

[0110] In summary, the ant colony algorithm for finding the minimum function value uses the path length from the starting point, passing through a certain point on some Maklink links, to the destination as the objective function, and the points on the traversed Maklink links as the independent variables. To facilitate the solution, the traversed Maklink links are normalized. In each calculation, the specific positions on these Maklink links are de-normalized based on the normalization result. Through multiple iterations, the optimal path for the mobile robot to transition between regions is obtained.

[0111] The basic idea of ​​triangulation pruning (geometric optimization) is: if multiple consecutive nodes in the path... This forms a multi-segment broken line. and If the direct connection path does not pass through any obstacles, then it can be used and Replace the straight line segments between arrive Multiple broken line segments. For example... Figure 9 As shown, the green line represents the initial planned path, and the red line represents the planned path optimized using triangulation.

[0112] Finally, the Boustrophedon path is used to obtain the optimal path through all sub-regions on the Maklink map.

[0113] The mobile robot takes the shortest path to the vicinity of a vertex in a sub-region that needs to be traversed, such as... Figure 6 and Figure 7 As shown by the blue dashed line, the robot moves along the longest side of the sub-region in a "bow" shape to the other vertex of that side. Upon reaching the other vertex, it then moves back and forth along the longest side again, achieving path planning for full coverage by the mobile robot. Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown by the solid red line in the image.

[0114] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0115] This invention establishes a system that uses free link lines in a Maklink graph to divide the entire two-dimensional planar space into multiple sub-regions (each sub-region is a convex polygon). The Maklink graph algorithm can perform map modeling on any complex two-dimensional environment, with low information storage requirements, high decision-making efficiency, and strong robustness.

[0116] The connection order of the sub-regions is transformed into the "Traveling Salesman Problem", and the optimal access order of the sub-regions is given by the one-dimensional ant colony algorithm. Local pheromone is added during the access process, that is, the number of different paths taken by the ants is increased in one iteration.

[0117] A network space model for robot mobility is constructed using free link lines in a Maklink graph, and the optimal path for robot transitions between sub-regions is given by an ant colony algorithm that finds the minimum function value. This increases the number of possible positions for the transition path on each free link line.

[0118] The system can plan the "bow"-shaped movement path that moves parallel to a certain edge within a sub-region in real time, thus realizing path planning for global traversal.

[0119] Another embodiment of the present invention provides a two-dimensional full-coverage path planning method for mobile robots.

[0120] The operating environment for this path planning simulation experiment is: Windows 11 Home Chinese Edition; Matlab R2017b; 12th Gen Intel(R) Core(TM) i5-12500H processor; 2.5GHz clock speed; 16GB memory. A two-dimensional full-coverage path planning method for mobile robots based on Maklink graphs and Boustrophedon paths is presented.

[0121] I. Modeling the Working Environment of Mobile Robots

[0122] Currently, commonly used environmental modeling methods for mobile robots include grids, Maklink graphs, and visibility graphs. Among them, grids suffer from problems such as large map information content and low decision-making efficiency in complex environments. This invention uses Maklink graphs to build an environmental model.

[0123] Assuming the mobile robot moves in a static two-dimensional space, obstacles are represented by concave and convex polygons, with the height of the polygons perpendicular to the XY plane. The boundaries of the obstacles are expanded based on the robot's maximum size and the minimum range required for normal perception. The mobile robot is simplified to a point mass, and obstacles are represented by vertices. The following assumptions are made regarding the experimental environment: [The text abruptly ends here, so the translation stops as well.] The first obstacle, the second One obstacle have ( If there are 10 vertices, then the obstacles and the environment are represented as follows:

[0124]

[0125]

[0126] in: Indicates the first The first obstacle The coordinates of each vertex are then determined. Subsequently, the principles and basic requirements of free link lines in Maklink graph theory are used to construct the Maklink graph and establish free link lines. The establishment of free link lines is based on Professor Maki K. Habib's 1991 research, which uses concave and convex polygons to represent obstacles in the environment and uses Maklink link lines to connect the vertices of different obstacles. These link lines do not pass through obstacles, and the external angle formed by the link lines with the obstacle boundaries is no greater than [value missing]. Furthermore, the connecting lines do not intersect each other. Using the connecting lines, obstacle boundaries, and the boundaries of the 2D map, the workspace is divided into multiple convex polygons to construct traversable sub-regions for the mobile robot, such as... Figure 2 As shown.

[0127] II. Ant Colony Algorithm for Establishing Sub-Region Access Order

[0128] Let the number of ants in the entire ant colony be . The number of sub-regions is subregion sub-region The distance between them is , Time sub-region sub-region The pheromone concentration along the connection path is Initially, the pheromone concentrations on the connection paths between each sub-region are the same; let's assume they are 100%. .

[0129] Ant The next sub-region to be visited is determined by the pheromone concentration along the connection paths between sub-regions. Let... express Time Ant From sub-region Transfer to sub-region The probability of is calculated using the following formula:

[0130]

[0131] in, For heuristic functions, , representing the expected degree of ant movement from subregion i to subregion j; Let k be the set of subregions visited by ant k. Initially, There is Each element includes, except for ants. As time progresses, all other subregions of the starting subregion... The number of elements in the array decreases continuously until it is empty, which means that all sub-regions have been visited.

[0132] This is a pheromone importance factor; the higher the value, the greater the role of pheromone concentration in the transfer process. This is the importance factor of the heuristic function. The larger the value, the greater the role of the heuristic function in the transition, meaning that ants will have a higher probability of moving to the shorter sub-region.

[0133] The updating of pheromones consists of two parts: local updating and global updating. Local updating refers to the reduction of pheromones at a point when an ant passes through it. The purpose of local updating is to increase the probability of the ant searching for points it has not yet visited, thus achieving the goal of global searching. Local pheromone updating continues as the ant searches, and the pheromone update formula is:

[0134]

[0135] in, sub-region sub-region The pheromone value carried along the connection path; The decay coefficient of pheromones.

[0136] As ants release pheromones, the pheromone concentration along the connecting paths between different sub-regions gradually disappears. Let parameters... This indicates the degree of pheromone volatilization. Therefore, after all ants complete one cycle, the pheromone concentration along the connecting paths between sub-regions needs to be updated in real time.

[0137]

[0138] in, Indicates the first Only ants in the sub-region sub-region The concentration of pheromones released along the connection path; This indicates that all ants are in the sub-region. sub-region The sum of pheromone concentrations released along the connection path.

[0139] Ants on shorter paths release more pheromones. As time progresses, the pheromone concentration on shorter paths gradually increases, and more and more ants choose these paths. Eventually, under the influence of positive feedback, all the ants will converge on the optimal path. This corresponds to the optimal solution to the problem being optimized, obtaining the best access order for the sub-region, such as... Figure 4 As shown.

[0140] III. Establishing an Ant Colony Algorithm for Finding the Shortest Path Using the Minimum Function Value

[0141] Then, the ant colony algorithm, which minimizes the function value, is used to obtain the optimal path for the robot to switch between sub-regions.

[0142]

[0143]

[0144] in: The nodes that the path passes through in sequence, and the corresponding free link lines are: S and T represent the starting point and the ending point, respectively.

[0145] set up and L respectively i The two endpoints of the link are then represented as follows: Within the movable space corresponding to one side of the obstacle, other points on the link are:

[0146]

[0147] in: For proportional parameters, Then a group Corresponding to a set of paths, This represents the solution obtained using the minimum function ant colony algorithm and geometry optimization.

[0148] Minimum function value is one method for finding the minimum path between two points. The following example uses a three-segment path minimum function value algorithm to illustrate the algorithm principle.

[0149] Let the starting coordinates be The endpoint coordinates are The first path in the three-segment path has the following start and end points: The vector representation of this path segment is as follows ,in ; Then there is ;

[0150] The start and end points of the second segment are respectively The start and end points of the third path are respectively Similarly, the following can be concluded:

[0151] ;

[0152] ;

[0153]

[0154] Therefore, the path length from the starting point to the ending point can be expressed as:

[0155]

[0156] The ant colony algorithm is used to iteratively solve the expression for the path length to find the optimal value. The optimal value includes the minimum value of the function obtained in each iteration and the value of its corresponding independent variable.

[0157] For each iteration, get The solution and its corresponding path length value Let the maximum value among them be The minimum value is Then, pheromones are defined as:

[0158]

[0159] In the iterative process using the ant colony algorithm, the expression for its heuristic function is:

[0160]

[0161] The state transition probability expression for this ant is:

[0162]

[0163] The probability values ​​for local search and global search are median value The smaller the function value, the greater the corresponding transition probability, and the more necessary a local search should be; the larger the function value, the smaller the corresponding transition probability, and the more necessary a global search should be.

[0164] During the iterative optimization process of the ant colony, if the state transition probability is greater than... The ant colony then performs a local search, and during the local process... The search scope is ,in The iteration number is given; if the state transition probability is less than... Then the ant colony performs a global search, during which it searches for... The search scope is until obtained Each corresponds to a certain value, such that the path length Minimum.

[0165] If during the iterative solution process, Then let If it appears Then let Then, substitute it into the next iteration calculation. Continue until the number of iterations is exhausted or the optimal value in the iteration process remains unchanged for several generations, and the minimum function value based on the ant colony algorithm can be obtained.

[0166] The basic idea of ​​triangular pruning is: if multiple consecutive nodes in the path This forms a multi-segment broken line. and If the direct connection path does not pass through any obstacles, then it can be used and Replace the straight line segments between arrive Multiple bends in the line segment.

[0167] IV. Establish the Boustrophedon path

[0168] The mobile robot takes the shortest path to the sub-region that needs to be traversed, and moves back and forth along the longest side of the sub-region in a "bow" shape to the other vertex of that side. When it reaches the other vertex of the side, it moves back and forth along the longest side again, thus achieving path planning that covers the entire area.

[0169] V. A Two-Dimensional Full-Coverage Path Planning Method for Mobile Robots Based on Maklink Graphs and Boustrophedon Paths

[0170] This invention first uses Maklink graph free link lines to divide the entire two-dimensional planar space into multiple sub-regions (each sub-region is a convex polygon); then, the connection order of the sub-regions is converted into a "Traveling Salesman Problem," and a one-dimensional ant colony algorithm is used to determine the visiting order of the sub-regions; next, a network space model that the robot can move in is constructed using Maklink graph free link lines, and an ant colony algorithm that minimizes the function value is used to determine the optimal path for the robot to switch between sub-regions; finally, a "bow"-shaped motion path that moves parallel to an edge within a sub-region is planned in real time, achieving global traversal path planning. The process is analyzed in detail below with reference to an example map.

[0171] The map's horizontal axis ranges from [0, 200], and its vertical axis ranges from [0, 200].

[0172] The coordinates of the obstacle vertices are as follows:

[0173] The first obstacle: [40,140], [60,160], [100,140], [60,120];

[0174] The second obstacle: [50,30], [30,40], [80,80], [100,40];

[0175] The third obstacle: [120,160], [140,100], [180,170], [165,180];

[0176] The fourth obstacle: [120,40], [170,40], [140,80];

[0177] The fifth obstacle: [180,20], [220,80], [200,160];

[0178] The initial position of the mobile robot is [-0.2, -0.2];

[0179] The distance between two adjacent "bow"-shaped paths is 5;

[0180] Parameters for one-dimensional and two-dimensional ant colony algorithms:

[0181] The number of ants is 50;

[0182] The maximum number of iterations is 30;

[0183] The pheromone importance factor is 2;

[0184] The importance factor of the heuristic function is 7;

[0185] The local pheromone evaporation factor is 0.5;

[0186] The global pheromone evaporation factor is 0.8;

[0187] The constant coefficient is 5;

[0188] The result of the mobile robot traversing within the instance map is as follows: Figure 8 As shown.

[0189] like Figure 10 As shown, the present invention also provides a two-dimensional full-coverage path planning system for mobile robots, comprising:

[0190] Partitioning and Construction Module: Used to generate Maklink lines to partition traversed sub-regions and construct a two-dimensional path planning feasible space on a map with obstacles, using Maklink graph theory.

[0191] The calculation module is used to determine the optimal access order for traversing sub-regions using a one-dimensional ant colony algorithm, and then to obtain the optimal path for the robot to switch between sub-regions using an ant colony algorithm that finds the minimum function value based on the feasible space of two-dimensional path planning.

[0192] Traversal module: Used to perform a bow-shaped traversal within subregions using Boustrophedon paths, following the optimal access order and the optimal path for subregion transformation.

[0193] In the computation module, the steps for obtaining the optimal path for the robot to transition between sub-regions using the ant colony algorithm to find the minimum function value based on the feasible space of two-dimensional path planning are as follows:

[0194] The objective function is the path length from the starting point, through some points on the Maklink links, to the destination. The independent variables are the points on the Maklink links traversed. These Maklink links are normalized. In each calculation, the specific positions on these Maklink links are back-normalized based on the normalization result. Through multiple iterations, the optimal path for the mobile robot to transition between regions is obtained. Then, the optimal path for the mobile robot to transition between regions is further optimized using triangulation pruning. Specifically, if there are multiple consecutive nodes in the path... This forms a multi-segment broken line. and If the direct connection path does not pass through any obstacles, then it can be used and Replace the straight line segments between arrive Multiple bends in the line segment.

[0195] An embodiment of the present invention provides a terminal device. This terminal device includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0196] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0197] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0198] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0199] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0200] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0201] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art, guided by the specification, can make many other modifications without departing from the scope of the claims of the present invention, and all of these modifications are within the scope of protection of the present invention.

Claims

1. A two-dimensional full-coverage path planning method for a mobile robot, characterized in that, include: On a map containing obstacles, Maklink graph theory is used to generate Maklink lines to divide the traversed sub-regions and construct a two-dimensional path planning feasible space. The optimal access order for traversing sub-regions is obtained using a one-dimensional ant colony algorithm. Then, based on the feasible space of two-dimensional path planning, the optimal path for the robot to switch between sub-regions is obtained using an ant colony algorithm that finds the minimum function value. Using the Boustrophedon path, the subregions are traversed in a "bow" shape according to the best access order and the optimal path for subregion transformation; The steps for obtaining the optimal path for the robot to transition between sub-regions using the ant colony algorithm to find the minimum function value based on the feasible space of two-dimensional path planning are as follows: Ants on shorter paths release more pheromones. As time progresses, the pheromone concentration on shorter paths gradually increases, and more and more ants choose these paths. Eventually, the entire ant population will converge on the optimal path under positive feedback. This corresponds to the optimal solution to the optimization problem. Then, the ant colony algorithm, which minimizes the function value, is used to obtain the optimal path for the robot to switch between sub-regions. in: The nodes that the path passes through in sequence, and the corresponding free link lines are: S and T represent the starting point and the ending point, respectively. set up and They are respectively The two endpoints of the link are then represented as follows: Within the movable space corresponding to one side of the obstacle, other points on the link are: in: For proportional parameters, Then a group Corresponding to a set of paths, This is the solution optimized by the minimum function ant colony algorithm. Minimum function value is a method for finding the shortest path between two points. The following example uses a three-segment path minimum function value algorithm to illustrate the algorithm's principle. Let the starting coordinates be The endpoint coordinates are The first path in the three-segment path has the following start and end points: The vector representation of this path segment is as follows ,in ; Then there is ; The start and end points of the second segment are respectively The start and end points of the third path are respectively Similarly, the following can be concluded: ； ； Therefore, the path length from the starting point to the ending point can be expressed as: The ant colony algorithm is used to iteratively solve the expression for the path length to find the optimal value. The optimal value includes the minimum value of the function obtained in each iteration and the value of its corresponding independent variable. For each iteration, get The solution and its corresponding path length value Let the maximum value among them be The minimum value is Then, pheromones are defined as: In the iterative process using the ant colony algorithm, the expression for its heuristic function is: The state transition probability expression for this ant is: The smaller the function value, the greater the corresponding transition probability, and the more necessary a local search should be; the larger the function value, the smaller the corresponding transition probability, and the more necessary a global search should be. During the iterative optimization process of the ant colony, if the state transition probability is greater than... Then the ant colony performs a local search, and during the local process... The search scope is ,in The iteration number is given; if the state transition probability is less than... Then the ant colony performs a global search, during which it searches for... The search scope is until obtained Each corresponds to a certain value, such that the path length Minimum; If during the iterative solution process, Then let If it appears Then let Then, substitute it into the next iteration calculation until the number of iterations is exhausted or the optimal value in the iteration process does not change for several generations, and the minimum function value based on the ant colony algorithm can be obtained.

2. The two-dimensional full-coverage path planning method for a mobile robot according to claim 1, characterized in that, The specific steps for generating Maklink lines to partition traversed subregions and constructing a feasible space for two-dimensional path planning using Maklink graph theory are as follows: First, the obstacles and environment of the experimental space are represented. Then, convex and concave polygons are used to represent the obstacles in the environment. Maklink links are used to connect the vertices of different obstacles. The links do not pass through the obstacles, and the external angle formed by the links and the boundary of the obstacles is no greater than 1 / 3. Furthermore, the connecting lines do not intersect each other. By using the connecting lines, the boundary lines of obstacles, and the boundary of the two-dimensional map, the working space is divided into multiple convex polygons to construct the traversable sub-regions of the mobile robot.

3. The two-dimensional full-coverage path planning method for a mobile robot according to claim 1, characterized in that, The specific steps for deriving the optimal access order for traversing subregions using the one-dimensional ant colony algorithm are as follows: First, identify the sub-regions with adjacent edges. Set the connection weight of any two sub-regions with connecting edges to 1. Treat each sub-region as a node and give the adjacency matrix corresponding to each sub-region. Based on the adjacency matrix, give the path between any two sub-regions. Use the one-dimensional ant colony algorithm for solving the "traveling salesman problem" to obtain the order in which the robot visits the sub-regions.

4. The two-dimensional full-coverage path planning method for a mobile robot according to claim 1, characterized in that, Finally, the Boustrophedon path is used to perform a bow-shaped traversal within the sub-regions according to the best access order and the optimal path for sub-region transformation. The specific steps are as follows: The mobile robot moves to the sub-region that needs to be traversed according to the optimal path of sub-region transformation in the best access order of sub-regions. It moves back and forth along the longest edge of the sub-region in a "bow" shape to the other vertex of that edge. When it reaches the other vertex of this edge, it moves back and forth along the longest edge again, thus realizing the path planning of full coverage of the mobile robot.

5. A two-dimensional full-coverage path planning system for a mobile robot, characterized in that, A method for implementing a two-dimensional full-coverage path planning method for a mobile robot as described in any one of claims 1-4 includes: Partitioning and Construction Module: Used to generate Maklink lines to partition traversed sub-regions and construct a two-dimensional path planning feasible space on a map with obstacles, using Maklink graph theory. The calculation module is used to determine the optimal access order for traversing sub-regions using a one-dimensional ant colony algorithm, and then to obtain the optimal path for the robot to switch between sub-regions using an ant colony algorithm that finds the minimum function value based on the feasible space of two-dimensional path planning. Traversal module: Used to perform a bow-shaped traversal within subregions using Boustrophedon paths, following the optimal access order and the optimal path for subregion transformation.

6. A two-dimensional full-coverage path planning system for a mobile robot according to claim 5, characterized in that, In the computation module, the steps for obtaining the optimal path for the robot to transition between sub-regions using the ant colony algorithm to find the minimum function value based on the feasible space of two-dimensional path planning are as follows: The objective function is the path length from the starting point, through some points on the Maklink links, to the destination. The independent variables are the points on the Maklink links traversed. These Maklink links are normalized. In each calculation, the specific positions on these Maklink links are back-normalized based on the normalization result. Through multiple iterations, the optimal path for the mobile robot to transition between regions is obtained. Then, the optimal path for the mobile robot to transition between regions is further optimized using triangulation pruning. Specifically, if there are multiple consecutive nodes in the path... This forms a multi-segment broken line. and If the direct connection path does not pass through any obstacles, then it can be used and Replace the straight line segments between arrive Multiple bends in the line segment.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the two-dimensional full-coverage path planning method for a mobile robot as described in any one of claims 1 to 4.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the two-dimensional full-coverage path planning method for a mobile robot as described in any one of claims 1 to 4.

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