Multi-robot sea rescue path planning method based on multi-objective particle swarm optimization

Abstract

The application discloses a kind of multi-robot sea rescue path planning method based on multi-objective particle swarm optimization, S1: the region to be searched is converted into two-dimensional search area;S2: grid decomposition is carried out to two-dimensional search area;S3: probability map is obtained by mixed Gaussian model;S4: unmanned aerial vehicle search multi-objective collaborative optimization function is established;S5: function is solved based on hybrid particle swarm optimization algorithm, and the optimal solution is obtained;According to the optimal solution solved, the specific search path of unmanned aerial vehicle is generated.The application establishes unmanned aerial vehicle search multi-objective collaborative optimization function, and the task of unmanned aerial vehicle is guided to execute search and rescue task with resource balanced allocation, maximum path safety, priority coverage high-risk area and minimization of energy consumption as target, improves task allocation, path planning and energy management, realizes multi-robot search path planning multi-objective optimization, formulates accurate flight path for each unmanned aerial vehicle, ensures comprehensive coverage of search and rescue task, and significantly improves search and rescue efficiency and success rate.

Description

Technical Field

[0001] This invention relates to the field of maritime search and rescue path planning technology, and in particular to a multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization. Background Technology

[0002] Natural disasters and human factors frequently lead to maritime accidents, causing enormous loss of life and property. The complexity of maritime accidents and the urgency of search and rescue missions necessitate rapid and accurate rescue of distressed personnel or vessels to minimize losses. Therefore, improving the efficiency and success rate of maritime search and rescue missions is crucial. Traditional search and rescue methods rely on ships and helicopters, but these have many limitations in terms of cost, risk, and handling of adverse sea conditions. With the rapid development of remote operation, sensors, and other related technologies, drones, with their advantages of flexible deployment, low cost, and low risk, can cover vast sea areas, conduct long-term searches and monitoring, operate in dangerous or inaccessible areas, and function in various weather conditions, demonstrating great potential in maritime search and rescue missions. Therefore, given the limited survival time of distressed personnel and the complex and changeable marine environment, scientifically and efficiently planning drone search and rescue routes, ensuring comprehensive coverage of the search area, and optimizing resource allocation are of great significance for improving the efficiency of maritime search and rescue.

[0003] Multi-UAV maritime search and rescue operations are complex tasks involving multiple aspects such as multi-target optimization, path planning, task allocation, and collaborative control. While existing technologies provide theoretical and practical guidance for UAV-based maritime search and rescue, they still lack consideration for the complex relationships between multiple performance objectives such as safety, economy, and timeliness. Specifically, firstly, in multi-UAV collaborative search and rescue, the workload of each UAV varies greatly. UAVs with fewer tasks may complete their missions in a shorter time, while others have to handle a larger area. This results in some important areas not being fully covered, prolonging the overall search and rescue operation and increasing the overall time cost. Insufficient coverage or search and rescue delays may cause the best opportunity to rescue trapped personnel in a short period of time, thus affecting the success rate of the search and rescue. Secondly, in multi-UAV collaborative missions, unreasonable path planning can lead to overlapping search paths between different UAVs, spending too much time in low-priority or repetitive areas and missing opportunities to cover high-priority areas, resulting in a slow overall search and rescue process. Thirdly, the endurance of UAVs is a major challenge in maritime search and rescue missions, especially when performing long-term missions in vast sea areas. Due to limited energy resources, how to plan the optimal path to achieve maximum search coverage with minimal energy consumption is a key challenge.

[0004] In summary, the existing technological planning path may lead to problems such as low mission efficiency, waste of resources, and increased safety risks for drones. Furthermore, it is difficult to find the optimal balance when facing target conflicts, thereby affecting the success rate and overall effectiveness of search and rescue missions. Summary of the Invention

[0005] This invention provides a multi-UAV maritime search and rescue path planning method based on multi-target particle swarm optimization, which overcomes the problems of low mission efficiency, resource waste, and increased UAV safety risks that may result from the path planning of existing technologies. Furthermore, it is difficult to find the optimal balance when facing target conflicts, thus affecting the success rate and overall effectiveness of search and rescue missions.

[0006] To achieve the above objectives, the technical solution of this invention is: a multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization, the specific steps of which include:

[0007] S1: Based on the initial information of the UAV search and rescue mission, extract the area to be searched from the Earth satellite map; by projecting the area to be searched onto a two-dimensional map, the area to be searched is transformed into a two-dimensional search and rescue area for UAV path planning.

[0008] S2: The two-dimensional search and rescue area is decomposed into a grid using a quadrilateral mesh decomposition method to obtain the decomposed search and rescue area;

[0009] S3: Calculate the distribution probability of the target to be searched within the decomposed search area using a Gaussian mixture model to obtain a probability map;

[0010] S4: Establish a multi-objective collaborative optimization function for UAV search and rescue, which includes: a task balancing objective function to ensure a balanced distribution of the area covered by each UAV and the workload; a path safety objective function to prevent path intersections or overlaps between UAVs; a priority coverage objective function based on a probability map to search for high-probability areas where targets appear; and an energy consumption minimization objective function to optimize flight paths and energy consumption, maximizing the UAV's endurance.

[0011] S5: Solve the multi-objective collaborative optimization function for UAV search and rescue based on the hybrid particle swarm optimization algorithm to obtain the optimal solution; generate the specific search and rescue path for the UAV based on the obtained optimal solution.

[0012] Furthermore, in S4, the established multi-objective cooperative optimization function for UAV search and rescue is expressed as:

[0013] minF=ω1Ls(t)+ω2Lc(t)-ω3Le(t)+ω4Lh(t)

[0014]

[0015] In the formula: ω1, ω2, ω3, and ω4 are the evaluation weights for balanced resource allocation, path safety, high-priority area coverage, and energy consumption minimization, respectively; Ls(t) is the objective function for balanced task allocation during UAV search and rescue; Lc(t) is the objective function for path safety; Le(t) is the objective function for priority coverage of high-probability areas; and Lh(t) is the objective function for minimizing energy consumption.

[0016] Furthermore, the objective function for balanced task allocation is expressed as:

[0017]

[0018] In the formula, c i (t) represents the number of points covered by drone i at time t. p is the average number of points covered by all drones at time t. i w(t) is the probability of UAV i detecting a target within its coverage area at time t. i (t) is the weight of the region at time t;

[0019] The objective function for path security is expressed as:

[0020]

[0021] In the formula, A i (t) and A j (t) represent the coverage areas of drones i and j at time t, respectively, O(A) i (t),A j (t) represents A i (t) and A j The number of overlaps between (t) at time t, I i,j (t) represents the number of intersections between drones i and j at time t, and K and K′ are constants used to ensure the cost of collision and overlap.

[0022] The objective function for prioritizing the coverage of high-probability regions is expressed as:

[0023]

[0024] In the formula, m is the number of grids on the UAV's path, and p i (t) is the detection probability of the i-th grid at time t, and λ is the weight decay coefficient, which is used to prioritize regions with high detection probabilities and decreases with time.

[0025] The objective function for minimizing energy consumption is expressed as:

[0026]

[0027] In the formula, m is the number of grids on the UAV's path, and d i,i+1 (t) is the distance between the i-th point and the (i+1)-th point at time t, v i (t) is the flight speed of UAV i at time t, E i (t) is the energy consumption of drone i at time t.

[0028] Furthermore, in S2, the process of decomposing the two-dimensional search and rescue area using a quadrilateral mesh decomposition method to obtain the decomposed search and rescue area is as follows:

[0029] The boundary range S of the two-dimensional search and rescue area is defined as follows:

[0030] S=[min(x),max(x);min(y),max(y)]

[0031] In the formula, x and y are the horizontal and vertical coordinates of a vertex on the boundary of the two-dimensional search and rescue area, respectively.

[0032] The number of grid cells B required to cover the entire two-dimensional search and rescue area is represented as:

[0033] B = [S / d]

[0034] Each grid B ij The position in the coordinate system is defined as the coordinates of its center point, expressed as:

[0035] B ij =[i·d,j·d]+l

[0036] In the formula, i and j are the row and column indices, d is the grid size, and l represents the offset from the grid start point to the target point;

[0037] Adjust the positions of all grids according to actual needs to ensure that all grids are within and completely cover the 2D search and rescue area. Adjustments include rotation and translation operations. The formula for grid rotation is:

[0038] Nc=R(θ)(cr c )+r c

[0039] In the formula, θ is the rotation angle; R(θ) is the rotation matrix, R(θ)=[-(sinθ)] 2 (cosθ) 2 ], c represents the coordinates of the center point of the rotated mesh, r c These are the coordinates of the rotation center;

[0040] The mesh is translated based on the movement vector Δ. The formula for calculating the movement vector Δ is:

[0041] Δ=δ[cos(-θ),sin(-θ)]

[0042] In the formula, δ is the step size that needs to be moved;

[0043] After adjusting the positions of all grids, the decomposed search and rescue area is obtained.

[0044] Furthermore, in S3, the process of calculating the probability distribution of the target to be searched within the decomposed search area using a Gaussian mixture model to obtain the probability map is as follows:

[0045] S31: Based on historical rescue data, expert experience and environmental information, identify several high-probability points in the environmental map. These high-probability points represent the locations where the search target is most likely to appear.

[0046] S32: Calculate the distance between each high-probability point and all grid center points in the decomposed search and rescue area, and replace the original high-probability point with the grid center point that is closest to the high-probability point as the new high-probability point;

[0047] S33: Based on new high-probability points, compare the credibility of each new high-probability point by comprehensively analyzing expert experience and environmental information;

[0048] S34: Based on the confidence levels of each new high-probability point after comparison, define the corresponding mixed weight π for each new high-probability point. k The probability distribution of the target to be searched in each grid cell was calculated using a Gaussian mixture model. The mathematical expression of the Gaussian mixture model is as follows:

[0049]

[0050] In the formula, x' represents the data point, K is the number of Gaussian distributions, and π k It is the mixture weight of the k-th distribution, and satisfies and π k ≥0; μ represents a two-dimensional Gaussian distribution. k The mean value represents the possible central location of the target; ∑ k The covariance matrix represents the uncertainty of the region;

[0051] The probability distribution of the search target in each grid is normalized to ensure that the sum of the probability values ​​in the probability map is 1. The normalization formula is as follows:

[0052]

[0053] In the formula, c(i,j) represents the grid with indices i and j, and Pn(c i,j) and P(c i,j The numbers () represent the normalized and unnormalized discovery probabilities of the corresponding grid points, respectively. This represents the sum of the unnormalized probability values ​​of all grid cells;

[0054] The parameters of each Gaussian distribution are adjusted according to different sea area conditions to simulate the possible locations of the target to be searched under different sea area conditions, and the final probability map is obtained.

[0055] Furthermore, the traditional particle swarm optimization algorithm is improved to obtain the hybrid particle swarm optimization algorithm. Specifically, the steps for improving the traditional particle swarm optimization algorithm include:

[0056] 1) An adaptive weight adjustment mechanism is introduced into the particle velocity update rule of the traditional particle swarm optimization algorithm to replace the fixed inertia weights. The improved particle velocity update rule is expressed as follows:

[0057]

[0058] x i (t+1)=x i (t)+v i (t+1)

[0059] In the formula, w max and w min These are the maximum and minimum inertia weights, respectively, where J is the current iteration number. m This represents the maximum number of iterations.

[0060] 2) In the individual optimal and global optimal update stages of the traditional particle swarm optimization algorithm, an elite mechanism is introduced to create an individual optimal set for each particle and record the optimal position it experiences during the iteration process; at the same time, a group optimal set is created for the entire swarm to record the global optimal position of all particles; and a crossover operation is added to the elite mechanism. In each iteration, the crossover operation first allows each particle to cross over with its individual optimal set, and then cross over with the group optimal set.

[0061] 3) A penalty mechanism is introduced into the fitness function of the traditional particle swarm optimization algorithm. That is, a penalty term is added to deal with solutions that violate the constraints. The expression of the penalty function is:

[0062]

[0063] In the formula, f p f(x) is the fitness function after adding the penalty term, f(x) is the original fitness function, and h k (x) represents the degree of violation of the k-th constraint, λ k Where K is the penalty coefficient and K is the number of constraints.

[0064] Beneficial Effects: This invention uses a quadrilateral mesh decomposition method to decompose the two-dimensional search and rescue area, simplifying the complex search area and process, and more effectively covering the entire search area. It also introduces a Gaussian mixture model to calculate the probability of the target's appearance, estimating the target's presence probability in different areas and prioritizing the search of high-probability regions. Based on this, a multi-objective collaborative optimization function for UAV search and rescue is established, guiding UAVs to perform search and rescue missions with objectives such as balanced resource allocation, maximum path safety, priority coverage of high-risk areas, and minimized energy consumption. This improves task allocation, path planning, and energy management, achieving multi-objective optimization of multi-UAV search and rescue path planning. A hybrid particle swarm optimization algorithm is proposed to enhance the algorithm's global search capability and convergence speed. This method can formulate precise flight paths for each UAV, ensuring comprehensive coverage of the search and rescue mission and significantly improving search and rescue efficiency and success rate. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 This is a flowchart of the multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization in this invention;

[0067] Figure 2 This is a schematic diagram illustrating the acquisition of the accident location and the area to be searched in an embodiment of the present invention;

[0068] Figure 3 This is a schematic diagram of the camera footprint of the drone in an embodiment of the present invention;

[0069] Figure 4 This is a schematic diagram showing that the search area in an embodiment of the present invention is decomposed into grid cells;

[0070] Figure 5 This is a scene diagram of a maritime search and rescue mission in an embodiment of the present invention;

[0071] Figure 6 This is a flowchart of the hybrid particle swarm optimization algorithm in an embodiment of the present invention;

[0072] Figure 7 This is a diagram illustrating the effect of dynamic weight adjustment in an embodiment of the present invention.

[0073] Figure 8 This is a schematic diagram of the search and rescue area for a test case in an embodiment of the present invention;

[0074] Figure 9 This is a schematic diagram of the test case grid decomposition and high probability points in an embodiment of the present invention;

[0075] Figure 10 This is a three-dimensional probability distribution diagram of the existence of the target to be searched in the test case of the embodiment of the present invention;

[0076] Figure 11 The drone path in the probability map in this embodiment of the invention;

[0077] Figure 12 The drone path generated by the method proposed in the embodiments of the present invention;

[0078] Figure 13 and 14 This is a comparison chart of the results calculated using multiple algorithms in the embodiments of the present invention. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0080] This embodiment provides a multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization, such as... Figure 1 As shown, the specific steps include:

[0081] S1: Based on the initial information of the UAV search and rescue mission, extract the area to be searched from the Earth satellite map; by projecting the area to be searched onto a two-dimensional map, the area to be searched is transformed into a two-dimensional search and rescue area for UAV path planning.

[0082] Specifically, high-resolution satellite map data is acquired through Earth observation satellites or online mapping services (such as Google Earth). In the initial stage of a maritime search and rescue mission, the boundaries of the search area are determined based on the last known location of the missing persons or vessels and their possible drift paths. This search area is then marked on an Earth satellite map, transforming it into a graph composed of vertices and edges. Figure 2 As shown, its boundary can be represented as a polygon, and the set of vertices on the polygon boundary is {v1, v2, v3, ..., v...}. n Then, the area to be searched in the three-dimensional Earth coordinate system is projected onto a two-dimensional map, thereby transforming the area to be searched into a two-dimensional search area for UAV path planning.

[0083] S2: The two-dimensional search and rescue area is decomposed into a grid using a quadrilateral mesh decomposition method to obtain the decomposed search and rescue area;

[0084] S3: Maritime search and rescue missions typically involve large search areas. To improve search and rescue efficiency and success rate, a probability map is obtained by calculating the distribution probability of the target to be searched within the decomposed search area using a Gaussian mixture model.

[0085] S4: Drone search and rescue path planning not only needs to efficiently search for targets, but also needs to consider economy and safety. That is, when performing tasks, drones should maximize search efficiency and minimize energy consumption to adapt to large-scale searches and avoid collisions. Therefore, this embodiment comprehensively considers target search efficiency, resource balance allocation, path safety, and energy consumption during the search and rescue process, and establishes a multi-objective collaborative optimization function for drone search and rescue. The multi-objective collaborative optimization function for drone search and rescue includes: a task balance allocation objective function to ensure a balance between the area covered by each drone and the workload; a path safety objective function to prevent path intersections or overlaps between drones; a priority coverage objective function based on the probability map to prioritize searching for high-probability areas where targets appear; and an energy consumption minimization objective function to optimize flight paths and energy consumption to maximize the drone's endurance.

[0086] S5: Based on the hybrid particle swarm optimization algorithm, solve the multi-objective collaborative optimization function for UAV search and rescue to obtain a set of optimal solutions that can satisfy different objectives (balanced task allocation, path safety, priority coverage of high-risk areas, and minimization of energy consumption). Based on the obtained optimal solutions, generate the specific search and rescue path for the UAV. In practical applications, the planned path can also be dynamically adjusted based on real-time data feedback during the search and rescue process. By quickly recalculating or locally adjusting the flight path, search and rescue efficiency can be further improved.

[0087] In a specific embodiment, UAVs need to perform precise regional decomposition of the search and rescue area before performing path planning in maritime search and rescue missions. By simplifying the complex maritime environment into visual planning units, search and rescue paths can be optimized, search and rescue efficiency can be improved, and efficient search coverage can be achieved. Currently, commonly used regional decomposition methods include hexagonal grid decomposition, Voronoi diagram decomposition, adaptive decomposition, and quadrilateral grid decomposition. Among them, quadrilateral grid decomposition is widely used due to its simplicity, adaptability, and ability to be combined with various algorithms. It is an effective method for discretizing real maps. Therefore, in this embodiment, the quadrilateral grid decomposition method is used to perform grid decomposition on the two-dimensional search and rescue area.

[0088] Specifically, in S2, the two-dimensional search and rescue area is decomposed into a grid using a quadrilateral mesh decomposition method, resulting in the following: Figure 4 The process of decomposing the search and rescue area as shown is as follows:

[0089] The boundary range S of the two-dimensional search and rescue area is defined as follows:

[0090] S=[min(x),max(x);min(y),max(y)]

[0091] In the formula, x and y are the horizontal and vertical coordinates of a vertex on the boundary of the two-dimensional search and rescue area, respectively.

[0092] The number of grid cells B required to cover the entire two-dimensional search and rescue area is represented as:

[0093] B = [S / d]

[0094] Each grid B ij The position in the coordinate system is defined as the coordinates of its center point, expressed as:

[0095] B ij =[i·d,j·d]+l

[0096] In the formula, i and j are the row and column indices, d is the grid size, and l represents the offset from the grid start point to the target point;

[0097] Specifically, the grid size d is designed based on the drone's flight altitude and the camera's field of view to ensure that the size of each grid matches the drone's coverage area.

[0098] Specifically, since the drone's camera viewpoint is circular, the region is divided into equal-sized grids during area decomposition. The grid size should be determined based on the circular area covered by the drone's camera viewpoint. Each grid's size must be less than or equal to the drone's camera viewpoint coverage area to ensure that the drone's line of sight completely covers the area when moving within each cell, thus achieving comprehensive search coverage. Figure 3 As shown, in order to ensure effective visual coverage of the UAV at its flight altitude, and at the same time reduce the total number of grids to improve processing efficiency, the grid size is generally selected as the largest square grid within the UAV's circular field of view.

[0099] In practical applications, based on the UAV's starting position or ocean dynamic data such as wind direction and ocean currents, it may be necessary to appropriately rotate or translate the grid to adapt to the actual environment. This can be achieved by selecting a reference edge, calculating the rotation angle, and applying a rotation matrix to adjust the coordinates of each grid, ensuring that all grids are within the two-dimensional search and rescue area and completely cover it. The formula for the grid rotation operation is as follows:

[0100] Nc=R(θ)(cr c )+r c

[0101] In the formula, R(θ) is the rotation matrix, R(θ)=[-(sinθ)] 2 (cosθ) 2 ], c represents the coordinates of the center point of the rotated mesh, r c θ is the coordinate of the rotation center; θ is the rotation angle, which can be determined by analyzing the direction of wind, waves and ocean currents to ensure that the UAV's search path is consistent with the direction of ocean currents, thereby increasing the chance of detecting the target.

[0102] To ensure that all meshes completely cover the target area and to avoid overlaps and omissions, a translation operation needs to be performed on the meshes. Specifically, the meshes are translated according to the translation vector Δ, which is calculated using the following formula:

[0103] Δ=δ[cos(-θ),sin(-θ)]

[0104] In the formula, δ is the step size that needs to be moved.

[0105] After adjusting the positions of all grids, the decomposed search and rescue area is obtained.

[0106] In a specific embodiment, S3, the process of calculating the distribution probability of the target to be searched within the decomposed search area using a Gaussian mixture model to obtain the probability map is as follows:

[0107] S31: Based on historical rescue data, expert experience and environmental information, identify several high-probability points in the environmental map. These high-probability points represent the locations where the search target is most likely to appear.

[0108] S32: Since the selected high-probability point has a certain deviation from the grid center, in order to improve the accuracy of the search, the distance between each high-probability point and all grid center points in the decomposed search area is calculated, and the original high-probability point is replaced by the grid center point that is closest to the high-probability point as the new high-probability point;

[0109] S33: Based on new high-probability points, compare the credibility of each new high-probability point by comprehensively analyzing expert experience and environmental information;

[0110] S34: Based on the confidence levels of each new high-probability point after comparison, define the corresponding mixed weight π for each new high-probability point. k The probability distribution of the target to be searched in each grid cell was calculated using a Gaussian mixture model. The mathematical expression of the Gaussian mixture model is as follows:

[0111]

[0112] In the formula, x' represents the data point, K is the number of Gaussian distributions, and π kIt is the mixture weight of the k-th distribution, and satisfies and π k ≥0; μ represents a two-dimensional Gaussian distribution. k The mean value represents the possible central location of the target; ∑ k The covariance matrix represents the uncertainty of the region;

[0113] The probability distribution of the search target in each grid is normalized to ensure that the sum of the probability values ​​in the probability map is 1. The normalization formula is as follows:

[0114]

[0115] In the formula, c(i,j) represents the grid with indices i and j, and Pn(c i,j ) and P(c i,j The numbers () represent the normalized and unnormalized discovery probabilities of the corresponding grid points, respectively. This represents the sum of the unnormalized probability values ​​of all grid cells;

[0116] The parameters of each Gaussian distribution are adjusted according to different sea conditions to simulate the possible location of the target to be searched under different sea conditions, so as to obtain the final probability map. Based on the probability map, the UAV is guided to prioritize the search in the area where the target is most likely to be found.

[0117] Specifically, in this embodiment, as the search and rescue operation progresses, the drone will continuously report real-time data such as sea surface conditions and target information. This data allows for dynamic adjustment of the parameters of the Gaussian mixture model. Based on the real-time updated probability map, the drone can adjust its search path, prioritizing coverage of new high-probability areas and improving search and rescue efficiency. Figure 5 As shown, drones are assigned to cover their respective areas in a predetermined order. Through real-time data links, the drones continuously transmit images and other monitoring data back to the command center, which then uses this data for real-time analysis and adjusts its search strategy.

[0118] In a specific embodiment, the multi-target cooperative optimization function for UAV search and rescue established in S4 is expressed as follows:

[0119] minF=ω1Ls(t)+ω2Lc(t)-ω3Le(t)+ω4Lh(t)

[0120]

[0121] In the formula: ω1, ω2, ω3, and ω4 are the evaluation weights for balanced resource allocation, path safety, high-priority area coverage, and energy consumption minimization, respectively, and their values ​​are determined according to the target priority of different search and rescue scenarios; Ls(t) is the objective function for balanced task allocation during UAV search and rescue; Lc(t) is the objective function for path safety; Le(t) is the objective function for priority coverage of high-probability areas; and Lh(t) is the objective function for minimizing energy consumption.

[0122] In a specific embodiment, uniform task allocation facilitates collaborative work among drones, ensuring that each drone covers a roughly equal area. This guarantees reasonable resource allocation and a balanced drone workload, while ensuring drone coverage of every important area for early target detection. The objective function for balanced task allocation during drone search and rescue is set as Ls(t). This balance is achieved by balancing the target detection probability within each drone's coverage area. The objective function for balanced task allocation is expressed as:

[0123]

[0124] In the formula, c i (t) represents the number of points covered by drone i at time t. p is the average number of points covered by all drones at time t. i w(t) is the probability of UAV i detecting a target within its coverage area at time t. i (t) is the weight of the region at time t;

[0125] Specifically, the path safety objective function Lc(t) is used to evaluate the ability of UAVs to avoid path overlap and intersection during search and rescue operations. It detects intersections and overlaps between UAVs and self-intersections of individual UAV flight paths, avoiding resource waste, efficiency reduction, and collision risks caused by overlaps and intersections. The path safety objective function is expressed as:

[0126]

[0127] In the formula, A i (t) and A j (t) represent the coverage areas of drones i and j at time t, respectively, O(A) i (t),A j (t) represents A i (t) and A j The number of overlaps between (t) at time t, I i,j (t) represents the number of intersections between drones i and j at time t, and K and K′ are constants used to ensure the cost of collision and overlap.

[0128] Specifically, the high-priority region coverage objective function Le(t) is a probability-weighted path optimization that enables the UAV to prioritize searching for key regions with a high probability of target existence at the start of the mission. The objective function for prioritizing high-probability region coverage is expressed as:

[0129]

[0130] In the formula, m is the number of grids on the UAV's path, and p i (t) is the detection probability of the i-th grid at time t, and λ is the weight decay coefficient, which is used to prioritize regions with high detection probabilities and decreases with time.

[0131] Specifically, the energy consumption minimization objective function Lh(t) aims to optimize the UAV's energy consumption by reducing the total flight path length and flight energy consumption, thereby accelerating search and rescue speed, improving UAV endurance, and enhancing search and rescue efficiency and expanding the search area. The energy consumption minimization objective function is expressed as:

[0132]

[0133] In the formula, m is the number of grids on the UAV's path, and d i,i+1 (t) is the distance between the i-th point and the (i+1)-th point at time t, v i (t) is the flight speed of UAV i at time t, E i (t) is the energy consumption of drone i at time t.

[0134] Traditional Particle Swarm Optimization (PSO) algorithms mainly include the following parts: particle initialization, fitness evaluation, individual and global optimum updates, velocity and position updates, iterative process, and termination conditions. When using traditional PSO algorithms, they may get stuck in local optima, failing to explore other possible better solutions. This can easily lead to an inability to expand the search, missing the optimal search and rescue path, wasting valuable computation and execution time, delaying search and rescue operations, and struggling to find the optimal balance when facing target conflicts, thus affecting the success rate and overall effectiveness of the search and rescue mission. Therefore, this embodiment introduces an adaptive weight adjustment mechanism, an elite mechanism, and a penalty mechanism. By dynamically adjusting search weights, constructing an optimal solution set, and adding a penalty function, the algorithm's global search capability and convergence speed are improved, enabling the optimization algorithm to run efficiently in actual search and rescue missions, ensuring rapid response to complex and changing marine environments, and achieving efficient solutions to the UAV maritime search and rescue coverage path planning problem. Figure 6As shown, the basic process of the hybrid particle swarm optimization algorithm is as follows: First, the particle swarm is initialized by setting key parameters; then, particle data is read during the iteration process to generate the initial flight path of the UAV; next, the optimization path is strengthened through violation suppression and constraint; at the same time, an elite mechanism is introduced to retain the optimal solution, and the diversity of solutions is increased through updates of individual optimal and group optimal solutions, as well as crossover and mutation operations; in addition, adaptive dynamic weight adjustment is used to balance global search and local exploitation; in each iteration cycle, the current global optimal path is recorded and updated; finally, the algorithm stops when the preset optimization termination condition is met, thus obtaining the optimal UAV flight path.

[0135] In a specific embodiment, the traditional particle swarm optimization algorithm is improved to obtain the hybrid particle swarm optimization algorithm. The specific steps for improving the traditional particle swarm optimization algorithm include: 1) introducing an adaptive weight adjustment mechanism into the particle velocity update rule of the traditional particle swarm optimization algorithm to replace the fixed inertia weights. The improved particle velocity update rule is expressed as:

[0136]

[0137] x i (t+1)=x i (t)+v i (t+1)

[0138] In the formula, w max and w min These are the maximum and minimum inertia weights, respectively, where J is the current iteration number. m v is the maximum number of iterations. i (t) and x i (t) represents the velocity and position of the i-th particle in generation t, respectively; c1 and c2 are acceleration constants used to control the particle's optimal position pbest. i The degree to which the global optimal position gbest is followed; rand1 and rand2 are random numbers between 0 and 1;

[0139] Specifically, traditional PSO lacks an effective balancing mechanism, allowing particles to perform simple random searches. When particles deviate from the global optimum, effective adjustments are difficult, easily leading to local optima. To improve the search capability of the PSO algorithm, this embodiment introduces an adaptive weight adjustment mechanism. This mechanism dynamically adjusts the weights of individual particles and the global optimum based on the search progress, enabling particles to explore the entire search space more effectively, thereby improving the ability to find the global optimum. The basic idea is: during algorithm iteration, the inertia weight is dynamically adjusted based on the particle's fitness value. If some particles have better fitness values, it means they may be close to the global optimum, and they should be given larger dynamic weight values ​​to move them closer to the global optimum faster. Conversely, particles with poor fitness values ​​may have deviated from the global optimum and should be given smaller dynamic weight values ​​to pull them back onto the global search path. Figure 7 The image shows the effect of dynamic weight changes, representing the relationship between dynamic weights and the current position and current velocity. By adjusting the weights, particles can more effectively approach the global optimal position.

[0140] 2) In the individual optimal and global optimal update stages of the traditional particle swarm optimization algorithm, an elite mechanism is introduced to create an individual optimal set for each particle and record the optimal position it experiences during the iteration process; at the same time, a group optimal set is created for the entire swarm to record the global optimal position of all particles; and a crossover operation is added to the elite mechanism. In each iteration, the crossover operation first allows each particle to cross over with its individual optimal set, and then cross over with the group optimal set.

[0141] Specifically, traditional PSO often suffers from premature convergence and is prone to getting trapped in local optima due to a lack of sufficient diversity. To address this issue, an elitist mechanism is introduced to preserve high-quality potential solutions, increase population diversity, and significantly improve algorithm performance. Specifically, an individual optimal set is created for each particle, recording its optimal position during iteration; simultaneously, a population optimal set is created for the entire population, recording the global optimal position of all particles. In each iteration, the crossover operation first crosses with each individual particle's individual optimal set, and then with the population optimal set. This approach not only preserves high-fitness elite individuals, ensuring their continuation, but also combines the crossover operation with the elitist mechanism, increasing population diversity through the crossover operation and significantly improving global search capability and convergence performance.

[0142] 3) A penalty mechanism is introduced into the fitness function of the traditional particle swarm optimization algorithm. That is, a penalty term is added to deal with solutions that violate the constraints. The expression of the penalty function is:

[0143]

[0144] In the formula, fp f(x) is the fitness function after adding the penalty term, f(x) is the original fitness function, and h k (x) represents the degree of violation of the k-th constraint, λ k Where K is the penalty coefficient and K is the number of constraints.

[0145] Specifically, in multi-objective optimization problems, there are often constraints that need to be satisfied. If a particle's position update violates these constraints, its fitness value needs to be penalized. Traditional particle swarm optimization algorithms lack effective penalty mechanisms, which can easily lead the algorithm into infeasible solution regions, affecting the optimization effect. This embodiment introduces a penalty mechanism and designs a penalty function to effectively avoid infeasible solutions, improve the feasibility of solutions, and enhance the robustness of the algorithm. Specifically, the degree of constraint violation for each particle is calculated, and solutions that violate the constraints are penalized, significantly increasing their fitness values ​​and reducing the influence of these particles in the population, thereby guiding the particle swarm to evolve towards the feasible solution space.

[0146] In this embodiment, the effectiveness of the proposed multi-UAV cooperative maritime search and rescue path planning method is verified through simulation experiments. The experiments simulate various search and rescue mission environments, such as... Figure 8 As shown, three drones are set up to conduct search and rescue operations in three different search and rescue areas. The polygons of each search and rescue area are randomly generated, and their sizes are controlled within the drones' flight range. The starting point of the drones can be freely chosen. Table 1 lists the relevant parameters for the simulation test.

[0147] Table 1:

[0148]

[0149]

[0150] Specifically, such as Figure 9 The diagram illustrates the process of decomposing the search and rescue area and determining high-probability points. Using a quadrilateral grid decomposition method, the search and rescue area is precisely discretized into multiple planning units. Furthermore, by combining historical search and rescue data with marine environmental characteristics, several key high-probability points are identified, providing decision support for prioritizing UAV search areas. A Gaussian mixture model is used to calculate the probability of target presence within each grid unit, generating a model as shown below. Figure 10 The probability distribution maps of the Gaussian mixture models for each region shown reflect the distribution probability of the target in different regions, providing a basis for UAV search and rescue path planning. Furthermore, the search and rescue paths generated according to the multi-objective optimization algorithm proposed in this embodiment are as follows: Figure 11As shown in the figure, the drone prioritizes detection of areas with a high probability of target location, enabling it to locate targets in a shorter time, thus improving search and rescue efficiency and success rate. Furthermore, the even distribution of tasks across high-probability areas improves resource utilization and avoids waste. Figure 12 As shown, three different colors represent the search paths of the three drones. The drone search path map generated by the method proposed in this embodiment shows a high degree of optimization, prioritizing the exploration of areas with high confidence while considering path safety and energy consumption. Each path demonstrates high rationality and efficiency. Figure 11 and 12 As shown, the drone achieved 100% search coverage in each search and rescue area, with 0% overlap in all search areas, and significantly improved the efficiency of path planning and the success rate of search and rescue.

[0151] The simulation results compare several similar algorithms, including the traditional Particle Swarm Optimization (PSO) algorithm, Simulated Annealing (SA) algorithm, and Genetic Algorithm (GA). The rationality of the path planning results is further verified through comparative analysis with existing algorithms, such as... Figure 13 and 14 As shown, within the same time frame, the improved PSO algorithm converges the fastest, indicating that it finds the optimal solution the fastest. The traditional PSO, simulated annealing (SA), and genetic algorithm (GA) converge slower. Therefore, the improved PSO outperforms the traditional PSO, SA, and GA in terms of both objective function value and fitness value convergence speed, demonstrating that the method proposed in this embodiment can converge to the global optimal solution more quickly.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization, characterized in that, The specific steps include: S1: Based on the initial information of the UAV search and rescue mission, extract the area to be searched from the Earth satellite map; by projecting the area to be searched onto a two-dimensional map, the area to be searched is transformed into a two-dimensional search and rescue area for UAV path planning. S2: The two-dimensional search and rescue area is decomposed into a grid using a quadrilateral mesh decomposition method to obtain the decomposed search and rescue area; S3: Calculate the distribution probability of the target to be searched within the decomposed search area using a Gaussian mixture model to obtain a probability map; S4: Establish a multi-target cooperative optimization function for UAV search and rescue, which includes: The objective function for balanced task allocation is expressed as: ， In the formula, It is a drone i In time t Number of points covered at the time Is all drones in time The average number of coverage points at any given time. It is a drone In time The probability of detecting targets within the coverage area. Is this region in time t Weight of time; The objective function for path security is expressed as: ， In the formula, and These are drones and In time Coverage area at that time express and Between in time Number of overlaps at time Indicates drone and In time The number of intersections at time, and It is a constant used to ensure collision and overlap costs; The objective function for prioritizing coverage of high-probability regions is expressed as: ， In the formula, m It is the number of grids along the drone's path. p i ( t ) is the first i Each grid in time t Detection probability at time, λ It is a weight decay coefficient, used to prioritize regions with high detection probability and decreases over time; The objective function for minimizing energy consumption is expressed as: ， In the formula, m It is the number of grids along the drone's path. d i, i+1 ( t ) is the first i The point and the first i +1 point in time t The distance between time, v i ( t (This refers to drones) i In time t Flight speed at that time E i ( t (This refers to drones) i In time t Energy consumption per hour; S5: Solve the multi-objective collaborative optimization function for UAV search and rescue based on the hybrid particle swarm optimization algorithm to obtain the optimal solution; generate the specific search and rescue path for the UAV based on the obtained optimal solution.

2. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 1, characterized in that, In S4, the established multi-target cooperative optimization function for UAV search and rescue is expressed as: ， ， In the formula: ω 1. ω 2. ω 3. ω 4 are the evaluation weights for balanced resource allocation, path security, high-priority area coverage, and energy consumption minimization, respectively. Ls ( t The objective function for task balancing in drone search and rescue; Lc ( t ) is the objective function for path security; Le ( t The objective function is to prioritize covering high-probability regions. Lh ( t ) is the objective function for minimizing energy consumption.

3. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 1, characterized in that, In S2, the two-dimensional search and rescue area is decomposed into a mesh using a quadrilateral mesh decomposition method. The process of obtaining the decomposed search and rescue area is as follows: Determine the boundary of the two-dimensional search and rescue area. S , represented as: ， In the formula, x and y These are the x and y coordinates of a vertex on the boundary of the two-dimensional search and rescue area, respectively. Determine the number of grids required to cover the entire two-dimensional search and rescue area. B , represented as: ， Each grid B ij The position in the coordinate system is defined as the coordinates of its center point, expressed as: ， In the formula, i and j These are row and column indices, d For grid size, l This represents the offset from the grid start point to the target point; Adjust the positions of all grids according to actual needs to ensure that all grids are within and completely cover the 2D search and rescue area. Adjustments include rotation and translation operations. The formula for grid rotation is: ， In the formula, θ The rotation angle; R ( θ ) is a rotation matrix. R ( θ ) = [ - (sin θ ) 2 (cos θ ) 2 ], c Indicates the coordinates of the center point of the rotated grid. r c These are the coordinates of the rotation center; According to the movement vector Δ Perform a translation operation on the mesh, moving the vector. Δ The calculation formula is: ， In the formula, δ It is the step size that needs to be moved; After adjusting the positions of all grids, the decomposed search and rescue area is obtained.

4. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 3, characterized in that, In S3, the probability distribution of the target to be searched within the decomposed search area is calculated using a Gaussian mixture model to obtain the probability map. S31: Based on historical rescue data, expert experience and environmental information, identify several high-probability points in the environmental map. These high-probability points represent the locations where the search target is most likely to appear. S32: Calculate the distance between each high-probability point and all grid center points in the decomposed search and rescue area, and replace the original high-probability point with the grid center point that is closest to the high-probability point as the new high-probability point; S33: Based on new high-probability points, compare the credibility of each new high-probability point by comprehensively analyzing expert experience and environmental information; S34: Based on the confidence levels of each new high-probability point after comparison, define the corresponding mixed weight for each new high-probability point. π k The probability distribution of the target to be searched in each grid cell was calculated using a Gaussian mixture model. The mathematical expression of the Gaussian mixture model is as follows: ， In the formula, Represents data points, K It is the number of Gaussian distributions. π k It is the first k Mixed weights of distributions, and satisfying and π k ≥0; Represents a two-dimensional Gaussian distribution; The mean value represents the possible central location of the target; ∑ k The covariance matrix represents the uncertainty of the region; The probability distribution of the search target in each grid is normalized to ensure that the sum of the probability values ​​in the probability map is 1. The normalization formula is as follows: ， In the formula, c ( i , j ) indicates that the index is i , j The grid, Pn ( c i, j )and P ( c i, j The numbers () represent the normalized and unnormalized discovery probabilities of the corresponding grid points, respectively. This represents the sum of the unnormalized probability values ​​of all grid cells; The parameters of each Gaussian distribution are adjusted according to different sea area conditions to simulate the possible locations of the target to be searched under different sea area conditions, and the final probability map is obtained.

5. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 3, characterized in that, The hybrid particle swarm optimization algorithm is obtained by improving the traditional particle swarm optimization algorithm. Specifically, the steps for improving the traditional particle swarm optimization algorithm include: 1) An adaptive weight adjustment mechanism is introduced into the particle velocity update rule of the traditional particle swarm optimization algorithm to replace the fixed inertia weights. The improved particle velocity update rule is expressed as follows: ， ， In the formula, w max and w min represents the maximum and minimum inertia weights, respectively. J This represents the current iteration number. J m is the maximum number of iterations; 2) In the individual optimal and global optimal update stages of the traditional particle swarm optimization algorithm, an elite mechanism is introduced to create an individual optimal set for each particle and record the optimal position it experiences during the iteration process; at the same time, a group optimal set is created for the entire swarm to record the global optimal position of all particles; and a crossover operation is added to the elite mechanism. In each iteration, the crossover operation first allows each particle to cross over with its individual optimal set, and then cross over with the group optimal set. 3) A penalty mechanism is introduced into the fitness function of the traditional particle swarm optimization algorithm. This involves adding a penalty term to handle solutions that violate the constraints. The expression for the penalty function is: ， In the formula, f p ( x () represents the fitness function after adding a penalty term. f ( x ) represents the original fitness function. h k ( x ) is the first k The degree of violation of a constraint, λ k The penalty coefficient is... K To constrain the number of constraints.

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