A multi-agent cooperative coverage exploration planning model and method for complex polygonal regions

Abstract

The application discloses a multi-agent cooperative coverage exploration planning model and method for a complex polygon area, and improves and designs a multi-agent cooperative area coverage model and algorithm for a complex irregular sea area, so that the area coverage efficiency under the exploration cost and the optimal cost in the complex sea area condition can be improved, and sudden threats can be avoided in time, and the multi-agent cooperative exploration technology in the complex sea area needs to coordinate and control and plan multiple agents according to the actual demand of the exploration work, the exploration precision and the exploration speed are taken into account, accurate measurement data are provided for various marine engineering in the later period, and the safety and the economy of the marine engineering are maximally ensured.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperation, specifically referring to a multi-agent cooperative coverage exploration planning model and method for complex polygonal regions. Background Technology

[0002] With the development of artificial intelligence, many complex tasks cannot be completed by a single intelligent agent or are too time-consuming to complete. Therefore, multiple intelligent agents need to work together to complete the tasks, making multi-agent collaboration a hot research topic.

[0003] Region coverage is a common task involving multi-agent collaboration. The goal is to achieve comprehensive coverage of a target region by coordinating multiple agents under limited conditions, minimizing both the number of agents and time required—that is, completing the task most efficiently with the lowest total cost.

[0004] This invention primarily addresses the problem of multi-agent collaboration in covering complex and irregular sea areas. Because marine resources are abundant today, and human exploration is too dangerous, unmanned intelligent agents are needed to explore complex sea areas. The first step in this exploration is to utilize multi-agent collaboration for area coverage.

[0005] Domestic and international researchers have achieved certain results in addressing the problem of regional coverage in irregular sea areas based on multi-agent cooperation. They have improved the efficiency and accuracy of regional coverage by optimizing algorithms, improving cooperation mechanisms, and applying advanced communication technologies. However, some challenges remain, such as the complexity of the marine environment, communication limitations, and the optimization of path planning, requiring further research and exploration. Future work can focus on algorithm improvement, system optimization, and application expansion to enhance the performance and application scope of regional coverage in irregular sea areas based on multi-agent cooperation. Summary of the Invention

[0006] This invention addresses the aforementioned problems by resolving the issue of pre-set trajectories intersecting with existing trajectories during path planning in multi-agent collaborative coverage of complex and irregular sea areas.

[0007] Most current multi-agent cooperative region coverage algorithms are ill-suited for complex, irregular polygonal sea areas. They suffer from repetitive agent traversal, trajectory overlap, and convergence issues, failing to avoid sudden threats and thus unable to achieve optimal region coverage in complex sea conditions. This invention, based on a hybrid particle swarm optimization algorithm, improves upon this by designing a multi-agent cooperative region coverage model algorithm for complex, irregular sea areas. This algorithm enhances exploration cost and region coverage efficiency at optimal cost in complex sea conditions, while also enabling timely avoidance of sudden threats. The invention achieves these technical objectives through the following technical solutions.

[0008] This invention proposes a multi-agent cooperative regional coverage planning model and algorithm for complex irregular polygonal sea areas, including an optimal coverage direction selection module, an optimal preset trajectory generation module, an optimal cooperative path planning module, a threat avoidance module, and an optimal path dynamic solution algorithm;

[0009] The optimal coverage direction selection module is used to select the overall movement direction of the intelligent agent to cover the complex polygonal sea area.

[0010] The optimal preset trajectory generation module is used to generate a preset trajectory with the fewest turning angles for the agent to cover the entire area.

[0011] The optimal collaborative path planning module: given a fixed number of agents, establishes an optimization mathematical model with the minimum coverage cost as the optimization objective;

[0012] Threat avoidance module: After the agent detects a threat target, it promptly replans the local path to avoid the danger.

[0013] The optimal path dynamic solution algorithm is based on the above-mentioned optimal cooperative path planning module. When a target is encountered during the coverage process, the planned path is dynamically corrected to ensure that the globally optimal multi-agent cooperative regional coverage path is obtained without entering the threat range.

[0014] Furthermore, the optimal coverage direction selection module is specifically designed as follows:

[0015] This invention assumes that the intelligent agent moves back and forth along a preset trajectory perpendicular to a given sweeping direction over the area to be covered, such as... Figure 2 As shown.

[0016] While flying along these preset trajectories, the agent maintains a stable attitude, with the camera vertically aimed at the sea level. However, at the end of each trajectory, it forms a curve outside the area to return to the next preset trajectory. Furthermore, the number of loops is directly related to the coverage time of a given area. Therefore, the first step of this invention is to find the optimal coverage direction, which is perpendicular to the direction of the minimum height of the irregular polygonal area. In this direction, the area can be covered with the fewest number of trajectories, and therefore also with the fewest curves, as... Figure 2 As shown, when considering costs such as path length, time, and energy, a path with fewer turns is more efficient.

[0017] To find the optimal coverage direction for a given polygonal region. For example... Figure 3 As shown, the polygon is rotated in a two-dimensional coordinate system (the two-dimensional coordinate system is based on the two-dimensional coordinate system of the screen where the polygon region is located) and its height in different directions is measured. The optimal scanning trajectory direction is the direction with the minimum height.

[0018] Furthermore, the optimal preset trajectory generation module, after finding the optimal scanning direction, can distribute the preset trajectories across the area. The distance (m) between two trajectories is chosen as a function of the coverage area of ​​the airborne camera on the sea surface. Given that the scanning width of the agent is L, and L is 150m, the number of preset trajectories covered can be obtained:

[0019]

[0020] In the formula, N l h is the number of rows in the preset trajectory. min The minimum height of the irregular polygonal sea area is given by ; L is the scanning width of the agent; s∈(0,1) represents the overlapping portion between two images, which is usually necessary for connecting images to form an aerial image. The distance d between the two preset trajectories can then be obtained. l for:

[0021]

[0022] Assuming the polygon representing the region is rotated parallel to the x-axis of the global reference 2D coordinate system in the optimal coverage direction, the coverage trajectory can be derived from two planar points (x, y) with the same y-coordinate:

[0023]

[0024] The x-coordinate is derived from the y-coordinate. i The intersection of the horizontal line and the boundary of the area to be covered is obtained. Once the points are calculated, they are rotated back to their original direction.

[0025] The extreme points of the covered trajectory, and the coordinates of the agent's starting position (base or warehouse), are represented by the point set V of graph G = (V, E). Each node in the graph is numbered; therefore, the starting point of the first agent is numbered 1, and the starting points of other agents are numbered accordingly. Nodes associated with the first row of the covered trajectory are numbered 2 and 3, nodes associated with the second row are numbered 4 and 5, and so on. Finally, each row of the covered trajectory is associated with subsequent even- and odd-numbered nodes. The edge set E consists of all lines connecting the N nodes of the graph, forming a complete graph, which is the optimal preset trajectory, as shown below. Figure 4 As shown.

[0026] Representing graph G as an N×N cost matrix C, with elements C ij It is derived from the Euclidean distance between the spatial coordinates of nodes i and j. Here, C is symmetric, i.e. Its elements satisfy the triangle inequality, that is

[0027] Furthermore, the optimal cooperative path planning module, after creating a graph associated with the area to be covered, treats the optimal cooperative path planning problem as a VRP (Vehicle Routing Problem). In this type of problem, a group of agents must visit a group of customers. To transform the optimal cooperative path planning problem into a VRP, each agent is considered an agent, and each extreme point of the coverage trajectory is considered a customer. Additionally, by introducing new constraints, agents can be forced to use some pre-specified edges in their path graph. Therefore, agents will definitely follow the coverage trajectory. Finally, by solving the VRP, a set of routes that each agent must execute can be obtained. Specifically:

[0028] The element C in the cost matrix C ij , representing the traversal cost of the edge (i,j) between nodes i and j. To indicate whether the k-th agent should move from vertex i to vertex j, a binary variable is used. in, This indicates that the k-th agent needs to move from vertex i to vertex j, and vice versa. Furthermore, let a constant be... Represents the flight speed of the k-th agent as it moves from vertex i to vertex j; a constant. Set time for individuals; L k Let be the battery life of the k-th agent. The number of agents designed for the task; The total number of available agents; The number of control programs for the intelligent agent; Let be the number of nodes in the graph. Finally, the variable d... k This represents the additional time required to launch the k-th agent, which is the preparation time required to launch an agent.

[0029] Based on the variables defined above, the time T spent by the k-th agent traversing its route can be obtained. k :

[0030]

[0031] The primary objective of this invention is to minimize task time, which can be achieved by minimizing the flight time of the longest path among all agent paths. Therefore, the problem this invention addresses is essentially a task to minimize T. k The min-max problem. To transform the min-max problem into a linear problem, this invention introduces an additional variable υ, which represents the longest agent path. The resulting optimization model is:

[0032] min(υ)

[0033]

[0034] Among them, t s (min) represents the preparation time required to launch an agent; O represents the maximum number of agents that can be launched from each starting point.

[0035] Since the setup time for the intelligent agent's takeoff is negligible, the subsequent steps of this invention regarding t... s This is not considered. To complete the task, and to ensure that each agent cannot repeatedly visit path nodes in the graph during the full graph traversal, the following constraints apply:

[0036]

[0037]

[0038] The constraints in the above formula enforce that each node can only be accessed by one agent, and guarantee that the agent that arrives at a given node is the same agent that leaves that node.

[0039] To ensure that each agent's path starts from the initial point and ends after all traversals are completed, and to guarantee that the path has no internal loops, standard sub-circuit is used to eliminate constraints:

[0040]

[0041] in, This represents the number of vertices the agent traverses to reach the i-th vertex.

[0042] To ensure that the solution of VRP can cover the entire polygonal sea area transformed into graph G, the following constraints are added:

[0043]

[0044] This constraint mandates that each agent must visit another node in the same line of the trajectory after visiting one node. It also guarantees that agents visiting even-numbered nodes will also visit the next odd-numbered node. Furthermore, agents visiting odd-numbered nodes must visit the previous even-numbered node.

[0045] To prevent the agent from traversing the coverage area along a pre-defined trajectory that is not parallel to the edge of the coverage area, two optional constraints can be added to the optimization model above.

[0046]

[0047]

[0048] In practice, the two constraints above can prevent the agent from making sharp turns and taking photos from different directions. If these issues are not important to the given task, these two constraints can be ignored without affecting the task's execution.

[0049] Finally, considering the number of available agents, the following constraints can be established:

[0050]

[0051] The invention primarily addresses the scenario where the number of agents is fixed. Therefore, with a fixed number of agents, the invention mainly optimizes the minimization of the maximum flight path length of the agents.

[0052] Design of an algorithm for covering irregular sea areas based on multi-agent cooperation

[0053] This design primarily uses the Yalmip toolbox on the front end and the Gurobi solver on the back end to solve the optimal traversal model of the entire graph.

[0054] First, based on the task scope, the `findwaypoints` function is used to obtain waypoints for the appropriate coverage trajectory. The input consists of a graph model point set V representing the irregular sea area and a point set X representing the locations to be traversed. Based on the agent's mobility capabilities, and constrained by traversing all required locations, the function iteratively outputs waypoints for the coverage trajectory of the irregular sea area.

[0055] Table 1-1 Findwaypoints function

[0056]

[0057] After obtaining waypoints covering the entire map of the preset trajectory, the Gurobi solver, combined with a linear iterative algorithm, can be used to solve for the optimal path. The input consists of a graph model point set V representing the irregular sea area, agent information (movement speed, start-up time, maximum flight time), and Gurobi optimizer configuration parameters h and O. Based on the calculated Euclidean distance, a suitable optimizer configuration is selected for path planning, and the planned path and agent assignments are output.

[0058] Table 1-2 lip function

[0059]

[0060]

[0061] During the full map traversal, the exploration of all static targets must also be completed. The agent is input with its coordinates and detection range. Within this range, a search is performed; if a static target exists, its coordinates are output.

[0062] Table 1-3 SearchTargets Function

[0063]

[0064] The beneficial effects of this invention are:

[0065] 1. This invention addresses the issue that multi-agent reinforcement learning requires a large number of scenarios to train the model and cannot effectively handle some sudden and complex working conditions. For safety reasons, this invention proposes a rule-based region coverage path planning strategy, which is easier and faster to implement, in order to solve the problem of multi-agent collaboration in exploring complex regions.

[0066] 2. Based on the hybrid particle swarm optimization algorithm, this invention improves and designs a multi-agent cooperative region coverage model algorithm for complex and irregular sea areas, which can improve the exploration cost and region coverage efficiency under the optimal cost in complex sea areas, and avoid sudden threats in a timely manner.

[0067] 3. This invention addresses the need for multi-agent collaborative exploration technology in complex sea areas to coordinate and control multiple agents according to the actual needs of the exploration work, balancing exploration accuracy and speed, providing accurate measurement data for various marine engineering projects in the future, and maximizing the safety and economy of marine engineering projects. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the overall implementation process of the present invention;

[0069] Figure 2 A map showing the coverage of complex polygonal sea areas;

[0070] Figure 3 To conduct static target reconnaissance for regional coverage;

[0071] Figure 4 A process for multi-agent collaborative algorithm for covering complex and irregular sea areas. Detailed Implementation

[0072] The invention will now be further described with reference to the accompanying drawings.

[0073] like Figure 1 As shown, the specific implementation of the present invention is as follows:

[0074] Step 1: Decomposition of Irregular Polygonal Sea Area

[0075] This invention assumes that the intelligent agent moves back and forth along a preset trajectory perpendicular to a given sweeping direction over the area to be covered, such as... Figure 2 As shown;

[0076] While flying along these preset trajectories, the agent maintains a stable attitude, with the camera vertically aimed at the sea level. However, at the end of each trajectory, it forms a curve outside the area to return to the next preset trajectory. Furthermore, the number of loops is directly related to the coverage time of a given area. Therefore, the first step of the method of this invention is to find the optimal coverage direction, which is perpendicular to the minimum height of the irregular polygonal area. In this direction, the area can be covered with the fewest number of trajectories, and therefore also with the fewest curves, such as... Figure 2 As shown, when considering costs such as path length, time, and energy, a path with fewer turns is more efficient.

[0077] To find the optimal coverage direction for a given polygonal region, a simple search process can be used, such as... Figure 3 As shown, the polygon is rotated in a two-dimensional coordinate system, and its height in different directions is measured. The optimal scanning trajectory direction is the direction with the minimum height.

[0078] Furthermore, the optimal preset trajectory generation module, after finding the optimal scanning direction, can distribute the preset trajectories across the area. The distance (m) between two trajectories is chosen as a function of the coverage area of ​​the airborne camera on the sea surface. Given that the scanning width of the agent is L = 150m, the number of preset trajectories covered can be obtained:

[0079]

[0080] In the formula, N l h is the number of rows in the preset trajectory. min The minimum height of the irregular polygonal sea area is given by ; L is the scanning width of the agent; s∈(0,1) represents the overlapping portion between two images, which is usually necessary for connecting images to form an aerial image. The distance d between the two preset trajectories can then be obtained. l for:

[0081]

[0082] Assuming the polygon representing the region is rotated parallel to the x-axis of the global reference frame in the optimal coverage direction, the coverage trajectory can be derived from two planar points (x, y) with the same y-coordinate:

[0083]

[0084] The x-coordinate is derived from the y-coordinate. i The intersection of the horizontal line and the boundary of the area to be covered is obtained. Once the points are calculated, they are rotated back to their original direction.

[0085] The extreme points of the covered trajectory, and the coordinates of the agent's starting position (base or warehouse), are represented by the set of points V of the graph G = (V, E). Each node in the graph is numbered; therefore, the starting point of the first agent is numbered 1, and the starting points of other agents are numbered accordingly. Nodes associated with the first row of the covered trajectory are numbered 2 and 3, nodes associated with the second row are numbered 4 and 5, and so on. Finally, each row of the covered trajectory is associated with subsequent even and odd-numbered nodes. The edge set E consists of all lines connecting the N nodes of the graph, forming a complete graph, as shown below. Figure 4 As shown.

[0086] Representing graph G as an N×N cost matrix C, with elements C ij It is derived from the Euclidean distance between the spatial coordinates of nodes i and j. Here, C is symmetric, i.e. Its elements satisfy the triangle inequality, that is

[0087] Step 2: Agent Path Planning Strategy

[0088] Furthermore, the optimal cooperative path planning model, after creating a graph associated with the area to be covered, first treats the coverage problem as a VRP (Virtual Resource Planning) problem. In this type of problem, a group of agents must visit a group of clients. To transform the previous problem into a VRP, each agent is considered an execution vehicle, and each extreme point of the coverage trajectory is considered a client. Moreover, by introducing new constraints, agents can be forced to use some pre-specified edges in their path graph. Therefore, one of the launched agents will definitely follow the coverage trajectory. Finally, by solving the VRP, a set of routes that each agent must execute can be obtained.

[0089] The value C in cost matrix C ij , representing the traversal cost of the edge (i,j) between nodes i and j. To indicate whether the k-th agent should move from vertex i to vertex j, a binary variable is used. In addition, let constants be used. Represents the flight speed of the k-th agent as it moves from vertex i to vertex j; a constant. Set time for individuals; L k Let be the battery life of the k-th agent. The number of agents designed for the task; The total number of available agents; The number of control programs for the intelligent agent; Let be the number of nodes in the graph. Finally, the variable d... k This represents the additional time required to launch the k-th agent.

[0090] Based on the variables defined above, the time T spent by the k-th agent traversing its route can be obtained.k :

[0091]

[0092] The primary objective of this invention is to minimize task time, which can be achieved by minimizing the flight time of the longest path among all agent paths. Therefore, the problem this invention addresses is essentially a task to minimize T. k The min-max problem. To transform the min-max problem into a linear problem, this invention introduces an additional variable υ, which represents the longest agent path. The resulting optimization model is:

[0093] min(υ)

[0094]

[0095] Since the setup time for the intelligent agent's takeoff is negligible, the subsequent steps of this invention regarding t... s This is not considered. To complete the task, and to ensure that each agent cannot repeatedly visit path nodes in the graph during the full graph traversal, the following constraints apply:

[0096]

[0097]

[0098] The constraints in the above formula enforce that each node can only be accessed by one agent, and guarantee that the agent that arrives at a given node is the same agent that leaves that node.

[0099] To ensure that each agent's path starts from the initial point and ends after all traversals are completed, and to guarantee that the path has no internal loops, standard sub-circuit is used to eliminate constraints:

[0100]

[0101] in,

[0102] To ensure that the solution of VRP can cover the entire polygonal sea area transformed into graph G, the following constraints also need to be added:

[0103]

[0104] This constraint mandates that each agent must visit another node in the same line of the trajectory after visiting one node. It also guarantees that agents visiting even-numbered nodes will also visit the next odd-numbered node. Furthermore, agents visiting odd-numbered nodes must visit the previous even-numbered node.

[0105] To prevent the agent from traversing a pre-defined trajectory across the coverage area along an edge that is not parallel to the coverage area, two optional constraints can be added to the optimization model of this invention.

[0106]

[0107]

[0108] In practice, the two constraints above can prevent the agent from making sharp turns and taking photos from different directions. If these issues are not important to the given task, these two constraints can be ignored without affecting the task's execution.

[0109] Finally, considering the number of available agents, the following constraints can be established:

[0110]

[0111] The invention primarily addresses the scenario where the number of agents is fixed. Therefore, with a fixed number of agents, the invention mainly optimizes the minimization of the maximum flight path length of the agents.

[0112] Step 3: Design of a Multi-Agent Collaborative Algorithm for Covering Irregular Sea Areas

[0113] This invention primarily uses the Yalmip toolbox at the front end and the Gurobi solver at the back end to solve the optimal traversal model of the entire graph.

[0114] First, based on the task scope, the findwaypoints function is used to find the appropriate waypoints to cover the trajectory.

[0115] Table 1-1 FindWayPoints function

[0116]

[0117] After obtaining waypoints that cover the entire map of the preset trajectory, the Gurobi solver can be used in conjunction with a linear iterative algorithm to find the optimal path.

[0118] Table 1-2 lip function

[0119]

[0120]

[0121] During the full graph traversal, the exploration of all static targets must also be completed, which is achieved by the following algorithm.

[0122] Table 1-3 SearchTargets Function

[0123]

[0124] In summary, this invention addresses the problem that most current multi-agent cooperative region coverage algorithms are unsuitable for complex, irregular polygonal sea areas. These algorithms suffer from repetitive agent traversal, trajectory overlap, and convergence issues, failing to avoid sudden threats and thus unable to achieve optimal region coverage in complex sea conditions. Based on a hybrid particle swarm optimization algorithm, this invention improves upon the design of a multi-agent cooperative region coverage model algorithm for complex, irregular sea areas. This model enhances exploration cost and region coverage efficiency at optimal cost in complex sea conditions, while also enabling timely avoidance of sudden threats.

[0125] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. All equivalent methods or modifications that do not depart from the technology of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-agent collaborative coverage exploration planning model for complex polygonal regions, characterized in that, include: Optimal coverage direction selection module, optimal preset trajectory generation module, and optimal collaborative path planning module; The optimal coverage direction selection module is used to select the overall movement direction of the intelligent agent to cover the complex polygonal sea area. The optimal preset trajectory generation module is used to generate a preset trajectory with the fewest turning angles for the agent to cover the entire area. The optimal preset trajectory generation module is as follows: Given that the scanning width of the agent is L, the number of preset trajectories covered is obtained: In the formula, The number of rows in the preset trajectory; The minimum height for an irregular polygonal sea area; The scan width of the intelligent agent; This represents the overlapping portion between two images. This overlap is often necessary to connect the images to form an aerial image, and the distance between the two preset tracks can then be obtained. for: Assume the polygon representing the region is parallel to the global reference frame in the optimal coverage direction. Rotation along the axis, covering the trajectory with the same Two plane points of coordinates Conclusion: The coordinates are from the vertical coordinate. The intersection of the horizontal line and the boundary of the area to be covered is obtained. Once the points are calculated, they are rotated back to their original direction. The extreme points of the covered trajectory, and the coordinates of the agent's starting position, are shown in the figure. point set Each node in the diagram is numbered. The starting point of the first agent is numbered 1, the nodes associated with the first row of covered trajectories are numbered 2 and 3, the nodes associated with the second row are numbered 4 and 5, and so on. Finally, each row of covered trajectories is associated with subsequent even and odd-numbered nodes, forming an edge set. From the connection diagram The line segments of each node form a complete graph, which is the optimal preset trajectory. The optimal collaborative path planning module, given a fixed number of agents, establishes an optimization mathematical model with the minimum coverage cost as the optimization objective. Specifically, it transforms the optimal collaborative path planning problem into a VRP problem, treating each agent as an agent and each extreme point of the coverage trajectory as a client. By proposing new constraints, it forces agents to use some pre-specified edges in their path graphs. Finally, by solving the VRP, it obtains a set of path routes executed by each agent.

2. The multi-agent cooperative coverage exploration planning model for complex polygonal regions according to claim 1, characterized in that, The overall movement direction of the optimal coverage direction selection module is perpendicular to the minimum height direction of the irregular polygonal region. Specifically, the polygonal region is rotated in a two-dimensional coordinate system, and its height in different directions is measured. The optimal scanning trajectory direction is the direction with the minimum height.

3. The multi-agent cooperative coverage exploration planning model for complex polygonal regions according to claim 1, characterized in that, It also includes the diagram Represented as Cost Matrix Its elements By node and The Euclidean distance between spatial coordinates is obtained, where the matrix... Symmetry, that is Its elements satisfy the triangle inequality, that is .

4. The multi-agent cooperative coverage exploration planning model for complex polygonal regions according to claim 1, characterized in that, The optimal collaborative path planning module is as follows: Cost matrix elements in , represented as a node and The edge between The traversal cost, in order to indicate the traversal cost of the first... Should an agent start from the vertex? Movement to the peak Using binary variables Furthermore, let constants be used. , indicating the first An agent from the top Movement to the peak Flight speed; constant Set time for individuals; For the first Battery life of an individual intelligent agent; Assume The number of agents designed for the task; , where is the total number of available agents; , where is the number of control programs for the intelligent agent; , where is the number of nodes in the graph; variable Indicates the launch number Additional time required for each agent; Based on the variables defined above, we can obtain the first... The time it takes for an agent to traverse its route : 。 5. A multi-agent cooperative coverage exploration planning model for complex polygonal regions according to claim 4, characterized in that, Also includes: Introducing variables , representing the longest agent route; the optimized model can be obtained as follows: 。 6. A multi-agent cooperative coverage exploration planning model for complex polygonal regions according to claim 5, characterized in that, Establish the following constraints: The constraint in the above formula forces each node to be accessed by only one agent, and guarantees that the agent that arrives at a given node is the same agent that leaves the node.

7. A multi-agent cooperative coverage exploration planning model for complex polygonal regions according to claim 6, characterized in that, Also includes: To ensure that each agent's path starts from the initial point and ends after all traversals are completed, and to guarantee that the path has no internal loops, standard sub-circuit is used to eliminate constraints: in, ; To ensure that the solution of VRP can transform the agent coverage into a graph For the entire polygonal sea area, the following constraints are applied: This constraint mandates that after visiting one node in the covered trajectory, each agent must visit another node in that trajectory. It also ensures that agents visiting even-numbered nodes also visit the next odd-numbered node. Furthermore, agents visiting odd-numbered nodes must visit the previous even-numbered node. To prevent the agent from traversing the coverage area along a preset trajectory that is not parallel to the edge of the coverage area, two optional constraints are added to the optimization model described above. Finally, considering the number of available agents, the following constraints are established: 。 8. A coverage trajectory planning method for a multi-agent cooperative coverage exploration planning model for complex polygonal regions as described in any one of claims 1-7, characterized in that, Includes the following steps: S1. First, based on the task scope, the findwaypoints function is used to obtain the waypoints for the appropriate coverage trajectory. The specific process is as follows: S11. Input the boundary of the irregular sea area and the location to be traversed; S12, constrained by the agent's mobility and the ability to traverse all required objectives; S13. Find the waypoints for the trajectory of an irregularly covered sea area; S2. After obtaining the waypoints that cover the preset trajectory on the full map, the Gurobi solver is used in conjunction with a linear iterative algorithm to solve for the optimal path. The specific process is as follows: S21. Construct a cost matrix based on the Euclidean distance between waypoints on the covered trajectory and the speed of the agent; S22. With a fixed number of agents, the optimization objective is to minimize the total cost. S23. Constraints include the maximum movement time of the agent, only one agent visiting a waypoint at a time, and traversing all waypoints. S23. Find the optimal route planning for multi-agent collaboration to achieve coverage of irregular sea areas; S3. During the full map traversal, complete the exploration of all static targets. The specific process is as follows: S31. When the agent is executing the planned route, it should keep exploring the surroundings within a fixed range; S32. When an unknown stationary target appears within the detection range of the agent, output the position of the stationary target; S33. When the number of known static targets reaches the given value of the task, complete the exploration of all static targets.

Images