Multi-unmanned aerial vehicle maritime search and rescue path planning method based on multi-target particle swarm optimization

Abstract

The invention discloses a multi-unmanned aerial vehicle maritime search and rescue path planning method based on multi-target particle swarm optimization. The method comprises the steps that S1, an area to be searched and rescued is converted into a two-dimensional search and rescue area; s2, performing grid decomposition on the two-dimensional search and rescue area; s3, obtaining a probability map through a Gaussian mixture model; s4, establishing an unmanned aerial vehicle search and rescue multi-target collaborative optimization function; s5, solving the function based on a hybrid particle swarm optimization algorithm to obtain an optimal solution; and generating a specific search and rescue path of the unmanned aerial vehicle according to the solved optimal solution. According to the method, an unmanned aerial vehicle search and rescue multi-target collaborative optimization function is established, the unmanned aerial vehicle is guided to execute the search and rescue task by taking resource balanced allocation, maximum path safety, preferential coverage of a high-risk area and minimum energy consumption as targets, task allocation, path planning and energy management are improved, multi-target optimization of multi-unmanned aerial vehicle search and rescue path planning is realized, and the search and rescue efficiency is improved. An accurate flight path is formulated for each unmanned aerial vehicle, comprehensive coverage of search and rescue tasks is ensured, and the search and rescue efficiency and success rate are remarkably improved.

Description

Technical Field

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

[0002] Natural disasters and human factors cause maritime accidents from time to time, causing huge losses of life and property. The complexity of maritime accidents and the urgency of search and rescue missions require quick and accurate rescue of people or ships in distress to minimize losses. Therefore, it is crucial to improve the efficiency and success rate of maritime search and rescue missions. Traditional search and rescue methods rely on ships and helicopters, but there are many limitations in terms of cost, risk, and coping with severe sea conditions. With the rapid development of related technologies such as remote operation and sensors, drones can cover vast sea areas, conduct long-term searches and monitoring, operate in dangerous or difficult-to-reach areas, and operate in a variety of weather conditions with their advantages of flexible deployment, low cost, and low risk, showing great potential in maritime search and rescue missions. Therefore, in the case of limited survival time for people in distress and complex and changeable marine environment, scientifically and efficiently planning the search and rescue path of drones, ensuring comprehensive coverage of the search and rescue area, and optimizing resource allocation are of great significance to improving the efficiency of maritime search and rescue.

[0003] Multi-UAV maritime search and rescue operations are a complex task, involving multiple aspects such as multi-objective optimization, path planning, task allocation, and collaborative control. Although existing technologies provide theoretical and practical guidance for UAV maritime search and rescue, they still lack consideration of the complex relationship between multiple performance objectives such as safety, economy, and timeliness. Specifically, first, in multi-UAV collaborative search and rescue, the amount of regional tasks that each UAV is responsible for varies greatly. UAVs with too few tasks may complete their tasks in a shorter time, while other UAVs have to deal with a larger area, resulting in some important areas not being fully covered and the overall search and rescue operation being prolonged, increasing the overall time cost of the search and rescue. Insufficient coverage or delayed search and rescue may miss the best time to rescue trapped people in a short time, thereby affecting the success rate of search and rescue. Secondly, in multi-UAV collaborative tasks, unreasonable path planning will lead to overlapping search paths between different UAVs, spending too much time in low-priority areas or repeated areas, missing the opportunity to cover high-priority areas, and slowing down the 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 conditions, how to plan the optimal path to achieve maximum search coverage with the least energy consumption is a key challenge.

[0004] In summary, the paths planned by existing technologies may lead to problems such as low mission efficiency, waste of resources, and increased safety risks of drones. In addition, it is difficult to find the best balance when facing conflicting targets, thus affecting the success rate and overall effect of the search and rescue mission. Summary of the invention

[0005] The present invention provides a multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization to overcome the problems that the paths planned by the prior art may lead to low mission efficiency, waste of resources, increase the safety risk of UAVs, and it is difficult to find the best balance when facing target conflicts, thus affecting the success rate and overall effect of the search and rescue mission.

[0006] In order to achieve the above object, the technical solution of the present invention is: a multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization, the specific steps include:

[0007] S1: Based on the initial information of the UAV search and rescue mission, the search and rescue area is extracted from the earth satellite map; by projecting the search and rescue area onto the two-dimensional map, the search and rescue area is converted into a two-dimensional search and rescue area for UAV path planning;

[0008] S2: Decomposing the two-dimensional search and rescue area by using a quadrilateral mesh decomposition method to obtain a decomposed search and rescue area;

[0009] S3: Calculate the distribution probability of the target to be searched and rescued in the decomposed search and rescue area by using a mixed Gaussian model to obtain a probability map;

[0010] S4: Establishing a multi-objective collaborative optimization function for UAV search and rescue, the multi-objective collaborative optimization function for UAV search and rescue includes: a task balance allocation objective function for ensuring that the size of the area covered by each UAV and the amount of tasks are balanced; a path safety objective function for preventing paths between UAVs from crossing or overlapping; a high probability area priority coverage objective function for preferentially searching for high probability areas where targets appear according to a probability map; an energy consumption minimization objective function for optimizing flight paths and energy consumption and maximizing the endurance of UAVs;

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

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

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

[0014]

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

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

[0017]

[0018] In the formula, c i (t) is the number of points covered by UAV i at time t, is the average number of coverage points of all drones at time t, p i (t) is the detection probability of the target in the coverage area of ​​UAV i at time t, w i (t) is the weight of the region at time t;

[0019] The path safety objective function is expressed as:

[0020]

[0021] In the formula, A i (t) and A j (t) are the coverage areas of UAV i and UAV j at time t, 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 collision and overlap costs.

[0022] The objective function of preferentially covering high probability areas is expressed as:

[0023]

[0024] Where m is the number of grids on the drone path, p i (t) is the detection probability of the i-th grid at time t, λ is the weight decay coefficient, which is used to give priority to areas with high detection probability and decreases with time;

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

[0026]

[0027] Where m is the number of grids on the drone path, 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 UAV i at time t.

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

[0029] Determine the boundary range S of the two-dimensional search and rescue area, expressed as:

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

[0031] Where x and y are the horizontal and vertical coordinates of a vertex on the boundary of the two-dimensional search and rescue area;

[0032] Determine the number of grids B required to cover the entire two-dimensional search and rescue area, expressed 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] Where i and j are 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 the two-dimensional search and rescue area and completely cover the two-dimensional search and rescue area. The adjustment includes rotation or translation operations. The formula for grid rotation operation is:

[0038] Nc=R(θ)(cr c )+r c

[0039] Where 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 rotation grid, r c is the coordinate of the rotation center;

[0040] The grid is translated according to the moving vector Δ. The calculation formula of the moving vector Δ is:

[0041] Δ=δ[cos(-θ),sin(-θ)]

[0042] In the formula, δ is the step size required to move;

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

[0044] Further, in S3, the distribution probability of the target to be searched and rescued in the decomposed search and rescue area is calculated by the mixed Gaussian model, and the process of obtaining the probability map is as follows:

[0045] S31: Determine a number of high-probability points in the environmental map based on historical rescue data, expert experience and environmental information. These high-probability points represent the most likely locations for the search target 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 closest to the high probability point as a new high probability point;

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

[0048] S34: According to the credibility of each new high probability point after comparison, the mixed weight π of each new high probability point is defined accordingly k , and use the mixed Gaussian model to calculate the distribution probability of the target to be rescued in each grid. The mathematical expression of the mixed Gaussian model is as follows:

[0049]

[0050] Where x' represents the data point, K is the number of Gaussian distributions, and π k is the mixing weight of the kth distribution and satisfies and π k ≥0; represents a two-dimensional Gaussian distribution; μ k is the mean, representing the possible central location of the target; ∑ k is the covariance matrix, representing the uncertainty of the region;

[0051] The distribution probability of the search and rescue 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:

[0052]

[0053] Where c(i,j) represents the grid with index i and j, Pn(c i,j) and P(c i,j ) represent the normalized and unnormalized discovery probability values ​​of the corresponding grid points, respectively. represents the sum of the unnormalized probability values ​​of all grids;

[0054] The parameters of each Gaussian distribution are adjusted according to different sea conditions to simulate the possible locations of the search and rescue targets under different sea conditions and obtain the final probability map.

[0055] Furthermore, the traditional particle swarm optimization algorithm is improved to obtain the hybrid particle swarm optimization algorithm. The specific steps of 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 weight. The improved particle velocity update rule is expressed as:

[0057]

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

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

[0060] 2) An elite mechanism is introduced in the individual optimal and global optimal update stages of the traditional particle swarm optimization algorithm. An individual optimal set is created for each particle, and the optimal position experienced during the iteration is recorded. At the same time, a group optimal set is created for the entire group, and the global optimal position of all particles is recorded. A crossover operation is added to the elite mechanism. In each iteration, the crossover operation first allows a single particle to cross with its individual optimal set, and then cross 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, by adding a penalty term to deal with solutions that violate the constraints. The expression of the penalty function is:

[0062]

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

[0064] Beneficial effects: The present invention uses a quadrilateral mesh decomposition method to decompose the two-dimensional search and rescue area to simplify the complex search and rescue area and the search and rescue process, more effectively cover the entire search and rescue area, and introduce a mixed Gaussian model to calculate the probability of the search and rescue target, estimate the probability of the target in different areas, and give priority to searching high-probability areas; on this basis, a multi-objective collaborative optimization function for unmanned aerial vehicle search and rescue is established, and the unmanned aerial vehicle is guided to perform search and rescue tasks with the goals of balanced resource allocation, maximum path safety, priority coverage of high-risk areas and minimization of energy consumption, which improves task allocation, path planning and energy management, and realizes multi-objective optimization of multi-unmanned aerial vehicle search and rescue path planning; a hybrid particle swarm optimization algorithm is proposed to improve the global search capability and convergence speed of the algorithm. This method can formulate an accurate flight path for each unmanned aerial vehicle, ensure comprehensive coverage of the search and rescue mission, and significantly improve the search and rescue efficiency and success rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

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

[0067] Figure 2 A schematic diagram of obtaining the accident occurrence point and the area to be searched in an embodiment of the present invention;

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

[0069] Figure 4 is a schematic diagram of a search area in an embodiment of the present invention being decomposed into grid units;

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

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

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

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

[0074] Fig. 9 A schematic diagram of the test case grid decomposition and high probability points in an embodiment of the present invention;

[0075] Fig.10 A three-dimensional probability distribution diagram of the existence of a target to be searched and rescued in a test case in an embodiment of the present invention;

[0076] Fig.11 is the drone path in the probability map in the embodiment of the present invention;

[0077] Fig.12 The drone path generated by the method proposed in the embodiment of the present invention;

[0078] Fig.13 and 14 This is a comparison chart of calculation results using various algorithms in an embodiment of the present invention. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work 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. Figure 1 As shown, the specific steps include:

[0081] S1: Based on the initial information of the UAV search and rescue mission, the search and rescue area is extracted from the earth satellite map; by projecting the search and rescue area onto the two-dimensional map, the search and rescue area is converted into a two-dimensional search and rescue area for UAV path planning;

[0082] Specifically, high-resolution satellite map data is obtained through earth observation satellites or online map services (such as Google Earth); in the early stages of the maritime search and rescue mission, the boundaries of the search and rescue area are determined based on the last known location of the missing person or ship and the possible drift path, and then the search and rescue area is marked on the earth satellite map, and the search and rescue area is converted into a graph composed of vertices and edges, such as Figure 2 As shown, its boundary can be represented as a polygon, and the vertex set on the polygon boundary is {v1,v2,v3,...,v n}, and then project the search and rescue area in the three-dimensional earth coordinate system onto the two-dimensional map, thereby converting the search and rescue area into a two-dimensional search and rescue area for UAV path planning.

[0083] S2: Decomposing the two-dimensional search and rescue area by using a quadrilateral mesh decomposition method to obtain a decomposed search and rescue area;

[0084] S3: Maritime search and rescue missions usually involve a large search area. In order to improve the search and rescue efficiency and success rate, the distribution probability of the search and rescue target in the decomposed search and rescue area is calculated by a mixed Gaussian model to obtain a probability map;

[0085] S4: The path planning of UAV search and rescue requires not only efficient target search, but also economic and safety considerations, that is, when performing tasks, UAVs should improve search efficiency and reduce energy consumption as much as possible to adapt to large-scale searches and avoid collisions. Therefore, this embodiment comprehensively considers the target search efficiency, balanced resource allocation, path safety and energy consumption in the search and rescue process, and establishes a multi-objective collaborative optimization function for UAV search and rescue. The multi-objective collaborative optimization function for UAV search and rescue includes: a task balance allocation objective function for ensuring that the size of the area covered by each UAV and the amount of tasks are balanced; a path safety objective function for preventing paths between UAVs from crossing or overlapping; an objective function for preferentially covering high-probability areas according to a probability map to prioritize search targets appearing in high-probability areas; an energy consumption minimization objective function for optimizing flight paths and energy consumption and maximizing the endurance of UAVs;

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

[0087] In a specific embodiment, the path planning of the UAV during the execution of the maritime search and rescue mission needs to be accurately decomposed in advance in the search and rescue sea area. By simplifying the complex maritime environment into visual planning units, the search and rescue path can be optimized, the search and rescue efficiency can be improved, and efficient search coverage can be achieved. Currently, the commonly used regional decomposition methods include hexagonal grid decomposition method, Voronoi diagram decomposition method, adaptive decomposition method and quadrilateral grid decomposition method. Among them, the quadrilateral grid decomposition method is widely used for its simplicity, strong adaptability, and combination with a variety of algorithms. It is an effective method for discretizing real maps. Therefore, in this embodiment, the quadrilateral grid decomposition method is used to decompose the grid of the two-dimensional search and rescue area.

[0088] Specifically, in S2, the two-dimensional search and rescue area is meshed by using a quadrilateral mesh decomposition method to obtain the following: Figure 4 The process of decomposing the search and rescue area shown is:

[0089] Determine the boundary range S of the two-dimensional search and rescue area, expressed as:

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

[0091] Where x and y are the horizontal and vertical coordinates of a vertex on the boundary of the two-dimensional search and rescue area;

[0092] Determine the number of grids B required to cover the entire two-dimensional search and rescue area, expressed 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] Where i and j are 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 according to the flight altitude of the UAV and the camera viewing range, ensuring that the size of each grid matches the coverage of the UAV.

[0098] Specifically, since the camera angle of the drone is circular, when decomposing the area, the area is divided into grids of equal size. The size of the grid should be determined according to the circular area covered by the drone camera angle. The size of each grid must be less than or equal to the coverage of the drone camera angle to ensure that when the drone moves in each unit, its line of sight can completely cover the area, thereby achieving comprehensive search coverage. Figure 3 As shown, in order to ensure effective visual coverage of the UAV at the flight altitude and reduce the total number of grids to improve processing efficiency, the grid size is generally selected to take the largest square grid within the circular field of view of the UAV.

[0099] In practical applications, based on the starting position of the drone or ocean dynamic data such as wind direction and current, the grid may need to be rotated or translated appropriately to adapt to the actual environment. The rotation angle can be calculated by selecting a reference edge and applying the rotation matrix to adjust the coordinates of each grid to ensure that all grids are within the two-dimensional search and rescue area and completely cover the two-dimensional search and rescue area. The formula for the grid rotation operation is:

[0100] Nc=R(θ)(cr c )+r c

[0101] Where R(θ) is the rotation matrix, R(θ)=[-(sinθ) 2 (cosθ) 2 ], c represents the coordinates of the center point of the rotation grid, r c is the coordinate of the rotation center; θ is the rotation angle, which can be determined by analyzing the wind, waves and current direction to ensure that the search path of the UAV is consistent with the current direction to increase the chance of finding the target.

[0102] To ensure that all grids completely cover the target area and avoid overlap and omission, the grids need to be translated. Specifically, the grids are translated according to the moving vector Δ. The calculation formula of the moving vector Δ is:

[0103] Δ=δ[cos(-θ),sin(-θ)]

[0104] Where δ is the step size required to move.

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

[0106] In a specific embodiment, in S3, the distribution probability of the target to be searched and rescued in the decomposed search and rescue area is calculated by a mixed Gaussian model, and the process of obtaining the probability map is as follows:

[0107] S31: Determine a number of high-probability points in the environmental map based on historical rescue data, expert experience and environmental information. These high-probability points represent the most likely locations for the search target to appear;

[0108] S32: Since there is a certain deviation between the position of the selected high probability point and the grid center, in order to improve the accuracy of the search, the distance between each high probability point and all the grid center points in the decomposed search and rescue area is calculated respectively, and the grid center point closest to the high probability point is used to replace the original high probability point as the new high probability point;

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

[0110] S34: According to the credibility of each new high probability point after comparison, the mixed weight π of each new high probability point is defined accordingly k , and use the mixed Gaussian model to calculate the distribution probability of the target to be rescued in each grid. The mathematical expression of the mixed Gaussian model is as follows:

[0111]

[0112] Where x' represents the data point, K is the number of Gaussian distributions, and π kis the mixing weight of the kth distribution and satisfies and π k ≥0; represents a two-dimensional Gaussian distribution; μ k is the mean, representing the possible central location of the target; ∑ k is the covariance matrix, representing the uncertainty of the region;

[0113] The distribution probability of the search and rescue 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:

[0114]

[0115] Where c(i,j) represents the grid with index i and j, Pn(c i,j ) and P(c i,j ) represent the normalized and unnormalized discovery probability values ​​of the corresponding grid points, respectively. represents the sum of the unnormalized probability values ​​of all grids;

[0116] The parameters of each Gaussian distribution are adjusted according to different sea conditions to simulate the possible locations of the search and rescue targets under different sea conditions, and the final probability map is obtained. Based on the probability map, the UAV is guided to search in the area where the target is most likely to be found.

[0117] Specifically, in this embodiment, as the search and rescue operation proceeds, the drone will continuously feed back real-time data such as sea surface conditions and target information, through which the parameters of the mixed Gaussian model can be dynamically adjusted. Based on the real-time updated probability map, the drone can adjust the search path, give priority to covering new high-probability areas, and improve the 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, drones continuously transmit images and other monitoring data to the command center, which uses these data for real-time analysis and adjusts search strategies.

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

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

[0120]

[0121] Where: ω1, ω2, ω3, ω4 are the evaluation weights of 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 of balanced task allocation during UAV search and rescue; Lc(t) is the objective function of path safety; Le(t) is the objective function of giving priority to covering high probability areas; Lh(t) is the objective function of minimizing energy consumption.

[0122] In a specific embodiment, evenly distributing tasks helps the coordinated work between drones, making the coverage area of ​​each drone basically equal, so as to ensure the reasonable allocation of resources and the balance of drone task load. At the same time, each important area is covered by drones, and the target can be found early. The objective function of balanced task allocation during drone search and rescue is set to Ls(t), and the balance of task volume is achieved by balancing the target detection probability in the coverage area of ​​each drone. The objective function of balanced task allocation is expressed as:

[0123]

[0124] In the formula, c i (t) is the number of points covered by UAV i at time t, is the average number of coverage points of all drones at time t, p i (t) is the detection probability of the target in the coverage area of ​​UAV i at time t, w 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 the drone to avoid path overlap and intersection during the search and rescue process, detect the intersection and overlap between drones and the self-intersection of a single drone's flight path, and avoid resource waste and efficiency reduction caused by overlap and intersection, as well as collision risks. The path safety objective function is expressed as:

[0126]

[0127] In the formula, A i (t) and A j (t) are the coverage areas of UAV i and UAV j at time t, 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 collision and overlap costs.

[0128] Specifically, the high-priority area coverage objective function Le(t) is a detection probability weighted path optimization, which enables the UAV to preferentially search for key areas with high probability of target existence at the beginning of the mission. The objective function of preferentially covering high-probability areas is expressed as:

[0129]

[0130] Where m is the number of grids on the drone path, p i (t) is the detection probability of the i-th grid at time t, λ is the weight decay coefficient, which is used to give priority to areas with high detection probability and decreases with time;

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

[0132]

[0133] Where m is the number of grids on the drone path, 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 UAV i at time t.

[0134] The traditional particle swarm optimization algorithm (PSO) mainly includes the following parts: particle initialization, fitness evaluation, individual optimal and global optimal update, speed and position update, iterative process, and termination condition. When using the traditional particle swarm optimization algorithm for searching, it may fall into the local optimal solution and fail to continue to explore other possible better solutions, which may easily lead to the inability to continue to expand the search, miss the best search and rescue path, waste precious computing and execution time, delay the search and rescue operation, and it is difficult to find the best balance when facing target conflicts, thus affecting the success rate and overall effect of the search and rescue mission. Therefore, in this embodiment, an adaptive weight adjustment mechanism, an elite mechanism and a penalty mechanism are introduced to improve the global search capability and convergence speed of the algorithm by dynamically adjusting the search weight, constructing the optimal solution set and adding a penalty function, so that the optimization algorithm can run efficiently in actual search and rescue missions, ensure rapid response to complex and changeable marine environments, and achieve efficient solution to the problem of drone maritime search and rescue coverage path planning. Figure 6As shown in the figure, the basic process of the hybrid particle swarm optimization algorithm is as follows: first, the particle swarm is initialized by setting key parameters; then, the particle data is read during the iteration process to generate the initial flight path of the UAV; then, the optimization path is strengthened by 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 the update of individual optimal and group optimal, as well as crossover and mutation operations; in addition, adaptive dynamic weight adjustment is used to balance global search and local development; in each iteration cycle, the current global optimal path is recorded and updated; finally, the algorithm stops when it meets the preset optimization termination condition, thereby 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 of 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 weight. 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 are the maximum and minimum inertia weights respectively, J is the current iteration number, J m is the maximum number of iterations; v i (t) and x i (t) are the velocity and position of the ith particle in the tth generation; c1 and c2 are acceleration constants used to control the optimal position of the particle for each individual, pbest i and the degree of following the global optimal position gbest; rand1 and rand2 are random numbers between 0 and 1;

[0139] Specifically, traditional PSO lacks an effective balancing mechanism, and particles can only perform simple random searches. When particles deviate from the global optimal position, it is difficult to make effective adjustments and they are prone to fall into local optimal solutions. In order to improve the search capability of the PSO algorithm, an adaptive weight adjustment mechanism is introduced in this embodiment to dynamically adjust the weights of individual and global optimal solutions according to the search process, so that particles can explore the entire search space more effectively, thereby improving the ability to find the global optimal solution. The basic idea is: during the algorithm iteration process, the inertia weight is dynamically adjusted according to the fitness value of the particle. If the fitness value of some particles is better, it means that these particles may be close to the global optimal position. At this time, a larger dynamic weight value should be assigned to make them approach the global optimal position faster; conversely, particles with poor fitness values ​​may have deviated from the global optimal position and should be assigned smaller dynamic weight values ​​in order to pull these particles back to the global search path. Figure 7 As shown, the dynamic weight change effect is shown, which represents the relationship between the dynamic weight and the current position and current speed. By adjusting the weight, the particle can more effectively approach the global optimal position.

[0140] 2) An elite mechanism is introduced in the individual optimal and global optimal update stages of the traditional particle swarm optimization algorithm. An individual optimal set is created for each particle, and the optimal position experienced during the iteration is recorded. At the same time, a group optimal set is created for the entire group, and the global optimal position of all particles is recorded. A crossover operation is added to the elite mechanism. In each iteration, the crossover operation first allows a single particle to cross with its individual optimal set, and then cross with the group optimal set.

[0141] Specifically, traditional PSO often leads to premature convergence due to the lack of sufficient diversity and is prone to falling into local optimality. To solve this problem, the introduction of an elite mechanism can retain high-quality potential solutions, increase the diversity of the population, and significantly improve the performance of the algorithm. Specifically, an individual optimal set is created for each particle, and the optimal position experienced during the iteration is recorded; at the same time, a group optimal set is created for the entire group, and the global optimal position of all particles is recorded. In each iteration, the crossover operation first allows a single particle to cross with its individual optimal set, and then cross with the group optimal set. This method not only retains elite individuals with high fitness values ​​and ensures their continuation; it also combines the crossover operation with the elite mechanism, increases the diversity of the population through the crossover operation, and significantly improves the 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, by adding a penalty term to deal with solutions that violate the constraints. The expression of the penalty function is:

[0143]

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

[0145] Specifically, in multi-objective optimization problems, there are often some constraints that need to be met. If the position update of a particle violates these constraints, its fitness value needs to be punished. The traditional particle swarm optimization algorithm lacks an effective penalty mechanism, which easily causes the algorithm to fall into an infeasible solution area, affecting the optimization effect. This embodiment introduces a penalty mechanism and designs a penalty function, which can effectively avoid infeasible solutions, improve the feasibility of the solution and the robustness of the algorithm. Specifically, the degree of constraint violation of each particle is calculated, and the solution that violates the constraint condition is punished, so that its fitness value is significantly increased, and the influence of these particles in the population is reduced, thereby guiding the particle swarm to evolve to a feasible solution space.

[0146] In this embodiment, the effectiveness of the proposed multi-UAV collaborative maritime search and rescue path planning method is verified through simulation experiments. In the experiment, various search and rescue mission environments are simulated, such as Figure 8 As shown in the figure, three drones are set to search and rescue three different search and rescue areas respectively. The polygon of each search and rescue area is randomly generated, and the size is controlled within the range of the drone's endurance. The starting point of the drone can be freely selected. Table 1 lists the relevant parameters of the simulation test.

[0147] Table 1:

[0148]

[0149]

[0150] Specifically, Fig. 9 As shown in the figure, the decomposition of the search and rescue area and the determination of high probability points are shown. The search and rescue area is accurately discretized into multiple planning units through the quadrilateral grid decomposition method, and several key high probability points can be determined by combining historical search and rescue data and marine environmental characteristics to provide decision support for the priority search area of ​​the drone. The mixed Gaussian model is used to calculate the probability of the target existing in each grid unit, generating Fig.10 The probability distribution diagram of the mixed Gaussian model of each region shown in FIG. 1 reflects the distribution probability of the target in different regions, providing a basis for the search and rescue path planning of the UAV. Further, the search and rescue path generated by the multi-objective optimization algorithm proposed in this embodiment is shown in FIG. Fig.11As shown in the figure, it can be seen that the drone prioritizes detection of areas with high target positioning probability, so that the drone can find the target in a shorter time, improve the efficiency and success rate of search and rescue, and the tasks in each high probability area are evenly distributed, which can improve resource utilization and avoid resource waste. Fig.12 As shown in the figure, three different colors are used to 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, giving priority to exploring areas with high confidence, while considering the safety and energy consumption of the path. Each path shows high rationality and efficiency. Fig.11 and 12 As shown in the figure, the search coverage rate of the UAV in each search and rescue area reached 100%, the overlap rate of the search areas was 0%, and the efficiency of path planning and the success rate of search and rescue were significantly enhanced.

[0151] The simulation results compare several similar algorithms, including the traditional particle swarm optimization algorithm (PSO), simulated annealing algorithm (SA), and genetic algorithm (GA). The rationality of the path planning results is further verified by comparative analysis with existing algorithms, such as Fig.13 and 14 As shown in the figure, within the same time, 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 at a slower speed. Therefore, the improved PSO is superior to the traditional PSO, SA and GA in terms of convergence speed of both objective function value and fitness value, indicating 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, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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, the search and rescue area is extracted from the earth satellite map; by projecting the search and rescue area onto the two-dimensional map, the search and rescue area is converted into a two-dimensional search and rescue area for UAV path planning; S2: Decomposing the two-dimensional search and rescue area by using a quadrilateral mesh decomposition method to obtain a decomposed search and rescue area; S3: Calculate the distribution probability of the target to be searched and rescued in the decomposed search and rescue area by using a mixed Gaussian model to obtain a probability map; S4: Establishing a multi-objective collaborative optimization function for UAV search and rescue, the multi-objective collaborative optimization function for UAV search and rescue includes: a task balance allocation objective function for ensuring that the size of the area covered by each UAV and the amount of tasks are balanced; a path safety objective function for preventing paths between UAVs from crossing or overlapping; a high probability area priority coverage objective function for preferentially searching for high probability areas where targets appear according to a probability map; an energy consumption minimization objective function for optimizing flight paths and energy consumption and maximizing the endurance of UAVs; S5: Solve the multi-objective collaborative optimization function of the UAV search and rescue based on the hybrid particle swarm optimization algorithm to obtain the optimal solution; generate a specific search and rescue path for the UAV according to the optimal solution obtained.

2. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 1 is characterized in that: In S4, the established UAV search and rescue multi-objective collaborative optimization function is expressed as: minF=ω1Ls(t)+ω2Lc(t)-ω3Le(t)+ω4Lh(t) Where: ω1, ω2, ω3, ω4 are the evaluation weights of resource balanced allocation, path safety, high priority area coverage and energy consumption minimization, respectively; Ls(t) is the objective function of balanced task allocation during UAV search and rescue; Lc(t) is the objective function of path safety; Le(t) is the objective function of giving priority to covering high probability areas; Lh(t) is the objective function of minimizing energy consumption.

3. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 2 is characterized in that: The task balanced allocation objective function is expressed as: In the formula, c i (t) is the number of points covered by drone i at time t, c(t) is the average number of points covered by all drones at time t, and p i (t) is the detection probability of the target in the coverage area of ​​UAV i at time t, w i (t) is the weight of the region at time t; The path safety objective function is expressed as: In the formula, A i (t) and A j (t) are the coverage areas of UAV i and UAV j at time t, 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, K and K′ are constants used to ensure collision and overlap costs; The objective function of preferentially covering high probability areas is expressed as: Where m is the number of grids on the drone path, p i (t) is the detection probability of the i-th grid at time t, λ is the weight decay coefficient, which is used to give priority to areas with high detection probability and decreases with time; The energy consumption minimization objective function is expressed as: Where m is the number of grids on the drone path, 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 UAV i at time t.

4. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 1 is characterized in that: In S2, the two-dimensional search and rescue area is meshed by using a quadrilateral mesh decomposition method, and the process of obtaining the decomposed search and rescue area is as follows: Determine the boundary range S of the two-dimensional search and rescue area, expressed as: S=[min(x),max(x);min(y),max(y)] Where x and y are the horizontal and vertical coordinates of a vertex on the boundary of the two-dimensional search and rescue area; Determine the number of grids B required to cover the entire two-dimensional search and rescue area, expressed as: B=[S / d] Each grid B ij The position in the coordinate system is defined as the coordinates of its center point, expressed as: B ij =[i·d,j·d]+l Where i and j are row and column indices, d is the grid size, and l 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 the two-dimensional search and rescue area and completely cover the two-dimensional search and rescue area. The adjustment includes rotation or translation operations. The formula for grid rotation operation is: Nc6R(θ)(cr c )+r c Where 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 rotation grid, r c is the coordinate of the rotation center; The grid is translated according to the moving vector Δ. The calculation formula of the moving vector Δ is: Δ=δ[cos(-θ),sin(-θ)] In the formula, δ is the step size required to move; After adjusting the positions of all grids, the decomposed search and rescue area is obtained.

5. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 4 is characterized in that: In S3, the distribution probability of the target to be searched and rescued in the decomposed search and rescue area is calculated by the mixed Gaussian model, and the process of obtaining the probability map is as follows: S31: Determine a number of high-probability points in the environmental map based on historical rescue data, expert experience and environmental information. These high-probability points represent the most likely locations for the search target 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 closest to the high probability point as a new high probability point; S33: Based on the new high probability points, the credibility of each new high probability point is compared by comprehensively analyzing expert experience and environmental information; S34: According to the credibility of each new high probability point after comparison, the mixed weight π of each new high probability point is defined accordingly k , and use the mixed Gaussian model to calculate the distribution probability of the target to be rescued in each grid. The mathematical expression of the mixed Gaussian model is as follows: Where x' represents the data point, K is the number of Gaussian distributions, and π k is the mixing weight of the kth distribution and satisfies and π k ≥0; represents a two-dimensional Gaussian distribution; μ k is the mean, representing the possible central location of the target; ∑ k is the covariance matrix, representing the uncertainty of the region; The distribution probability of the search and rescue 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: Where c(i,j) represents the grid with index i and j, Pn(c i,j ) and P(c i,j ) represent the normalized and unnormalized discovery probability values ​​of the corresponding grid points, respectively. represents the sum of the unnormalized probability values ​​of all grids; The parameters of each Gaussian distribution are adjusted according to different sea conditions to simulate the possible locations of the search and rescue targets under different sea conditions and obtain the final probability map.

6. The multi-UAV maritime search and rescue path planning method based on multi-objective particle swarm optimization according to claim 3 is characterized in that: The traditional particle swarm optimization algorithm is improved to obtain the hybrid particle swarm optimization algorithm. The specific steps of 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 weight. The improved particle velocity update rule is expressed as: x i (t+1)=x i (t)+v i (t+1) In the formula, w max and w min are the maximum and minimum inertia weights respectively, J is the current iteration number, J m is the maximum number of iterations; 2) An elite mechanism is introduced in the individual optimal and global optimal update stages of the traditional particle swarm optimization algorithm. An individual optimal set is created for each particle, and the optimal position experienced during the iteration is recorded. At the same time, a group optimal set is created for the entire group, and the global optimal position of all particles is recorded. A crossover operation is added to the elite mechanism. In each iteration, the crossover operation first allows a single particle to cross with its individual optimal set, and then cross with the group optimal set. 3) A penalty mechanism is introduced into the fitness function of the traditional particle swarm optimization algorithm, that is, by adding a penalty term to deal with solutions that violate the constraints. The expression of the penalty function is: In the formula, f p (x) is the fitness function after adding the penalty term, f(x) is the original fitness function, h k (x) is the violation degree of the kth constraint, λ k is the penalty coefficient, and K is the number of constraints.

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