Multi-robot patrol path planning method and system considering differentiated access

Abstract

The application discloses the technical field of robot multi-target point path planning and discloses a multi-robot patrol path planning method and system considering differentiated access, solves the technical problems of unreasonable resource allocation and insufficient important target access caused by not considering the actual access demand of target points in the prior art, generates virtual nodes according to the access period constraints of each target point, decomposes tasks through space clustering with load balancing constraints, and establishes a path planning model with time window constraints to generate an initial path; based on the geometric centers of the virtual nodes covered by each robot, a cooperative pair is constructed according to the spatial neighbor principle, and merging and re-planning are performed, and iterative adjustment is performed with total distance reduction as the target until convergence is achieved, and a final path scheme is obtained. The application can strictly meet the differentiated access period requirements of each target point, avoid uneven allocation of patrol resources, and obtain a high-quality patrol path scheme under limited computing resources.

Description

Technical Field

[0001] This invention relates to the field of multi-target point path planning technology for robots, specifically to a multi-robot patrol path planning method and system that considers differentiated access for patrol tasks where each target point has different access cycle constraints. Background Technology

[0002] In recent years, multi-robot systems have been increasingly widely used in various fields such as logistics, healthcare, agriculture, park security, disaster relief, environmental monitoring, and home services, with patrolling being one of the typical application scenarios. In most patrol tasks, robots need to periodically visit multiple target points within an area. In real-world scenarios, different target points often have different access requirements due to differences in importance, security level, or data collection needs. The most direct manifestation of this is the different access cycles, i.e., the different maximum allowable idle time for each target point.

[0003] However, most existing multi-robot patrol path planning strategies assume that all target points are of equal importance, typically aiming to minimize weighted metrics such as the average or maximum idle time of each target point. This "one-size-fits-all" approach can lead to risks for important targets due to insufficient access frequency, while less important targets are over-accessed, resulting in a waste of patrol resources (such as robot range and working time). Furthermore, in scenarios such as environmental monitoring, excessively frequent access can lead to redundant collected data, and minimizing idle time does not align with actual needs.

[0004] Reasonable path planning should effectively reduce the robot's total travel distance while strictly meeting the differentiated access cycle requirements of each target point. This is key to improving the resource utilization efficiency and task execution quality of multi-robot systems. Therefore, it is necessary to develop a multi-robot patrol path planning method and system that can take into account differentiated access. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-robot patrol path planning method and system that considers differentiated access, solving the technical problems of unreasonable resource allocation and insufficient access to important targets caused by the failure to consider the actual access needs of target points in the prior art. This solution can strictly meet the differentiated access cycle requirements of each target point and obtain a high-quality patrol path under limited computing resources.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: This invention provides a multi-robot patrol path planning method considering differentiated access, comprising the following steps: S1. Obtain the task duration, base location, location and access cycle of each target point, as well as the number of robots performing the task and their movement speed; S2. Based on the task duration and the access cycle of each target point, calculate the minimum number of accesses for each target point within the task duration, and construct an extended node set by generating virtual nodes; S3. Perform spatial clustering on the virtual nodes in the extended node set, set an upper and lower limit for the number of virtual nodes in each cluster, divide the virtual nodes into several task clusters equal to the number of robots, and number each task cluster as follows: Each task cluster corresponds to one robot, which is assigned the same number. S4. For each task cluster, with the goal of minimizing the total distance, establish a path planning model with time window constraints, and call the solver to generate the initial path for a single robot; S5. For each robot, calculate the geometric center of the virtual nodes covered by its initial path; select one robot in order of robot number and select the other robot whose geometric center is closest to it to form a cooperative pair; S6. Merge the task clusters of the selected collaboration pairs, establish a path planning model and solve it to obtain the replanning path of the collaboration pair; S7. If the sum of the distances of the replanned paths of the cooperative pair is less than the sum of the distances of its initial paths, then replace the original path with the replanned path; otherwise, keep the original path. Repeat S5 to S7 until the iteration stopping condition is met to obtain the final multi-robot patrol path. S8. Output the final multi-robot patrol path.

[0007] Furthermore, in S2, the original target point Minimum number of accesses within task duration H for:

[0008] in, · This is the floor function. For the target point Access cycle; The specific method for generating virtual nodes is as follows: for nodes with a access count of [number missing], [method missing]. target point ,generate Each of the following virtual nodes corresponds to the first to the second iteration of the target point. Each visit constructs a set of virtual nodes. It contains the virtual nodes corresponding to each visit to the original target point; construct the extended node set. , where node 0 represents the base.

[0009] Furthermore, the spatial clustering in S3 includes: S31. Based on the total number of virtual nodes And the number of robots Set a lower limit for the number of virtual nodes that each task cluster can contain. and upper limit value :

[0010] S32. Random selection Each virtual node serves as the initial center point for each task cluster; S33. For each unassigned virtual node, calculate its distance to the center point of each task cluster, and assign it to the nearest virtual node whose current number of virtual nodes has not reached the upper limit. Task clusters; S34. After each assignment, update the center point coordinates of the task cluster based on the positions of all virtual nodes currently contained in the cluster:

[0011] In the formula, Indicates the first A cluster of tasks This represents the number of virtual nodes within the cluster.

[0012] S35. After all virtual nodes have been allocated, check if there are any task clusters whose number of virtual nodes is lower than the lower limit. If the clustering scheme exists, the current clustering is considered invalid; otherwise, the total intra-cluster distances for this clustering scheme are calculated.

[0013] In the formula, For the first A cluster of tasks For the first The coordinates of the center point of each task cluster; S36. Repeat steps S32 to S35 until the maximum number of iterations is reached, then select... The minimum clustering scheme is used as the final task cluster partitioning.

[0014] Furthermore, the constraints for establishing the path planning model in S4 and S6 include time window constraints, specifically: Access cycle constraints:

[0015] In the formula, For virtual nodes The predecessor node is determined as follows: if a virtual node corresponds to the first visit of a target point, its predecessor node is base node 0; if it corresponds to a subsequent visit, its predecessor node is the virtual node that was visited before the target point. For virtual nodes The access cycle corresponding to the original target point. Task duration; Represents virtual nodes Whether this is the last visit to a certain target point, 1 if yes, 0 if no; And robot return time constraints: the robot must return to base no later than the mission duration. .

[0016] Furthermore, the constraints for establishing the path planning model in S4 and S6 also include: Node allocation constraint: Each virtual node must be accessed by one and only one robot; Path continuity constraint: The robot starts from the base, returns to the base after completing the visit, and the number of paths to and from each visited node is conserved; Time continuity constraint: When the robot moves along the path, the time to visit the next node is not less than the time to visit the previous node plus the travel time between the two points. Sub-path elimination constraint: Eliminates independent loops that do not contain a base; 2-Cyclic Elimination Constraints: Eliminate low-order elimination constraints of special sub-loops; Path prohibition constraint between virtual nodes with the same target point: Direct connection paths are prohibited between multiple virtual nodes generated at the same target point.

[0017] Furthermore, in S5, when selecting robots sequentially according to their robot numbers, if the current robot has already participated in the merging optimization as a partner in a previous iteration, then the robot is skipped and the next one is selected; otherwise, the Euclidean distance between the geometric center of the virtual node covered by the current robot's path and the geometric centers of other robots is calculated, and the other robot with the smallest distance is selected to form a partner.

[0018] Furthermore, the iteration stopping condition in S7 is: constructing and optimizing cooperative pairs sequentially according to the robot number order, when a whole round of traversal is completed and the total distance in that round remains unchanged.

[0019] The present invention also provides a multi-robot patrol path planning system that considers differentiated access, comprising: The data acquisition module is used to acquire task duration, base location, location and access cycle of each target point, as well as the number of robots performing the task and robot movement speed; The node expansion module, connected to the data acquisition module, is used to calculate the minimum number of times each target point is accessed within the task duration based on the task duration and the access cycle of each target point, and to construct an expansion node set by generating virtual nodes. The node clustering module, connected to the node expansion module, is used to spatially cluster the virtual nodes and divide them into task clusters equal to the number of robots. The initial path generation module, connected to the node clustering module, is used to establish and solve a path planning model for each task cluster to generate an initial path for a single robot. The cooperative pair selection module, connected to the initial path generation module, is used to select the reference robot sequentially according to the robot number order and match the nearest neighbor to form a cooperative pair; The replanning path solving module is connected to the collaboration pair selection module. It is used to merge the task clusters of the collaboration pair, establish a path planning model and solve it to obtain the replanning path of the collaboration pair. The iterative optimization module is connected to the initial path generation module, the cooperative pair selection module, and the replanning path solving module, respectively. It is used to determine whether to replace the original path with a replanning path and to repeatedly trigger the cooperative pair selection module and the replanning path solving module until the iteration stop condition is met. The path output module, connected to the iterative optimization module, is used to output the final multi-robot patrol path.

[0020] Furthermore, the node clustering module includes: The upper and lower limit setting unit is used to set the upper and lower limits of the number of virtual nodes in each task cluster based on the total number of virtual nodes and the number of robots. The clustering iterative unit is used to randomly select the initial center point in each iteration, enforce the upper limit constraint when allocating virtual nodes, check whether the lower limit constraint is satisfied after allocation, and calculate the total intra-cluster distance. The scheme selection unit is used to select the effective clustering scheme with the smallest distance within the total cluster from multiple iterations as the final task cluster partition.

[0021] Furthermore, the iterative optimization module includes: A condition judgment unit is used to determine whether the iteration stopping condition is met, wherein the iteration stopping condition is that a full round of traversal iteration is completed and the total distance remains unchanged; The path replacement decision unit is used to compare the sum of the path distances before and after replanning in the collaborative pair and decide whether to replace the original path with the replanned path.

[0022] By adopting the above technical solution, the present invention has the following advantages: 1. This invention provides a multi-robot patrol path planning method that considers differentiated access. By transforming the access cycle constraint into a time window constraint between virtual nodes and integrating it into a mathematical programming model, it can strictly ensure that each target point is visited within its required access cycle. The planning scheme meets the differentiated requirements and completely solves the problems of unreasonable resource allocation and insufficient access to important targets in the prior art.

[0023] 2. This invention provides a multi-robot patrol path planning method that considers differentiated access, employing a hierarchical solution framework of "decomposition-cooperation". First, large-scale complex problems are decomposed into multiple small-scale sub-problems through spatial clustering with load balancing, significantly reducing the computational complexity of the initial solution. Then, through an iterative replanning mechanism based on spatial nearest neighbor cooperation, the task allocation at the cluster boundaries is intelligently adjusted, overcoming the limitations of "one-size-fits-all" decomposition. This significantly improves the quality of the final path scheme under limited computational resources, approaching the global optimum and achieving a high balance between computational efficiency and scheme quality.

[0024] 3. This invention provides a multi-robot patrol path planning system that considers differentiated access. By introducing target allocation constraints, it mathematically ensures that all access tasks for the same target point are handled by a single robot. This not only avoids the complex online coordination and communication synchronization problems caused by multiple robots cooperating to access the same target point, reducing the difficulty and cost of system implementation, but also improves the feasibility and robustness of the entire patrol scheme in actual operation. Attached Figure Description

[0025] Figure 1 This is a flowchart of the multi-robot patrol path planning method of the present invention that considers differentiated access; Figure 2 This is a flowchart of the spatial clustering steps of the present invention; Figure 3 This is a flowchart of the iterative optimization steps of the present invention; Figure 4 This is a structural block diagram of the multi-robot patrol path planning system of the present invention, which considers differentiated access. Detailed Implementation

[0026] The technical solution of the present invention will be specifically described below with reference to the accompanying drawings. It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0027] like Figure 1 As shown, this embodiment discloses a multi-robot patrol path planning method that considers differentiated access, including the following steps: S1. Obtain the task duration, base location, location and access cycle of each target point, as well as the number of robots performing the task and their movement speed; S2. Based on the task duration and the access cycle of each target point, calculate the minimum number of accesses for each target point within the task duration, and construct an extended node set by generating virtual nodes; Specifically, the original target point Minimum number of accesses within task duration H for:

[0028] In the formula, · This is the floor function. For the target point Access cycle.

[0029] The specific method for generating virtual nodes is as follows: for nodes with a access count of [number missing], [method missing]. target point ,generate There are 1 virtual nodes, corresponding sequentially to the 1st, 2nd, ..., 1st virtual nodes. This is the second visit. A set of virtual nodes is constructed as follows: It contains the virtual nodes corresponding to each visit to the original target point; construct the extended node set. , where node 0 represents the base.

[0030] S3. Perform spatial clustering on the virtual nodes in the extended node set, set an upper and lower limit for the number of virtual nodes in each cluster, divide the virtual nodes into several task clusters equal to the number of robots, and number each task cluster as follows: Each task cluster corresponds to one robot, which is assigned the same number. Specifically, set the maximum number of iterations for spatial clustering. Spatial clustering process as follows Figure 2 As shown, the specific steps include the following: S31. Based on the total number of virtual nodes And the number of robots Set a lower limit for the number of virtual nodes that each task cluster can contain. and upper limit value ; S32, Random Selection Each virtual node serves as the initial center point for each task cluster; S33. For each unassigned virtual node, calculate its distance to the center point of each task cluster, and assign it to the nearest virtual node whose current number of virtual nodes has not reached the upper limit. Task clusters; S34. After each allocation, update the center point coordinates of the task cluster based on the positions of all virtual nodes currently included in the task cluster. ,in, Indicates the first A cluster of tasks This represents the number of virtual nodes within the cluster. S35. After all virtual nodes are allocated, check if there are any task clusters whose number of virtual nodes is lower than the lower limit. If the clustering scheme exists, the current clustering is deemed invalid; otherwise, the total intra-cluster distances for this clustering scheme are calculated. ,in, For the first A cluster of tasks For the first The coordinates of the center point of each task cluster; S36. Repeat steps S32 to S35 until the maximum number of iterations is reached. Select The minimum clustering scheme is used as the final task cluster partitioning.

[0031] S4. For each task cluster, with the goal of minimizing the total distance, establish a path planning model with time window constraints, and call the solver to generate the initial path for a single robot; Specifically, the decision variables for the path planning model are defined as follows: A binary variable representing a robot. From node Move to node ,in If yes, it is 1; otherwise, it is 0. A binary variable representing a robot. Access virtual node? If yes, it is 1; otherwise, it is 0. For continuous variables, representing virtual nodes The time of access; Let be a continuous variable, representing the robot. The moment to return to base.

[0032] The above path planning model can be expressed as:

[0033] Equation (1) is the objective function, where, For the assembly of robots, For nodes To node The distance. Equations (2)-(14) are the constraints. The constraints include time window constraints, specifically: Equations (2) and (3) are access cycle constraints. For virtual nodes The predecessor node is determined as follows: if a virtual node corresponds to the first visit of a target point, its predecessor node is base node 0; if it corresponds to a subsequent visit, its predecessor node is the virtual node that was visited before the target point. For virtual nodes The access cycle corresponding to the original target point. For task duration, Represents virtual nodes Whether it is the last visit to a certain target point is 1 if yes and 0 if no. Equation (4) is the robot return time constraint.

[0034] The constraints also include: Equation (5) assigns constraints to nodes: each virtual node must be accessed by one and only one robot; Equations (6), (7), (8), and (9) represent path continuity constraints: the robot starts from the base, returns to the base after completing the visit, and the number of paths entering and leaving each visited node is conserved; Equations (10) and (11) are time continuity constraints: when the robot moves along the path, the time of visiting the next node is not less than the time of visiting the previous node plus the travel time between the two points. Equation (12) is the sub-path elimination constraint: eliminating independent loops that do not contain a base; Equation (13) is a 2-cycle elimination constraint: a low-order elimination constraint for eliminating special sub-loops; Equation (14) is a path prohibition constraint between virtual nodes with the same target point: it prohibits the establishment of direct paths between multiple virtual nodes generated at the same target point.

[0035] In equation (10), For the node To node Travel time; For a sufficiently large positive number, this example takes... In equation (12), Let be a non-negative continuous variable, representing the robot. For virtual nodes The order of access; For a set of virtual nodes The number of elements. In equation (14), For the original set of target points, Original target point The set consisting of all corresponding virtual nodes.

[0036] When solving for the initial path of a single robot, the number of robots is 1, and the set of virtual nodes is... , Indicates the first The set of all virtual nodes within a task cluster, and the extended node set. The initial path is obtained by calling a commercial solver (such as Gurobi or CPLEX).

[0037] S5. For each robot, calculate the geometric center of the virtual nodes covered by its initial path; select one robot in order of robot number and select the other robot whose geometric center is closest to it to form a cooperative pair; Specifically, according to the robot numbering sequence ( Select robots in sequence. If the current robot has participated in the merging optimization as a partner in a previous iteration, skip the robot and continue to select the next one; otherwise, calculate the Euclidean distance between the geometric center of the virtual node covered by the current robot's path and the geometric centers of other robots, and select the other robot with the smallest distance to form a cooperative pair.

[0038] S6. Merge the task clusters of the selected collaboration pairs, establish a path planning model and solve it to obtain the replanning path of the collaboration pair; Specifically, the number of robots in the solution model is 2, and the set of virtual nodes is... , and These are the virtual node sets of the merged task clusters and the expanded node set, respectively. The solution is obtained by calling a commercial solver (such as Gurobi or CPLEX) to solve the problem and obtain the replanning path for the cooperative pair.

[0039] S7. If the sum of the distances of the replanned paths of the cooperative pair is less than the sum of the distances of its initial paths, then replace the original path with the replanned path; otherwise, keep the original path. Repeat S5 to S7 until the iteration stopping condition is met to obtain the final multi-robot patrol path.

[0040] Specifically, the iteration stopping condition is: constructing and optimizing cooperative pairs in the order of robot numbers, and stopping when a full round of traversal is completed (all robots have participated in the merging optimization at least once) and the total distance in that round remains unchanged.

[0041] S8. Output the final multi-robot patrol path.

[0042] Specifically, the specific steps of iterative optimization are as follows: Figure 3 As shown, the patrol paths of all robots after the iterative optimization (including the order of visiting nodes and the estimated arrival time) will be output in the form of visualization charts and data files.

[0043] like Figure 4 As shown, the present invention also provides a system for implementing the above-described multi-robot patrol path planning method considering differentiated access, comprising: The data acquisition module is used to acquire task duration, base location, location and access cycle of each target point, as well as the number of robots performing the task and robot movement speed; The node extension module, connected to the data acquisition module, is used to calculate the minimum number of times each target point is accessed within the task duration based on the task duration and the access cycle of each target point, and to build an extended node set by generating virtual nodes. The node clustering module, connected to the node expansion module, is used to spatially cluster virtual nodes and divide them into task clusters equal to the number of robots. Specifically, the node clustering module includes: The upper and lower limit setting unit is used to set the upper and lower limits of the number of virtual nodes in each task cluster based on the total number of virtual nodes and the number of robots. The clustering iterative unit is used to randomly select the initial center point in each iteration, enforce the upper limit constraint when allocating virtual nodes, check whether the lower limit constraint is satisfied after allocation, and calculate the total intra-cluster distance. The scheme selection unit is used to select the effective clustering scheme with the smallest distance within the total cluster from multiple iterations as the final task cluster partition.

[0044] The initial path generation module, connected to the node clustering module, is used to establish and solve a path planning model for each task cluster, generating the initial path for a single robot. The cooperative pair selection module, connected to the initial path generation module, is used to select the baseline robot in order of robot number and match the nearest neighbor to form a cooperative pair. The replanning path solving module is connected to the collaboration pair selection module. It is used to merge the task clusters of collaboration pairs, establish a path planning model and solve it to obtain the replanning path of the collaboration pair. The iterative optimization module is connected to the initial path generation module, the cooperative pair selection module, and the replanning path solving module, respectively. It is used to determine whether to replace the original path with a replanning path and to repeatedly trigger the cooperative pair selection module and the replanning path solving module until the iteration stopping condition is met. Specifically, the iterative optimization module includes: The condition judgment unit is used to determine whether the iteration stopping condition is met. The iteration stopping condition is that a full round of traversal iteration is completed and the total distance remains unchanged. The path replacement decision unit is used to compare the sum of the path distances before and after replanning in the collaborative pair and decide whether to replace the original path with the replanned path.

[0045] The path output module, connected to the iterative optimization module, is used to output the final multi-robot patrol path.

[0046] This embodiment proposes a multi-robot patrol path planning method and system that considers differentiated access. At the modeling level, it breaks away from the limitation of traditional patrol strategies that treat all target points equally. By generating virtual nodes and introducing time window constraints, it expresses the differentiated access of each target point, avoiding the problem of unreasonable resource allocation. At the solution level, it employs spatial clustering with load balancing constraints to decompose large-scale problems into sub-problems to reduce computational complexity. Combined with an iterative optimization framework, it allows dynamic adjustments between adjacent robots, obtaining high-quality path solutions under limited computational resources. At the application level, by introducing target allocation constraints, it avoids the dependence on real-time communication and high-precision synchronization caused by multi-robot coordinated access, improving the executability and robustness of the patrol scheme. This method provides an efficient patrol path planning scheme that meets differentiated cycle requirements for typical multi-robot patrol scenarios such as park security, disaster relief, and environmental monitoring.

[0047] Finally, it should be noted that although the present invention has been described with reference to specific embodiments, those skilled in the art should recognize that the above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Various equivalent changes or substitutions can be made without departing from the concept of the present invention. Therefore, any changes or modifications to the above embodiments within the essential spirit of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A multi-robot patrol path planning method considering differentiated access, characterized in that, Includes the following steps: S1. Obtain the task duration, base location, location and access cycle of each target point, as well as the number of robots performing the task and their movement speed; S2. Based on the task duration and the access cycle of each target point, calculate the minimum number of accesses for each target point within the task duration, and construct an extended node set by generating virtual nodes; In S2, the original target point Task duration Minimum number of visits for: in, · This is the floor function. For the target point Access cycle; The specific method for generating virtual nodes is as follows: for nodes with a access count of [number missing], [method missing]. target point ,generate Each of the following virtual nodes corresponds to the first to the second iteration of the target point. Each visit constructs a set of virtual nodes. It contains the virtual nodes corresponding to each visit to the original target point; construct the extended node set. Node 0 represents the base; S3. Perform spatial clustering on the virtual nodes in the extended node set, set an upper and lower limit for the number of virtual nodes in each cluster, divide the virtual nodes into several task clusters equal to the number of robots, and number each task cluster as follows: Each task cluster corresponds to one robot, which is assigned the same number. S4. For each task cluster, with the goal of minimizing the total distance, establish a path planning model with time window constraints, and call the solver to generate the initial path for a single robot; S5. For each robot, calculate the geometric center of the virtual nodes covered by its initial path; select one robot in order of robot number and select the other robot whose geometric center is closest to it to form a cooperative pair; S6. Merge the task clusters of the selected collaboration pairs, establish a path planning model and solve it to obtain the replanning path of the collaboration pair; S7. If the sum of the distances of the replanned paths of the cooperative pair is less than the sum of the distances of its initial paths, then replace the original path with the replanned path; otherwise, keep the original path. Repeat S5 to S7 until the iteration stopping condition is met to obtain the final multi-robot patrol path. S8. Output the final multi-robot patrol path; The constraints for establishing the path planning model in S4 and S6 include time window constraints, specifically: Access cycle constraints: In the formula, For continuous variables, representing virtual nodes The time of visit, For virtual nodes The predecessor node is determined as follows: if a virtual node corresponds to the first visit of a target point, its predecessor node is base node 0; if it corresponds to a subsequent visit, its predecessor node is the virtual node that was visited before the target point. For virtual nodes The access cycle corresponding to the original target point. Task duration; Represents virtual nodes Whether this is the last visit to a certain target point, 1 if yes, 0 if no; And robot return time constraints: the robot must return to base no later than the mission duration. Let be a continuous variable, representing the robot. The moment of returning to base, For the assembly of robots; The constraints for establishing the path planning model in S4 and S6 also include: Node allocation constraint: Each virtual node must be accessed by one and only one robot; Path continuity constraint: The robot starts from the base, returns to the base after completing the visit, and the number of paths to and from each visited node is conserved; Time continuity constraint: When the robot moves along the path, the time to visit the next node is not less than the time to visit the previous node plus the travel time between the two points. Sub-path elimination constraint: Eliminates independent loops that do not contain a base; 2-Cyclic Elimination Constraints: Eliminate low-order elimination constraints of special sub-loops; Path prohibition constraint between virtual nodes with the same target point: Direct connection paths are prohibited between multiple virtual nodes generated at the same target point.

2. The multi-robot patrol path planning method considering differentiated access according to claim 1, characterized in that, The spatial clustering in S3 includes: S31. Based on the total number of virtual nodes And the number of robots Set a lower limit for the number of virtual nodes that each task cluster can contain. and upper limit value : S32. Random selection Each virtual node serves as the initial center point for each task cluster; S33. For each unassigned virtual node, calculate its distance to the center point of each task cluster, and assign it to the nearest virtual node whose current number of virtual nodes has not reached the upper limit. Task clusters; S34. After each assignment, update the center point coordinates of the task cluster based on the positions of all virtual nodes currently contained in the cluster: In the formula, Indicates the first A cluster of tasks This represents the number of virtual nodes within the cluster. S35. After all virtual nodes have been allocated, check if there are any task clusters whose number of virtual nodes is lower than the lower limit. If the clustering scheme exists, the current clustering is considered invalid; otherwise, the total intra-cluster distances for this clustering scheme are calculated. In the formula, For the first A cluster of tasks For the first The coordinates of the center point of each task cluster; S36. Repeat steps S32 to S35 until the maximum number of iterations is reached, then select... The minimum clustering scheme is used as the final task cluster partitioning.

3. The multi-robot patrol path planning method considering differentiated access according to claim 1, characterized in that, In step S5, when selecting robots sequentially according to their robot numbers, if the current robot has already participated in the merging optimization as a partner in a previous iteration, then skip that robot and continue to select the next one; otherwise, calculate the Euclidean distance between the geometric center of the virtual node covered by the current robot's path and the geometric centers of other robots, and select the other robot with the smallest distance to form a partner.

4. The multi-robot patrol path planning method considering differentiated access according to claim 1, characterized in that, The iteration stopping condition in S7 is: constructing and optimizing cooperative pairs in the order of robot numbers, and stopping when a whole round of traversal is completed and the total distance in that round remains unchanged.

5. A multi-robot patrol path planning system considering differentiated access, used to implement the multi-robot patrol path planning method considering differentiated access as described in any one of claims 1 to 4, characterized in that, include: The data acquisition module is used to acquire task duration, base location, location and access cycle of each target point, as well as the number of robots performing the task and robot movement speed; The node expansion module, connected to the data acquisition module, is used to calculate the minimum number of times each target point is accessed within the task duration based on the task duration and the access cycle of each target point, and to construct an expansion node set by generating virtual nodes. The node clustering module, connected to the node expansion module, is used to spatially cluster the virtual nodes and divide them into task clusters equal to the number of robots. The initial path generation module, connected to the node clustering module, is used to establish and solve a path planning model for each task cluster to generate an initial path for a single robot. The cooperative pair selection module, connected to the initial path generation module, is used to select the reference robot sequentially according to the robot number order and match the nearest neighbor to form a cooperative pair; The replanning path solving module is connected to the collaboration pair selection module. It is used to merge the task clusters of the collaboration pair, establish a path planning model and solve it to obtain the replanning path of the collaboration pair. The iterative optimization module is connected to the initial path generation module, the cooperative pair selection module, and the replanning path solving module, respectively. It is used to determine whether to replace the original path with a replanning path and to repeatedly trigger the cooperative pair selection module and the replanning path solving module until the iteration stop condition is met. The path output module, connected to the iterative optimization module, is used to output the final multi-robot patrol path.

6. A multi-robot patrol path planning system considering differentiated access according to claim 5, characterized in that, The node clustering module includes: The upper and lower limit setting unit is used to set the upper and lower limits of the number of virtual nodes in each task cluster based on the total number of virtual nodes and the number of robots. The clustering iterative unit is used to randomly select the initial center point in each iteration, enforce the upper limit constraint when allocating virtual nodes, check whether the lower limit constraint is satisfied after allocation, and calculate the total intra-cluster distance. The scheme selection unit is used to select the effective clustering scheme with the smallest distance within the total cluster from multiple iterations as the final task cluster partition.

7. A multi-robot patrol path planning system considering differentiated access according to claim 5, characterized in that, The iterative optimization module includes: A condition judgment unit is used to determine whether the iteration stopping condition is met, wherein the iteration stopping condition is that a full round of traversal iteration is completed and the total distance remains unchanged; The path replacement decision unit is used to compare the sum of the path distances before and after replanning in the collaborative pair and decide whether to replace the original path with the replanned path.

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