Underwater target search and tracking cooperative path planning method based on AUV and multiple USVs

Abstract

This invention provides a collaborative path planning method for underwater target search and tracking based on AUVs and multiple USVs. It employs a distributed, cross-domain, heterogeneous collaborative path planning architecture. By setting different fitness functions in the search and tracking phases, the USV cluster and AUVs can dynamically adjust their path planning strategies according to mission requirements, achieving close collaboration between cross-domain platforms within the same time period and overcoming the information transmission lag problem in traditional phased collaborative modes. In the tracking phase, this invention introduces a dynamic periodic underwater target position prediction method to predict the target's future trajectory, enabling the AUV to switch from tracking mode to interception mode, improving the target acquisition success rate. The algorithm effectively balances global exploration capability and local development accuracy by introducing adaptive explosion radius, Levy flight strategy, and Gaussian mutation operation, resulting in stronger global optimization capability and faster convergence speed in the optimization of multi-USV and AUV collaborative path planning.

Description

Technical Field

[0001] This invention belongs to the field of unmanned system cooperative control technology, specifically involving a cooperative path planning method for underwater target search and tracking based on AUV and multiple USVs. Background Technology

[0002] With the rapid development of unmanned systems technology, utilizing low-cost, reusable unmanned platforms to perform maritime missions has become an industry consensus. Unmanned swarm platforms can complete complex tasks without human intervention, featuring high mission efficiency, reusability, and significant cost advantages, and have become an important component of future intelligent and unmanned maritime equipment systems. Collaborating unmanned surface vehicles (USVs) and autonomous underwater vehicles (AUVs) to form a cross-domain heterogeneous system of AUVs and multiple USVs can fully leverage the complementary advantages of USVs' high-precision surface positioning and strong real-time communication capabilities, and AUVs' fine underwater detection capabilities. Through economies of scale and synergistic gains, the reliability of underwater target search and tracking missions can be significantly improved.

[0003] However, the primary technical challenge in achieving efficient collaboration between AUVs and multiple USVs in a cross-domain heterogeneous system is path planning. Due to significant differences between USVs and AUVs in terms of dynamic characteristics, working media, communication capabilities, and sensing range, traditional path planning methods are difficult to apply directly, mainly exhibiting the following technical shortcomings:

[0004] (1) For example, the artificial potential field method, The A-Star algorithm (also known as the A-Star algorithm) is a classic path planning algorithm for swarm intelligence optimization. It performs well in static environments or single-machine path planning, but it has significant limitations when facing dynamic environments, multi-agent cooperation, and heterogeneous platform constraints. In particular, the artificial potential field method is prone to getting trapped in local optima, which can prevent the target from being reached. As the dimension of the state space increases, the computational complexity of the algorithm rises sharply, resulting in excessively long convergence times and making it difficult to meet the real-time requirements of path planning. For example, swarm intelligence optimization algorithms such as genetic algorithms and particle swarm optimization algorithms, although possessing certain global search capabilities, mostly adopt a centralized planning architecture. Under this planning architecture, the algorithm's operation is highly dependent on a central node that serves as a global information exchange hub. This central node is responsible for collecting the states of all individuals and distributing unified optimization instructions. Once this central node fails, the entire optimization system will come to a standstill. Therefore, this type of swarm intelligence algorithm, due to its excessive reliance on the central node, suffers from high communication overhead and high failure risk, making it difficult to adapt to the actual operating environment where underwater communication is limited.

[0005] (2) In existing technologies, the collaboration between USVs and AUVs often adopts a phased collaboration mode, which divides the entire task into several independent phases. For example, after the USV completes the search phase, it transmits the underwater target information to the AUV, which then independently performs the tracking phase. This phased collaboration is essentially a serial operation, and the USV and AUV do not form a true collaborative cooperation within the same time period. Taking the underwater target tracking task as an example, in traditional methods, after the AUV detects the underwater target, it relies solely on the AUV to complete the subsequent tracking. Since the underwater positioning error of the AUV accumulates over time and its communication capability is limited, when the underwater target moves, the AUV has difficulty obtaining the new position of the underwater target in time and is prone to losing the underwater target. Therefore, this traditional collaboration method fails to fully utilize the advantages of the USV's high-precision surface positioning and real-time communication, and the efficiency and reliability of task completion need to be improved.

[0006] (3) In swarm intelligence algorithms, the fireworks algorithm has received widespread attention due to its advantages such as simple structure, few parameters, and fast convergence speed. However, in practical applications, the traditional fireworks algorithm uses a fixed explosion radius to generate offspring fireworks, a short step displacement strategy for position updates, and Gaussian mutation with a fixed mutation probability to maintain population diversity. These technical strategies, to some extent, restrict the performance of the fireworks algorithm in solving complex optimization problems. Summary of the Invention

[0007] The inventive concept of this invention:

[0008] Through in-depth research, the inventors of this application not only recognized the technical limitations of traditional fireworks algorithms, such as fixed explosion radius, short step size displacement, and fixed mutation probability, but also discovered that these technical limitations are related to the following in the specific scenario of path planning for cross-domain heterogeneous systems involving AUVs and multiple USVs:

[0009] (1) The fixed explosion radius leads to a mismatch in the search range, the short step size displacement leads to a local optimum dilemma, and the fixed mutation probability causes the loss of population diversity. These three problems seem independent, but in fact they are coupled: if the fixed explosion radius is set too large, although it can expand the search range in the early stage of the algorithm, it will cause the offspring fireworks to be too scattered in the later stage of iteration, making it difficult to focus on the vicinity of the optimal solution for fine search; if the fixed explosion radius is set too small, it is difficult to jump out of the local range of the initial solution in the early stage of the algorithm, that is, the global exploration ability is insufficient, it is easy to fall into local optima, and the convergence speed is slow. The short step size displacement is prone to repeatedly searching in the current local area and falling into local optima; if the initial solution is far from the global optimum, the short step size displacement requires a lot of iterations to gradually approach it, and the search efficiency is low. The fixed explosion radius exacerbates the locality of the short step size displacement, and the mutation mechanism of the fixed mutation probability cannot introduce new genes to maintain population diversity when the population falls into local optima, which easily leads to premature convergence of the algorithm. The three together form a local convergence trap, which makes the algorithm very easy to fail in the high-dimensional solution space of AUV and multi-USV cross-domain heterogeneous systems. (2) The differences in working media, dynamic characteristics, and communication capabilities between USVs and AUVs result in a highly nonlinear and multimodal solution space for path planning. The shortcomings that traditional fireworks algorithms can tolerate in conventional optimization problems are amplified in the specific scenario of cross-domain heterogeneous systems of AUVs and multiple USVs. Fixed explosion radius cannot meet the differentiated requirements of large-scale surface search by USVs and fine underwater tracking by AUVs; short step displacement is difficult to cross the solution space faults formed by cross-media cooperation; and fixed mutation probability cannot cope with the continuous uncertainty brought about by the dynamic marine environment.

[0010] To address the aforementioned technical limitations, this invention introduces three major strategies: adaptive explosion radius, Levy flight strategy, and adaptive Gaussian mutation. These strategies respectively address the search imbalance caused by a fixed radius, the weakening of the global search due to short step size displacement, and the loss of population diversity due to a fixed mutation probability, forming a complete solution. The proposed three strategies work together synergistically to improve the algorithm's global optimization capability, convergence speed, and solution accuracy. Furthermore, as long as each individual in the AUV and multiple USV cross-domain heterogeneous system has sensors and connectors, the method of this invention can be used to jointly plan paths for USVs and AUVs located in different domains, thereby realizing path planning for cross-domain heterogeneous systems.

[0011] The technical solution provided by this invention is:

[0012] A cooperative path planning method for underwater target search and tracking based on AUVs and multiple USVs includes the following steps:

[0013] Step 1: Establish a kinematic model describing the motion characteristics of USV, AUV and underwater targets, and set underwater target constraints as well as constraints that USV and AUV must satisfy during the search and tracking task.

[0014] Step 2: Divide the underwater target search and tracking task into a search phase and a tracking phase. Construct fitness functions for the USV cluster and AUV for the task objectives of different phases, which will serve as optimization objectives for subsequent periodic path planning. In the tracking phase, when constructing the fitness function for the AUV, introduce an underwater target position prediction method based on dynamic periods to predict the future position of the underwater target according to the planning period.

[0015] The underwater target position prediction method based on dynamic cycles includes: calculating the speed of the underwater target based on the historical position information of the underwater target, dynamically adjusting the prediction cycle number according to the current distance between the AUV and the underwater target, predicting the future position of the underwater target, and using the predicted future position of the underwater target as the input for the fitness function calculation of the AUV in the tracking phase, so that the AUV can go to the position where the underwater target will arrive in advance.

[0016] Step 3: At the beginning of each planning cycle, based on the current task stage, select a set of fitness functions from the fitness functions constructed in Step 2 as the optimization objective for the path planning of this cycle; at the same time, if the current stage is the tracking stage, call the underwater target position prediction method based on dynamic cycle in Step 2 to update the future position of the underwater target and substitute it into the fitness function of the selected tracking stage AUV.

[0017] Step 4: Using the fitness function selected in Step 3 as the optimization objective, the distributed improved genetic-fireworks algorithm is used to independently perform path iteration optimization on the USV cluster and AUV within the current planning period, and solve for the optimal path scheme of the USV cluster and AUV in the current planning period.

[0018] The distributed improved genetic-fireworks algorithm includes: initializing the population to generate initial path solutions; calculating the fitness value of each firework in the population according to the selected fitness function; generating explosion sparks around the parent firework based on the adaptive explosion radius; introducing the Levy flight strategy to perform displacement operations on the explosion sparks to generate new sparks after displacement; introducing the adaptive Gaussian mutation operator to perform Gaussian mutation operations on the new sparks after displacement to generate Gaussian mutated sparks; handling out-of-bounds sparks in the explosion sparks, new sparks after displacement, and Gaussian mutated sparks using an improved mapping rule; determining the next generation population through an elite retention strategy and roulette wheel method, repeating the iteration until the maximum number of iterations is reached, and then outputting the optimal path scheme for the current planning cycle.

[0019] Step 5: At the end of the current planning cycle, control the movement of the USV and AUV according to the optimal path scheme output in Step 4, update the status of the USV, AUV and underwater target, and return to Step 3 to enter the next planning cycle. Repeat Step 3 to Step 5 until the mission ends, realizing dynamic path planning throughout the entire process.

[0020] Furthermore, in step 2, fitness functions for the USV cluster and AUV are constructed for different stages of the task objectives, including:

[0021] During the search phase, the fitness function of the USV cluster is constructed with the optimization objectives of maximizing the joint search domain of the USV cluster and satisfying the communication distances between USVs and AUVs, as well as the USV-USV communication distances. :

[0022]

[0023] In the formula, Indicates the first One planning cycle; It is the USV-USV connectivity fitness function during the search phase, which is obtained by comparing the distance between each USV with the effective detection radius of the USV during the search phase. It is the fitness function for the connectivity between the USV and AUV during the search phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connectivity domain between the USV and AUV during the search phase. It is the fitness function of the joint search domain, which is calculated based on the intersection of the joint search domain of the USV cluster and the working sea area; It is the fitness function for updating the search domain, which is calculated based on the intersection of the newly added search domain and the joint search domain in the current planning cycle; , , All three are non-negative weight coefficients, representing the weights of the corresponding fitness functions during the search phase, and their sum is 1.

[0024] During the search phase, with the optimization objectives of maintaining communication between the AUV and the USV and ensuring path security, a fitness function for the AUV during the search phase is constructed. :

[0025]

[0026] In the formula, It is the fitness function for the connectivity between the USV and AUV during the search phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connectivity domain between the USV and AUV during the search phase. It is the underwater path safety fitness function of the AUV, which is obtained based on the collision detection results between the path and obstacles.

[0027] During the tracking phase, the fitness function of the USV swarm during the tracking phase is constructed with the optimization objectives of maintaining the detection of underwater targets by the USV swarm and satisfying the communication distance between the AUV and the USV. :

[0028]

[0029] In the formula, It is the USV-USV connectivity fitness function during the tracking phase, which is obtained by comparing the distance between each USV during the tracking phase with the effective detection radius of the USV. It is the fitness function for the connection between the USV and AUV during the tracking phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connection domain between the USV and AUV during the tracking phase. It is a fitness function for the proximity of the USV swarm to the underwater target during the tracking phase, which is calculated based on the distance between the USV and the underwater target; , , All three are non-negative weight coefficients, representing the weights of the corresponding fitness function during the tracking phase, and their sum is 1.

[0030] During the tracking phase, with path safety and minimizing the distance between the AUV and the underwater target as optimization objectives, a fitness function for the AUV during the tracking phase is constructed. Furthermore, a dynamic periodic underwater target position prediction method is introduced into the fitness function; wherein the fitness function of the AUV during the tracking phase... for:

[0031]

[0032] In the formula, This is a fitness function for assessing the proximity of the AUV to the underwater target during the tracking phase; when the underwater target does not enter the AUV's search domain... Based on real-time distance calculation between the AUV and the underwater target; when the underwater target has entered the AUV's search domain, Calculation based on the distance between the AUV and the predicted future location of the underwater target; It is the fitness function for underwater path safety of AUV, which is obtained based on the collision detection results between the path and obstacles.

[0033] Furthermore, in step 2, the USV-USV connectivity fitness function during the search phase... for:

[0034]

[0035] In the formula, The connectivity coefficient of the USV cluster represents the maximum number of communication links in the USV cluster, and its value is the total number of USVs minus 1. Indicates the first The distance between any two USVs within a planning cycle; Indicates the effective detection radius of the USV; The communication radius between USVs;

[0036] Search phase: USV and AUV connected fitness function for:

[0037]

[0038] In the formula, This indicates the distance between the nearest USV and the AUV during the search phase; It is the communication radius between the USV and AUV. Represents an exponential function;

[0039] Joint search domain fitness function for:

[0040]

[0041] In the formula, It is the first Sea-level search section of a USV , This represents the total number of USVs. It is the sea level of the working area;

[0042] Search domain update degree fitness function for:

[0043]

[0044] In the formula, It is a preset planning period interval, with a value range of 1 to 3 planning periods;

[0045] AUV underwater path safety fitness function for:

[0046]

[0047] In the formula, This is the symbol for a binary logical variable in Boolean algebra. This indicates that no collision occurred; This indicates that a collision has occurred;

[0048] USV-USV Connectivity Fitness Function during Tracking Phase for:

[0049]

[0050] In the formula, case 1 represents the case where a USV not connected to an AUV searches for an underwater target. In this case, the expression of the USV-USV connectivity fitness function is the same as the USV-USV connectivity fitness function during the search phase. The expressions are the same; case 2 indicates the case where an AUV or a USV connected to an AUV searches for an underwater target. In this case, it is assumed that the USV not connected to the AUV has completed its own mission, and the connection status between USVs is no longer considered, so the expression is set to... ;

[0051] Tracking Phase USV and AUV Connectivity Fitness Function for:

[0052]

[0053] In the formula, This represents the straight-line distance from the center of the communicating USV and the searching USV to the AUV during the tracking phase. The communicating USV refers to the USV that is in communication with the AUV and is closest to the AUV, while the searching USV refers to the USV that has detected the underwater target and is closest to the underwater target. It is the communication radius between the USV and AUV. Represents an exponential function;

[0054] Fitness function for proximity between USV swarm and underwater target during the tracking phase for:

[0055]

[0056] In the formula, This is the threshold for the maximum effective tracking distance of the USV to underwater targets; The distance between the nearest USV and the underwater target is used to represent the distance between the USV cluster and the underwater target during the tracking phase. When the underwater target is not within the search range of the USV cluster, for ease of calculation, [the distance is set to -1]. The value is set to a fixed value, and takes... , The effective detection radius of the USV; when the underwater target is within the search range of the USV swarm, the distance between the USV closest to the underwater target and the underwater target is used as the effective detection radius. The value of .

[0057] Furthermore, the underwater target position prediction method based on dynamic periods in step 2 specifically includes:

[0058] First, obtain the number underwater target location for each planning cycle , No. underwater target location for each planning cycle and the duration of AUV path planning during the tracking phase Calculate the velocity of the underwater target:

[0059]

[0060] In the formula, Indicates the first Predicted values ​​of underwater target velocity for each planning cycle; Indicates the first Predicted values ​​of underwater target yaw angle for each planning cycle; Indicates the first Predicted values ​​of underwater target pitch angle for each planning cycle; It is the first Underwater target location for each planning cycle , It is the first The location coordinates of underwater targets within each planning cycle; It is the first Underwater target location for each planning cycle It is the first The location coordinates of underwater targets within each planning cycle; This refers to the AUV path planning time during the tracking phase; Norm symbol; Represents the arcsine function; Represents the arctangent function;

[0061] The AUV path planning time during the tracking phase is adaptively adjusted according to the following formula. :

[0062]

[0063] In the formula, To track the real-time distance between the AUV and the underwater target, It is the radius of the AUV search domain;

[0064] Then, based on the real-time distance between the AUV and the underwater target, the number of prediction cycles is dynamically determined. :

[0065]

[0066] In the formula, It represents the real-time distance between the AUV and the underwater target during the tracking phase; It is the radius of the AUV search domain; when At that time, the AUV can only obtain the location of underwater targets by relying on its communication with the USV;

[0067] Next, according to the current number The underwater target location, underwater target velocity, and number of prediction periods for each planning cycle. Predicting the first Underwater target locations for each planning cycle:

[0068]

[0069] In the formula, It is the first Underwater target locations for each planning cycle; For the first Underwater target locations for each planning cycle; Indicates the first Predicted values ​​of underwater target velocity for each planning cycle; Indicates the first Predicted values ​​of underwater target yaw angle for each planning cycle; Indicates the first Predicted values ​​of underwater target pitch angle for each planning cycle; This refers to the AUV path planning time during the tracking phase;

[0070] Finally, the predicted number underwater target location for each planning cycle As the fitness function of AUV during the tracking phase The input for the calculation is the fitness of the AUV during the tracking phase.

[0071] Furthermore, in step 4, depending on the current task stage, the following steps are performed independently and in parallel for both the USV and AUV fireworks populations:

[0072] Step 4.1: Independently and randomly generate initial fireworks populations for the USV and AUV respectively within the solution space to form initial path solutions; where:

[0073] During the search phase:

[0074] During the search phase, the linear acceleration of all USVs in the initial fireworks is as follows: The yaw rate of all USVs is randomly selected according to a Gaussian distribution within the positive range. Values ​​are randomly selected from a uniform distribution within the range; where It is the upper limit of linear acceleration of USV. This is the upper limit of the yaw rate of the USV. The negative value corresponding to the upper limit of the yaw rate of the USV;

[0075] During the search phase, the linear acceleration of the AUV in the initial fireworks of the AUV is at... The yaw rate of the AUV is randomly selected from values ​​within the positive range according to a Gaussian distribution. Within a range, values ​​are randomly selected from a uniform distribution; the pitch angular velocity of the AUV is within... Values ​​are randomly selected from a uniform distribution within the range; where, This is the upper limit of the linear acceleration of an AUV. It is the upper limit of the yaw rate of an AUV. This is the upper limit of the pitch angular velocity of the AUV;

[0076] During the tracking phase:

[0077] The linear acceleration of all USVs in the initial fireworks during the tracking phase is at Within a range, values ​​are randomly selected from a uniform distribution, and the yaw rate is within... Values ​​are randomly selected from a uniform distribution within the range;

[0078] The linear acceleration of the AUV during the initial fireworks of the tracking phase is at... The yaw rate of the AUV is randomly selected from values ​​within a Gaussian distribution within a certain range. Within a range, values ​​are randomly selected from a uniform distribution; the pitch angular velocity of the AUV is within... Values ​​are randomly selected from a uniform distribution within the range;

[0079] Step 4.2: Calculate the fitness value of each firework in the current population based on the fitness function selected in Step 3, and obtain the optimal fitness value and the corresponding optimal firework in the current population;

[0080] Step 4.3: Using each firework in the current population as the parent, calculate the number of sparks generated based on its fitness value, and introduce an adaptive explosion radius. Dynamically adjust the explosion radius based on the comparison between the current fitness value of the firework and the fitness value of its parent, generating explosion sparks around the parent to obtain new candidate path solutions; wherein, when the current fitness value of the firework is better than the fitness value of its parent, the explosion radius is reduced for local fine search; when the current fitness value of the firework is worse than the fitness value of its parent, the explosion radius is expanded for global exploration;

[0081] Step 4.4: Introduce the Levy flight strategy, calculate the explosion offset for the randomly selected dimension position of the explosion spark, generate a new spark position with Levy distribution characteristics, and obtain the updated candidate path solution;

[0082] Step 4.5: Perform Gaussian mutation operation on the new sparks after displacement, introduce an adaptive Gaussian mutation operator, dynamically control the mutation amplitude according to the current iteration algebra, and use the best individual of the parent generation to guide the mutation direction, generate Gaussian mutated sparks, and obtain diverse candidate path solutions;

[0083] Step 4.6: For the out-of-bounds sparks generated in steps 4.3 to 4.5 that exceed the solution space boundary, an improved mapping rule is used to process the out-of-bounds position back into the solution space, while preserving the characteristics of the out-of-bounds sparks in the original dimensional direction, thus obtaining effective candidate path solutions;

[0084] Step 4.7: Merge the parent fireworks, the explosion sparks generated in Step 4.3, the new sparks after displacement in Step 4.4, the Gaussian mutation sparks generated in Step 4.5, and the sparks after mapping in Step 4.6 into a candidate solution set. Use the elite retention strategy to directly retain the parent fireworks with the best fitness and the offspring sparks with the best fitness to the next generation. Select the remaining candidate solutions by roulette wheel according to their fitness values ​​to form the next generation of fireworks population.

[0085] Step 4.8: Repeat steps 4.2 to 4.7 until the maximum number of iterations within the current planning period is reached, and output the optimal path scheme for the current planning period.

[0086] Furthermore, in step 4.3, the specific method for generating explosion sparks based on adaptive explosion radius is as follows:

[0087] Step 4.3.1: Calculate the actual number of sparks produced by a single firework. :

[0088] First, obtain the number Fireworks at the current number The fitness values ​​of the current generation and its parents, as well as the optimal fitness value in the current population, are used to initially calculate the fitness value of the current generation. The generation The number of sparks produced by a single firework explosion:

[0089]

[0090] In the formula, For the preliminary calculation of the first Fireworks at the current number The number of sparks that should be generated by the explosion; This represents the total number of sparks produced by all fireworks explosions, typically set to 50. The adjustment factor is calculated using a minimum value, ranging from 10. -6 ; It is the first Fireworks at the current number Fitness value of the generation; It is the current number The optimal fitness value in the generation population;

[0091] Then, to After limiting and rounding, the result is the first... The actual number of sparks produced by each firework:

[0092]

[0093] In the formula, For the first The actual number of sparks produced by a single firework; This represents the total number of explosive sparks allowed to be produced by all fireworks. Its value is obtained empirically and is generally taken as a number similar to... The same as or multiple of it, The total number of sparks produced by all fireworks explosions; , These represent the lower and upper limits of the allowed percentage of explosive sparks produced by a single firework relative to the total allowed explosive sparks produced by all fireworks, respectively. The value range is from 0.05 to 0.1. The value range is from 0.8 to 0.9; This represents the rounding function;

[0094] Step 4.3.2: Compare the first The fitness value of a firework in the current generation is compared with the fitness value of its parent generation, and the fitness value of the firework is dynamically adjusted based on the comparison results. The adaptive blast radius of a firework: When the firework's fitness value in the current generation is better than that of its parent generation, the blast radius is reduced for fine-grained local search; when the firework's fitness value in the current generation is worse than that of its parent generation, the blast radius is expanded for global exploration.

[0095] First, calculate the basic explosion radius:

[0096]

[0097] In the formula, For the first Fireworks at the current number The basic blast radius of the generation; It is the first Fireworks at the current number Fitness value of the generation; It is the optimal fitness value in the current population; The adjustment factor is calculated using a minimum value, ranging from 10. -6 ;

[0098] Then determine the number according to the following formula. Adaptive blast radius of a firework :

[0099]

[0100] In the formula, Based on the blast radius; For the first Fireworks at the current number The adaptive explosion radius of the generation; It is the first Fireworks at the current number Fitness value of the generation; It is the first The fitness value of a firework in its parent generation; and All are preset constants. , ;

[0101] Step 4.3.3: According to the first The actual number of sparks produced by each firework and adaptive blast radius , with the first Centered on a single firework, explosive sparks are randomly generated in a uniform distribution around it. All the generated explosion sparks constitute new candidate path solutions.

[0102] Furthermore, the specific method for using the Levy flight strategy to displace the explosion sparks in step 4 is as follows:

[0103] Step 4.4.1: For each explosion spark generated in step 4.3 Randomly select from all dimensions of its solution vector There are several dimensions, among which This is a preset constant, taking the value 1 or 2; it generates Levy-distributed random numbers for each selected dimension. :

[0104]

[0105] In the formula, For the selected explosion spark Levy-distributed random numbers in the dimension; and All are random numbers that follow a normal distribution, i.e. , ; is a constant and ; It is the step size scaling factor of the Levy distribution, used to control the overall magnitude of the random step size; ,in , ; ! represents the standard gamma function; ! represents the factorial operation; The explosion sparks were selected in the first... Position value in dimension ; This represents a complete individual explosion spark, whose solution vector contains multiple dimensions;

[0106] Step 4.4.2: For each selected dimension, based on the Levy distribution random numbers generated in Step 4.4.1 and the adaptive blast radius determined in Step 4.3, independently calculate the blast spark at the selected dimension. Adaptive Explosion Offset in Dimension :

[0107]

[0108] in, For the first Fireworks at the current number The adaptive explosion radius of the generation; For the selected explosion spark Levy-distributed random numbers in the dimension;

[0109] Step 4.4.3: Generate a new spark after displacement based on the adaptive explosion offset. :

[0110] For the selected number Dimensions:

[0111]

[0112] In the formula, For the selected explosion spark Adaptive explosion offset in dimensions; Is the new spark after displacement in the selected first... Position in dimensions; The explosion sparks were selected in the first... Position value in dimension;

[0113] For dimensions that are not selected, the original position value of the explosion spark in that dimension remains unchanged;

[0114] Step 4.4.4: All new sparks generated by the displacement operation in step 4.4.3 will be processed. As a candidate path solution after displacement:

[0115] If the new spark generated after displacement If a value in any dimension exceeds the boundary of the solution space, then the out-of-bounds processing is performed according to the improved mapping rule in step 4.6, and the out-of-bounds value is mapped back to the feasible region of the solution space.

[0116] Furthermore, in step 4.5, Gaussian mutation sparks are generated according to the following adaptive mutation formula. :

[0117]

[0118] In the formula, and These are the first and second mutation magnitude control terms of the adaptive Gaussian mutation operator, respectively. and These are the first directional control item and the second directional control item, respectively. and These are the first and second parental genetic control terms, respectively. Their values ​​are related to the current iteration generation. Automatic linear decrease; the later the planning period, the smaller the influence of paternal inheritance, and the closer it is to the optimal solution. and This is the optimal reference control term, and its value is a preset fixed constant value; , These are the values ​​in the parent generation's online acceleration and yaw rate dimensions, respectively. , These are the values ​​in the online acceleration dimension and yaw angle acceleration dimension of the generated Gaussian mutated spark, respectively; , These are the values ​​of the optimal fireworks in the parent population in terms of online acceleration and yaw rate, respectively. , , , All are random real numbers in the range [0,1].

[0119] For dimensions that are not selected, the values ​​of the parent fireworks in that dimension remain unchanged; if the generated Gaussian mutated fireworks are... If a value in any dimension exceeds the boundary of the solution space, then the out-of-bounds processing is performed according to the improved mapping rule in step 4.6, and the out-of-bounds value is mapped back to the feasible domain of the solution space.

[0120] The formulas for calculating the first and second mutation magnitude control terms of the adaptive Gaussian mutation operator are as follows:

[0121]

[0122] In the formula, This is the upper limit of the yaw rate of a USV; This is the upper limit of linear acceleration for a USV;

[0123] First paternal genetic control term Second paternal genetic control terms The calculation formula is:

[0124]

[0125] In the formula, and These are the first paternal genetic control terms. The upper and lower limits; and These are the genetic control terms of the second paternal parent. Upper and lower limits; first paternal genetic control term Second paternal genetic control terms The upper limit is set to 0.9 and the lower limit is set to 0.4. The maximum number of iterations within a single planning period;

[0126] First direction control item Second direction control item Determined according to the following methods:

[0127]

[0128] In the formula, +1 represents a positive perturbation, that is, during the mutation process, the gene in this dimension shifts in the direction of increasing value; -1 represents a negative perturbation, that is, during the mutation process, the gene in this dimension shifts in the direction of decreasing value.

[0129] Furthermore, the kinematic models established in step 1 describing the motion characteristics of the USV, AUV, and underwater target are as follows:

[0130] Three-dimensional kinematic model of an underwater target:

[0131]

[0132] In the formula, It is the pose of an underwater target within the terrestrial system; These are the position coordinates of the underwater target, where These represent the displacements of the underwater target on each coordinate axis in the ground system; It is the yaw angle of the underwater target; It is the pitch angle of the underwater target; It is the velocity of the underwater target in the velocity system; It is the translational speed of the underwater target; It is the yaw rate of the underwater target; It is the pitch angular velocity of the underwater target;

[0133] Two-dimensional kinematic model of USV:

[0134]

[0135]

[0136] In the formula, Indicates the USV number; It is the first in the terrestrial system The position of the USV For the first The location coordinates of the USV, among which , , They represent the first Displacement of the USV along each axis in the ground system Constant; The first in the Earth system Yaw angle of a USV; The first in the velocity system The speed of the USV, among which For the first The translational speed of the USV; For the first Yaw rate of a USV;

[0137] AUV's three-dimensional kinematic model:

[0138]

[0139] In the formula, It is the pose of the AUV in the ground system; These are the position coordinates of the AUV, where , , These represent the displacements of the AUV on each coordinate axis in the ground system; It is the yaw angle of the AUV; It is the pitch angle of the AUV; Let be the velocity of the AUV in the velocity system, where It is the translational speed of the AUV. It is the pitch rate of the AUV. It is the yaw rate of the AUV.

[0140] Furthermore, in step 1, the underwater target constraints include the underwater target's workspace constraints and the underwater target's operational performance constraints, wherein:

[0141] The workspace constraints for underwater targets are:

[0142]

[0143] In the formula, , These are the upper and lower limits of the known sea area along the x-axis, respectively; , These are the upper and lower limits of the known sea area along the y-axis, respectively. It is the maximum operating depth of an underwater target. These represent the displacements of the underwater target on each coordinate axis in the ground system;

[0144] Performance constraints of underwater targets:

[0145]

[0146] In the formula, It is the upper limit of the translational speed of an underwater target; It is the upper limit of the yaw rate of an underwater target; It is the upper limit of the pitch angular velocity of an underwater target; It is the upper limit of linear acceleration for underwater targets; It is the translational speed of the underwater target; It is the yaw rate of the underwater target; It is the pitch angular velocity of the underwater target; It is the linear acceleration of the underwater target;

[0147] USV constraints include USV isomorphic platform constraints, search capability constraints, USV inter-communication constraints, USV-AUV communication constraints, USV motion performance constraints, and workspace constraints; among which:

[0148] USV isomorphic platform constraint: The USVs involved in the work are of the same model and have the same performance indicators;

[0149] USV search capability constraints: Assuming the search domain of the USV is sphere-shaped, with the centroid of the USV as the center of the search domain, the effective detection radius of the USV is defined as follows: When an underwater target enters the effective detection radius of the USV, the USV is considered to have successfully detected the underwater target.

[0150]

[0151] In the formula, Indicates the first The location coordinates of the USV Indicates the position coordinates of the underwater target. Indicates the effective detection radius of the USV;

[0152] USV's information connectivity constraints:

[0153] When the information exchange target of a USV is another USV on the water surface, assuming that the water surface information exchange domain of each USV is a planar circle, and taking the centroid of the USV as the center of the information connectivity domain, the exchange radius of the information connectivity domain between USVs is defined as follows: When the distance between any two USVs does not exceed At that time, it was assumed that the two USVs could sense each other and freely exchange information. The formula for information communication between USVs was:

[0154]

[0155] In the formula, Indicates the first The distance between any two USVs within a planning cycle; Indicates the first The planning cycle, the first The coordinates of the USV on the horizontal plane; Indicates the first The planning cycle, the first The coordinates of the USV on the horizontal plane. It is the communication radius of the information connectivity domain between USVs, representing the maximum communication distance between USVs;

[0156] When the USV's information transmission target is an underwater AUV, assuming the underwater information communication domain of the USV is hemispherical in shape, and with the USV's center of mass as the center of the sphere, the communication radius between the USV and the AUV is defined as follows: When the distance between the USV and AUV does not exceed If we assume that the two can sense each other, then the formula for information communication between the USV and AUV is:

[0157]

[0158] In the formula, Indicates the first The location coordinates of the USV Constant; These are the position coordinates of the AUV; It is the communication radius between the USV and AUV.

[0159] USV performance constraints: Due to the inherent structural limitations of USVs, there are upper limits to their speed and acceleration during navigation.

[0160]

[0161] in, It is the first The translational speed of the USV; It is the first Yaw rate of a USV; It is the first The linear acceleration of a USV; This is the upper limit of the translational speed of the USV; This is the upper limit of the yaw rate of a USV; This is the upper limit of linear acceleration for a USV;

[0162] USV's workspace constraints: USVs search for underwater targets within bounded sea areas where underwater targets are more likely to be present.

[0163]

[0164] In the formula, , These represent the upper and lower limits of the known sea area along the x-axis, respectively. , These are the upper and lower limits of the known sea area along the y-axis, respectively.

[0165] AUV constraints include AUV search capability constraints, information transmission constraints, target acquisition constraints, performance constraints, and workspace constraints; among which:

[0166] AUV search capability constraints: Since AUVs operate underwater, we assume their search domain is a sphere, with the AUV's center of mass as the center of the search domain. The radius of the AUV's search domain is defined as... When the distance between the underwater target and the AUV is less than For an AUV to be considered to have successfully detected an underwater target, the following constraints must be met:

[0167]

[0168] In the formula, These are the position coordinates of the AUV; These are the position coordinates of the underwater target; It is the radius of the AUV search domain;

[0169] AUV information transmission constraints: satisfy the information communication formula between USV and AUV;

[0170] AUV target acquisition constraint: The AUV's mission requirement during the tracking phase is to successfully acquire underwater targets. This is achieved when the distance between the AUV and the underwater target is less than a set AUV acquisition distance threshold. At this point, it is considered that the AUV has completed its underwater target acquisition mission:

[0171]

[0172] Performance constraints of AUVs:

[0173]

[0174] in, It is the translational speed of the AUV; It is the pitch rate of the AUV; It is the yaw rate of the AUV; It is the linear acceleration of the AUV; This is the upper limit of the translational speed of the AUV; This is the upper limit of the pitch rate of an AUV; This is the upper limit of the yaw rate of an AUV; This is the upper limit of linear acceleration for AUVs;

[0175] AUV working space constraints:

[0176]

[0177] in, These are the position coordinates of the AUV; , These are the upper and lower limits of the known sea area along the x-axis, respectively; , These are the upper and lower limits of the known sea area along the y-axis, respectively. This is the maximum operating depth of an AUV underwater. In order to successfully capture underwater targets, it needs to meet certain requirements. ; It is the maximum operating depth of an underwater target.

[0178] The advantages of this invention are:

[0179] 1. The underwater target search and tracking collaborative path planning method proposed in this invention, based on AUV and multiple USVs, adopts a distributed cross-domain heterogeneous collaborative path planning architecture. By setting different fitness functions in the search and tracking phases, the USV cluster and AUV can dynamically adjust the path planning strategy according to the mission requirements, realizing close collaboration between cross-domain platforms within the same time period and overcoming the problem of information transmission lag in the traditional phased collaborative mode.

[0180] 2. This invention introduces an underwater target position prediction method based on dynamic cycles during the tracking phase. By analyzing the target's historical position information through the USV, the future trajectory of the target is predicted, and the predicted future position of the underwater target is transmitted to the AUV. This enables the AUV to switch from tracking mode to interception mode and travel to the future position of the underwater target in advance, significantly shortening the mission completion time and improving the success rate of target acquisition.

[0181] 3. The present invention makes the following improvements to the traditional fireworks algorithm: (1) An adaptive explosion radius is introduced, and the explosion range is dynamically adjusted according to the changing trend of individual fitness: when the current fitness value of the fireworks is better than that of the parent generation, the explosion radius is reduced to perform local fine search; when the current fitness value of the fireworks is worse than that of the parent generation, the explosion radius is expanded to perform global exploration, which effectively balances the global exploration capability in the early stage of the algorithm and the local development accuracy in the later stage of the algorithm; (2) The Levy flight strategy is introduced to perform displacement operation, and its characteristic of alternating short step size and long step size is used to enhance the ability to jump out of the local optimum, which balances the global exploration capability and local development capability of the algorithm, so that the algorithm focuses on the fast search of USV in the early stage and the precise approach of AUV in the later stage of the algorithm; (3) An adaptive Gaussian mutation operator is proposed, which uses the best individual in the population to guide the mutation direction and dynamically controls the mutation amplitude according to the iteration number, which maintains the population diversity while accelerating convergence. The above improvements enable the algorithm to have stronger global optimization capability and faster convergence speed when dealing with complex optimization problems such as multi-USV and AUV cooperative path planning.

[0182] 4. This invention is applicable not only to path planning for single agents, homogeneous unmanned clusters, and heterogeneous unmanned clusters, but also to path planning tasks for cross-domain heterogeneous clusters composed of USV clusters and AUVs. Attached Figure Description

[0183] Figure 1 This is a flowchart of the underwater target search and tracking cooperative path planning method based on AUV and multiple USVs of the present invention;

[0184] Figure 2 This is a flowchart of the distributed improved genetic-fireworks algorithm proposed in this invention;

[0185] Figure 3 This is a comparison chart showing the explosion results of fireworks with different adaptability under the action of explosion operators of different scales in this invention. Figure 3 (a) shows the results of a small-radius, multi-spark explosion of fireworks with good adaptability. Figure 3 (b) shows the results of a large-radius, low-spark explosion of fireworks with poor adaptability;

[0186] Figure 4 This is a diagram showing the results of acceleration and angular velocity variations on the search path of a single USV in this invention.

[0187] Figure 5 This is a two-dimensional top view of the path of each individual in the cross-domain heterogeneous system of AUV and multiple USV in the embodiment of the present invention from the start of the search to the completion of target tracking. The dashed circle represents the search range of the individual.

[0188] Figure 6This is a schematic diagram illustrating the changes in the distance between the USV and the underwater target, and the distance between the AUV and the underwater target, during the entire process of collaborative path planning between the AUV and multiple USV cross-domain heterogeneous systems in this embodiment of the invention.

[0189] Figure 7 This is a schematic diagram illustrating the real-time changes in the distance between the AUV and each USV during the entire process of collaborative path planning between the AUV and multiple USVs in a cross-domain heterogeneous system according to an embodiment of the present invention.

[0190] Figure 8 This is a schematic diagram illustrating the depth changes of the AUV and underwater targets during the entire process of collaborative path planning between the AUV and multiple USV cross-domain heterogeneous systems in an embodiment of the present invention.

[0191] Figure 9 This is a comparison of the convergence characteristic curves of the algorithm of this invention and the traditional algorithm under the same experimental environment. Detailed Implementation

[0192] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0193] Reference Figure 1 and Figure 2 This embodiment provides a cooperative path planning method for underwater target search and tracking based on AUV and multiple USVs, including the following steps:

[0194] Step 1: Establish a kinematic model describing the motion characteristics of USV, AUV and underwater targets, and set the constraints that USV and AUV must satisfy during the execution of search and tracking tasks.

[0195] Step 1.1: Establish a three-dimensional kinematic model of the underwater target.

[0196] The three-dimensional motion model of the underwater target is as follows:

[0197] (1)

[0198] in, It is the pose of an underwater target within the terrestrial system; These are the position coordinates of the underwater target, where These represent the displacements of the underwater target on each coordinate axis in the ground system; It is the yaw angle of the underwater target; It is the pitch angle of the underwater target; It is the velocity of the underwater target in the velocity system; It is the translational speed of the underwater target; It is the yaw rate of the underwater target; It is the pitch angular velocity of the underwater target.

[0199] The three-dimensional motion of an underwater target is decomposed into translational motion and rotational motion, which are described by the following equations:

[0200] (2)

[0201] (3)

[0202] (4)

[0203] Formula (2) is the translational motion equation of the underwater target, which expresses the displacement vector of the underwater target in the ground system. The first derivative and the translational velocity of an underwater target along the x-axis in the velocity system. The relationship. Equations (3) and (4) are the equations of motion for the underwater target's rotation. Since the underwater target is considered as a point mass, the angular velocities are independent of each other. In equation (4), It is the linear acceleration of the underwater target.

[0204] Step 1.2: Establish a two-dimensional kinematic model of the USV.

[0205] Since the USV moves in a two-dimensional plane at sea level, its two-dimensional kinematic model is established as follows:

[0206] (5)

[0207] In the formula, Indicates the USV number; It is the first in the terrestrial system The position of the USV For the first The location coordinates of the USV, among which , , They represent the first Displacement of the USV along each axis in the ground system Constant; The first in the Earth system Yaw angle of a USV; The first in the velocity system The speed of the USV, among which For the first The translational speed of the USV; For the first Yaw angle rate of a USV.

[0208] Step 1.3, establish the three-dimensional kinematic model of the AUV:

[0209] (6)

[0210] In the formula, It is the pose of the AUV in the ground system; These are the position coordinates of the AUV, where , , These represent the displacements of the AUV on each coordinate axis in the ground system; It is the yaw angle of the AUV; It is the pitch angle of the AUV; Let be the velocity of the AUV in the velocity system, where It is the translational speed of the AUV. It is the pitch rate of the AUV. It is the yaw rate of the AUV.

[0211] (7)

[0212] (8)

[0213] In the formula, These represent the velocity components of the AUV on each coordinate axis in the ground coordinate system.

[0214] Step 1.4: Set the constraints that the USV and AUV must meet during the mission, including underwater target constraints, USV constraints, and AUV constraints.

[0215] Underwater target constraints:

[0216] The constraints on underwater targets include the working space constraints and the operational performance constraints of underwater targets.

[0217] Workspace constraints for underwater targets: Underwater targets move in known sea areas, and their maximum diving depth range is set based on their own pressure-bearing capacity.

[0218] (9)

[0219] In the formula, , These are the upper and lower limits of the known sea area along the x-axis, respectively; , These are the upper and lower limits of the known sea area along the y-axis, respectively. This refers to the maximum operating depth of the underwater target in this embodiment. ; These represent the displacements of the underwater target on each coordinate axis in the ground system.

[0220] Performance constraints of underwater targets:

[0221] (10)

[0222] In the formula, It is the upper limit of the translational speed of an underwater target; It is the upper limit of the yaw rate of an underwater target; It is the upper limit of the pitch angular velocity of an underwater target; It is the upper limit of linear acceleration for underwater targets; It is the translational speed of the underwater target; It is the yaw rate of the underwater target; It is the pitch angular velocity of the underwater target; It is the linear acceleration of the underwater target.

[0223] USV constraints:

[0224] USV constraints include isomorphic platform constraints, information connectivity constraints between USVs, information connectivity constraints between USVs and AUVs, motion performance constraints of USVs, and workspace constraints.

[0225] (1) Homogeneous platform constraint: In order to facilitate the cooperation of USVs on the water surface, the USVs involved in the work are of the same model and have the same performance indicators.

[0226] (2) Search capability constraint: Assuming the search domain of the USV is sphere-shaped, with the centroid of the USV as the center of the search domain, the effective detection radius of the USV is defined as follows: When an underwater target enters the effective detection radius of the USV, the USV is considered to have successfully detected the underwater target.

[0227] (11)

[0228] In the formula, Indicates the first The location coordinates of the USV Indicates the position coordinates of the underwater target. This indicates the effective detection radius of the USV.

[0229] (3) Information Connectivity Constraints: The USV cluster requires information exchange and collaboration for underwater target searching. When the information exchange target of a USV is another USV on the water surface, assuming the surface information exchange domain of each USV is a planar circle, and taking the centroid of the USV as the center of the information connectivity domain, the radius of the information connectivity domain between USVs is defined as follows: When the distance between any two USVs does not exceed At that time, it was assumed that the two USVs could sense each other and freely exchange information. The formula for information communication between USVs is as follows:

[0230] (12)

[0231] In the formula, Indicates the first The distance between any two USVs within a planning cycle; Indicates the first The planning cycle, the first The coordinates of the USV on the horizontal plane; Indicates the first The planning cycle, the first The coordinates of the USV on the horizontal plane. It is the communication radius between USVs, representing the maximum communication distance between USVs.

[0232] When the USV's information transmission target is an underwater AUV, assuming the underwater information communication domain of the USV is hemispherical in shape, and with the USV's center of mass as the center of the sphere, the communication radius between the USV and the AUV is defined as follows: When the distance between the USV and AUV does not exceed If it is assumed that these two can perceive each other, then the formula for information communication between USV and AUV is:

[0233] (13)

[0234] In the formula, Indicates the first The location coordinates of the USV Constant; These are the position coordinates of the AUV; It is the communication radius between the USV and AUV.

[0235] (4) Performance constraints: Due to the structural limitations of the USV itself, there are upper limits on its speed and acceleration during navigation, as shown in the following formula:

[0236] (14)

[0237] in, It is the first The translational speed of the USV; It is the first Yaw rate of a USV; It is the first The linear acceleration of a USV; This is the upper limit of the translational speed of the USV; This is the upper limit of the yaw rate of a USV; It is the upper limit of linear acceleration for a USV.

[0238] (5) Workspace constraints: The USV searches for underwater targets in bounded sea areas where the probability of underwater target presence is high.

[0239] (15)

[0240] In the formula, , These represent the upper and lower limits of the known sea area along the x-axis, respectively. , These are the upper and lower limits of the known sea area along the y-axis, respectively.

[0241] AUV constraints:

[0242] AUV constraints include AUV search capability constraints, information transmission constraints, target acquisition constraints, performance constraints, and workspace constraints.

[0243] (1) Search capability constraint: Since the AUV operates underwater, it is assumed that the search domain of the AUV is a sphere, with the center of mass of the AUV as the center of the search domain, and the radius of the AUV search domain is defined as follows: When the distance between the underwater target and the AUV is less than If the AUV is considered to have successfully detected an underwater target, then the following constraints must be met:

[0244] (16)

[0245] In the formula, These are the position coordinates of the AUV; These are the position coordinates of the underwater target; It is the radius of the AUV search domain.

[0246] (2) Information transmission constraints: Due to the limitations of the underwater environment, in order to search and track more efficiently, the AUV can communicate with the USV. The information communication constraint formula between the AUV and the USV has been given in the USV constraint conditions, as shown in formula (13).

[0247] (3) Target acquisition constraint: The task requirement for the AUV during the tracking phase is to successfully acquire the underwater target. When the distance between the AUV and the underwater target is less than or equal to the set AUV acquisition distance threshold, the target acquisition constraint is met. When the target is captured, it is considered that the AUV has completed its underwater target acquisition mission.

[0248] (17)

[0249] (4) Performance constraints: Due to the limitations of the AUV's own components, there are upper limits on its speed and acceleration during navigation:

[0250] (18)

[0251] in, It is the translational speed of the AUV; It is the pitch rate of the AUV; It is the yaw rate of the AUV; It is the linear acceleration of the AUV; This is the upper limit of the translational speed of the AUV; This is the upper limit of the pitch rate of an AUV; This is the upper limit of the yaw rate of an AUV; It is the upper limit of linear acceleration for AUVs.

[0252] (5) Workspace constraints: When an AUV searches for underwater targets in a bounded sea area where the probability of underwater targets appearing is relatively high, then:

[0253] (19)

[0254] in, These are the position coordinates of the AUV; , These are the upper and lower limits of the known sea area along the x-axis, respectively; , These are the upper and lower limits of the known sea area along the y-axis, respectively. This refers to the maximum operating depth of the AUV underwater, as described in this embodiment. In order to successfully capture underwater targets, the following conditions must be met. ; It is the maximum operating depth of an underwater target.

[0255] Step 2: Construct the fitness function in stages.

[0256] The underwater target search and tracking task is divided into a search phase and a tracking phase. Based on the current task phase (search phase or tracking phase), fitness functions for the USV cluster and AUV are constructed respectively, which serve as optimization objectives for subsequent periodic path planning. In the tracking phase, when constructing the fitness function for the AUV, an underwater target position prediction method based on dynamic periods is introduced to predict the future position of the underwater target according to the planning period.

[0257] (1) Construct the fitness function for the search phase:

[0258] During the search phase, distributed path planning is employed for both the USV cluster and AUVs, thus their fitness functions are set separately. The USV cluster plays a leading role in the search, and the online path fitness evaluation of the USV cluster mainly considers three aspects: information connectivity between USVs, information connectivity between USVs and AUVs, the joint search domain of the USV cluster, and the update degree of the search domain. Therefore, the fitness function of the USV cluster during the search phase is constructed with the optimization objectives of maximizing the joint search domain of the USV cluster and satisfying the communication distances between USVs and AUVs and between USVs. :

[0259] (20)

[0260] In the formula, Indicates the first One planning cycle; It is the USV-USV connectivity fitness function during the search phase, which is obtained by comparing the distance between each USV with the effective detection radius of the USV during the search phase. It is the fitness function for the connectivity between the USV and AUV during the search phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connectivity domain between the USV and AUV during the search phase. It is the fitness function of the joint search domain, which is calculated based on the intersection of the joint search domain of the USV cluster and the working sea area; It is the fitness function for updating the search domain, which is calculated based on the intersection of the newly added search domain and the joint search domain in the current planning cycle; , , All three are non-negative weight coefficients, representing the weights of the corresponding fitness functions during the search phase, and their sum is 1. In this embodiment, to find underwater targets more quickly, the search range needs to be expanded as much as possible during the search phase; therefore, the three non-negative weight coefficients are respectively set to values ​​of... , , .

[0261] Search phase USV-USV connectivity fitness function for:

[0262] (twenty one)

[0263] In the formula, The connectivity coefficient of the USV cluster represents the maximum number of communication links in the USV cluster, and its value is the total number of USVs minus 1. Indicates the first The distance between any two USVs within a planning cycle; Indicates the effective detection radius of the USV; The communication radius between USVs is defined as the communication range between USVs.

[0264] Search phase: USV and AUV connected fitness function for:

[0265] (twenty two)

[0266] In the formula, This indicates the distance between the nearest USV and the AUV during the search phase; It is the communication radius between the USV and AUV. This represents an exponential function.

[0267] Joint search domain fitness function for:

[0268] (twenty three)

[0269] In the formula, It is the first Sea-level search section of a USV , This represents the total number of USVs. It is the sea level of the working area.

[0270] Search domain update degree fitness function for:

[0271] (twenty four)

[0272] In the formula, It is the preset planning period interval, with a value range of 1 to 3 planning periods.

[0273] During the search phase, the AUV should maintain continuous communication with the USV cluster to ensure it obtains the underwater target's location information as quickly as possible. Simultaneously, due to its underwater operation, the AUV needs to consider the impact of obstacles on path safety. Therefore, during the search phase, with the optimization objectives of maintaining communication between the AUV and USVs and ensuring path safety, a fitness function for the AUV during the search phase is constructed. :

[0274] (25)

[0275] In the formula, It is the fitness function of USV and AUV connectivity during the search phase, which is calculated based on the distance between USV and AUV and the communication radius of the information connectivity domain between USV and AUV during the search phase; the specific expression of the fitness function of USV and AUV connectivity during the search phase is shown in formula (21). It is the fitness function for underwater path safety of AUV, which is obtained based on the collision detection results between the path and obstacles.

[0276] AUV underwater path safety fitness function for:

[0277] (26)

[0278] In the formula, This is the symbol for a binary logical variable in Boolean algebra. This indicates that no collision occurred; This indicates that a collision has occurred.

[0279] (2) Construct the fitness function for the tracking phase:

[0280] The search phase ends once any USV or AUV detects an underwater target. During the tracking phase, the fitness function for the multi-USV and AUV cross-domain heterogeneous system path planning is evaluated based on whether the current path is beneficial for the AUV to track the target. Distributed path planning is also used for the USV cluster and AUVs in this phase, with separate fitness functions set for each. The task of the USV cluster in this phase is to transmit underwater target location information to the AUVs. Therefore, the evaluation criteria for the USV cluster path solution are: whether the working path can maintain awareness of the underwater target's location and whether it can transmit the target's location to the AUVs. Thus, in this phase, the optimization objectives are for the USV cluster to maintain underwater target detection and to satisfy the communication distance between the AUVs and USVs, and the fitness function for the USV cluster in the tracking phase is constructed accordingly. :

[0281] The general formula for the fitness function of the USV cluster during the tracking phase is:

[0282] (27)

[0283] In the formula, It is the USV-USV connectivity fitness function during the tracking phase, which is obtained by comparing the distance between each USV during the tracking phase with the effective detection radius of the USV. It is the fitness function for the connection between the USV and AUV during the tracking phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connection domain between the USV and AUV during the tracking phase. It is a fitness function for the proximity of the USV swarm to the underwater target during the tracking phase, which is calculated based on the distance between the USV and the underwater target; , , All three are non-negative weight coefficients, representing the weights of the corresponding fitness function during the tracking phase; the sum of the three is 1. In this embodiment... , , .

[0284] Among them, the USV-USV connectivity fitness function during the tracking phase for:

[0285] (28)

[0286] In formula (28), based on the underwater target situation at the end of the previous stage, the expression for the USV-USV connectivity fitness function during the tracking stage is divided into two cases:

[0287] In the case where a USV not connected to an AUV detects an underwater target (case 1), the USV cluster still needs to maintain inter-USV connectivity to transmit underwater target location information. In this situation, the expression for the USV-USV connectivity fitness function during the tracking phase differs from the expression for the USV-USV connectivity fitness function during the search phase. The expressions are the same.

[0288] In the case where an AUV or a USV connected to an AUV detects an underwater target (case 2), it is assumed that USVs not connected to the AUV have completed their missions. Therefore, the connectivity status between USVs is no longer considered, and the following settings are made: .

[0289] Tracking Phase USV and AUV Connectivity Fitness Function for:

[0290] (29)

[0291] In the formula, This represents the straight-line distance from the center of the communicating USV and the searching USV to the AUV during the tracking phase. The communicating USV refers to the USV that is in communication with the AUV and is closest to the AUV, while the searching USV refers to the USV that has detected the underwater target and is closest to the underwater target. It is the communication radius between the USV and AUV. This represents an exponential function.

[0292] Fitness function for proximity between USV swarm and underwater target during the tracking phase for:

[0293] (30)

[0294] In the formula, This is the threshold for the maximum effective tracking distance of the USV to underwater targets; The distance between the nearest USV and the underwater target is used to represent the distance between the USV cluster and the underwater target during the tracking phase. When the underwater target is not within the search range of the USV cluster, for ease of calculation, [the distance is set to -1]. The value is set to a fixed value, and takes... , The effective detection radius of the USV; when the underwater target is within the search range of the USV swarm, the distance between the USV closest to the underwater target and the underwater target is used as the effective detection radius. The value of .

[0295] During the tracking phase, the AUV needs to gradually approach the underwater target and complete the target acquisition task. Simultaneously, the AUV needs to consider the impact of underwater obstacles on path safety. Therefore, with path safety and minimizing the distance between the AUV and the underwater target as optimization objectives, a fitness function for the AUV during the tracking phase is constructed. Furthermore, a dynamic periodic underwater target position prediction method is introduced into the fitness function. Specifically, the fitness function of the AUV during the tracking phase... for:

[0296] (31)

[0297] In the formula, This is a fitness function for assessing the proximity of the AUV to the underwater target during the tracking phase; when the underwater target does not enter the AUV's search domain... Based on real-time distance calculation between the AUV and the underwater target; when the underwater target has entered the AUV's search domain, Calculation based on the distance between the AUV and the predicted future location of the underwater target; It is the fitness function for underwater path safety of AUV, which is obtained based on the collision detection results between the path and obstacles.

[0298] The core task of the AUV during the tracking phase is to acquire underwater targets; therefore, the distance from the underwater target at the end of the AUV's path is used to evaluate the first phase. The merits of AUV path solutions over a planning cycle: When the distance between the AUV and the underwater target is greater than the radius of the USV's search domain. Initially, the primary objective of an AUV is to include underwater targets within its search domain, and the corresponding fitness function is the real-time distance between the AUV and the target. Once the underwater target is already within the AUV's search domain, the performance of the path is evaluated using the distance between the AUV and the predicted position of the underwater target, replacing the target's position coordinates with the predicted location. Specifically, during the tracking phase, the AUV's underwater path safety fitness function... Same as formula (26).

[0299] During the tracking phase, since the underwater target is constantly moving underwater, if the USV only provides the AUV with the target's current position information, the target information held by the AUV will lag behind the target's actual movement information. Therefore, the USV needs to reliably predict the future position of the underwater target and transmit the prediction result to the AUV, enabling the AUV to pre-position the target and successfully capture it. The underwater target position prediction method based on dynamic periods provided by this invention is as follows:

[0300] First, obtain the number underwater target location for each planning cycle , No. underwater target location for each planning cycle and the duration of AUV path planning during the tracking phase Calculate the velocity of the underwater target:

[0301] (32)

[0302] In the formula, Indicates the first Predicted values ​​of underwater target velocity for each planning cycle; Indicates the first Predicted values ​​of underwater target yaw angle for each planning cycle; Indicates the first Predicted values ​​of underwater target pitch angle for each planning cycle; It is the first Underwater target location for each planning cycle , It is the first The location coordinates of underwater targets within each planning cycle; It is the first Underwater target location for each planning cycle It is the first The location coordinates of underwater targets within each planning cycle; This refers to the AUV path planning time during the tracking phase; Norm symbol; Represents the arcsine function; This represents the arctangent function.

[0303] During the tracking phase, as the distance between the AUV and the underwater target continues to decrease, The size should also be gradually reduced to match the AUV's approach to underwater targets. The size of the path planning time during the tracking phase is related to the radius of the AUV search domain and the distance between the AUV and the underwater target. In this embodiment, the AUV path planning time during the tracking phase is adaptively adjusted according to the following formula. :

[0304] (33)

[0305] in, To track the real-time distance between the AUV and the underwater target, It is the radius of the AUV search domain.

[0306] Then, based on the real-time distance between the AUV and the underwater target, the number of prediction cycles is dynamically determined. .

[0307] During the AUV search process, the distance between the AUV and the current position of the underwater target needs to be dynamically set. The value of is used to control the direction of movement of the AUV. This is because the number of prediction cycles... As the number of prediction cycles increases, the accuracy of underwater target location prediction will continuously decrease, thus reducing the number of prediction cycles. The threshold should be within a reasonable range. In this invention, the number of prediction periods... Dynamic value retrieval is performed, and the rules for dynamic value retrieval are as follows:

[0308] (34)

[0309] In the formula, It represents the real-time distance between the AUV and the underwater target during the tracking phase; This is the radius of the AUV search domain. It's important to note that when... At that time, the AUV can only obtain the location of underwater targets by relying on its communication with the USV.

[0310] Next, according to the current number The underwater target location, underwater target velocity, and number of prediction periods for each planning cycle. Predicting the first The underwater target location for each planning cycle. The underwater target locations for each planning cycle are:

[0311] (35)

[0312] In the formula, It is the first Underwater target locations for each planning cycle; For the first Underwater target locations for each planning cycle; Indicates the first Predicted values ​​of underwater target velocity for each planning cycle; Indicates the first Predicted values ​​of underwater target yaw angle for each planning cycle; Indicates the first Predicted values ​​of underwater target pitch angle for each planning cycle; This refers to the AUV path planning time during the tracking phase.

[0313] Finally, the predicted number underwater target location for each planning cycle As shown in formula (31), the fitness function of the AUV in the tracking phase The input for the calculation is the fitness of the AUV during the tracking phase.

[0314] Step 4: Based on the current task stage, select the corresponding fitness function as the optimization objective, and use the distributed improved genetic-fireworks algorithm to independently perform path iteration optimization for the USV cluster and AUV within the current planning period, and solve for the optimal path scheme for the USV cluster and AUV in the current planning period.

[0315] Because the USV cluster and AUV have different priorities in different mission phases, centralized path planning would result in too many constraints in dynamic path planning, leading to unsatisfactory results. Therefore, this invention employs distributed path planning in both the search and tracking phases. It should be noted that when the mission phase switches from the search phase to the tracking phase, the fireworks populations of both the USV cluster and AUV need to be regenerated according to the initialization strategy of the tracking phase, rather than inheriting the population from the end of the search phase. In this step, the USV cluster and AUV each maintain independent fireworks populations and execute steps 4.1-4.8 independently and in parallel, using their respective fitness functions only during fitness function calculation. This embodiment uses a cross-domain heterogeneous system including 3 USVs and 1 AUV as an example, setting the population size... Both are 20, representing the maximum number of iterations of the algorithm within a single planning period. It is 100.

[0316] Step 4.1: Initialize the population.

[0317] Define the improved genetic-fireworks algorithm. The first planning cycle The generation population is:

[0318] (36)

[0319] in, Indicates the first One planning cycle, Indicates the first Generation population, representing the first generation Population at the next iteration. Indicates the first The first planning cycle Generational population; Indicates the first The first planning cycle Within the first generation of the population Fireworks; the first Each firework represents the first There are several feasible solutions.

[0320] The USV cluster and AUV each perform initialization independently. Based on the current task stage (search stage or tracking stage) and the current platform type to be optimized (USV cluster or AUV), the initial fireworks populations of the USV and AUV are randomly generated in the solution space according to the following strategies.

[0321] (1) Population initialization during the search phase:

[0322] USV Fireworks: The solution vector of the USV fireworks has a dimension of 6, containing the linear acceleration and yaw rate of each of the three USVs. The USV fireworks are set as... ,in These are the search phases. The linear acceleration and yaw rate of the first USV in the USV fireworks display. These are the search phases. The linear acceleration and yaw rate of the second USV in the USV fireworks display. These are the search phases. The linear acceleration and yaw rate of the third USV in the USV fireworks display.

[0323] USV Initial Fireworks Swarm Generation: Considering that the USV swarm needs to conduct thorough searches over a large area, the higher the sailing speed, the larger the search range per cycle. Therefore, to expand the search range, the initial fireworks of the USVs during the search phase... Linear acceleration of three USVs , , All in The yaw rate of the three USVs is randomly selected from Gaussian distributions within the positive range. , , All in Values ​​are randomly selected from a uniform distribution within the range. It is the upper limit of linear acceleration of USV. This is the upper limit of the yaw rate of the USV. The negative value corresponding to the upper limit of the yaw rate of the USV.

[0324] AUV Fireworks: The solution vector of the AUV fireworks has a dimension of 3, including the linear acceleration, pitch rate, and yaw rate of the AUV. The AUV fireworks are set as... ,in These represent the search phases. The linear acceleration, pitch rate, and yaw rate of the AUV in the AUV fireworks.

[0325] AUV Initial Fireworks Swarm Generation: During the search phase, the AUV is primarily responsible for following the USV to obtain real-time location information for underwater target searches. Considering that the AUV's navigation capability is weaker than that of the USV, to maintain communication between the AUV and the USV, the AUV's initial fireworks swarm generation during the search phase... Linear acceleration of a medium-sized AUV exist The yaw rate of an AUV is randomly selected from values ​​within the positive range according to a Gaussian distribution. exist The values ​​are randomly selected within a uniform distribution within the range; because the working depth has little impact on the AUV during the initial search, the pitch velocity of the AUV... exist Values ​​are randomly selected from a uniform distribution within the range. This is the upper limit of the linear acceleration of an AUV. It is the upper limit of the yaw rate of an AUV. This is the upper limit of the pitch angular velocity of the AUV.

[0326] (2) Population initialization during the tracking phase

[0327] USV initial fireworks population generation: Solution vector dimension is the same as in the search phase. To assist AUV tracking, the USV initial fireworks are generated during the tracking phase. Linear acceleration of three USVs , , All in Yaw angular velocity is randomly selected from a uniform distribution within the range. , , All in Values ​​are randomly selected from a uniform distribution within the range. , and The tracking phase is respectively The linear acceleration of the first, second, and third USVs in the initial USV fireworks display. , and The tracking phase is respectively The yaw rate of the first, second, and third USVs in the initial USV fireworks.

[0328] AUV Initial Fireworks Population Generation: Tracking Phase AUV Initial Fireworks Linear acceleration of a medium-sized AUV exist The yaw rate of an AUV is randomly selected from values ​​within a Gaussian distribution within a given range. exist The pitch angular velocity of the AUV is randomly selected within a uniform distribution within a certain range. exist Values ​​are randomly selected from the range according to a uniform distribution.

[0329] Step 4.2: Based on the current task stage and the type of platform being optimized (USV cluster or AUV), select the corresponding fitness function from the fitness functions constructed in Step 3, calculate and record the fitness value of each firework in the current population, and obtain the optimal fitness value of the current population. And the corresponding optimal fireworks The firework with the highest fitness value in the population is the optimal firework. When the current optimized platform type is a USV cluster, the fitness function is selected from formula (20) or formula (27). When the current optimized platform type is an AUV, the fitness function is selected from formula (25) or formula (31).

[0330] The following describes the specific process of generating the optimal path scheme for the USV at the end of the current planning cycle using the distributed improved genetic-fireworks algorithm of this invention, taking USV fireworks as an example; the process of generating the optimal path scheme for AUV is the same as that for USV.

[0331] Step 4.3: Generate explosion sparks.

[0332] This step uses USV fireworks as an example to describe the specific process of generating offspring fireworks through explosion:

[0333] Using each firework in the current population as the parent, the number of sparks generated is calculated based on its fitness value. An adaptive explosion radius is introduced, dynamically adjusting the explosion radius based on a comparison between the firework's current fitness value and its parent's fitness value. Explosion sparks are generated around the parent, yielding new candidate path solutions. Specifically, if the current firework's fitness value is better than its parent's, the explosion radius is reduced for a local fine-grained search; if the current firework's fitness value is worse than its parent's, the explosion radius is expanded for a global exploration. Taking the first... Taking fireworks as an example, the specific method for generating explosion sparks based on adaptive explosion radius is as follows:

[0334] Step 4.3.1: Calculate the first... The actual number of explosion sparks produced by each firework .

[0335] First, obtain the number Fireworks at the current number The fitness values ​​of the current generation, its parents, and the best fitness value in the current population are used to initially calculate the fitness value of the current generation. The generation The number of sparks produced by a single firework explosion:

[0336] (37)

[0337] In the formula, For the preliminary calculation of the first Fireworks at the current number The number of sparks that should be generated by the explosion; This represents the total number of sparks produced by all fireworks explosions, typically set to 50. To calculate the adjustment factor, which is a very small value, it typically takes a value in the range of 10. -6 ; It is the first Fireworks at the current number Fitness value of the generation; It is the current number The optimal fitness value in the generation population.

[0338] Then, to After limiting and rounding, the result is the first... The actual number of sparks produced by each firework :

[0339] (38)

[0340] In the formula, For the first The actual number of sparks produced by a single firework; This represents the total number of explosive sparks allowed to be produced by all fireworks. Its value is obtained empirically and is generally taken as a number similar to... Same as or the same as Multiple relationship, In this embodiment, the total number of sparks produced by all fireworks explosions is [not specified]. The value is 50; , These represent the lower and upper limits of the allowed percentage of explosive sparks produced by a single firework relative to the total allowed explosive sparks produced by all fireworks, respectively. The value range is from 0.05 to 0.1. The value range is from 0.8 to 0.9; This represents the rounding function.

[0341] Step 4.3.2: Compare the first The fitness value of a firework in the current generation is compared with the fitness value of its parent generation, and the fitness value of the firework is dynamically adjusted based on the comparison results. Adaptive blast radius of a firework .

[0342] In traditional fireworks algorithms, the explosion radius depends only on the current generation of the individual. Since fireworks algorithms use a roulette wheel selection method, there's a possibility of the fitness value deteriorating over time. To address this issue, this invention introduces an adaptive explosion radius mechanism: if the current fireworks' fitness value is worse than its parent's, the explosion radius is increased for global exploration; if the current fireworks' fitness value is better than its parent's, the explosion radius is decreased for local fine-grained search; if the current fireworks' fitness value is equal to its parent's, the base explosion radius is maintained.

[0343] Basic blast radius The calculation formula is:

[0344] (39)

[0345] In the formula, For the first Fireworks at the current number The basic blast radius of the generation; It is the first Fireworks at the current number Fitness value of the generation; It is the optimal fitness value in the current population; To calculate the adjustment factor, which is a very small value, it typically takes a value in the range of 10. -6 .

[0346] The number is determined according to the following formula. Adaptive blast radius of a firework :

[0347] (40)

[0348] In the formula, Based on the blast radius; For the first Fireworks at the current number The adaptive explosion radius of the generation; It is the first Fireworks at the current number Fitness value of the generation; It is the first The fitness value of a firework in its parent generation; and All are preset constants. , .

[0349] Step 4.3.3: According to the first The actual number of sparks produced by each firework and adaptive blast radius , with the first Centered on a single firework, explosive sparks are randomly generated in a uniform distribution around it. All the generated explosion sparks constitute new candidate path solutions, which are used in subsequent displacement, mutation, and selection steps.

[0350] like Figure 3 As shown in (a), for fireworks with better fitness values, the calculated adaptive explosion radius is smaller and the actual number of sparks produced by the fireworks is greater. Spatially, the explosion sparks are closely distributed around the parent fireworks (represented by pentagrams in the figure). Performing a refined local search can improve the convergence accuracy; as shown in (a), the explosion sparks are closely distributed around the parent fireworks (represented by pentagrams in the figure). Figure 3 As shown in (b), for fireworks with poor fitness values, the corresponding adaptive explosion radius is larger and the number of sparks actually generated by the fireworks is smaller. In space, the explosion sparks are spread to a wider solution space, and a global search is performed, which can guide the population to escape local optima.

[0351] Step 4.4: Introduce the Levy flight strategy to process the explosion sparks generated in Step 4.3. Calculate the explosion offset at a randomly selected dimension location to generate a new spark with Levy distribution characteristics. This yields the updated candidate path solution.

[0352] In traditional fireworks algorithms, the same explosion offset is typically applied to all dimensions of the offspring fireworks generated by the explosion spark, severely reducing the algorithm's local search capability during iteration. Experiments have shown that, in reality, a better solution may appear near the individual as iterations progress. Therefore, this invention introduces a Levy displacement flight technique, causing the explosion spark offset to decrease with increasing algorithm iterations. By combining gamma functions, sine functions, and normally distributed random numbers, a Levy distribution is constructed, characterized by frequent short steps and occasional long steps. This ultimately helps the algorithm balance global exploration and local exploitation capabilities, improving optimization efficiency. The specific method is as follows:

[0353] Step 4.4.1: For each explosion spark generated in step 4.3 Randomly select from all dimensions of its solution vector There are several dimensions, among which This is a preset constant, taking the value 1 or 2; it generates Levy-distributed random numbers for each selected dimension. :

[0354] (41)

[0355] In the formula, For the selected explosion spark Levy-distributed random numbers in the dimension; and All are random numbers that follow a normal distribution, i.e. , ; is a constant and ; It is the step size scaling factor of the Levy distribution, used to control the overall magnitude of the random step size; ,in , ; ! represents the standard gamma function; ! represents the factorial operation; The explosion sparks were selected in the first... Position value in dimension ; It represents a complete explosion spark individual, whose solution vector contains multiple dimensions.

[0356] Step 4.4.2: For each selected dimension, based on the Levy distribution random numbers generated in Step 4.4.1 and the adaptive blast radius determined in Step 4.3, independently calculate the blast spark at the selected dimension. Adaptive Explosion Offset in Dimension :

[0357] (42)

[0358] in, For the first Fireworks at the current number The adaptive explosion radius of the generation; For the selected explosion spark Levy-distributed random numbers in the dimension.

[0359] Step 4.4.3: Generate a new spark after displacement based on the explosion offset. :

[0360] For the selected number Dimensions:

[0361] (43)

[0362] In the formula, For the selected explosion spark Adaptive explosion offset in dimensions; Is the new spark after displacement in the selected first... Position in dimensions; The explosion sparks were selected in the first... Position value in a dimension.

[0363] For dimensions that are not selected, the original position value of the explosion spark in that dimension remains unchanged.

[0364] Step 4.4.4: All new sparks generated by the above displacement operation will be processed. As a candidate path solution after displacement.

[0365] If the new spark generated after displacement If a value in any dimension exceeds the boundary of the solution space, then the out-of-bounds processing is performed according to the improved mapping rule defined in step 4.6, and the out-of-bounds value is mapped back to the feasible region of the solution space.

[0366] Step 4.5: Generate Gaussian mutation sparks.

[0367] Gaussian mutation is performed on some of the new sparks in the current population after the displacement in step 4.4. An adaptive Gaussian mutation operator is introduced to dynamically control the mutation amplitude according to the current iteration number and to guide the mutation direction using the best individual in the population to generate Gaussian mutated sparks and obtain diverse candidate path solutions.

[0368] Taking USV fireworks as an example, their mutable dimensions are linear acceleration and yaw rate. Gaussian mutated sparks are then generated according to the following adaptive mutation formula. :

[0369] (44)

[0370] In the formula, and These are the first and second mutation magnitude control terms of the adaptive Gaussian mutation operator, respectively. and These are the first directional control item and the second directional control item, respectively. and These are the first and second parental genetic control terms, respectively. Their values ​​are related to the current iteration generation. Automatic linear decrease; the later the planning period, the smaller the influence of paternal inheritance, and the closer it is to the optimal solution. and This is the optimal reference control term, and its value is a preset fixed constant value, which is set to 0.5 in this embodiment. , These are the values ​​in the parent generation's online acceleration and yaw rate dimensions, respectively. , These are the values ​​in the online acceleration dimension and yaw angle acceleration dimension of the generated Gaussian mutated spark, respectively; , These are the values ​​of the optimal fireworks in the parent population in terms of online acceleration and yaw rate, respectively. , , , All are random real numbers in the range [0,1].

[0371] For dimensions that are not selected, keep the value of the parent fireworks in that dimension unchanged.

[0372] The formulas for calculating the first and second mutation magnitude control terms of the adaptive Gaussian mutation operator are as follows:

[0373] (45)

[0374] In the formula, This is the upper limit of the yaw rate of a USV; It is the upper limit of linear acceleration for a USV.

[0375] First paternal genetic control term Second paternal genetic control terms The calculation formula is:

[0376] (46)

[0377] In the formula, and These are the first paternal genetic control terms. The upper and lower limits; and These are the genetic control terms of the second paternal parent. Upper and lower limits; first paternal genetic control term Second paternal genetic control terms The upper limit is set to 0.9 and the lower limit is set to 0.4. This represents the maximum number of iterations within a single planning cycle.

[0378] First direction control item Second direction control item The purpose of this setting is to allow offspring individuals to randomly select the direction of mutation in the dimensionality during the mutation phase, which is determined according to the following methods:

[0379] (47)

[0380] In the formula, the direction control term determines whether the mutation operation adds or subtracts a value from the original dimension. +1 represents a positive perturbation, that is, during the mutation process, the gene of this dimension (such as linear acceleration or yaw rate) shifts in the direction of increasing value; -1 represents a negative perturbation, that is, during the mutation process, the gene of this dimension shifts in the direction of decreasing value.

[0381] If the Gaussian mutation spark generated after step 4.5 If a value in any dimension exceeds the boundary of the solution space, then the out-of-bounds processing is performed according to the improved mapping rule defined in step 4.6, and the out-of-bounds value is mapped back to the feasible region of the solution space.

[0382] Figure 4 This diagram illustrates the impact of different dimensional variations on the path when the search path for a single USV is varied in both linear acceleration and yaw rate. Only the start and end points of the cycle are used as simplified navigation trajectories for that planning cycle. Paths 1-4 represent four different search paths, with paths 2-4 being the results of different variations of path 1. L1, L2, L3, and L4 represent four consecutive search cycles. Paths 2 and 3 are new paths obtained by varying yaw rate and linear acceleration in search cycle L2, respectively; path 4 is the result of varying yaw rate in search cycle L4. Figure 4 The comparison of the paths shows that the variations in linear acceleration (path 3) and yaw rate (paths 2 and 4) have distinctly different impacts on the generated paths. The magnitude of the linear acceleration variation directly affects the length of the search path in the current and subsequent planning cycles, while the magnitude of the yaw rate variation directly affects the direction of the search path in the current and subsequent planning cycles, and these effects accumulate over the planning cycles. Comparing paths 2 and 3 reveals that, within the same search cycle, the yaw rate variation has a more significant impact on the search path than the linear acceleration variation. Therefore, it is necessary to dynamically adjust and control the magnitude of gene variation according to different dimensions.

[0383] Step 4.6: For the out-of-bounds sparks exceeding the solution space boundary in the explosion sparks generated in Step 4.3, the new sparks after displacement in Step 4.4, and the Gaussian mutation sparks after mutation in Step 4.5, an improved mapping rule is used for out-of-bounds processing. The improved mapping rule refers to mapping the out-of-bounds sparks back into the solution space with reference to the original position information, while preserving the characteristics of the out-of-bounds sparks in the original dimensional direction, thus obtaining effective candidate path solutions.

[0384] This embodiment uses cross-boundary sparks. The first one beyond the boundary Taking the value on the dimension as an example, using the improved mapping rule described above, for the value on the dimension, respectively Mapping values ​​that exceed the lower boundary and values ​​that exceed the upper boundary to obtain the mapped positions:

[0385] (48)

[0386] in, Is the spark after mapping in the first The value of the dimension; It was the spark that crossed the line in the first The original value on the dimension, , The solution space is respectively in the th The upper and lower boundaries of the dimension are determined by the boundary symmetry of the feasible region of the solution space, i.e. ; The % symbol represents the identity sign; the % symbol represents modular arithmetic. Represents absolute value operation; It is a symbolic function.

[0387] The improved mapping rule proposed in this invention can preserve the original dimensional direction of the outbound spark and map the outbound spark with reference to its original position, so that the outbound spark still retains its typical characteristics, rather than being a random mapping in the solution space.

[0388] Step 4.7: Form the next generation of fireworks population.

[0389] The parent fireworks, the explosion sparks generated in step 4.3, the new sparks after displacement in step 4.4, the Gaussian mutation sparks generated in step 4.5, and the sparks after mapping in step 4.6 are merged into a candidate solution set. After eliminating infeasible candidates, the best-fit parent fireworks and the best-fit offspring sparks are directly retained to the next generation using an elite retention strategy. The remaining candidate solutions are selected by roulette wheel selection based on their fitness values ​​to form the next generation of fireworks population.

[0390] Specifically, the elite retention strategy directly retains the parent firework with the best fitness and the offspring firework with the best fitness as the next generation firework. After eliminating infeasible candidates with extremely negative fitness values, the remaining candidates are selected using a roulette wheel method based on their fitness values, with the next generation being selected first. Taking one candidate as an example, the probability of being selected is calculated using the following formula:

[0391] (49)

[0392] In the formula, Indicates the first One planning cycle; Indicates the first The probability that a candidate individual is selected by the roulette wheel; Indicates the first Fitness values ​​of each candidate individual; This represents the maximum fitness value among all current candidate individuals, corresponding to the current optimal solution; This represents the total number of candidates participating in the roulette wheel selection process. ; This represents the sum of the fitness differences among all candidates, used to normalize the probability of a candidate being selected. between.

[0393] As can be seen from formula (49), if the fitness value of a candidate is high, the probability of the candidate being selected will be slightly increased, but it does not have a major advantage. Candidates with poor fitness may also be selected. The selection operation of the elite retention strategy can ensure the diversity of fireworks.

[0394] Step 4.8: Repeat steps 4.2 to 4.7 until the maximum number of iterations within the current planning period is reached, and output the optimal path scheme for the current planning period.

[0395] Step 5: At the end of the current planning cycle, control the movement of the USV and AUV according to the optimal path scheme of the USV and AUV generated in Step 4, update the status of the USV, AUV and underwater target, and return to Step 3 to enter the next planning cycle. Repeat Step 3 to Step 5 until the mission ends, realizing dynamic path planning throughout the entire process.

[0396] The simulation example in this embodiment:

[0397] Reference Figure 5 The initial simulation settings were as follows: a Cartesian coordinate system was established with the center of the search area as the origin, and three USVs and one AUV were distributed near the origin. The USV search radius was set to 500m, the communication radius between USVs was set to 1000m, and the communication radius between USVs and the AUV was set to 800m; the AUV search radius was set to 300m, the AUV capture distance threshold was set to 5m, and the maximum number of prediction cycles was set to 5; the underwater target moved continuously in three-dimensional space. The above settings simulated a typical scenario of collaborative search and tracking of cross-domain heterogeneous systems in a real marine environment.

[0398] Simulation parameter settings: Set the fireworks scale for the USV cluster and AUV. Maximum number of iterations within a single planning period The total number of sparks produced by all fireworks explosions The lower limit of the proportion of the explosive sparks produced by a single firework to the total number of explosive sparks produced by all fireworks. The maximum percentage of explosive sparks produced by a single firework relative to the total number of explosive sparks produced by all fireworks. Based on the complexity of tasks on heterogeneous platforms, the upper limit of the planning cycle is set to 300 in this embodiment.

[0399] Based on the above simulation parameters, path planning is performed according to the distributed improved genetic-fireworks algorithm proposed in this invention. The planning process and results are as follows: Figures 5-8 As shown, where:

[0400] Figure 5The path of three USVs and an AUV from the start of the search to the completion of target tracking is clearly shown. The initial positions of the three USVs are approximately 500m, 1000m, and 1500m on the X-axis, respectively, while the AUV is initially located around 1000m on the X-axis and 3000m on the Y-axis, with all distances between them within a communicable range. During the t=0 to 100s phase, the trajectories of each vehicle exhibit a divergent search path. After t=200s, the AUV, assisted by USV1 (representing the first USV), gradually approaches the underwater target, eventually forming an encirclement distribution with USV1 around the underwater target. This verifies that the fitness function set according to different mission phases in this invention can maintain information stability and continuous underwater target acquisition capability even when the detection node and communication node are different.

[0401] Figure 6 Real-time distance variation curves between each vehicle (USV and AUV) and the underwater target are presented. Figure 6 As can be seen, although the distances between each vehicle and the underwater target varied slightly, they all maintained a rapid and monotonous downward trend, ultimately achieving high-precision convergence. Specifically: initially, the maximum distance between the USV and the underwater target was approximately 1900m, and the distance between the AUV and the underwater target was approximately 1700m. Between 0 and 200 seconds, the three USVs and AUV rapidly narrowed their distances to the underwater target through divergent searching. Around 200 seconds, USV1 located the underwater target and transmitted the information to the AUV via USV2 (representing the second USV). At this time, USV3 (representing the third USV) neither located the underwater target nor communicated with the AUV, and therefore stopped recording its position. Subsequently, the two USVs and the AUV continuously shortened their distances to the underwater target. Around 250 seconds, USV2 ceased its communication task and stopped recording its position. Subsequently, the AUV and USV1, which was tracking the underwater target, continued to narrow their distances, eventually converging the distance between the AUV and the underwater target to within 5m. This demonstrates that the distributed improved genetic-fireworks algorithm used in this invention has good global optimization capabilities when handling dynamic target tracking.

[0402] Figure 7 This demonstrates the real-time distance changes between each USV and AUV during the mission. According to... Figure 7As shown in the real-time distance change curve, the distance between the USV and AUV remained within the effective range of 100m to 800m throughout the entire path planning process. No collision risk occurred below 100m or communication interruption risk occurred above 800m, verifying the role of the fitness function based on communication cost in ensuring the stability of the communication link in cross-domain heterogeneous systems. In the figure, around t=200s, USV3 completed its search task, and around t=250s, USV2 completed its communication task with the AUV, after which its distance from the AUV was no longer recorded. Furthermore, the distance between the USV and AUV rapidly increased from 150m at 200s to 400m, and then dropped back to 180m at t=230s. This fluctuation and subsequent rapid recovery demonstrates the autonomous path reconstruction capability of the Levy flight strategy and adaptive Gaussian mutation strategy in the algorithm of this invention under obstacle avoidance conflicts, indicating that the algorithm possesses good dynamic adjustment robustness.

[0403] Figure 8 The depth variation curves of the AUV and the underwater target throughout the mission are presented. As can be seen from the figure, the underwater target depth does not change significantly from 0 to 100 seconds. From 100 to 200 seconds, the underwater target depth gradually increases from 150m to 200m, while the AUV's search depth fluctuates between 50m and 200m. Its depth curve exhibits phase lag from 0 to 100 seconds; after 200 seconds, the AUV's depth curve almost completely overlaps with the underwater target's depth curve. The results show that even with nonlinear fluctuations in the underwater target depth, the AUV can still achieve rapid fitting of the underwater target's depth changes through real-time parameter adjustments. From t=200s onwards, the AUV's depth curve is highly synchronized with the underwater target's depth curve, demonstrating excellent tracking accuracy and stability. This result verifies the efficient optimization capability of the distributed improved genetic-fireworks algorithm of this invention in the three-dimensional solution space.

[0404] To further illustrate the effectiveness of the distributed improved genetic-fireworks algorithm of this invention, this embodiment demonstrates the average convergence trend of 50 experimental runs, and compares in detail the distributed improved genetic-fireworks algorithm of this invention with the traditional path planning algorithm. The convergence characteristics of (ACO, DDPG) are compared, and the results are as follows: Figure 9 As shown in the figure, the initial fitness value of the distributed improved genetic-fireworks algorithm of this invention is 0.3, reaching 0.83 after 20 iterations and 0.97 after 50 iterations; the fitness value of the DDPG algorithm (Deep Deterministic Policy Gradient Algorithm) is 0.75 after 50 iterations and reaches 0.85 after 100 iterations; the fitness value of the ACO algorithm (Ant Colony Optimization Algorithm) is below 0.8 throughout the process. The algorithm (Optimal Fast Expanding Random Tree Algorithm) achieved a fitness of 0.88 after 50 iterations and 0.92 after 100 iterations. The results show that the distributed improved genetic-fireworks algorithm of this invention exhibits a significant lead-gap convergence advantage in the early stages of iteration, with its fitness growth curve consistently exceeding that of other algorithms throughout the entire iteration cycle, ultimately reaching the highest steady-state fitness value. In contrast, the ACO and DDPG algorithms both suffer from slow convergence or premature convergence. This comparison fully demonstrates that this invention achieves significant results in resolving the inherent contradiction between convergence speed and solution accuracy in complex spatial optimization problems, and the overall operational efficiency of the cross-domain heterogeneous system composed of AUV and multiple USVs outperforms existing mainstream algorithms.

[0405] Although simulation embodiments of the present invention have been described above, they are exemplary. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments based on the invention without departing from the principles and spirit of the invention.

Claims

1. A cooperative path planning method for underwater target search and tracking based on AUV and multiple USVs, characterized in that, Includes the following steps: Step 1: Establish a kinematic model describing the motion characteristics of USV, AUV and underwater targets, and set underwater target constraints as well as constraints that USV and AUV must satisfy during the search and tracking task. Step 2: Divide the underwater target search and tracking task into a search phase and a tracking phase. Construct fitness functions for the USV cluster and AUV for the task objectives of different phases, which will serve as optimization objectives for subsequent periodic path planning. In the tracking phase, when constructing the fitness function for the AUV, introduce an underwater target position prediction method based on dynamic periods to predict the future position of the underwater target according to the planning period. The underwater target position prediction method based on dynamic periodicity includes: calculating the speed of the underwater target based on the historical position information of the underwater target; dynamically adjusting the prediction period number based on the current distance between the AUV and the underwater target; predicting the future position of the underwater target; and using the predicted future position of the underwater target as the input for the fitness function calculation of the AUV during the tracking phase, so that the AUV can travel to the position where the underwater target will arrive in advance. Step 3: At the beginning of each planning cycle, based on the current task stage, select a set of fitness functions from the fitness functions constructed in Step 2 as the optimization objective for the path planning of this cycle; at the same time, if the current stage is the tracking stage, call the underwater target position prediction method based on dynamic cycle described in Step 2 to update the future position of the underwater target and substitute it into the fitness function of the selected tracking stage AUV. Step 4: Using the fitness function selected in Step 3 as the optimization objective, the distributed improved genetic-fireworks algorithm is used to independently perform path iteration optimization on the USV cluster and AUV within the current planning period, and solve for the optimal path scheme of the USV cluster and AUV in the current planning period. The distributed improved genetic-fireworks algorithm includes: initializing the population to generate initial path solutions; calculating the fitness value of each firework in the population according to the selected fitness function; generating explosion sparks around the parent firework based on the adaptive explosion radius; introducing a Levy flight strategy to perform displacement operations on the explosion sparks to generate new sparks after displacement; introducing an adaptive Gaussian mutation operator to perform Gaussian mutation operations on the new sparks after displacement to generate Gaussian mutated sparks; handling out-of-bounds sparks in the explosion sparks, new sparks after displacement, and Gaussian mutated sparks using an improved mapping rule; determining the next generation population through an elite retention strategy and a roulette wheel method, repeating the iteration until the maximum number of iterations is reached, and then outputting the optimal path scheme for the current planning cycle. Step 5: At the end of the current planning cycle, control the movement of the USV and AUV according to the optimal path scheme output in Step 4, update the status of the USV, AUV and underwater target, and return to Step 3 to enter the next planning cycle. Repeat Step 3 to Step 5 until the mission ends, realizing dynamic path planning throughout the entire process.

2. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 1, characterized in that, Step 2 involves constructing fitness functions for the USV cluster and AUV respectively, based on the task objectives at different stages, including: During the search phase, the fitness function of the USV cluster is constructed with the optimization objectives of maximizing the joint search domain of the USV cluster and satisfying the communication distances between USVs and AUVs, as well as the USV-USV communication distances. : In the formula, Indicates the first One planning cycle; It is the USV-USV connectivity fitness function during the search phase, which is obtained by comparing the distance between each USV with the effective detection radius of the USV during the search phase. It is the fitness function for the connectivity between the USV and AUV during the search phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connectivity domain between the USV and AUV during the search phase. It is the fitness function of the joint search domain, which is calculated based on the intersection of the joint search domain of the USV cluster and the working sea area; It is the fitness function for updating the search domain, which is calculated based on the intersection of the newly added search domain and the joint search domain in the current planning cycle; , , All three are non-negative weight coefficients, representing the weights of the corresponding fitness functions during the search phase, and their sum is 1. During the search phase, with the optimization objectives of maintaining communication between the AUV and the USV and ensuring path security, a fitness function for the AUV during the search phase is constructed. : In the formula, It is the fitness function for the connectivity between the USV and AUV during the search phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connectivity domain between the USV and AUV during the search phase. It is the underwater path safety fitness function of the AUV, which is obtained based on the collision detection results between the path and obstacles. During the tracking phase, the fitness function of the USV swarm during the tracking phase is constructed with the optimization objectives of maintaining the detection of underwater targets by the USV swarm and satisfying the communication distance between the AUV and the USV. : In the formula, It is the USV-USV connectivity fitness function during the tracking phase, which is obtained by comparing the distance between each USV during the tracking phase with the effective detection radius of the USV. It is the fitness function for the connection between the USV and AUV during the tracking phase, which is calculated based on the distance between the USV and AUV and the communication radius of the information connection domain between the USV and AUV during the tracking phase. It is a fitness function for the proximity of the USV swarm to the underwater target during the tracking phase, which is calculated based on the distance between the USV and the underwater target; , , All three are non-negative weight coefficients, representing the weights of the corresponding fitness function during the tracking phase, and their sum is 1. During the tracking phase, with path safety and minimizing the distance between the AUV and the underwater target as optimization objectives, a fitness function for the AUV during the tracking phase is constructed. Furthermore, a dynamic periodic underwater target position prediction method is introduced into the fitness function; wherein the fitness function of the AUV during the tracking phase... for: In the formula, This is a fitness function for assessing the proximity of the AUV to the underwater target during the tracking phase; when the underwater target does not enter the AUV's search domain... Based on real-time distance calculation between the AUV and the underwater target; when the underwater target has entered the AUV's search domain, Calculation based on the distance between the AUV and the predicted future location of the underwater target; It is the fitness function for underwater path safety of AUV, which is obtained based on the collision detection results between the path and obstacles.

3. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 2, characterized in that, In step 2, the USV-USV connectivity fitness function during the search phase. for: In the formula, The connectivity coefficient of the USV cluster represents the maximum number of communication links in the USV cluster, and its value is the total number of USVs minus 1. Indicates the first The distance between any two USVs within a planning cycle; Indicates the effective detection radius of the USV; The communication radius between USVs; Search phase: USV and AUV connected fitness function for: In the formula, This indicates the distance between the nearest USV and the AUV during the search phase; It is the communication radius between the USV and AUV. Represents an exponential function; Joint search domain fitness function for: In the formula, It is the first Sea-level search section of a USV , This represents the total number of USVs. It is the sea level of the working area; Search domain update degree fitness function for: In the formula, It is a preset planning period interval, with a value range of 1 to 3 planning periods; AUV underwater path safety fitness function for: In the formula, This is the symbol for a binary logical variable in Boolean algebra. This indicates that no collision occurred; This indicates that a collision has occurred; USV-USV Connectivity Fitness Function during Tracking Phase for: In the formula, case 1 represents the case where a USV not connected to an AUV searches for an underwater target. In this case, the expression of the USV-USV connectivity fitness function is the same as the USV-USV connectivity fitness function during the search phase. The expressions are the same; case 2 indicates the case where an AUV or a USV connected to an AUV searches for an underwater target. In this case, it is assumed that the USV not connected to the AUV has completed its own mission, and the connection status between USVs is no longer considered, so the expression is set to... ; Tracking Phase USV and AUV Connectivity Fitness Function for: In the formula, This represents the straight-line distance from the center of the communicating USV and the searching USV to the AUV during the tracking phase. The communicating USV refers to the USV that is in communication with the AUV and is closest to the AUV, while the searching USV refers to the USV that has detected the underwater target and is closest to the underwater target. It is the communication radius between the USV and AUV. Represents an exponential function; Fitness function for proximity between USV swarm and underwater target during the tracking phase for: In the formula, This is the threshold for the maximum effective tracking distance of the USV to underwater targets; The distance between the nearest USV and the underwater target is used to represent the distance between the USV cluster and the underwater target during the tracking phase. When the underwater target is not within the search range of the USV cluster, for ease of calculation, [the distance is set to -1]. The value is set to a fixed value, and takes... , The effective detection radius of the USV; when the underwater target is within the search range of the USV swarm, the distance between the USV closest to the underwater target and the underwater target is used as the effective detection radius. The value of .

4. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 2, characterized in that, The underwater target position prediction method based on dynamic period described in step 2 specifically includes: First, obtain the number underwater target location for each planning cycle , No. underwater target location for each planning cycle and the duration of AUV path planning during the tracking phase Calculate the velocity of the underwater target: In the formula, Indicates the first Predicted values ​​of underwater target velocity for each planning cycle; Indicates the first Predicted values ​​of underwater target yaw angle for each planning cycle; Indicates the first Predicted values ​​of underwater target pitch angle for each planning cycle; It is the first Underwater target location for each planning cycle , It is the first The location coordinates of underwater targets within each planning cycle; It is the first Underwater target location for each planning cycle It is the first The location coordinates of underwater targets within each planning cycle; This refers to the AUV path planning time during the tracking phase; Norm symbol; Represents the arcsine function; Represents the arctangent function; The AUV path planning time during the tracking phase is adaptively adjusted according to the following formula. : In the formula, To track the real-time distance between the AUV and the underwater target, It is the radius of the AUV search domain; Then, based on the real-time distance between the AUV and the underwater target, the number of prediction cycles is dynamically determined. : In the formula, It represents the real-time distance between the AUV and the underwater target during the tracking phase; It is the radius of the AUV search domain; when At that time, the AUV can only obtain the location of underwater targets by relying on its communication with the USV; Next, according to the current number The underwater target location, underwater target velocity, and number of prediction periods for each planning cycle. Predicting the first Underwater target locations for each planning cycle: In the formula, It is the first Underwater target location for each planning cycle; For the first Underwater target location for each planning cycle; Indicates the first Predicted values ​​of underwater target velocity for each planning cycle; Indicates the first Predicted values ​​of underwater target yaw angle for each planning cycle; Indicates the first Predicted values ​​of underwater target pitch angle for each planning cycle; This refers to the AUV path planning time during the tracking phase; Finally, the predicted number underwater target location for each planning cycle As the fitness function of AUV during the tracking phase The input for the calculation is the fitness of the AUV during the tracking phase.

5. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 1, characterized in that, In step 4, depending on the current task stage, the following steps are performed independently and in parallel on the USV and AUV fireworks populations: Step 4.1: Independently and randomly generate initial fireworks populations for the USV and AUV respectively within the solution space to form initial path solutions; where: During the search phase: During the search phase, the linear acceleration of all USVs in the initial fireworks is as follows: The yaw rate of all USVs is randomly selected according to a Gaussian distribution within the positive range. Values ​​are randomly selected from a uniform distribution within the range; where It is the upper limit of linear acceleration of USV. This is the upper limit of the yaw rate of the USV. The negative value corresponding to the upper limit of the yaw rate of the USV; During the search phase, the linear acceleration of the AUV in the initial fireworks of the AUV is at... The yaw rate of the AUV is randomly selected from values ​​within the positive range according to a Gaussian distribution. Within a range, values ​​are randomly selected from a uniform distribution; the pitch angular velocity of the AUV is within... Values ​​are randomly selected from a uniform distribution within the range; where, This is the upper limit of the linear acceleration of an AUV. It is the upper limit of the yaw rate of an AUV. This is the upper limit of the pitch angular velocity of the AUV; During the tracking phase: The linear acceleration of all USVs in the initial fireworks during the tracking phase is at Within a range, values ​​are randomly selected from a uniform distribution, and the yaw rate is within... Values ​​are randomly selected from a uniform distribution within the range; The linear acceleration of the AUV during the initial fireworks of the tracking phase is at... The yaw rate of the AUV is randomly selected from values ​​within a Gaussian distribution within a certain range. Within a range, values ​​are randomly selected from a uniform distribution; the pitch angular velocity of the AUV is within... Values ​​are randomly selected from a uniform distribution within the range; Step 4.2: Calculate the fitness value of each firework in the current population based on the fitness function selected in Step 3, and obtain the optimal fitness value and the corresponding optimal firework in the current population; Step 4.3: Using each firework in the current population as the parent, calculate the number of sparks generated based on its fitness value, and introduce an adaptive explosion radius. Dynamically adjust the explosion radius based on the comparison between the current fitness value of the firework and the fitness value of its parent, generating explosion sparks around the parent to obtain new candidate path solutions; wherein, when the current fitness value of the firework is better than the fitness value of its parent, the explosion radius is reduced for local fine search; when the current fitness value of the firework is worse than the fitness value of its parent, the explosion radius is expanded for global exploration; Step 4.4: Introduce the Levy flight strategy, calculate the explosion offset for the randomly selected dimension position of the explosion spark, generate a new spark position with Levy distribution characteristics, and obtain the updated candidate path solution; Step 4.5: Perform Gaussian mutation operation on the new sparks after displacement, introduce an adaptive Gaussian mutation operator, dynamically control the mutation amplitude according to the current iteration algebra, and use the best individual of the parent generation to guide the mutation direction, generate Gaussian mutated sparks, and obtain diverse candidate path solutions; Step 4.6: For the out-of-bounds sparks generated in steps 4.3 to 4.5 that exceed the solution space boundary, an improved mapping rule is used to process the out-of-bounds position back into the solution space, while preserving the characteristics of the out-of-bounds sparks in the original dimensional direction, thus obtaining effective candidate path solutions; Step 4.7: Merge the parent fireworks, the explosion sparks generated in Step 4.3, the new sparks after displacement in Step 4.4, the Gaussian mutation sparks generated in Step 4.5, and the sparks after mapping in Step 4.6 into a candidate solution set. Use the elite retention strategy to directly retain the parent fireworks with the best fitness and the offspring sparks with the best fitness to the next generation. Select the remaining candidate solutions by roulette wheel according to their fitness values ​​to form the next generation of fireworks population. Step 4.8: Repeat steps 4.2 to 4.7 until the maximum number of iterations within the current planning period is reached, and output the optimal path scheme for the current planning period.

6. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 5, characterized in that, In step 4.3, the specific method for generating explosion sparks based on adaptive explosion radius is as follows: Step 4.3.1: Calculate the actual number of sparks produced by a single firework. : First, obtain the number Fireworks at the current number The fitness values ​​of the current generation and its parents, as well as the optimal fitness value in the current population, are used to initially calculate the fitness value of the current generation. The generation The number of sparks produced by a single firework explosion: In the formula, For the preliminary calculation of the first Fireworks at the current number The number of sparks that should be generated by the explosion; This represents the total number of sparks produced by all fireworks explosions, typically set to 50. The adjustment factor is calculated using a minimum value, ranging from 10. -6 ; It is the first Fireworks at the current number Fitness value of the generation; It is the current number The optimal fitness value in the generation population; Then, to After limiting and rounding, the result is the first... The actual number of sparks produced by each firework: In the formula, For the first The actual number of sparks produced by a single firework; This represents the total number of explosive sparks allowed to be produced by all fireworks. Its value is obtained empirically and is generally taken as a number similar to... The same as or multiple of it, The total number of sparks produced by all fireworks explosions; , These represent the lower and upper limits of the allowed percentage of explosive sparks produced by a single firework relative to the total allowed explosive sparks produced by all fireworks, respectively. The value range is from 0.05 to 0.

1. The value range is from 0.8 to 0.9; This represents the rounding function; Step 4.3.2: Compare the first The fitness value of a firework in the current generation is compared with the fitness value of its parent generation, and the fitness value of the firework is dynamically adjusted based on the comparison results. The adaptive blast radius of a firework: When the firework's fitness value in the current generation is better than that of its parent generation, the blast radius is reduced for fine-grained local search; when the firework's fitness value in the current generation is worse than that of its parent generation, the blast radius is expanded for global exploration. First, calculate the basic explosion radius: In the formula, For the first Fireworks at the current number The basic blast radius of the generation; It is the first Fireworks at the current number Fitness value of the generation; It is the optimal fitness value in the current population; The adjustment factor is calculated using a minimum value, ranging from 10. -6 ; Then determine the number according to the following formula. Adaptive blast radius of a firework : In the formula, Based on the blast radius; For the first Fireworks at the current number The adaptive explosion radius of the generation; It is the first Fireworks at the current number Fitness value of the generation; It is the first The fitness value of a firework in its parent generation; and All are preset constants. , ; Step 4.3.3: According to the first... The actual number of sparks produced by each firework and adaptive blast radius , with the first Centered on a single firework, explosive sparks are randomly generated in a uniform distribution around it. All the generated explosion sparks constitute new candidate path solutions.

7. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 6, characterized in that, The specific method for using the Levy flight strategy to manipulate the displacement of the explosion sparks in step 4 is as follows: Step 4.4.1: For each explosion spark generated in step 4.3 Randomly select from all dimensions of its solution vector There are several dimensions, among which This is a preset constant, taking the value 1 or 2; it generates Levy-distributed random numbers for each selected dimension. : In the formula, For the selected explosion spark Levy-distributed random numbers in the dimension; and All are random numbers that follow a normal distribution, i.e. , ; is a constant and ; It is the step size scaling factor of the Levy distribution, used to control the overall magnitude of the random step size; ,in , ; ! represents the standard gamma function; ! represents the factorial operation; The explosion sparks were selected in the first... Position value in dimension ; This represents a complete individual explosion spark, whose solution vector contains multiple dimensions; Step 4.4.2: For each selected dimension, based on the Levy distribution random numbers generated in Step 4.4.1 and the adaptive blast radius determined in Step 4.3, independently calculate the blast spark at the selected dimension. Adaptive Explosion Offset in Dimension : in, For the first Fireworks at the current number The adaptive explosion radius of the generation; For the selected explosion spark Levy-distributed random numbers in the dimension; Step 4.4.3: Generate a new spark after displacement based on the adaptive explosion offset. : For the selected number Dimensions: In the formula, For the selected explosion spark Adaptive explosion offset in dimensions; Is the new spark after displacement in the selected first... Position in dimensions; The explosion sparks were selected in the first... Position value in dimension; For dimensions that are not selected, the original position value of the explosion spark in that dimension remains unchanged; Step 4.4.4: All new sparks generated by the displacement operation in step 4.4.3 will be processed. As a candidate path solution after displacement: If the new spark generated after displacement If a value in any dimension exceeds the boundary of the solution space, then the out-of-bounds processing is performed according to the improved mapping rule in step 4.6, and the out-of-bounds value is mapped back to the feasible region of the solution space.

8. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 5, characterized in that, In step 4.5, Gaussian mutation sparks are generated according to the following adaptive mutation formula. : In the formula, and These are the first and second mutation magnitude control terms of the adaptive Gaussian mutation operator, respectively. and These are the first directional control item and the second directional control item, respectively. and These are the first and second parental genetic control terms, respectively. Their values ​​are related to the current iteration generation. Automatic linear decrease; the later the planning period, the smaller the influence of paternal inheritance, and the closer it is to the optimal solution. and This is the optimal reference control term, and its value is a preset fixed constant value; , These are the values ​​in the parent generation's online acceleration and yaw rate dimensions, respectively. , These are the values ​​in the online acceleration dimension and yaw angle acceleration dimension of the generated Gaussian mutated spark, respectively; , These are the values ​​of the optimal fireworks in the parent population in terms of online acceleration and yaw rate, respectively. , , , All are random real numbers in the range [0,1]. For dimensions that are not selected, the values ​​of the parent fireworks in that dimension remain unchanged; if the generated Gaussian mutated fireworks are... If a value in any dimension exceeds the boundary of the solution space, then the out-of-bounds processing is performed according to the improved mapping rule in step 4.6, and the out-of-bounds value is mapped back to the feasible domain of the solution space. The formulas for calculating the first and second mutation magnitude control terms of the adaptive Gaussian mutation operator are as follows: In the formula, This is the upper limit of the yaw rate of a USV; This is the upper limit of linear acceleration for a USV; First paternal genetic control term Second paternal genetic control terms The calculation formula is: In the formula, and These are the first paternal genetic control terms. The upper and lower limits; and These are the genetic control terms of the second paternal parent. Upper and lower limits; first paternal genetic control term Second paternal genetic control terms The upper limit is set to 0.9 and the lower limit is set to 0.

4. The maximum number of iterations within a single planning period; First direction control item Second direction control item Determined according to the following methods: In the formula, +1 represents a positive perturbation, that is, during the mutation process, the gene in this dimension shifts in the direction of increasing value; -1 represents a negative perturbation, that is, during the mutation process, the gene in this dimension shifts in the direction of decreasing value.

9. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 1, characterized in that, The kinematic models established in step 1 to describe the motion characteristics of USV, AUV, and underwater targets are as follows: Three-dimensional kinematic model of an underwater target: In the formula, It is the pose of an underwater target within the terrestrial system; These are the position coordinates of the underwater target, where These represent the displacements of the underwater target on each coordinate axis in the ground system; It is the yaw angle of the underwater target; It is the pitch angle of the underwater target; It is the velocity of the underwater target in the velocity system; It is the translational speed of the underwater target; It is the yaw rate of the underwater target; It is the pitch angular velocity of the underwater target; Two-dimensional kinematic model of USV: In the formula, Indicates the USV number; It is the first in the Earth system The position of the USV For the first The location coordinates of the USV, among which , , They represent the first Displacement of the USV along each axis in the ground system Constant; The first in the Earth system Yaw angle of a USV; The first in the velocity system The speed of the USV, among which For the first The translational speed of the USV; For the first Yaw rate of a USV; AUV's three-dimensional kinematic model: In the formula, It is the pose of the AUV in the ground system; These are the position coordinates of the AUV, where , , These represent the displacements of the AUV on each coordinate axis in the ground system; It is the yaw angle of the AUV; It is the pitch angle of the AUV; Let be the velocity of the AUV in the velocity system, where It is the translational speed of the AUV. It is the pitch rate of the AUV. It is the yaw rate of the AUV.

10. The underwater target search and tracking cooperative path planning method based on AUV and multiple USVs according to claim 9, characterized in that, In step 1, the underwater target constraints include the underwater target's workspace constraints and the underwater target's operational performance constraints, wherein: The workspace constraints for underwater targets are: In the formula, , These are the upper and lower limits of the known sea area along the x-axis, respectively; , These are the upper and lower limits of the known sea area along the y-axis, respectively. It is the maximum operating depth of an underwater target. These represent the displacements of the underwater target on each coordinate axis in the ground system; Performance constraints of underwater targets: In the formula, It is the upper limit of the translational speed of an underwater target; It is the upper limit of the yaw rate of an underwater target; It is the upper limit of the pitch angular velocity of an underwater target; It is the upper limit of linear acceleration for underwater targets; It is the translational speed of the underwater target; It is the yaw rate of the underwater target; It is the pitch angular velocity of the underwater target; It is the linear acceleration of the underwater target; USV constraints include USV isomorphic platform constraints, search capability constraints, USV inter-communication constraints, USV-AUV communication constraints, USV motion performance constraints, and workspace constraints; among which: USV isomorphic platform constraint: The USVs involved in the work are of the same model and have the same performance indicators; USV search capability constraints: Assuming the search domain of the USV is sphere-shaped, with the centroid of the USV as the center of the search domain, the effective detection radius of the USV is defined as follows: When an underwater target enters the effective detection radius of the USV, the USV is considered to have successfully detected the underwater target. In the formula, Indicates the first The location coordinates of the USV Indicates the position coordinates of the underwater target. Indicates the effective detection radius of the USV; USV's information connectivity constraints: When the information exchange target of a USV is another USV on the water surface, assuming that the water surface information exchange domain of each USV is a planar circle, and taking the centroid of the USV as the center of the information connectivity domain, the exchange radius of the information connectivity domain between USVs is defined as follows: When the distance between any two USVs does not exceed At that time, it was assumed that the two USVs could sense each other and freely exchange information. The formula for information communication between USVs was: In the formula, Indicates the first The distance between any two USVs within a planning cycle; Indicates the first The planning cycle, the first The coordinates of the USV on the horizontal plane; Indicates the first The planning cycle, the first The coordinates of the USV on the horizontal plane. It is the communication radius of the information connectivity domain between USVs, representing the maximum communication distance between USVs; When the USV's information transmission target is an underwater AUV, assuming the underwater information communication domain of the USV is hemispherical in shape, and with the USV's center of mass as the center of the sphere, the communication radius between the USV and the AUV is defined as follows: When the distance between the USV and AUV does not exceed If we assume that the two can sense each other, then the formula for information communication between the USV and AUV is: In the formula, Indicates the first The location coordinates of the USV Constant; These are the position coordinates of the AUV; It is the communication radius between the USV and AUV. USV performance constraints: Due to the inherent structural limitations of USVs, there are upper limits to their speed and acceleration during navigation. in, It is the first The translational speed of the USV; It is the first Yaw rate of a USV; It is the first The linear acceleration of a USV; This is the upper limit of the translational speed of the USV; This is the upper limit of the yaw rate of a USV; This is the upper limit of linear acceleration for a USV; USV's workspace constraints: USVs search for underwater targets within bounded sea areas where underwater targets are more likely to be present. In the formula, , These represent the upper and lower limits of the known sea area along the x-axis, respectively. , These are the upper and lower limits of the known sea area along the y-axis, respectively. AUV constraints include AUV search capability constraints, information transmission constraints, target acquisition constraints, performance constraints, and workspace constraints; among which: AUV search capability constraints: Since AUVs operate underwater, we assume their search domain is a sphere, with the AUV's center of mass as the center of the search domain. The radius of the AUV's search domain is defined as... When the distance between the underwater target and the AUV is less than For an AUV to be considered to have successfully detected an underwater target, the following constraints must be met: In the formula, These are the position coordinates of the AUV; These are the position coordinates of the underwater target; It is the radius of the AUV search domain; AUV information transmission constraints: satisfy the information connection formula between USV and AUV; AUV target acquisition constraint: The AUV's mission requirement during the tracking phase is to successfully acquire underwater targets. This is achieved when the distance between the AUV and the underwater target is less than a set AUV acquisition distance threshold. At this point, it is considered that the AUV has completed its underwater target acquisition mission: Performance constraints of AUVs: in, It is the translational speed of the AUV; It is the pitch rate of the AUV; It is the yaw rate of the AUV; It is the linear acceleration of the AUV; This is the upper limit of the translational speed of an AUV; This is the upper limit of the pitch rate of an AUV; This is the upper limit of the yaw rate of an AUV; This is the upper limit of linear acceleration for AUVs; AUV working space constraints: in, These are the position coordinates of the AUV; , These are the upper and lower limits of the known sea area along the x-axis, respectively; , These are the upper and lower limits of the known sea area along the y-axis, respectively. This is the maximum operating depth of an AUV underwater. In order to successfully capture underwater targets, it needs to meet certain requirements. ; It is the maximum operating depth of an underwater target.

Images