A Multi-Agent Cooperative Detection and Multi-Region Coverage Task Planning Method Based on Improved Discrete Gray Wolf Optimization Algorithm

Abstract

This invention provides a multi-agent cooperative detection multi-region coverage task planning method based on an improved discrete gray wolf optimization algorithm. This method aims to achieve comprehensive coverage detection of multiple non-overlapping target regions while significantly reducing the completion time of the cooperative coverage task. First, considering detection height, field of view, and image resolution requirements, an accurate mathematical model is constructed with the objective of minimizing the longest coverage path. Further, a multi-region coverage path generation method based on an improved rotating caliper method is proposed. This method can accurately locate the entry and exit points of each target region and optimize the transition paths between target regions and the coverage paths within each region. To address the complexity of solving large-scale problems, a discrete gray wolf optimization algorithm integrating heuristic population initialization, adaptive iterative update strategy, and variable neighborhood search operation is designed to improve task planning efficiency.

Description

Technical Field

[0001] This invention relates to the field of multi-agent task planning technology, and specifically to a multi-agent cooperative exploration multi-region coverage task planning method based on an improved discrete gray wolf optimization algorithm. Background Technology

[0002] The multi-agent collaborative detection and multi-area coverage task planning problem refers to the optimization objective of minimizing the coverage completion time while ensuring full coverage of the target areas, under certain constraints (such as range constraints, collision avoidance, and obstacle avoidance).

[0003] The multi-agent cooperative exploration and multi-region coverage task planning problem can be decomposed into two sub-problems: target region allocation and coverage path planning. Most current research focuses on coverage task planning for a single target region, with less consideration given to coverage task planning for multiple non-overlapping target regions. Multi-region coverage task planning has wider applications in real-world scenarios. For example, in disaster response and environmental monitoring tasks, there are sometimes multiple non-overlapping sub-regions that need to be covered. This requires not only considering coverage path planning within each region but also optimizing the access order between multiple sub-regions, making the solution more complex. A common solution currently is to use a decoupling optimization strategy, decoupling task allocation from path planning and using heuristic algorithms to approximate the solution. However, on the one hand, the decoupling optimization strategy may lead to infeasible or inefficient path planning after task allocation, making it difficult to achieve global optimum; on the other hand, the complexity of heuristic algorithms in design and their dependence on specific empirical rules result in poor scalability.

[0004] Furthermore, in practical applications, different target areas may have different image resolution detection requirements to ensure accurate identification of different targets. The detection flight altitude of the agent directly affects the sensor's field of view and image resolution. As the detection altitude increases, the sensor's field of view expands, but the image resolution decreases accordingly. Therefore, for target areas with high image resolution requirements, the detection altitude needs to be lowered to obtain higher quality images. For sea areas with lower image resolution requirements, the detection altitude can be appropriately increased to expand the sensor's field of view and thus shorten the task completion time. This difference in requirements leads to the heterogeneity of coverage paths within various target areas. This invention takes this heterogeneity into account, meaning that while multiple agents cover the target area, they need to rationally plan the detection altitude to ensure the image resolution requirements of the target area. Summary of the Invention

[0005] In view of the above problems and shortcomings, the present invention provides a multi-agent cooperative detection multi-region coverage task planning method based on an improved discrete gray wolf optimization algorithm, which can realize coupled optimization of coverage task allocation and path generation, improve the cooperative coverage effect and shorten the coverage task completion time.

[0006] To achieve the above objectives, this invention comprehensively considers key factors such as detection flight altitude, sensor field of view, and image resolution requirements, and constructs a multi-region coverage task planning model with minimizing the longest flight path as the optimization objective. Based on this, a multi-region coverage path generation method based on an improved rotating caliper method is proposed. This method can accurately determine the entry and exit points of each target region, while optimizing the transition paths between target regions and the coverage paths within the target regions. Given the high computational complexity of large-scale problems, to improve solution efficiency, a discrete gray wolf optimization algorithm integrating heuristic initialization methods, adaptive iterative update strategies, and variable neighborhood search operations is designed. This method can effectively balance the task load among multiple agents, optimize the access order between target regions, and ensure balanced task allocation and efficient path planning.

[0007] The present invention adopts the following technical solution:

[0008] A multi-agent cooperative exploration and multi-region coverage task planning method based on an improved discrete gray wolf optimization algorithm includes the following steps:

[0009] Step 1: Based on the given target area map and the parameter configuration information of each agent and its sensors, initialize the target area map, agent, and sensor models. Taking into account key factors such as detection height, field of view, and image resolution requirements, construct a multi-region coverage task model and fitness function with the optimization objective of minimizing the longest coverage path.

[0010] Step 2: Initialize the gray wolf population based on a heuristic method. Each gray wolf corresponds to a task allocation scheme, and ensure that each target area is visited by at least one agent in each task allocation scheme.

[0011] Assuming the number of agents is M and the number of target regions is N, the encoding length of each gray wolf is M+N. The encoding of each gray wolf includes two parts: the access sequence of target regions and the number of target regions allocated to each agent. The access sequence of target regions includes the target region sequence corresponding to each agent arranged in ascending order of agent number, and the target region sequence corresponding to each agent is formed by the access order of each agent.

[0012] Step 3: Calculate the fitness value of each gray wolf and determine the top three gray wolf individuals in the group in terms of fitness, α, β, and δ, where the fitness values ​​of α, β, and δ decrease in that order.

[0013] Step 4: Randomly select gray wolf individuals from the population, and perform a crossover operation on the selected individuals and gray wolf individuals α, β, δ to obtain new gray wolf individuals. Keep the gray wolf individuals with higher fitness values, and obtain three gray wolf individuals after the crossover operation.

[0014] Step 5: Generate a random number rand1 between [0,1]. When rand1≤s, apply the swap operator, insertion operator, and inversion operator to each of the three gray wolf individuals obtained in Step 3. Each operation yields a new gray wolf individual. Compare the fitness values ​​of the new gray wolf individuals obtained after each operation with those of the three gray wolf individuals obtained in Step 3. Retain the gray wolf individuals with higher fitness values ​​to obtain the three gray wolf individuals after adaptive probability perturbation control. When rand1>s, apply the disorder perturbation operator to each of the three gray wolf individuals obtained in Step 3. Compare the fitness values ​​of the three new gray wolf individuals obtained after the operation with those of the three gray wolf individuals obtained in Step 3. Retain the gray wolf individuals with higher fitness values ​​to obtain the three gray wolf individuals after adaptive probability perturbation control.

[0015] Where s is the convergence factor, and is the probability of selecting multiple neighborhood search operators to balance the results;

[0016] Step 6: Increment the iteration count by 1, and determine whether the maximum number of iterations has been reached. If yes, output the best individual among the three gray wolf individuals obtained in the last iteration and proceed to the next step. Otherwise, go back to step 3 and replace the gray wolf individuals α, β, and δ with the three gray wolf individuals obtained in the last iteration.

[0017] Step 7: Calculate the optimal path of the task allocation scheme corresponding to the optimal individual to obtain the final path. Further, in step 2, the specific method for heuristically initializing the population is as follows:

[0018] First, randomly select N target region indices and assign them to their respective sets; then, calculate the distance between target regions based on the centroid coordinates of each region; finally, unassigned regions will be inserted into the end of each set in turn, with the selection criterion being the region closest to the last region in the set.

[0019] Furthermore, in step 4, the specific method for the CROSS cross-operation is as follows:

[0020] Step 4.1: Generate a random number rand2. If rand2≤1 / 3, then α is the individual to be crossed. If rand2≥2 / 3, then β is the individual to be crossed. If 1 / 3<rand2<2 / 3, then δ is the individual to be crossed.

[0021] Step 4.2: Randomly generate the target region location to be crossed. Swap the target region location encoded by the selected gray wolf individual with the target region location to be crossed to obtain two new gray wolf individuals. Compare the fitness values ​​of α, β, δ with the two new gray wolf individuals, and select the three gray wolf individuals with the highest fitness as the three gray wolf individuals after the crossover operation.

[0022] Furthermore, in step 5, the exchange, insertion, and inversion operators are respectively:

[0023] The swap operator is defined as follows: randomly select two target region positions from the original gray wolf individual's encoding, swap the target regions of these two positions, and form a new gray wolf individual;

[0024] The definition of insertion is: randomly select two target region positions from the original gray wolf individual's encoding, insert the target region of the first position after the target region of the second position, and form a new gray wolf individual;

[0025] The inversion operator is defined as follows: randomly select two target region locations from the original gray wolf individual's encoding, reverse the target region sequence between these two target region locations, and form a new gray wolf individual;

[0026] The disorder perturbation operator is defined as follows: while maintaining the same length of the target region access sequence for each agent, a random interval is selected from the target region sequence of each agent. Then, within this selected interval, the target region sequence is randomly recombined to form a new gray wolf individual.

[0027] Furthermore, in step 5, the formula for calculating s is:

[0028]

[0029] In the formula, iter is the current iteration number, and u is the preset control factor value.

[0030] Compared with the prior art, the present invention, by adopting the above technical solution, has the following advantages:

[0031] This invention addresses a coverage path planning problem in a practical application scenario. The goal is to achieve visual coverage detection of a series of non-intersecting polygonal target regions while satisfying the target region's image resolution. To effectively solve this problem, this invention first models and analyzes the airborne sensors, deriving a mathematical expression relating the detection flight altitude to the image resolution. This ensures that the agent performs visual coverage at the maximum detection flight altitude while meeting the image resolution requirements. Furthermore, this invention innovatively proposes a discrete gray wolf optimization algorithm that integrates multiple strategies. This method comprehensively considers the detection flight altitude, the access order of target regions, and the coverage path for each region, achieving coupled optimization. Simulation experiments in task scenarios of different scales verify that the proposed method not only effectively solves large-scale multi-region coverage task planning problems but also significantly outperforms many existing solutions.

[0032] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0034] Figure 2 A schematic diagram of a multi-agent, multi-region visual coverage scenario;

[0035] Figure 3 This is a schematic diagram of the projected area of ​​the photoelectric load;

[0036] Figure 4 This is a schematic diagram of the image resolution of the photoelectric payload;

[0037] Figure 5 This is a schematic diagram of the optimal coverage path for a single area;

[0038] Figure 6 A diagram illustrating the coding of individual gray wolves;

[0039] Figure 7 This is a schematic diagram of a set-based encoding representation method;

[0040] Figure 8 This is a diagram illustrating the CROSS operation.

[0041] Figure 9 This is a schematic diagram of the out-of-order perturbation operator;

[0042] Figure 10 A schematic diagram of the commutation operator;

[0043] Figure 11 A schematic diagram of the insertion operator;

[0044] Figure 12 This is a schematic diagram of the inversion operator;

[0045] Figure 13 The top view and 3D view of the IDGWO-based path planning under scenario one.

[0046] Figure 14 The top view and 3D view of the IDGWO-based path planning under scenario two conditions;

[0047] Figure 15 The top view and 3D view of the IDGWO-based path planning under scenario three conditions;

[0048] Figure 16 Box plot of Monte Carlo simulation results for scenario one;

[0049] Figure 17 Box plot of Monte Carlo simulation results for scenario two;

[0050] Figure 18 Box plot of Monte Carlo simulation results for scenario 3. Detailed Implementation

[0051] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0052] 1. Problem Description and Model Building

[0053] 1.1 Problem Description

[0054] like Figure 2 As shown, consider the following task scenario: Deployment An intelligent agent carrying a photoelectric sensor Visual coverage is applied to several target areas, all located within the same geographic space and without overlap. Let S... i ,i∈[N] represents the i-th target region, whose location, size, and shape are known, determined by its vertices. The decision was made. Among them, P i The j-th row stores the position information of the j-th vertex in the i-th vertex region. This represents the number of vertices in region i. All agents start from the same base and return to that base after completing their tasks. The location of the base is known and is represented as . The number 0 indicates the starting position.

[0055] In practical applications, monitoring tasks in different areas have varying requirements for image clarity. Therefore, when an agent moves from one target area to another to perform a task, it should adjust its detection flight altitude according to the new task requirements to ensure that the image resolution requirements of each area are met.

[0056] 1.2 Model Assumptions

[0057] To simplify the model, the following assumptions are made:

[0058] 1) An existing boundary processing method can simplify any irregular concave polygonal region into a convex polygonal region. Therefore, without loss of generality, this invention assumes that all target regions are convex polygonal regions.

[0059] 2) Assume that each target area is a two-dimensional plane without terrain undulations, in order to avoid the complexity caused by changes in height or occlusion.

[0060] 3) Assume that the image resolution requirement is uniform within a single target area, and that the height and velocity of the agent within that area remain constant.

[0061] 4) When the agent moves between target areas, it can dynamically adjust the flight altitude according to the image resolution requirements of the target area. This process is not included in the path planning process.

[0062] 5) Assume that the visual coverage task for each target area is completed independently by a single agent. The maximum range of each agent under the maximum energy constraint is L. max .

[0063] Based on the above assumptions, the goal of multi-agent collaborative detection and multi-region coverage path planning is to ensure that all target areas can be effectively covered and monitored while meeting the image resolution requirements of each target area and the range limitations of the agents.

[0064] 1.3 Sensor Model

[0065] like Figure 3 As shown, the projection area of ​​the photoelectric sensor onto the sea can be approximated as a rectangle. At a given field of view, its area is related to the spatial state parameters of the sensor.

[0066] Assume the projected area is S o = W×L. The straight-line distance between the camera and the target area is l. Considering W≈l·γ, Then S o It can be represented as:

[0067]

[0068] In the formula, h is the detection flight altitude, and θ is the line-of-sight depression angle (the angle between the photoelectric payload and the horizontal plane). This refers to the field of view of the camera lens.

[0069] As can be seen from the formula, the projected area S o It is directly proportional to the square of the detection flight altitude and inversely proportional to the cube of the sine function of the camera's line-of-sight angle. Field of view. Determined by the camera's focal length, and considering the low image distortion and good stability when shooting with a fixed focal length, it is assumed that a fixed focal length is used for visual coverage. Therefore, the projected area is only related to the detection flight altitude and the line-of-sight angle.

[0070] For optical images, the more pixels per unit area, the higher the image resolution. For example... Figure 4 As shown, the agent provides visual coverage of the target area at height h. The pixel size of the CCD camera is N. H ×N V (Unit: pixels / cm). Assume the projected dimensions of the sea surface target in the horizontal and vertical directions are W0×L0.

[0071] According to the imaging principle, the pixel size of the target on the image sensor can be expressed as:

[0072]

[0073] Combining the above equation with formula (1), we get:

[0074]

[0075] Therefore, the number of pixels per unit area corresponding to the target is:

[0076]

[0077] As can be seen from the formula, when the photoelectric load pixel size N H ×N V At a given time, the target resolution of the electro-optical payload is proportional to the cube of the sine function of the tilt angle of the electro-optical payload's line of sight, and proportional to the square of the detection flight altitude and the field of view. Inversely proportional. Assume the image resolution required by the task is no less than R. d ,Right now:

[0078] N″ H ×N″ V ≥R d (5)

[0079] Combining equations (4) and (5), we can obtain the maximum detection flight altitude as follows:

[0080]

[0081] To ensure minimal image distortion during visual coverage, the downward angle of the photoelectric sensor's line of sight is assumed to be a constant 90°. After determining the lens field of view and pixel size parameters, the flight altitude is adjusted to meet the image resolution requirements of the target area. In this invention, each agent performs visual coverage at its maximum detection flight altitude while meeting the image resolution requirements. This strategy not only ensures image clarity but also effectively increases the field of view, improving task completion efficiency.

[0082] 1.4 Construction of Fitness Function

[0083] When constructing the fitness function, five decision variables need to be considered: the target area detection flight altitude, the number of target areas allocated, the target area access order, the entry and exit points of the target areas, and the coverage path within the target areas. These decision variables are coupled with each other and jointly influence the final planned multi-agent cooperative detection scheme. Therefore, a binary decision variable x is introduced. ij ,i,j∈[N]∪{0}, when the variable value is 1, it indicates that the agent is in the region S i Move to area S j Otherwise, the variable value is 0. Where x 0i This indicates that the intelligent agent is traveling from the base to the target area S. i x i0 This indicates that the intelligent agent is composed of the target region S. i Return to base. Therefore, the following constraints can be obtained:

[0084]

[0085] Specifically, formulas (7)-(8) ensure that each region is covered only once. Formulas (9)-(10) ensure that all M agents start from the same base and return to the same base after completing their tasks. Formula (11) is used to prevent the generation of sub-loops, where |S| represents the total cardinality of the target region set. Formula (12) represents the variable x ij The values ​​that can be assigned.

[0086] In addition, variables are introduced to describe the coverage path of each target area. Indicates the target region S i The agent follows a coverage path to achieve complete coverage of the target area. Where c im Let n represent the m-th path point in this path. i C represents the total number of path nodes on this path. i Indicates target region S i The set of all possible coverage paths. i1 and These represent the target region S respectively. iThe in-point and out-point of the coverage are determined. Based on... The order of access to the specified target area is determined by connecting the overlay path. Given a base S0, we can obtain a set T of trajectories for M agents covering all target regions, where |T| = M. Let τ ∈ T represent the trajectory of one of the agents, and S... τ Let τ represent the set of all target regions covered by the trajectory τ, satisfying the following constraints:

[0087]

[0088] In the formula, This indicates that for set S τ Target area access order, S τ The absolute value indicates that each agent is assigned a minimum of one target region and a maximum of M target regions. Since the agent's maximum range is L... max Then the length of each flight trajectory τ needs to satisfy the following constraints:

[0089]

[0090] In the formula, L τ The total length of the flight trajectory τ can be calculated using the following formula:

[0091]

[0092] The formula consists of three parts: the first part represents the distance from each agent's base location to the entry point of the first target region; the second part represents the path distance for each agent to transfer between target regions; and the third part represents the coverage path distance for each agent within the target region. In the formula, the function D(p1,p2) represents the Euclidean distance from position p1 to position p2, and the function... The coverage path c was calculated. i The total length.

[0093] Under the condition that the motion parameters of each agent are the same, the completion time of the multi-region cooperative detection task depends on the longest coverage path. Therefore, this invention aims to minimize the longest coverage path. The advantage of this strategy is that it can balance the task load among multiple agents and avoid waiting time caused by excessively long coverage paths of individual agents, thereby improving the overall task execution efficiency. Therefore, the fitness function is constructed as follows:

[0094]

[0095] stConstraint(7)-(12)

[0096] To address the multi-agent collaborative exploration and multi-region coverage task planning problem, this invention proposes a coupled optimization solution strategy. The target region allocation scheme and the target region access order are encoded and represented as the solution space. A metaheuristic algorithm is used to search for candidate solutions in the search space to gradually approach the optimal solution. A multi-region coverage path is generated based on an improved rotating caliper method, and the reciprocal of the longest coverage path is used as the fitness value to evaluate the merits of candidate solutions.

[0097] 2. A Multi-Region Coverage Path Generation Method Based on an Improved Rotating Caliper Method

[0098] Vasquez et al. proposed the rotating caliper method to solve the full-coverage path planning problem for a single convex region. The basic idea is to traverse the pairs of opposite points of the convex polygon, find the parallel support line that minimizes the distance between these opposite points, and then use the direction of this parallel support line to perform parallel path coverage of the target region. Figure 5 As shown. Since the rotating caliper method is only suitable for generating coverage paths for a single target area, this invention proposes an improved method for generating multi-area coverage paths based on the rotating caliper method.

[0099] Suppose that for the i-th agent, there are N i N target areas to be covered are obtained through a heuristic initialization method. i The order of access to each region. When the agent reaches the first target region, it starts from the task starting point P. start Start moving to the in-point P1 of the first area to be covered. in Following the parallel coverage pattern, the target area is scanned and traversed, and finally the process moves to the exit point P1 of the first area to be covered. out The parallel coverage model can locate a series of waypoints at the edges of the polygon. The combination of the mission starting point and these waypoints forms the coverage path for the current target area. Based on the rotating caliper method, the shortest full coverage path for the current target area can be obtained, denoted as... After completing the coverage of a target area, based on the access order of the target areas, a greedy strategy is used to start from the exit point P1 of the first area to be covered. out Move to the in-point P2 of the second area to be covered in This process continues in sequence, eventually returning to the mission termination point P after covering all target areas. end The overall optimal coverage path is obtained by connecting the shortest full-coverage path to each target area.

[0100] 3. Multi-strategy fusion discrete gray wolf optimization algorithm

[0101] 3.1 Standard Gray Wolf Optimization Algorithm

[0102] The standard Grey Wolf Optimization (GWO) algorithm is a swarm intelligence optimization method developed by simulating the social hierarchy and hunting behavior of grey wolves. It features strong convergence, few parameters, and ease of implementation. The GWO optimization process mainly includes the grey wolf's social hierarchy stratification, encirclement, hunting, and attacking prey. Its mathematical model is described below:

[0103] (1) Social stratification

[0104] When designing a Gray Wolf Wolf (GWO), the first step is to construct a hierarchical model of the gray wolf social hierarchy. The fitness value of each individual in the initial population is calculated, and the three gray wolves with the best fitness are labeled α, β, and δ, respectively, while the remaining gray wolves are labeled ω. In other words, the social hierarchy of the gray wolf pack, from highest to lowest, is α, β, δ, ω. The optimization process of the GWO is primarily guided by the three best solutions α, β, and δ from each generation of the population.

[0105] (2) Encircle

[0106] The mathematical model for a gray wolf's encirclement of its prey is as follows:

[0107] X(t+1)C=X P (t)-A⊙D (17)

[0108] D = |C·X P (t)-X(t)| (18)

[0109] In the formula: t is the current iteration number; ⊙ is the Hadamard product operation; A and C are the cooperative coefficient vectors; D is the distance between the prey and the gray wolf. X P Let A be the position vector of the prey; X(t) be the position vector of the gray wolf. The formulas for calculating A and C are:

[0110] A = 2·a·r1-a (19)

[0111] C = 2·r² (20)

[0112] In the formula, r1 and r2 are both random numbers in [0,1]; a is a linear convergence factor that decreases linearly from 2 to 0 as the number of iterations increases.

[0113] (3) Hunting

[0114] After encircling their prey, individuals within the wolf pack continue hunting by updating their own positions. The mathematical model for this process is as follows:

[0115]

[0116] In the formula, X(t+1) represents the updated position of an individual wolf in the pack, and the forward movement and direction of the individual wolf are jointly determined by X1(t), X2(t), and X3(t); X α (t), X β (t), X δ (t) represent the position vectors of α, β, and δ wolves, respectively; D α D β D δ Let α, β, δ represent the distances between α, β, δ wolves and ω wolves, respectively. The calculation formulas are as follows:

[0117]

[0118] (4) Attack

[0119] The hunting activity ends when the prey stops moving, and the wolf pack then launches an attack. In constructing the prey attack model, according to formula (19), a decrease in the value of 'a' will cause the value of 'A' to fluctuate accordingly; that is, 'A' is a random vector in the interval [-a, a]. Here, 'a' decreases linearly during the iteration process. When |A| < 1, an attack is launched on the prey.

[0120] 3.2 Improved Discrete Gray Wolf Optimization Algorithm

[0121] The standard Grey Wolf Optimization (GWO) method is suitable for solving continuous optimization problems, while the MTSP-HVCPP problem is a combinatorial optimization problem and cannot be solved directly using the GWO method. Therefore, this invention proposes an improved Discrete Grey Wolf Optimization (IDGWO) algorithm, which integrates heuristic population initialization, multi-population co-evolution, and neighborhood perturbation operations, based on the standard Grey Wolf Optimization (GWO) method.

[0122] 3.2.1 Gray Wolf Individual Encoding Representation

[0123] The multi-agent target region allocation scheme and target region access order are encoded as solution space for individual gray wolves. Each gray wolf in the population corresponds to a feasible solution. This invention employs a two-part sequence encoding method, such as... Figure 6 As shown. Assuming the number of agents is M and the number of target regions is N, the encoding length of a gray wolf individual is M+N. The gray wolf individual is divided into two parts by vertical lines. The numbers on the left represent the access sequence of the N target regions (excluding the starting position), and the numbers on the right represent the number of target regions assigned to each agent.

[0124] After encoding the individual gray wolves, the optimal gray wolf needs to be transformed into an optimization variable through decoding to obtain the extreme value of the objective function. The decoding method involves assigning a corresponding number of target regions to each agent for visual coverage detection according to the order of the target regions arranged to the left of the vertical line.

[0125] 3.2.2 Heuristic Population Initialization Strategy

[0126] During population initialization, we employ a set-based encoding representation method, such as... Figure 6 As shown. First, M target region sets are generated based on the number of agents; second, N target regions are assigned to these M sets using a heuristic initialization method based on the optimization objective; finally, the final gray wolf individual is generated based on the number of target regions in each set.

[0127] The heuristic initialization method first randomly selects M target region indices and assigns them to corresponding sets. Then, based on the centroid coordinates of each region, the distance between target regions is calculated. Unassigned regions are sequentially inserted at the end of each set, selected based on the region closest to the last region in the set. During each iteration, the updated sets are checked to reduce the risk of generating infeasible paths. This process continues until all regions have been assigned. Once the region assignment within each set is complete, the number of target regions each agent needs to cover is determined based on the number of regions in each set, and the corresponding encoding representation is performed.

[0128] 3.2.3 Cross-update and population elimination strategies

[0129] Since the multi-agent, multi-region coverage task planning problem is a combinatorial optimization problem, the standard Grey Wolf Optimization Algorithm cannot be directly applied to solve it. Therefore, borrowing the idea of ​​crossover and mutation from genetic methods, the Grey Wolf positions are updated using the following formula:

[0130]

[0131] For each individual gray wolf's position update, firstly, gray wolf individuals α, β, and δ are selected according to the aforementioned social hierarchy mechanism. Then, a random number rand between [0,1] is generated. Based on the different values ​​of rand, the current gray wolf individual's position is cross-checked with one of the gray wolf individuals α, β, or δ. Figure 8As shown. Assume there are 10 target regions, numbered 1 to 10, and 3 agents. All agents start from the same initial position. Define gray wolf individuals X1 and X2. Assume the intersection position is 3 to 6. Then, select the intersection segment [8,1,4,5] from X1 and replace it before X2. Then, delete the duplicate elements in X2 from beginning to end (excluding the last 3 elements). Finally, a new gray wolf individual X2 = [8,1,4,5,7,3,2,6,10,9,2,4,4].

[0132] After each iteration, the G worst-fitting gray wolves are selected for elimination, where G = k * population, k is the elimination ratio factor, and population is the total number of individuals in the population. New gray wolves are generated heuristically to replace the eliminated ones, and a greedy strategy is employed to ensure that the fitness of the newly generated wolves is always better than that of the original ones. This population elimination strategy removes poorly fit individuals from the population, preventing the search from stalling due to a fixed solution location in later stages, and promoting co-evolution of the population.

[0133] 3.2.4 Variable Neighborhood Search Strategy

[0134] To avoid the method getting trapped in local optima, a neighborhood search is performed on the α, β, and δ individuals of the gray wolf population after the position update to obtain better gray wolf individuals, thereby driving the population towards a more optimal update direction. Since the order of target region visits has a significant impact on fitness values, a random perturbation operator is introduced, combined with three classic neighborhood operators—exchange, insertion, and reversal—to perform local search. Simultaneously, to coordinate the inter-group communication strategy with local perturbation and effectively balance the global and local search of the method, an adaptive probabilistic perturbation control strategy is introduced. This strategy selects the perturbation method based on probability, resulting in a large perturbation amplitude in the early stages to maintain population diversity and prevent the method from getting trapped in local optima; in the middle and later stages, the strategy leans towards local search to enhance the method's expansive capabilities and improve convergence speed.

[0135] (1) Disorder perturbation operator

[0136] like Figure 9 As shown, for individual gray wolf X α First, it is converted into an encoding form X based on the target region set. L According to X L The length of each target region set is used to generate a corresponding non-repeating random integer sequence X. S Using X S Adjust X L The gene locations on the target region are used to obtain a new set of target regions, which are then encoded into a new gray wolf individual X′. α .

[0137] (2) Commutation operator

[0138] like Figure 10 As shown, two positions are randomly selected from individual gray wolf X, and the target areas of these two positions are swapped to form a new individual X′.

[0139] (3) Insertion operator

[0140] like Figure 11 As shown, two positions are randomly selected from individual gray wolf X, and the target area of ​​the first position is inserted after the target area of ​​the second position to form a new individual gray wolf X′.

[0141] (4) Inversion operator

[0142] like Figure 12 As shown, two positions are randomly selected from individual gray wolf X, and the target region sequence between these two positions is reversed to form a new individual gray wolf X′.

[0143] Clearly, the disordered perturbation operator is more suitable for fine-tuning searches, while the exchange, insertion, and reversal operators show their advantages in achieving efficient perturbations with large changes. To better balance the exploration and development of the method, neighborhood operators are adaptively selected based on their varying degrees of perturbation to the solution: in the early stages of the method, larger, more efficient perturbations are used to accelerate convergence; for later stages with more high-quality individuals, precise searches for fine-tuning are prioritized to improve solution accuracy. Therefore, the aforementioned neighborhood search operators are selected probabilistically to generate new solutions. Each time, a random number between [0,1] is generated. When rand≤s, exchange, insertion, and reversal are applied sequentially to the gray wolf individual. When rand>s, the disordered perturbation operator is used to generate new solutions for the gray wolf individual. Let s be the convergence factor, which is calculated by the following formula to balance the selection probabilities of various neighborhood search operators:

[0144]

[0145] In the formula, iter is the current iteration number, and u is the control factor. Changing the size of u can control the decay rate of s. The larger u is, the slower s decays. The corresponding method mainly uses transformation, insertion and reversal operations in the early stage, and mainly performs disordered adjustment within the set in the later stage.

[0146] 3.3 Solution Process

[0147] Let the gray wolf population size be *population*, the maximum number of iterations for the method be *max_iter*, the number of iterations for the optimal individual's fitness value to remain unchanged be *stop_iter*, the number of iterations for the neighborhood search operation be *search_iter*, the population elimination ratio factor be *k*, and the method terminates when the optimal gray wolf's α-fitness value remains unchanged for *stop_iter* generations or when the maximum number of iterations *max_iter* is reached. The main steps are as follows:

[0148] Step 1: Initialize method hyperparameters: max_iter, stop_iter, search_iter, population, k, initialize the gray wolf population.

[0149] Step 2: Calculate the fitness values ​​of all individuals in the population and determine the top three most fit gray wolf individuals α, β, and δ in the group.

[0150] Step 3: Select individual gray wolves in the population using the roulette wheel method, and perform the CROSS operation on the selected individuals.

[0151] Step 4: Perform neighborhood search based on the adaptive probability perturbation control strategy.

[0152] Step 5: If the method reaches the termination condition, output the global optimal solution; otherwise, repeat Step 2 to Step 4.

[0153] 4. Simulation Results and Analysis

[0154] 4.1 Parameter Settings

[0155] The simulation experiment was conducted using MATLAB R2023b, with a hardware environment configured as an Intel Core i9-11900H, 2.50GHz CPU and 16GB RAM. The simulation parameters were set as follows: photoelectric sensor viewing angle θ = 90°, lens field of view... The initial starting coordinates of the multi-agent system are (14km, 18km), with a speed of 20m / s and a maximum range of 40km. Considering the varying image resolution requirements of different target areas, different detection flight altitudes h are set for different target areas. i ,make Three different scale coverage task scenarios were set up. A certain number of target areas were randomly generated within task domains of different sizes, and different numbers of agents were deployed for cooperative detection. The parameters for each scenario are shown in Table 1.

[0156] Table 1 Parameters for Multi-Agent Multi-Region Coverage Scenarios

[0157]

[0158] 4.2 Method Comparison

[0159] This invention uses the IDGWO method to solve the problem, generating multi-region coverage paths in... Figures 13 to 15 The method was demonstrated in the paper. To verify the superiority of the proposed IDGWO method, three benchmark methods were selected for comparative analysis. These benchmark methods included two multi-region coverage task planning methods based on improved genetic algorithms: GASC and GA2PC, and a multi-region coverage path planning method combining heuristics and ant colony optimization: BETR-VAC. All these methods have been proven effective in solving multi-agent, multi-region coverage task planning problems. Table 2 details the parameter settings for these methods.

[0160] Table 2 Comparison Method Parameter Settings

[0161]

[0162] To eliminate the instability of single experiments, Monte Carlo simulations were used to conduct 100 experiments on each test method in scenario 4. In each experiment, these methods underwent a maximum of 200 iterations. To more clearly compare the results of each method, the changes in the optimal objective function value were plotted as box plots, such as... Figures 16-18 As shown in the table, the proposed method significantly outperforms other comparative methods in terms of stability, especially when facing large-scale problems, where IDGWO still exhibits good convergence. Statistical analysis of the performance of the four methods is presented in Table 3. According to Table 3, under scenario 1, when facing small-scale problems, IDGWO and the three baseline methods can all obtain near-optimal solutions, but IDGWO's method shows significantly better stability than the other three methods. Furthermore, the GA2PC method's solution quality is significantly inferior to the other methods, indicating that this method is prone to getting trapped in local optima. As the problem size increases, the superiority of the IDGWO method becomes increasingly apparent, outperforming the other methods in both solution quality and solution efficiency.

[0163] Table 3 Statistical Analysis of Monte Carlo Simulation Results

[0164]

[0165] 5. Conclusion

[0166] This invention addresses a coverage path planning problem in a practical application scenario. The goal is to achieve visual coverage detection of a series of non-intersecting polygonal target regions while satisfying the target region's image resolution. To effectively solve this problem, this invention first models and analyzes the airborne sensors, deriving a mathematical expression relating the detection flight altitude to the image resolution. This ensures that the agent performs visual coverage at the maximum detection flight altitude while meeting the image resolution requirements. Furthermore, this invention innovatively proposes a discrete gray wolf optimization algorithm that integrates multiple strategies. This method comprehensively considers the detection flight altitude, the access order of target regions, and the coverage path for each region, achieving coupled optimization. Simulation experiments in task scenarios of different scales verify that the proposed method not only effectively solves large-scale multi-region coverage task planning problems but also significantly outperforms many existing solutions.

[0167] The above description provides examples of the preferred embodiments of the present invention. Parts not detailed herein are common knowledge to those skilled in the art. The scope of protection of the present invention is determined by the claims. Any equivalent modifications based on the technical teachings of the present invention are also within the scope of protection of the present invention.

Claims

1. A multi-agent cooperative detection multi-region coverage task planning method based on an improved discrete grey wolf optimization algorithm, characterized in that, The method comprises the following steps: Step 1: according to the given target area map and the parameter configuration information of each agent and its sensor, the target area map, the agent and its sensor model are initialized; a multi-area coverage task model and a fitness function are constructed with the optimization goal of minimizing the longest coverage path; Step 2: the grey wolf population is initialized based on a heuristic method, each grey wolf corresponds to a task allocation scheme, and it is ensured that each target area is covered by at least one agent in each task allocation scheme; Assuming that the number of agents is M and the number of target areas is N, the coding length of each grey wolf individual is M+N, the coding of the grey wolf individual includes the access sequence of the target area and the number of target areas allocated to each agent, and the access sequence of the target area includes the target area sequence corresponding to each agent arranged in ascending order of agent number, and the target area sequence number visited by each agent in ascending order of access sequence forms the target area sequence corresponding to each agent; Step 3: the fitness value of each grey wolf is calculated, and the three grey wolf individuals with the highest fitness value in the group are determined as α, β and δ, wherein the fitness values of α, β and δ decrease; Step 4: randomly select a grey wolf individual in the population, and perform CROSS crossover operation on the selected individual and the grey wolf individuals α, β and δ to obtain new grey wolf individuals, and retain the grey wolf individual with a higher fitness value to obtain three grey wolf individuals after the crossover operation; Step 5: a random number rand1 between 0 and 1 is generated, when rand1≤s, the three grey wolf individuals obtained in step 4 are respectively subjected to the exchange operator, the insertion operator and the reverse operator operation, and a new grey wolf individual is obtained each time, the fitness values of the new grey wolf individuals obtained after each operation and the three grey wolf individuals obtained in step 4 are compared, and the grey wolf individual with a higher fitness value is retained to obtain three grey wolf individuals after adaptive probability disturbance regulation; when rand1>s, the three grey wolf individuals obtained in step 4 are subjected to the random disturbance operator operation, and the fitness values of the three new grey wolf individuals obtained after the operation and the three grey wolf individuals obtained in step 4 are compared, and the grey wolf individual with a higher fitness value is retained to obtain three grey wolf individuals after adaptive probability disturbance regulation; wherein s is a convergence factor, and is used to balance the selection probability of multiple neighborhood search operators; In step 5, the calculation formula of s is: In the formula, iter is the current iteration number, and u is a preset control factor value; step 6: the iteration number is increased by 1, and it is judged whether the maximum iteration number is reached, if yes, the optimal individual among the three grey wolf individuals obtained in the last iteration is output, and the next step is turned to, otherwise, step 3 is turned to, and the three grey wolf individuals obtained after the iteration are replaced by the grey wolf individuals α, β and δ; Step 7: the task allocation scheme corresponding to the optimal grey wolf individual is calculated, the optimal coverage path is generated based on the improved rotary caliper method according to the scheme, and the final full coverage path is obtained.

2. The multi-agent cooperative detection multi-region coverage task planning method based on the improved discrete grey wolf optimization algorithm according to claim 1, characterized in that, In step 2, the heuristic initialization method is as follows: first, randomly select N target region serial numbers and assign them to the corresponding sets; then, calculate the distance between the target regions based on the centroid coordinates of each region; finally, the unassigned regions will be sequentially inserted into the end of each set, and the selection criterion is the region closest to the last region in the set.

3. The multi-agent cooperative detection multi-region coverage task planning method based on the improved discrete grey wolf optimization algorithm according to claim 1, characterized in that, In step 4, the specific method of CROSS crossover operation is as follows: Step 4.1, generate a random number rand2, if rand2≤1 / 3, then take α as the individual to be crossed, if rand2≥2 / 3, then take β as the individual to be crossed, if 1 / 3<rand2<2 / 3, then take δ as the individual to be crossed; Step 4.2, randomly generate the target region position to be crossed, exchange the selected grey wolf individual and the coding of the target region position to be crossed of the individual to be crossed, obtain two new grey wolf individuals, compare the fitness values of α, β, δ and the two new grey wolf individuals, and select the top three grey wolf individuals with the highest fitness values as the three grey wolf individuals after the crossover operation.

4. The multi-agent cooperative detection multi-region coverage task planning method based on the improved discrete grey wolf optimization algorithm according to claim 1, characterized in that, In step 5, the exchange, insertion and reversal operator operations are as follows: The definition of the exchange operator is: randomly select two target region positions from the coding of the original grey wolf individual, exchange the target regions at these two positions to form a new grey wolf individual; The definition of insertion is: randomly select two target region positions from the coding of the original grey wolf individual, insert the target region at the first position after the target region at the second position to form a new grey wolf individual; The definition of the reversal operator is: randomly select two target region positions from the coding of the original grey wolf individual, and arrange the target regions between these two target region positions in reverse order to form a new grey wolf individual; The definition of the random disturbance operator is: select the target region access sequence corresponding to each agent from the coding of the original grey wolf individual, randomly select an interval under the condition that the total length of the target region sequence of each agent remains unchanged, and randomly recombine the target region sequence in the selected interval to form a new grey wolf individual.

5. The multi-agent cooperative detection multi-region coverage task planning method based on the improved discrete grey wolf optimization algorithm according to claim 1, characterized in that, An improved multi-region coverage path generation method based on the rotating caliper method is used to generate the optimal coverage path, and the reciprocal of the total path length is taken as the fitness value of the grey wolf individual, which includes the following steps: Step 1.1, determine the access order of each agent to different target areas according to the code of gray wolf, assuming that for the ith agent, there are N i target areas to be covered, and the access order of the N i areas has been planned, when the agent covers the first target area, it moves from the task starting point P start to the entry point P1 in of the first target area to be covered, follows a reciprocating path to scan and cover the target area, and finally moves to the exit point P1 out of the first target area to be covered; a parallel reciprocating coverage mode is adopted to cover the target area completely, and a series of waypoints are generated by calculating the intersection points of the coverage path and the target area boundary; Step 1.2, the set of the combination of the task starting point and the corresponding waypoint of each target area is the coverage path of the current target area, and the shortest path length is the optimization objective, and the optimal coverage path for the current area is obtained based on the rotating caliper method, and is represented as After completing the coverage of one target area, according to the target area access sequence, the starting point P1 of the first to-be-covered area is moved to the entry point of the next to-be-covered area based on the greedy strategy out , and the next to-be-covered area is covered. All target areas are covered in turn, and finally the task termination point P is returned after covering all target areas. end The optimal coverage path of each target area is sequentially connected to obtain the overall optimal coverage path. Step 1.3, calculate the total path length according to the overall optimal coverage path, and take the reciprocal of the total path length as the fitness value.

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