Cooperative path planning method for searching and tracking underwater target by multiple USV unmanned clusters

Abstract

The invention provides a cooperative path planning method for searching and tracking an underwater target by a multi-USV unmanned cluster, and the method comprises the steps: introducing a pose-control quantity-time to carry out the three-dimensional double-chain coding of a population in an improved genetic algorithm, enabling a control instruction and an accurate execution timestamp to serve as a genetic gene, and enabling the control instruction and the precise execution timestamp to serve as a genetic gene in the crossover and mutation operation, timestamps, control quantities and poses are transmitted synchronously, and it is ensured that offspring individuals can inherit an excellent cooperation mode of a parent; during population initialization, USV is guided to preferentially cover a high-value region through region division and weighted Gaussian distribution, so that blindness caused by random initialization of a traditional genetic algorithm is overcome, and invalid search is avoided; a target for avoiding secondary search is designed in a fitness function, and repeated access to recently searched areas is quantified by introducing a concept of confidence time intervals, so that an algorithm actively explores unexplored water areas, waste of search resources is avoided, and accuracy and planning efficiency of multi-USV collaborative path planning are improved.

Description

A cooperative path planning method for underwater target search and tracking by a multi-USV unmanned swarm Technical Field

[0001] This invention belongs to the field of unmanned swarm path planning technology, specifically relating to a collaborative path planning method for underwater target search and tracking by a multi-USV unmanned swarm. Background Technology

[0002] With the increasing demand for ocean observation and operations, utilizing unmanned systems has become an important development direction. Unmanned surface vessels (USVs) have attracted widespread attention for their platform characteristics in tasks such as surface support and underwater target detection. However, when a single USV performs large-scale underwater target search missions, it suffers from limitations such as limited sensing range and insufficient mission continuity due to the limitations of its sensor detection range and platform endurance. To address this, employing multiple USVs to form an unmanned USV swarm, through coordinated cooperation to expand the search range and improve mission reliability, has become a solution for enhancing operational efficiency.

[0003] To achieve unmanned swarm collaborative operation of USVs, the path planning problem for each USV within the swarm must first be solved. Currently, various algorithms exist in the field of path planning, such as dynamic programming, artificial potential field methods, etc. Algorithms and intelligent algorithms that simulate biological groups (such as ant colonies and bird flocks). However, these methods face many challenges when applied to specific scenarios of multi-USV cooperative search. For example, the optimization models of traditional swarm intelligence algorithms (such as ant colony algorithms and particle swarm algorithms) are usually based on scenarios with low complexity and weak constraints. However, the actual multi-USV isomorphic unmanned cluster cooperative search is an engineering problem that requires comprehensive consideration of multiple complex constraints such as platform motion constraints, communication link limitations, obstacle avoidance and regional boundaries. At the same time, the task requires that the path planning results not only achieve regional coverage, but also take into account the cooperative efficiency of the cluster and its adaptability to the dynamic environment. Existing swarm intelligence path planning algorithms (such as traditional genetic algorithms) have the following shortcomings when facing dynamic, cooperative, and strongly constrained continuous regional search tasks of isomorphic multi-USV unmanned clusters: (1) the randomly generated path may not conform to the kinematic / dynamic constraints of USV, resulting in a large number of invalid iterations; (2) the initialization and mutation process is blind and easily falls into local optima or generates redundant exploration, which may ultimately lead to unsatisfactory actual operability or cooperative efficiency of the planned path.

[0004] Furthermore, some existing unmanned swarm path planning schemes have different focuses compared to the requirements of "regional cooperative search." For example, invention CN117707210A, entitled "A Path Planning Method for Underwater AUV Swarms Based on Swarm Intelligence Algorithm," primarily addresses the problem of planning the swarm's navigation path from a known starting point to a destination, with optimization focusing on the optimality of the transfer process. However, for regional search tasks, the core objective is to plan a cooperative search path within a specified area that achieves efficient coverage, avoids collisions, and can be adjusted based on task status (such as target discovery). Simple "point-to-point" transfer planning methods cannot directly meet the specific requirements of regional coverage search in terms of efficiency and dynamism. Summary of the Invention

[0005] The purpose of this invention is to address the problem that existing swarm intelligence-based path planning technologies are prone to getting trapped in local optima or generating redundant explorations when facing dynamic, cooperative, and strongly constrained continuous area search tasks with homogeneous multi-USV unmanned swarms. This invention provides a cooperative path planning method for underwater target search and tracking using multiple USV unmanned swarms. This method designs a multi-target fitness function and introduces a three-dimensional double-chain encoding of the population based on pose, control variables, and time during initialization. The "timestamp" dimension enhances the spatiotemporal cooperation and heritability of cooperative operations within the swarm. During crossover and mutation operations, the timestamp is transmitted synchronously with the control variables and pose, ensuring that offspring inherit the cooperative patterns of their parents. This allows individual USVs in the swarm to plan paths while maintaining connectable distances, resulting in the optimal cooperative path planning scheme for the multi-USV unmanned swarm within a certain search area.

[0006] To achieve the above objectives, the technical solution provided by this invention is:

[0007] A collaborative path planning method for underwater target search and tracking by a multi-USV unmanned swarm includes the following steps:

[0008] Step 1: Model building and model constraint setting;

[0009] Establish a planar motion model for the USV and a motion model for the underwater target, and set constraints for the motion model for the underwater target and the planar motion model for the USV;

[0010] The constraints of the underwater target motion model include its workspace constraints and performance constraints; the constraints of the USV planar motion model include its performance constraints, workspace constraints, and search domain radius. Communication radius of the information connectivity domain within the cluster And collision avoidance constraints between USVs;

[0011] Step 2, based on the established USV planar motion model, underwater target motion model, and set model constraints, uses an improved genetic algorithm to periodically perform path collaborative planning; including the following steps:

[0012] Step 2.1, Three-dimensional double-stranded encoding and population initialization;

[0013] Based on the current actual pose state of the USV, a three-dimensional double-stranded encoding method of pose-control quantity-time is used to generate the current initial population. The three-dimensional double-stranded encoding refers to the joint encoding of the pose sequence, control quantity sequence and corresponding timestamp sequence of the USV, so that each USV chromosome in the population contains the pose sequence, control quantity sequence and corresponding timestamp sequence.

[0014] Step 2.2, Fitness Evaluation and Iterative Optimization;

[0015] Step 2.2.1, using the designed overall fitness function The initial population is evaluated to obtain a set of fitness values ​​corresponding one-to-one with each individual in the initial population; the overall fitness function is then used. The following metrics are used to optimize the cluster's joint search domain area, the degree to which secondary searches are avoided for recently searched regions, and the number of USVs that can maintain information connectivity within the cluster.

[0016] Step 2.2.2: Based on the fitness value set, an elite preservation strategy is used to select individuals from the initial population to obtain a set of elite individuals that will be retained for the next generation.

[0017] Step 2.2.3: The individuals remaining after the elite selection operation are used as parent individuals, and an adaptive Gaussian mutation operation is performed to generate a set of offspring individuals;

[0018] Step 2.2.4: Merge the elite individuals set with the offspring individuals set to form a new generation population, and repeat steps 2.2.1 to 2.2.3.

[0019] Step 2.3: Optimal path solution generation;

[0020] Determine whether the iteration termination condition within the current planning cycle has been met. If not, repeat step 2 until the iteration termination condition within the current planning cycle is met. If so, select the individual with the highest fitness value from the final generation population as the optimal individual, and decode the chromosome of the optimal individual to obtain the optimal pose sequence, optimal control quantity sequence and corresponding optimal timestamp sequence of each USV at the time of iteration termination, and generate the path scheme to be executed in the current planning cycle.

[0021] Step 3, Path Execution and Dynamic Programming;

[0022] After obtaining the path plan to be executed, immediately determine whether a feedback signal has been received from any USV indicating that an underwater target has been detected. If a feedback signal is received, discard the path plan to be executed, and output instructions to control all USVs to confirm the target or cooperate in encircling and capturing the underwater target, while terminating the subsequent path planning cycle.

[0023] If no feedback signal is received, the path plan to be executed is sent to the corresponding USV, so that the cluster moves according to the planned path to perform the search; and the current actual pose, control variables and timestamps of all USVs are used as the initial state of the next planning cycle, and the process returns to step 2 to perform a new round of path planning.

[0024] Furthermore, the three-dimensional bichain encoding of pose-control quantity-time in step 2.1 is specifically defined for one search cycle of a single USV as follows:

[0025]

[0026] in, Represents any ship In the Individual coded chromosomes within a search cycle, This indicates that the USV was in the Linear acceleration sequence within a search cycle , represents the real chain in a doubly chained encoding; This indicates that the USV was in the angular velocity sequence within a search cycle , representing the imaginary chain in doubly chained encoding; This indicates that the USV was in the A timestamp sequence within a search cycle ; The number of control steps within the cycle; and They represent the first The linear acceleration and angular velocity of each control step. Indicates the first The timestamp corresponding to each control step.

[0027] Furthermore, step 2.1 generates the current initial population, specifically including:

[0028] Classification and updating of working sea area value:

[0029] Before executing the search mission, an initial area value analysis map is received from the shore-based or command system based on the acquired prior information. According to the initial area value analysis map, the sea area to be searched is pre-divided into high-value areas and ordinary areas. High-value areas include unsearched areas and areas where the probability of the target presence is higher than a preset threshold. Ordinary areas are other sea areas besides high-value areas. Initial weights are assigned to high-value areas and ordinary areas based on historical search data.

[0030] After the search mission begins, the weights of each region are dynamically adjusted and the region divisions are updated based on the actual search feedback data of the unmanned surface vessel cluster. The specific method is as follows: if any region has been effectively searched, the confidence period interval of the searched region is updated based on historical search data; based on the updated confidence period interval and the search status of the region, the real-time value weight of the region is recalculated.

[0031] Based on the real-time value weight of each region, high-value areas and ordinary areas in the working sea area are dynamically redefined; the confidence period interval is defined as follows: if an area has been searched and identified as a high-safety area within a certain historical search period, then the historical search interval is defined as the confidence period interval.

[0032] Initial value generation of linear acceleration: in Within a certain range, the initial value of linear acceleration is selected according to a Gaussian distribution. Specifically, in the ordinary region, the mean value of the initial linear acceleration is set. The initial linear acceleration value is set to 0 to guide the initial movement direction of the population towards high-value areas and avoid ineffective energy consumption; the mean value of the initial linear acceleration value is set in high-value areas. The offset is positive, and its magnitude is:

[0033]

[0034] in, Energy consumption coefficient; Energy consumption per unit time; This is a stability correction coefficient, ranging from 0.8 to 1.0, used to balance the fluctuations of the Gaussian distribution and avoid sudden acceleration changes; The maximum linear acceleration of the USV, and as the USV moves toward the high-value area, the angle between the direction of its linear acceleration and the direction of the line connecting the current position of the USV and the center point of the high-value area remains less than 90°.

[0035] Initial angular velocity value generation: Based on the distance between the USV and the obstacle, the sampling range of the initial angular velocity value is dynamically adjusted using an adaptive uniform distribution to perform obstacle avoidance;

[0036] Initial timestamp sequence generation: For USV pairs whose initial position distance is less than the safety threshold, collision avoidance of the initial path is achieved by introducing a fixed time difference in the timestamp sequence encoded by one of the USVs.

[0037] Furthermore, in the initial angular velocity generation step, if the distance between the current position of the USV and the nearest obstacle is greater than or equal to a set safe distance threshold, then in Within the sampling range, an adaptive uniform distribution strategy is used to determine the initial value of the angular velocity; if the distance between the current position of the USV and the nearest obstacle is less than the safe distance threshold, the sampling range is reduced to... ;in, This is the maximum angular acceleration of the USV.

[0038] Furthermore, the degree to which secondary searches are avoided in recently searched areas in step 2.2.1 is evaluated using the following method:

[0039] Define confidence interval This indicates the time interval corresponding to the recently searched area; where the underwater target velocity information is unknown, The value is taken in the range of 2 to 4; when velocity estimation information for the underwater target exists, then [the value is taken as 4]. ,in The maximum speed of the USV The maximum speed of the underwater target. To optimize the coefficients, The value ranges from 0.7 to 1;

[0040] Calculate the first The joint search area of ​​all USVs under the time-planned path, and the first The overlapping area between all historical joint search areas of USVs under the time-planned path;

[0041] The smaller the overlap area, the more effectively the path planning avoids areas that have been recently searched.

[0042] Furthermore, in step 2.2.1, the total fitness function The specific expression is:

[0043]

[0044] In the formula, The defined confidence time interval; Indicates the first The fitness function of the area of ​​the joint search domain of all USVs at time 1. Indicates the first The fitness function for the area of ​​the joint search domain of all USVs at time t; This means that the distance between any two USVs is greater than the communication radius of the information connectivity domain within the cluster. USV, Number it; This indicates the number of USVs participating in the target search task; , , These are constant coefficients with different values, and In the initial stage of the search task, the values ​​of the three constant coefficients satisfy... In the later stages of the search mission, in order to balance the communication needs of high-value areas and USVs, and The value of gradually increases, but does not exceed . .

[0045] Furthermore, in the adaptive Gaussian mutation operation step 2.2.3, the mutation operator is an adaptive mutation operator guided by the parent optimal individual. This adaptive mutation operator makes the mutation direction of the offspring individual refer to the direction of the corresponding gene in the parent optimal individual.

[0046] No. The expression for the adaptive mutation operator for each USV individual in each iteration cycle is:

[0047]

[0048] In the formula, and The optimal reference control term is used to reference the optimal solution of the previous iteration. The first 60% of iterations are defined as the early stage of the algorithm. Considering the high requirements for population diversity in the early stage of the algorithm, the optimal reference control term takes a value of 0.2 to 0.3. The last 40% of iterations are defined as the late stage of the algorithm. Considering that the population tends to converge in the late stage of the algorithm, the optimal reference control term takes a value of 0.4 to 0.5. , The first The 1st iteration cycle The linear acceleration and angular velocity genes of each individual; , The first The linear acceleration gene and angular velocity gene of the optimal path solution for each iteration cycle; , , , All are random real numbers in the range [0,1].

[0049] If after the mutation operation, the first In the nth iteration cycle, the th If the specific values ​​of an individual's acceleration gene and angular velocity gene exceed the maximum acceleration and maximum angular velocity of the USV, then the maximum acceleration and maximum angular velocity will be used to replace the corresponding values ​​that exceed the range.

[0050]

[0051] In the formula, and These are the maximum linear acceleration and maximum angular velocity of the USV, respectively. and They represent the first The 1st iteration cycle The linear acceleration and angular velocity genes of each individual;

[0052] and The variation magnitude term of the mutation operator is expressed as follows:

[0053]

[0054] and The first The specific expressions for the first and second paternal genetic control terms in each iteration cycle are as follows:

[0055]

[0056] In the formula, , These are the maximum and minimum values ​​of the first paternal genetic control term, respectively; , These are the maximum and minimum values ​​of the second paternal genetic control term, respectively; This represents the maximum number of iterations.

[0057] and As a direction control term, it is used to make the offspring individuals randomly select the direction of gene mutation during the mutation stage. This can both make the mutation direction of the offspring individuals refer to the direction of the best parent individuals and ensure the randomness of the offspring individuals' mutation. and The method for determining the value is as follows: when it is determined that there is an obstacle near the USV, and Values ​​are taken within the range of 0.3 to 0.6 to enhance directional guidance; when it is determined that there are no obstacles near the USV, and Values ​​are taken within the range of 0.1 to 0.3 to reduce directional guidance and increase the diversity of variation.

[0058] Furthermore, the USV planar motion model established in step 1 is as follows:

[0059]

[0060]

[0061]

[0062] In the formula, The first in the Earth system Position of the USV; Indicates the first The location coordinates of the USV It is always 0; For the first The horizontal yaw angle of the USV; The first in the velocity system The speed of the USV; For the first USV along Translational speed of the axis; For the first USV around Angular velocity of the axis; For the first The linear acceleration of the USV.

[0063] Furthermore, the underwater target motion model established in step 1 is a three-dimensional kinematic model, which is used to estimate the target motion state to determine whether the USV unmanned cluster has detected the underwater target, and to assist in calculating the confidence time interval.

[0064] The three-dimensional kinematic model of the underwater target is as follows:

[0065]

[0066]

[0067]

[0068] in, This indicates the pose of an underwater target within a terrestrial system. Indicates the position coordinates of the underwater target. Indicates the horizontal yaw angle of an underwater target. This indicates the pitch angle of an underwater target on the depth surface of the sea area; Represents the velocity of an underwater target in the velocity frame. Indicates underwater target along Translational speed of the axis, Indicates underwater target orbiting angular velocity of the axis, Indicates underwater target orbiting Angular velocity of the axis; This represents the linear acceleration of an underwater target.

[0069] Furthermore, the constraints of the underwater target motion model are:

[0070] Workspace constraints: The underwater target moves within a known sea area, and its maximum diving depth is limited based on its pressure-bearing capacity.

[0071]

[0072] In the formula, and These are the known sea areas in Minimum and maximum values ​​in the direction; and These are known sea areas in Minimum and maximum values ​​in the direction; It is the maximum underwater working depth of the underwater target. ;

[0073] Performance constraints: Based on the underwater target's own performance range, set upper limits for velocity, acceleration, and linear acceleration.

[0074]

[0075] In the formula, It is the upper limit of the underwater target's own speed; Is it an underwater target? Maximum angular velocity of the shaft; Is it an underwater target? Maximum angular velocity of the shaft; It is the maximum linear acceleration of the underwater target;

[0076] The constraints of the USV planar motion model are:

[0077] Homogeneous platform constraint: All USVs participating in the search task in the cluster are of the same model and have consistent performance metrics;

[0078] Search capability constraints: Each USV has a fixed detection capability. The search domain of the USV is a sphere, the center of which is the center of mass of the USV; the radius of the search domain is... When an underwater target enters the search area of ​​the USV, the USV is considered to have successfully detected the underwater target.

[0079]

[0080] in, Indicates the first The location coordinates of the USV Indicates the position coordinates of the underwater target;

[0081] Information connectivity constraints: To maintain cluster collaboration, each USV participating in the search task maintains communication, achieving underwater target search through information exchange and collaboration. When the information transmission target of any USV is another USV on the water surface, it is assumed that the surface information exchange domain of each USV is a planar circle, with the centroid of the USV as the center of the information connectivity domain, and the exchange radius of the information connectivity domain is... When the distance between two USVs does not exceed the communication radius of the information connectivity domain. At that time, it was assumed that the two USVs could sense each other and freely exchange information;

[0082] Performance constraints: Due to the inherent structural limitations of the USV, there are upper limits on its speed, linear acceleration, and angular velocity during navigation, namely:

[0083]

[0084] in, , , These represent the USV's maximum translational velocity, maximum acceleration, and maximum angular velocity, respectively.

[0085] Workspace constraints: The USV searches for underwater targets within a two-dimensional bounded ocean area where underwater targets have been observed.

[0086]

[0087] In the formula, and They represent USV's Axis coordinates and Axis coordinates and These are known sea areas in Minimum and maximum values ​​in the direction; and These are known sea areas in Minimum and maximum values ​​in the direction;

[0088] USV Collision Avoidance Constraints: To prevent collisions between USVs during the search, the distance between any two USVs must be greater than a set safety distance. :

[0089]

[0090] Where, in the formula, express The distance between any two USVs at any given time; and Indicates the first

[0091] ships Horizontal coordinates and express The horizontal coordinates, where, ; This represents the safe distance between any two USVs.

[0092] The advantages of this invention are:

[0093] 1. The proposed method for collaborative path planning for underwater target search by a multi-USV unmanned swarm is based on an improved genetic algorithm iterative optimization strategy and a designed multi-objective fitness function. This enables individual USVs in the swarm to achieve continuous individual trajectory planning while maintaining connectable distances, reducing redundant exploration and improving the accuracy and efficiency of collaborative path planning by the multi-USV unmanned swarm in any search area.

[0094] 2. In the improved genetic algorithm adopted in this invention, a three-dimensional bichain encoding of the population is introduced, which combines pose-control quantity-time. The control commands (acceleration, angular velocity) and their precise execution timestamps are used as heritable genes. This encoding method ensures that the path represented by any individual is physically executable from the perspective of solution expression. The heritability of spatiotemporal collaboration and collaborative operations of the cluster is enhanced through the timestamp dimension, avoiding a large amount of resources being wasted on the evaluation and iteration of invalid solutions, thus improving the efficiency of the algorithm.

[0095] 3. In the improved genetic algorithm employed in this invention, a timestamp dimension is introduced into the encoding, making the spatiotemporal relationship of "which USV arrives at which place at what time" a heritable and optimizable object. During crossover and mutation operations, the timestamp is transmitted synchronously with the control variable and pose, ensuring that offspring individuals can inherit the superior cooperative patterns of their parents (such as formation maintenance and regional coverage). This strategy makes the cooperativeness of the cluster no longer merely a passive constraint, but rather something that can be actively optimized and continuously evolved in iterations, thereby obtaining a global path with better cooperativeness.

[0096] 4. During population initialization, this invention guides the USV to prioritize covering high-value areas (unsearched areas and / or areas that have been searched but where no target has been found) through region partitioning and weighted Gaussian distribution. This overcomes the blindness caused by random initialization in traditional genetic algorithms and avoids ineffective searches. The fitness function is designed to avoid secondary target searches. By introducing the concept of confidence time interval, the repeated visits to recently searched areas are quantified, enabling the algorithm to actively explore unexplored waters, effectively avoiding the waste of search resources and improving the area coverage rate per unit time. Simultaneously, the designed timestamp offset and obstacle avoidance verification strategies ensure collision-free initial paths, enhancing cluster collaboration. Continuous planning based on the pose of the previous cycle avoids path breakage, making it suitable for long-term continuous search tasks.

[0097] 5. To overcome the problem that random mutation operators in traditional genetic algorithms easily destroy high-quality solutions, this invention proposes an adaptive Gaussian mutation operator that integrates particle swarm optimization. By using the optimal individual of the parent generation to adaptively control the mutation direction, the mutation proceeds towards historically good solutions, thereby driving the continuous evolution of the population, improving the global search performance of the algorithm, reducing blind and redundant exploration, accelerating convergence, and avoiding the problem of cluster cooperation being destroyed by random mutation in traditional genetic algorithms.

[0098] 6. When performing path planning tasks using the method of this invention, the direction and magnitude of gene mutation can be dynamically adjusted and controlled by modifying the mutation magnitude term, parental genetic control term, and direction control term in combination with the different gene types of individuals in the population. This guides individuals in the population to evolve with reference to the direction of the optimal individual, ensuring that the traits of the offspring generated are controllable within a certain range and avoiding ineffective movements of the spacecraft.

[0099] 7. In the method of this invention, after obtaining the fitness of the population, an elite preservation strategy is used for selection operations, and superior individuals are selected and retained according to their fitness values. Under the premise of controlling the population size while meeting the high real-time requirements of USV cooperative path planning, the diversity of the population is maintained. Furthermore, in order to generate a better path solution for the next cycle, the motion control quantities of the USV unmanned swarm system (including the linear acceleration and angular acceleration of the USV) corresponding to the optimal path solution of the previous cycle are retained in the path scheme of the next cycle, ensuring that the optimal cooperative scheme of each generation is not lost, thereby improving the convergence stability and solution quality of the algorithm. Attached Figure Description

[0100] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0101] Figure 1 is a flowchart of the invention of a collaborative path planning method for underwater target search by a multi-USV unmanned swarm;

[0102] Figure 2 is a flowchart of the computation of the improved genetic algorithm proposed in this invention;

[0103] Figure 3 is a schematic diagram of the influence of linear acceleration and angular acceleration genes on the search path in an embodiment of the present invention;

[0104] Figure 4 is a two-dimensional top view of the planned path for target search by the USV unmanned swarm in an embodiment of the present invention;

[0105] Figure 5 is a diagram showing the real-time changes in the distance between each USV and the target within the USV unmanned cluster during the search process in an embodiment of the present invention.

[0106] Figure 6 is a comparison of the search time for target cooperative search using the improved genetic algorithm of this invention, the traditional genetic algorithm, and the particle swarm algorithm. Detailed Implementation

[0107] 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.

[0108] A preferred embodiment of the present invention provides a cooperative path planning method for underwater target search by a multi-USV unmanned surface vessel swarm. This method is applied to a swarm consisting of multiple homogeneous unmanned surface vessels (USVs) to perform cooperative search tasks for moving underwater targets within a specific sea area. The path planning method is executed by a control unit (a computer system deployed in a command and control center or a lead USV within the swarm) and specifically includes the following steps:

[0109] Step 1: Establish kinematic models of the USV and underwater targets, including information such as position, velocity, and angle.

[0110] Step 1.1, Model Establishment;

[0111] (1) Establishment of a three-dimensional motion model of an underwater target: Treating the target as a point mass, a three-dimensional kinematic model is established. The three-dimensional kinematic model of an underwater target can be decomposed into translational kinematics and rotational kinematics models:

[0112] Equations of translational kinematics

[0113] Displacement vector of an underwater target in a ground system Its first derivative and its translational velocity vector in the velocity system The relationship is:

[0114] (1)

[0115] rotational kinematic equations

[0116] Since the target is treated as a point mass, the angular velocities are independent of each other. Therefore, the relationship between attitude angle and angular velocity is as follows:

[0117] (2)

[0118] Based on the above analysis, the three-dimensional motion model of the underwater target can be represented as follows:

[0119] (3)

[0120] Acceleration should also be considered when establishing the kinematic model of the target. Existence:

[0121] (4)

[0122] In the above formula, This represents the pose vector of an underwater target in a ground-based system. This represents the velocity vector of an underwater target in the velocity system. Here are the position coordinates of the underwater target. The horizontal yaw angle of the underwater target. The pitch angle of the underwater target on the depth surface of the sea area. For underwater targets angular velocity of the axis, Indicates underwater target along Translational speed of the axis, Indicates underwater target orbiting Angular velocity of the axis.

[0123] As can be seen from formulas (3) and (4), the three-dimensional motion model of the underwater target describes the position of the underwater target. The relationship between velocity, attitude angle, and angular velocity is considered in the establishment of the three-dimensional motion model of the underwater target, taking into account the acceleration term and... The pitch angle of the axis makes the established three-dimensional motion model of the underwater target closer to the actual motion law of the underwater target, which can improve the accuracy and feasibility of path planning;

[0124] (2) Establishment of the USV motion model: Assuming that the USV performs two-dimensional planar motion on the water surface, its motion model is similar to that of an underwater target. The USV motion model can be expressed as:

[0125] , (5)

[0126] in, This represents the pose vector of the USV in the ground frame; Here are the position coordinates of the USV. Constant; The horizontal yaw angle of the USV; This represents the velocity vector of the USV in the velocity system; For USV along Translational speed of the axis; Let $\omega$ be the angular velocity of $USV around the z-axis. Let be the linear acceleration of the USV.

[0127] Accordingly, for the first in a USV unmanned swarm USV (notation) Its motion state is represented as:

[0128] (6)

[0129] In the formula, The first in the Earth system The pose vector of the USV; For the first The location coordinates of the USV; For the first The horizontal yaw angle of the USV; The first in the velocity system The velocity vector of the USV; For the first USV along Translational speed of the axis; For the first The angular velocity of the USV about the z-axis.

[0130] The equation for linear acceleration is expressed as:

[0131] (7)

[0132] In the formula, Indicates the first The linear acceleration of the USV.

[0133] Step 1.2, Setting Constraints. To ensure the physical feasibility of the path and the effectiveness of the task, the following constraints are set:

[0134] (1) Goal constraints

[0135] The constraints on a target mainly consider two aspects: the target's workspace and the target's performance.

[0136] Workspace constraints: The underwater target moves in a known sea area and has a maximum diving depth range set according to its own pressure resistance capacity.

[0137] (8)

[0138] In the formula, and These are known sea areas in Minimum and maximum values ​​in the direction; and These are the minimum and maximum values ​​in the y-direction of a known sea area; It is the maximum underwater working depth of the underwater target. .

[0139] (2) Performance constraints: The upper limits of the underwater target's velocity, angular velocity, and linear acceleration are set according to the target's own performance range, specifically expressed as follows:

[0140] (9)

[0141] In the formula, It is the upper limit of the underwater target's own speed; Is it an underwater target? Maximum angular velocity of the shaft; Is it an underwater target? Maximum angular velocity of the shaft; It is the maximum linear acceleration of the underwater target.

[0142] (3) USV Constraints: The constraints on USVs should be analyzed from several aspects, including the performance limitations of USVs themselves, the limitations of USV unmanned cluster collaboration, and the workspace of USVs.

[0143] 1) Homogeneous platform constraint: In order to facilitate USV cooperation on the water surface, all USVs participating in the search work in the USV unmanned swarm are of the same model and have the same performance indicators.

[0144] 2) Search Capability Constraints: Each USV has a fixed detection capability. Assume the USV's search domain is a sphere, with the USV's center of mass as the center of the search domain, and the radius of the search domain is... When an underwater target enters the search area of ​​the USV, the USV is considered to have successfully searched for the underwater target.

[0145] (10)

[0146] 3) Information Connectivity Constraints: To maintain cluster collaboration, all USVs need to communicate with each other to collaboratively search for underwater targets. When the information exchange target of any USV is another USV on the surface, assuming the surface information exchange domain of each USV is a planar circle, with the centroid of the USV as the center of the information connectivity domain, the exchange radius of the information connectivity domain is... When the distance between two USVs does not exceed the communication radius of the information connectivity domain. 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:

[0147] (11)

[0148] In the formula, express The distance between any two USVs at any given time; and Indicates the first USV (using) (represents) the horizontal coordinate; and Indicates the first USV (using) (represents) the horizontal coordinates, where, .

[0149] 4) Performance Constraints: Due to the inherent structural limitations of the USV, its speed and acceleration limits during navigation are as follows:

[0150] (12)

[0151] In the formula, , , These represent the maximum translational velocity, maximum linear acceleration, and maximum angular velocity of the USV, respectively.

[0152] 5) Workspace Constraints: The USV searches for targets within a two-dimensional bounded ocean area where underwater targets are more likely to appear. Therefore, we can conclude that:

[0153] (13)

[0154] In the formula, and They represent USV's Axis coordinates and Axis coordinates and These are known sea areas in Minimum and maximum values ​​in the direction; and These are known sea areas in Minimum and maximum values ​​of the direction.

[0155] 6) USV Collision Avoidance Constraints: To prevent collisions between USVs during navigation, the distance between any two USVs must be greater than a certain limit. The safe distance between any two USVs is set as follows: The collision avoidance formula between USVs is as follows:

[0156] (14)

[0157] In the formula, express The distance between any two USVs at any given time; and Indicates the first The horizontal coordinates of the USV and Indicates the first The horizontal coordinates of the USV, where, ; This represents the safe distance between any two USVs.

[0158] Step 2, design of multi-objective fitness function.

[0159] In genetic algorithms, the fitness of an individual in the population is the main indicator describing its performance. The algorithm uses fitness as the sole evaluation metric to assess and select individuals. Before path planning in a USV unmanned swarm system, it is necessary to design the optimization of the fitness function (i.e., the objective function) according to the specific requirements of the collaborative task to ensure that the final output path solution can more efficiently search for underwater targets. However, the single-objective fitness function in traditional genetic algorithms cannot meet the multi-USV search path planning requirements of this invention. Therefore, this invention adopts a multi-objective weighted fusion method to balance search efficiency and collaborative constraints, while optimizing the joint search domain area and avoiding secondary searches and information communication between USVs, thereby guiding the algorithm to find the collaborative path with the best overall performance.

[0160] The multi-objective weighted fitness function designed in this invention mainly includes three aspects: the joint search domain area of ​​the USV cluster, avoiding secondary search, and information connectivity between USVs.

[0161] (1) Joint search domain area of ​​USV cluster

[0162] When performing search missions, the search area covered by a USV swarm system needs to be as large as possible in order to locate underwater targets as quickly as possible. Compared to a single USV platform, the biggest advantage of a USV swarm system is that it can understand the current location information and search area of ​​each USV through mutual information communication. Therefore, the optimal cooperative path individual can be selected based on the overall search area size of the USV swarm system.

[0163] The USV is a stable hemisphere in the underwater search domain. The effective volume of the joint USV search domain needs to be calculated using the union of the volumes of each USV within the working sea area. Therefore, the optimization objective expression can be obtained as follows:

[0164] (15)

[0165] in, Represents any number of The search domain for USVs It refers to the scope of the working sea area.

[0166] However, accurately calculating the volume of formula (15) requires a significant amount of computational resources and time, which does not meet the real-time requirements of online path planning. Considering that the purpose of calculating the above formula is to select the USV unmanned swarm cooperative path solution with the largest search range within the population during this period rather than to obtain the volume value, an equivalent calculation method can be used to simplify formula (15) for the following reasons:

[0167] The centroids of each USV operate with high consistency. The search cross-section projected onto the sea level is the maximum search cross-section of the USVs, with equal area and shape. Furthermore, this maximum search cross-section accurately reflects whether the USV search domains overlap. Therefore, the sea level search cross-section can be used to represent the USV search domain, transforming the joint search domain volume calculation of the USV unmanned swarm into the joint area calculation of the sea level search cross-section of the USV unmanned swarm. Thus, the objective function for optimizing the area of ​​the joint search domain of all USVs simplifies to:

[0168] (16)

[0169] in, This represents the maximum area of ​​the joint search domain of all USVs; Indicates the first The sea-level search area of ​​the USV This indicates the area of ​​the working sea area.

[0170] Then, the fitness function for the area of ​​the joint search domain of all USVs is expressed as:

[0171] (17)

[0172] in, express The fitness function of the area of ​​the joint search domain of all USVs at time t.

[0173] (2) The degree to which secondary searches are avoided

[0174] To thoroughly search unexplored waters and efficiently locate underwater moving targets, the USV search process needs to avoid repeatedly searching high-safety areas that have been recently searched (meaning areas where no underwater targets have been found recently). To address this issue, this embodiment proposes the concept of a confidence time interval.

[0175] During the search, due to the speed difference between the underwater target and the USV (the USV's speed is higher than the underwater target's speed), at certain intervals... Within a given timeframe, if the maximum distance traveled by the underwater target does not exceed the distance traveled by the USV within a single planning cycle (i.e., the maximum displacement of the underwater target does not exceed the distance traveled by the USV within the search domain from the previous cycle to the current cycle), then it is considered that the target has been successfully tracked in the past timeframe. The areas searched by the USV are all high-safety areas; the corresponding time interval is called the confidence time interval, denoted as... To avoid the USV repeatedly searching areas within the confidence interval (recently searched), the USV is forced to explore new areas.

[0176] The maximum speed of the underwater target is The maximum speed of the USV is When the velocity of an underwater target can be estimated, the time interval satisfy:

[0177] (18)

[0178] In the formula, This is the search cycle for USV. And because... Therefore, we get:

[0179] (19)

[0180] In the formula, Indicates the confidence interval. To optimize the coefficients, the values ​​range from 0.7 to 1. When the target velocity information is unknown, It takes values ​​between 2 and 4. Based on the definition of the confidence interval, it is assumed... Time to The areas searched by USV at any given time are high-safety areas that should be avoided from being searched repeatedly. However, due to the short search cycle U of USV, USV... Time to The search domains at different times highly overlap, and merging calculations would waste a significant amount of computational memory. Furthermore, the difference between the search domain within the confidence interval and the search domain of the new search cycle is too small, resulting in no significant difference between the solutions of each path in the USV at this stage, thus rendering this stage useless. Therefore, to simplify the calculation, only... The search domain of USV at time step is used as the original search domain.

[0181] USV needs to search for new areas with the lowest possible security, so All USV joint search domains at any time The overlap of the joint search domain at any given time needs to be sufficiently small. The USV search domain for this part still uses the sea-level search section instead.

[0182] In summary, the objective function for avoiding secondary search is designed as follows:

[0183] (20)

[0184] in, express The fitness function for the area of ​​the joint search domain of all USVs at time t; express The fitness function of the area of ​​the joint search domain of all USVs at time t.

[0185] The objective function for avoiding secondary searches shown in Formula (20) aims to reduce the degree of repeated searches of the corresponding search area for the confidence time interval by the USV unmanned cluster and improve the search efficiency for underwater targets. The larger the value, the smaller the area that is repeatedly searched. This further indicates that the path planning system has more effectively avoided areas that have been recently searched, thereby reducing resource redundancy, improving search novelty, and enhancing information acquisition efficiency. Therefore, the higher the degree of optimization of this indicator (degree of avoidance of secondary searches), the higher the degree of optimization of the indicator.

[0186] (3) Maintain the number of USVs with information connectivity within the cluster

[0187] By transmitting information between USVs, USV swarms can avoid problems such as collisions and excessive proximity of search areas between USVs in the same period, helping USVs to better search for targets. Therefore, maintaining information connectivity between USVs is essential.

[0188] To ensure stable information exchange between USVs, the number of USVs capable of exchanging information needs to be maximized, i.e., maximizing the number of nodes within the cluster that can maintain communication connections. Therefore, the objective function expression for optimizing the number of USVs capable of maintaining communication connectivity is defined as follows:

[0189] (twenty one)

[0190] in, This indicates that the distance to other USVs is greater than the communication radius of the information connectivity domain. USV, Number it; This indicates the number of USVs participating in the target search task.

[0191] (4) Fitness function

[0192] In summary, due to the optimization function , , Both involve finding the maximum value, which is the overall optimization objective of USV unmanned swarm search path planning. The definition is as follows:

[0193] (twenty two)

[0194] The above three sub-objectives , , By weighted summation and fusion to obtain the total fitness function, the expression for the total fitness function is:

[0195] (twenty three)

[0196] in, , , These are constant coefficients with different values, and In the early stages of the search, to ensure a fast search, the values ​​of the three constant coefficients satisfy the following: In the later stages, to balance the high-security area and the communication needs of the USV, the [specific feature / mechanism] can be gradually improved. and The value can be any value, but cannot be greater than 1. ; This indicates the number of AUVs in the parameter search process.

[0197] Step 3, Population Encoding and Initialization.

[0198] At the start of each cycle, using the final state of the previous cycle as a starting point, the following improved genetic algorithm is run to perform a cluster USV cooperative path planning. The first step of cooperative path planning is to plan the path for each individual USV. Path planning first requires encoding the individuals to be generated by the genetic algorithm, transforming it into a mathematical problem that can be optimized by an algorithm.

[0199] Step 3.1: Population coding is performed based on the three-dimensional bichain coding method of pose-control quantity-time.

[0200] To address the periodicity, physical feasibility, and search efficiency requirements of collaborative path planning for multi-USV unmanned swarms, the population encoding and initialization processes are optimized. A three-dimensional bichain encoding based on pose-control quantity-time is employed. By retaining the bichain real-number encoding framework (acceleration + angular velocity), the encoding dimensions are expanded to adapt to periodic planning and swarm collaboration. Specifically, the pose-control quantity-time three-dimensional bichain encoding refers to using a special chromosome encoding for the path of a single USV within the same period. This chromosome encoding includes not only the control quantity sequence (including linear acceleration and angular velocity sequences) but also the corresponding timestamp sequence. Details are as follows:

[0201] at any time The navigation attitude can be represented as Therefore, it can be concluded that time The expression for the navigation attitude is:

[0202] (twenty four)

[0203] In the formula, This represents the position of the i-th USV at time k. Let represent the horizontal yaw angle of the i-th USV at time k.

[0204] Among them, with For example, we have:

[0205] (25)

[0206] In the formula, For the USV search cycle. In the... Within a search period, any ship Corresponding navigation attitude Due to its linear acceleration and angular velocity The only certainty is that any ship can be set. In the The individual coded chromosomes within each search cycle are:

[0207] (26)

[0208] The linear acceleration sequence is as follows: , representing the "real chain" in a doubly chained structure; the angular velocity sequence is , representing the "virtual chain" in a doubly chained network; the timestamp sequence is This is used to record the execution time of each control step. This represents the number of control steps within a cycle. Linear acceleration and angular velocity together determine the trajectory of the USV.

[0209] Therefore, in the IGA algorithm (improved genetic algorithm) The population record of the USV unmanned swarm at that time is as follows:

[0210] (27)

[0211] in: The period number of the current iteration. , This represents the upper limit of the algorithm's iteration cycle. The initial population size, i.e., the number of individuals in the initial population; Indicates the first Within the population of the 1st cycle The individual contains all the chromosomes of the USV. The first individual within the population... Individuals are set as follows:

[0212] (28)

[0213] In the formula, n is the number of USVs participating in the target search task. It represents a complete cluster path solution (i.e., a path individual).

[0214] In the population evolution process of the improved genetic algorithm of this invention, the two control variables, acceleration and angular velocity, on the same chromosome are genetically manipulated simultaneously.

[0215] Step 3.2, Population initialization.

[0216] When generating the initial path population, considering that the USV needs to conduct a thorough search of the working area, it is necessary to simultaneously satisfy physical feasibility (complying with USV operational constraints), environmental adaptability (obstacle avoidance), and search orientation (prioritizing coverage of the search area). Longer travel distances yield better results; therefore, the initial path population contains path individuals... linear acceleration in exist The angular velocity takes values ​​according to a Gaussian distribution within the positive range. exist Values ​​are selected within a range with uniform probability to maximize the feasible solution space.

[0217] This embodiment uses the following strategy to generate the initial population:

[0218] Area-guided search strategy: The working sea area is divided into high-value areas (such as unsearched areas or areas with high target probability) and ordinary areas, and different value weights are assigned based on historical search data (e.g., the value weight of high-value areas). Value weight of ordinary areas Before the search begins, high-value and ordinary areas are determined by target information output from the shore-based or command system. After the search begins, the high-value and ordinary areas are dynamically adjusted based on whether the area has been searched and the determined confidence interval. The target information is obtained based on the following process: Before the USV performs the search mission, the satellite detects underwater targets (prior information) and transmits it to the shore-based or command system. The shore-based or command system issues a search mission to the USV swarm. When issuing the search mission, the shore-based or command system analyzes the acquired information and outputs a predicted area value analysis map. This area value analysis map is the target information. The confidence interval mentioned in this embodiment refers to the probability estimate of the underwater target existing in a certain area, used to quantify the value of that area. The confidence interval is obtained through Bayesian updates and dynamic calculation of observation statistics. Its width directly reflects the reliability of the probability estimate. That is, areas with fewer observations have a wider interval and a higher degree of uncertainty, which will incentivize the USV swarm to explore; areas with sufficient observations have a narrower interval and a more reliable estimate, which can be used to confidently adjust the area's value level.

[0219] Initial value of linear acceleration generated At that time, Within the positive range, values ​​are selected according to a Gaussian distribution: in the high-value region, the mean of the initial value of the lower limit acceleration is set. For positive offset (e.g., In the normal zone direction, set its average value. The value is 0 to avoid wasted energy and guide the initial motion direction of the USV. The mean value is... Quantitative derivation results based on USV energy consumption, motion efficiency, and stability constraints.

[0220] (29)

[0221] in, The energy consumption factor (determined by the USV's power system, e.g., energy consumption factor = 0.05) ; Energy consumption per unit time; This is a stability correction coefficient, ranging from 0.8 to 1.0, used to balance the fluctuations of the Gaussian distribution and avoid sudden acceleration changes; The maximum linear acceleration of the USV is given, and the angle between the direction of the linear acceleration and the line connecting the USV coordinate point and the center point of the high-value zone is less than 90°.

[0222] Obstacle avoidance verification strategy: Initial angular velocity value generated At that time, an adaptive uniform distribution strategy is adopted. The sampling range is determined by the following method: if the distance between the current position of the USV and the nearest obstacle (including other USVs) is less than the set safe distance threshold (e.g., 50m), the sampling range is reduced to ±0.2rad / s to avoid collisions during sharp turns; if the USV is in open water, i.e., the distance between the current position of the USV and the nearest obstacle (including other USVs) is greater than or equal to the set safe distance threshold, the sampling range is expanded (±0.5rad / s) to increase path diversity, cover a wider area, and expand the feasible solution space as much as possible.

[0223] Timestamp strategy: When generating the initial timestamp sequence, the timestamp sequence is set according to the control step size. Increasing, that is Furthermore, a time offset strategy is used to avoid cluster conflicts. The time offset strategy is as follows: for USV pairs whose initial position distance is less than a preset safety distance (e.g., 100m), a time difference is set. This ensures that access times to the same spatial point do not overlap, thus avoiding path conflicts. In other words, it controls the step size. In addition, a fixed time difference is set. This ensures that nearby USVs do not overlap in their access times to the same spatial point, even if their paths intersect, and will be within a fixed time difference. Under the offset effect, USV pairs that are close together pass through the same area at different times, thereby avoiding path conflicts. For example, assuming there are two USVs, A and B, whose distance is less than a preset spacing of 100m, the timestamp sequence of A is set according to the control step size. Increasing, that is The timestamp sequence of B is according to The incrementing method is used.

[0224] The core of the population initialization strategy in this embodiment is to use a weighted Gaussian distribution to guide USVs to prioritize covering high-value areas, thereby improving search efficiency; to ensure that the initial path is collision-free through a timestamp offset strategy and an obstacle avoidance verification strategy, thereby enhancing cluster collaboration; the acceleration and angular velocity of the first control step need to be calculated based on the pose (including actual speed and heading) of the USV at the end of the optimal path in the previous cycle, so as to achieve continuous planning, avoid path breakage, and be suitable for long-term continuous search tasks.

[0225] Step 4, fitness calculation and iterative optimization solution, including:

[0226] Step 4.1, based on the overall fitness function designed in Step 2. Furthermore, for each individual in the current population, the fitness value is calculated based on the path scheme represented by its chromosome, resulting in a fitness value set that corresponds one-to-one with each individual in the population.

[0227] Step 4.2: Select the best performers using the elite preservation strategy.

[0228] From the current population, select the top e individuals with the highest fitness values ​​to obtain the elite individual set, which is then directly retained in the next generation population.

[0229] The selection operation involves choosing superior individuals to retain after obtaining the population fitness. Traditional genetic algorithms typically use a roulette wheel selection method. However, the roulette wheel selection method has a large selection error due to its randomness. In USV cooperative path planning, to achieve high real-time performance, it is necessary to control the population size. To improve the algorithm's real-time performance while maintaining population diversity, the improved genetic algorithm of this invention uses an elite preservation strategy instead of the selection operator. This strategy retains the superior individuals of the current path planning population and their corresponding USV motion control variables in the next generation path planning population, enabling the next generation to generate even better individuals, i.e., path solutions.

[0230] Step 4.3: Perform adaptive Gaussian mutation on the individuals in the population.

[0231] Due to the unique nature of chromosomes in the algorithm of this invention, the effect of some chromosomes is not significant when performing crossover. Therefore, this invention abandons the traditional crossover operation and uses all individuals in the population for mutation. The mutation operator causes a segment of chromosomes in an individual to mutate, resulting in a completely new individual. Mutation allows for a secondary search of regions not explored by previous generations, ensuring individual diversity and global optimality; however, general genetic algorithms blindly require randomness in the mutation process, causing the algorithm to degenerate into a random search for the optimal solution.

[0232] In this invention, the remaining Me individuals after the elite selection operation in step 4.1 are used to form the parent generation individuals, and a mutation operation is performed to generate a set of offspring individuals. In a preferred embodiment of this invention, the first... The mutation operator for each USV individual in each period is expressed as follows:

[0233] (30)

[0234] in, and This is the variation magnitude term of the mutation operator; and For direction control items; and They represent the first The values ​​of the first and second paternal genetic control terms in each cycle are related to the ordinal number of the current cycle. and The optimal reference control term serves as the core function of learning from previous optimal solutions to prevent the algorithm from degenerating into a random search. It needs to balance the "degree of learning from the best" and "mutation diversity". The first 60% of iterations of the algorithm are defined as the early stage of the algorithm. In the early stage of the algorithm, high population diversity is required, and the optimal reference control term takes a value of 0.2 to 0.3. The last 40% of iterations of the algorithm are defined as the late stage of the algorithm. In the late stage of the algorithm, considering that the population tends to converge, the optimal reference control term takes a value of 0.4 to 0.5. , The first The 1st iteration cycle Acceleration and angular velocity genes of each individual; , The first The acceleration and angular velocity genes of the optimal path solution for each iteration cycle; , , , All are random real numbers in the range [0,1].

[0235] The variation magnitude term in the above formula , and paternal genetic control items , The specific expression is as follows:

[0236] (31)

[0237] In the formula, and The first The first paternal genetic control term and the second paternal genetic control term in each iteration cycle; , These are the maximum and minimum values ​​of the first paternal genetic control term, respectively; , These are the maximum and minimum values ​​of the second paternal genetic control term, respectively. and This is a directional control term used to guide the random selection of the direction of gene mutation in offspring during the mutation phase. It balances the "directional guidance strength" and "mutation randomness." The specific value of the directional control term is determined when an obstacle is identified near the USV. and Values ​​are taken within the range of 0.3 to 0.6 to enhance directional guidance; when it is determined that there are no obstacles near the USV, and Values ​​are selected within the range of 0.1 to 0.3 to weaken directional guidance and increase variation diversity. In this embodiment of the invention, the presence of obstacles near the USV can be determined by the USV's own sensing hardware (such as radar) and corresponding control modules. Specifically, if the distance between the USV and obstacles (including other USVs) within 180° of its direction of travel is less than a preset safe distance threshold, then an obstacle is determined to exist; if no obstacle is detected or the distance between the USV and obstacles (including other USVs) within 180° of its direction of travel is greater than or equal to the set safe distance threshold, then the vicinity of the USV is determined to be open water, and no obstacles exist. Based on the corresponding judgment results, the algorithm of this invention randomly adjusts the directional control item within the specified value range. and To retrieve the value.

[0238] If the acceleration and angular velocity variables after the mutation operation exceed their respective maximum values, then the variables exceeding the range need to be replaced with critical values, i.e.:

[0239] (32)

[0240] The improved genetic algorithm of this invention incorporates a mutation magnitude term. , Direction control items Optimal reference control term and paternal genetic control items and This is a novel fusion mutation method. The algorithm adaptively guides the mutation direction using the best parent individual, thereby accelerating the algorithm's convergence speed. In formula (30), the direction control term... , The magnitude of variation determines whether the variation in offspring individuals proceeds in a positive direction. and Paternal genetic control items and and directional control and Together, they determine the upper and lower limits of individual variation. Paternal genetic control terms. and As the number of path cycles increases, offspring individuals gradually reduce their inheritance from their parents. In early planning cycles, maintaining reference to the parent path preserves the unique traits of the parent from the previous cycle, enhancing population diversity and maximizing the search of the solution space. In later planning cycles, linear descent reduces dependence on the parent, generating more superior individuals and gradually bringing the population closer to the optimal solution. The purpose of linear descent is to balance the conflict between early-stage diversity and rapid convergence in later stages. Early planning cycles rely on the parent to preserve its unique traits; a sudden reduction in dependence (e.g., jumping directly from 0.7 to 0.2) would cause the population to abruptly lose the diversity accumulated in the early stages, potentially missing potential optimal solutions. Linear descent aims to gradually reduce dependence, allowing the population to retain some parental characteristics while gradually incorporating new superior traits, achieving a smooth transition from diversity to convergence.

[0241] Optimal reference control term It can always guide the population to evolve in the direction of the best individual, ensuring that the traits of the offspring are controllable within a certain range and avoiding the spacecraft from making ineffective movements.

[0242] The innovation of the adaptive Gaussian mutation operation designed in this invention lies in:

[0243] (1) Adaptively control the mutation direction using the best individual from the parent generation. The best individual from the parent generation is the one closest to the global optimum, and is usually the one that is currently closest to the optimum. Therefore, to address the problem of insufficient mutation ability in genetic algorithms, the mutation operator in the improved genetic algorithm of this invention incorporates the evolutionary idea of ​​particle swarm optimization, allowing offspring individuals to mutate by referring to the direction of the best individual from the previous generation parent, thereby promoting the continuous evolution of the population and improving the global search performance of the algorithm.

[0244] (2) Dynamically control the variation range of different genes in an individual.

[0245] Figure 3 shows the results of applying acceleration and angular velocity variations to the search path of a single USV in this embodiment (the two are not superimposed and only have non-zero values ​​in a specified period). The path only takes the beginning and end points of the period as the simplified navigation trajectory for that period. Paths 1 to 4 represent four different search paths, where paths 2 to 4 are the results of different variations of path 1, with a, b, c, and d representing four consecutive search periods; paths 2 and 3 are respectively the results of path 1 in the specified period. The new path obtained by the variation in angular velocity and acceleration; path 4 is path 1 in the period The result of the angular velocity variation. In Figure 3, , The path direction deflection angle is caused by the variation in angular velocity. The direction of path 2 is deflected. (Corresponding to the directional deflection of path 4), demonstrating the impact of angular velocity variation on path direction; It is the change in path length caused by acceleration variation (corresponding to the length difference between path 3 and the original path 1), reflecting the impact of acceleration variation on path length.

[0246] As can be seen from the comparison of the paths in Figure 3, the effects of acceleration gene and angular velocity gene mutations on the generated paths are significantly different. The magnitude of acceleration mutation directly affects the length of the search path in the current and subsequent cycles, while the magnitude of angular velocity mutation directly affects the direction of the search path in the current and subsequent cycles, and the effect accumulates continuously during the cycle. Comparing paths 2 and 3, it can be seen that under the same cycle, angular velocity mutation has a more significant impact on the search path than acceleration mutation. Therefore, it is necessary to dynamically adjust and control the magnitude of gene mutations using formulas (30) to (32).

[0247] Step 4.4: Merge the set of elite individuals formed in step 4.2 with the set of offspring individuals obtained from mutation in step 4.3 to form a new generation population, and repeat steps 4.1-4.3.

[0248] Step 4.5: Determine whether the iteration termination condition within the current planning cycle has been met. If not, repeat steps 4.1-4.4 until the iteration termination condition within the current planning cycle is met. If yes, select the individual with the highest fitness from the final generation population as the optimal individual, and decode the chromosome of the optimal individual to obtain the optimal pose, optimal control quantity sequence, and corresponding optimal timestamp sequence of each USV at the time of iteration termination, thereby generating the path scheme to be executed in the current planning cycle.

[0249] In this embodiment of the invention, the iteration termination condition of the current planning cycle is any one or a combination of the following: reaching the preset maximum number of iterations, or any USV detecting an underwater target.

[0250] Step 5, Path Execution and Dynamic Programming.

[0251] In this invention, the control unit of the USV unmanned swarm platform monitors the latest actual attitude of all USVs in real time. After obtaining the path scheme to be executed in the current planning cycle, it first immediately determines the detection status of the underwater target, that is, whether there is any USV whose distance from the underwater target is less than or equal to the radius of the USV search domain. ,

[0252] If the control unit receives a "detected underwater target" feedback signal from any USV, it discards the path execution plan for the current planning cycle and terminates subsequent path planning cycles. If the control unit does not receive a "detected underwater target" feedback signal, it generates corresponding path control commands based on the current cycle's path execution plan and sends them to the corresponding USVs to control each USV to execute the corresponding path.

[0253] In other words, during the current planning period or at the end of the current planning period, there exists a USV whose distance from an underwater target is less than or equal to the radius of the USV's search domain. If the underwater target has been detected, the entire search mission is terminated. If the current planning cycle ends and no underwater target has been detected, the actual poses of all USVs at the end of the current planning cycle are used as the initial state of the next planning cycle, and the process returns to step 3 to perform a new round of path planning.

[0254] To verify the effectiveness of the present invention, the following simulation verification was performed in this embodiment:

[0255] In this simulation example, the number of cluster platforms executing the target search task is set to USV in an unmanned cluster, and the number of USVs is... The key parameters of the USV are as follows:

[0256] Communication radius of the USV inter-domain information connectivity The search domain radius of each USV Maximum working speed Maximum linear acceleration Maximum working angular velocity .

[0257] The specific settings for the motion parameters of the underwater target are as follows:

[0258] Maximum speed of underwater targets Maximum acceleration Maximum yaw rate When the target is performing three-dimensional motion, the maximum pitch angular velocity... .

[0259] Considering the real-time requirements of USV unmanned swarms searching for underwater moving targets, the algorithm needs to balance real-time performance and search performance requirements; therefore, the population size is set accordingly. Number of iterations (i.e., iteration period) Set the upper limit of the USV's working cycle (search cycle) based on the USV's endurance. Each search cycle lasts 5 seconds. Path planning is performed on the USV swarm in the simulation example according to the method of this invention. Figure 4 is a two-dimensional simulation screenshot of the process path of the USV swarm completing the underwater target search. It shows the simulation environment of the USV swarm and the initial movement state of the individual swarm members. During the search process, due to the information communication mechanism, the USVs maintain a certain distance from each other in each cycle, avoiding collisions while maximizing their respective search domains, and gradually expanding their search into new unknown spaces. As can be seen from Figure 4, the USV swarm maintains good cooperative formation during the search process, avoids collisions, and systematically covers the search area.

[0260] Figure 5 shows the real-time changes in the distance between each USV and the target during the search process within the USV swarm system. The black dashed line in the figure represents the search radius of the USVs. As can be seen from Figure 5, due to the existence of the information communication mechanism, the swarm advances its search formation towards the target as a whole during the search process, periodically reducing the distance to the target.

[0261] Figure 6 compares the optimization results of the improved genetic algorithm (IGA algorithm) of this invention with those of the traditional genetic algorithm (GA algorithm) and the traditional particle swarm optimization (PSO algorithm), using the time to find the target as the comparison metric. As shown in the timeboxes of Figure 6, the traditional genetic algorithm has an average discovery time of 212.8 seconds and a median of 212.1 seconds, performing the worst among the three algorithms. Its discovery time is the longest and relatively concentrated (mean and median are close), indicating that the traditional genetic algorithm has low search efficiency in solving this cooperative path planning problem, is prone to getting trapped in local optima, and thus has a slow convergence speed. The traditional particle swarm optimization (PSO) algorithm has an average discovery time of 179.5 seconds and a median of 177.3 seconds. PSO has a faster convergence speed and better global exploration capability, but its continuous vector encoding is simple, limiting its guidance capability. The improved genetic algorithm (IGA) of this invention has an average discovery time of 141.4 seconds and a median of 140.8 seconds, making it the best performing of the three algorithms. Its discovery time is the shortest and its distribution is symmetrical (mean and median are almost equal), indicating that the introduction of optimization measures such as three-dimensional double-chain encoding and dynamic partitioning collaboration significantly improves search efficiency and collaborative performance. The close proximity of the IGA's mean and median suggests good algorithm stability and minimal impact from outliers.

[0262] Based on the above analysis, it can be seen that when using the improved genetic algorithm of this invention, the target discovery time box curve has a shorter mean and median, indicating that the mutation direction guidance enables the algorithm to more effectively organize the USV search behavior, reduce random fluctuations in the search process, improve the robustness of the algorithm, and locate the target faster.

[0263] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A collaborative path planning method for underwater target search and tracking by a multi-USV unmanned swarm, characterized in that, Includes the following steps: Step 1, Model Establishment and Constraint Setting; Establish the USV planar motion model and the underwater target motion model, and set constraints for the underwater target motion model and the USV planar motion model; the constraints of the underwater target motion model include its workspace constraints and performance constraints; the constraints of the USV planar motion model include its performance constraints, workspace constraints, and search domain radius. Communication radius of the information connectivity domain within the cluster And collision avoidance constraints between USVs; Step 2, based on the established USV planar motion model, underwater target motion model, and set model constraints, use an improved genetic algorithm to periodically perform path collaborative planning; The process includes the following steps: Step 2.1, Three-dimensional double-stranded encoding and population initialization; Based on the current actual pose state of the USV, a three-dimensional double-stranded encoding method of pose-control quantity-time is used to generate the current initial population; The three-dimensional double-stranded encoding refers to jointly encoding the pose sequence, control quantity sequence, and corresponding timestamp sequence of the USV, so that each USV chromosome in the population contains the pose sequence, control quantity sequence, and corresponding timestamp sequence; Step 2.2, Fitness evaluation and iterative optimization; Step 2.2.1, Using the designed total fitness function The initial population is evaluated to obtain a set of fitness values ​​corresponding one-to-one with each individual in the initial population; the total fitness function The following metrics are used for synchronous optimization: the area of ​​the cluster joint search domain, the degree to which secondary searches are avoided for recently searched areas, and the number of USVs that can maintain information connectivity within the cluster; Step 2.2.2: Based on the fitness value set, an elite preservation strategy is used to select individuals from the initial population to obtain a set of elite individuals to be retained for the next generation; Step 2.2.3: The individuals remaining after the elite selection operation are used as parent individuals, and an adaptive Gaussian mutation operation is performed to generate a set of offspring individuals; Step 2.2.4: The set of elite individuals is merged with the set of offspring individuals to form a new generation population. Steps 2.2.1 to 2.2.3 are executed repeatedly. Step 2.3 generates the optimal path scheme. It is determined whether the iteration termination condition within the current planning cycle has been met. If not, step 2 is repeated until the iteration termination condition within the current planning cycle is met. If so, the individual with the highest fitness value is selected from the final generation population as the optimal individual, and the chromosome of the optimal individual is decoded to obtain the optimal pose sequence, optimal control quantity sequence, and corresponding optimal timestamp sequence of each USV at the time of iteration termination, generating the path scheme to be executed in the current planning cycle. Step 3 executes the path and performs dynamic programming. After obtaining the proposed path, it is immediately determined whether a feedback signal indicating the detection of an underwater target has been received from any USV. If the feedback signal is received, the proposed path is discarded, and instructions are output to control all USVs to confirm the target or coordinate to capture the underwater target, while terminating subsequent path planning cycles. If the feedback signal is not received, the proposed path is sent to the corresponding USV, causing the cluster to move according to the planned path to perform the search. The current actual pose, control variables, and timestamps of all USVs are used as the initial state for the next planning cycle, and the process returns to step 2 to perform a new round of path planning.

2. The method for collaborative path planning of underwater target search and tracking by a multi-USV unmanned swarm according to claim 1, characterized in that, The three-dimensional bichain encoding of pose-control quantity-time in step 2.1 is specifically defined for one search cycle of a single USV as follows: in, Represents any ship In the Individual coded chromosomes within a search cycle This indicates that the USV was in the Linear acceleration sequence within a search cycle , represents the real chain in a doubly chained encoding; This indicates that the USV was in the angular velocity sequence within a search cycle , representing the imaginary chain in doubly chained encoding; This indicates that the USV was in the A timestamp sequence within a search cycle ； The number of control steps within the cycle; and They represent the first The linear acceleration and angular velocity of each control step. Indicates the first The timestamp corresponding to each control step.

3. The method for collaborative path planning of underwater target search and tracking by a multi-USV unmanned swarm according to claim 1 or 2, characterized in that, Step 2.1, generating the current initial population, specifically includes: Classification and updating of the working sea area value: Before executing the search mission, an initial area value analysis map is received from the shore-based or command system based on acquired prior information; according to the initial area value analysis map, the working sea area to be searched is pre-divided into high-value areas and ordinary areas. The high-value areas include unsearched areas and areas where the probability of target presence is higher than a preset threshold, while the ordinary areas are other working sea areas besides the high-value areas; and initial weights are assigned to the high-value areas and the ordinary areas based on historical search data; after the search mission begins, the weights are updated according to the actual search data of the unmanned surface vessel cluster. The system retrieves feedback data, dynamically adjusts the weights of each region, and updates the region division. Specifically, if any region has been effectively searched, the confidence period interval for the searched region is updated based on historical search data. Based on the updated confidence period interval and the region's search status, the real-time value weight of that region is recalculated. Based on the real-time value weights of each region, high-value and ordinary regions in the working sea area are dynamically redefined. The confidence period interval is defined as follows: if a region has been searched and identified as a high-safety region within a certain historical search period, then the historical search interval is defined as the confidence period interval. Initial linear acceleration value generation: In Within a certain range, the initial value of the linear acceleration is selected according to a Gaussian distribution probability. Specifically, in the ordinary region, the mean value of the initial linear acceleration is set. The initial linear acceleration value is set to 0 to guide the initial movement direction of the population towards high-value areas, avoiding ineffective energy consumption; the mean value of the initial linear acceleration value is set in the high-value area. The offset is positive, and its magnitude is: in, Energy consumption coefficient; Energy consumption per unit time; This is a stability correction coefficient, ranging from 0.8 to 1.0, used to balance the fluctuations of the Gaussian distribution and avoid sudden acceleration changes; The maximum linear acceleration of the USV is defined as follows: During the USV's journey towards the high-value area, the angle between its linear acceleration direction and the line connecting the USV's current position and the center of the high-value area remains less than 90°. Initial angular velocity generation: Based on the distance between the USV and obstacles, an adaptive uniform distribution is used to dynamically adjust the sampling range of the initial angular velocity value for obstacle avoidance. Initial timestamp sequence generation: For USV pairs with initial position distances less than a safety threshold, a fixed time difference is introduced into the timestamp sequence encoded by one of the USVs to achieve collision avoidance on the initial path.

4. The multi-USV unmanned swarm cooperative path planning method for underwater target search and tracking according to claim 3, characterized in that, in the step of generating the initial angular velocity value, if the distance between the current position of the USV and the nearest obstacle is greater than or equal to a set safe distance threshold, then in Within the sampling range, an adaptive uniform distribution strategy is used to determine the initial value of the angular velocity; if the distance between the current position of the USV and the nearest obstacle is less than the safe distance threshold, the sampling range is narrowed to... ;in, This is the maximum angular acceleration of the USV.

5. The method for collaborative path planning of underwater target search and tracking by a multi-USV unmanned swarm according to claim 4, characterized in that, The degree to which secondary searches are avoided in recently searched areas, as described in step 2.2.1, is evaluated using the following method: defining a confidence time interval. This indicates the time interval corresponding to the recently searched area; where the underwater target velocity information is unknown, The value is taken in the range of 2 to 4; when velocity estimation information for the underwater target exists, then [the value is taken as 4]. ,in The maximum speed of the USV The maximum speed of the underwater target. To optimize the coefficients, The value ranges from 0.7 to 1; calculate the first... The joint search area of ​​all USVs under the time-planned path, and the first The overlapping area between all historical joint search areas of USVs under the planning path at any time; the smaller the overlapping area, the more effectively the recently searched areas are avoided in the path planning.

6. The method for cooperative path planning for underwater target search and tracking by a multi-USV unmanned swarm according to claim 5, characterized in that, In step 2.2.1, the total fitness function The specific expression is: In the formula, The defined confidence time interval; Indicates the first The fitness function of the area of ​​the joint search domain of all USVs at time 1. Indicates the first The fitness function for the area of ​​the joint search domain of all USVs at time t; This means that the distance between any two USVs is greater than the communication radius of the information connectivity domain within the cluster. USV, Number it; This indicates the number of USVs participating in the target search task; 、 、 These are constant coefficients with different values, and In the initial stage of the search task, the values ​​of the three constant coefficients satisfy... In the later stages of the search mission, in order to balance the communication needs of high-value areas and USVs, and The value of gradually increases, but does not exceed . 。 7. The method for cooperative path planning for underwater target search and tracking by a multi-USV unmanned swarm according to claim 6, characterized in that, In step 2.2.3, the adaptive Gaussian mutation operation is performed by an adaptive mutation operator guided by the optimal parent individual. This adaptive mutation operator causes the mutation direction of the offspring individual to reference the direction of the corresponding gene in the optimal parent individual. The expression for the adaptive mutation operator for each USV individual in each iteration cycle is: In the formula, and The optimal reference control term is used to reference the optimal solution of the previous iteration. The first 60% of iterations are defined as the early stage of the algorithm. Considering the high requirements for population diversity in the early stage of the algorithm, the optimal reference control term takes a value of 0.2 to 0.

3. The last 40% of iterations are defined as the late stage of the algorithm. Considering that the population tends to converge in the late stage of the algorithm, the optimal reference control term takes a value of 0.4 to 0.

5. 、 The first The 1st iteration cycle The linear acceleration and angular velocity genes of each individual; 、 The first The linear acceleration gene and angular velocity gene of the optimal path solution for each iteration cycle; 、 、 、 All are random real numbers in the range [0,1]; if after the mutation operation, the first... In the nth iteration cycle, the th If the specific values ​​of an individual's acceleration gene and angular velocity gene exceed the maximum acceleration and maximum angular velocity of the USV, then the maximum acceleration and maximum angular velocity will be used to replace the corresponding values ​​that exceed the range. In the formula, and These are the maximum linear acceleration and maximum angular velocity of the USV, respectively. and They represent the first The 1st iteration cycle The linear acceleration and angular velocity genes of each individual; and The variation magnitude term of the mutation operator is expressed as follows: and The first The specific expressions for the first and second paternal genetic control terms in each iteration cycle are as follows: In the formula, 、 These are the maximum and minimum values ​​of the first paternal genetic control term, respectively; 、 These are the maximum and minimum values ​​of the second paternal genetic control term, respectively; This represents the maximum number of iterations. and As a direction control term, it is used to make the offspring individuals randomly select the direction of gene mutation during the mutation stage. This can both make the mutation direction of the offspring individuals refer to the direction of the best parent individuals and ensure the randomness of the offspring individuals' mutation. and The method for determining the value is as follows: when it is determined that there is an obstacle near the USV, and Values ​​are taken within the range of 0.3 to 0.6 to enhance directional guidance; when it is determined that there are no obstacles near the USV, and Values ​​are taken within the range of 0.1 to 0.3 to reduce directional guidance and increase the diversity of variation.

8. The method for collaborative path planning of underwater target search and tracking by a multi-USV unmanned swarm according to claim 1, characterized in that, The USV planar motion model established in step 1 is as follows: In the formula, The first in the Earth system Position of the USV; Indicates the first The location coordinates of the USV It is always 0; For the first The horizontal yaw angle of the USV; The first in the velocity system The speed of the USV; For the first USV along Translational speed of the axis; For the first USV around Angular velocity of the axis; For the first The linear acceleration of the USV.

9. The method for cooperative path planning for underwater target search and tracking by a multi-USV unmanned swarm according to claim 5, characterized in that, The underwater target motion model established in step 1 is a three-dimensional kinematic model, used to estimate the target motion state to determine whether the USV unmanned swarm has detected the underwater target, and to assist in calculating the confidence time interval; the three-dimensional kinematic model of the underwater target is: in, This indicates the pose of an underwater target within a terrestrial system. Indicates the position coordinates of the underwater target. Indicates the horizontal yaw angle of an underwater target. This indicates the pitch angle of an underwater target on the depth surface of the sea area; Represents the velocity of an underwater target in the velocity frame. Indicates underwater target along Translational speed of the axis, Indicates underwater target orbiting angular velocity of the axis, Indicates underwater target orbiting Angular velocity of the axis; This represents the linear acceleration of an underwater target.

10. The method for cooperative path planning for underwater target search and tracking by a multi-USV unmanned swarm according to claim 9, characterized in that, The constraints of the underwater target motion model are as follows: Workspace constraint: The underwater target moves in a known sea area, and a maximum diving depth range is set according to its own pressure-bearing capacity: In the formula, and These are the known sea areas in Minimum and maximum values ​​in the direction; and These are the known sea areas in Minimum and maximum values ​​in the direction; It is the maximum underwater working depth of the underwater target. Performance constraints: Based on the underwater target's own performance range, set upper limits for velocity, acceleration, and linear acceleration. In the formula, It is the upper limit of the underwater target's own speed; Is it an underwater target? Maximum angular velocity of the shaft; Is it an underwater target? Maximum angular velocity of the shaft; This is the maximum linear acceleration of the underwater target; the constraints of the USV planar motion model are: isomorphic platform constraint: all USVs participating in the search mission in the cluster are of the same model, and all performance indicators are consistent; search capability constraint: each USV has a fixed detection capability, the search domain of the USV is a sphere, and the center of the sphere is the center of mass of the USV; the radius of the search domain is... When an underwater target enters the search area of ​​the USV, the USV is considered to have successfully detected the underwater target. in, Indicates the first The location coordinates of the USV Represents the position coordinates of the underwater target; Information connectivity constraints: To maintain cluster collaboration, each USV participating in the search task maintains communication, achieving the search for underwater targets through information exchange and collaboration; When the information transmission object of any USV is another USV on the water surface, it is assumed that the shape of the surface information exchange domain of each USV is a planar circle, with the centroid of the USV as the center of the information connectivity domain, and the communication radius of the information connectivity domain is... When the distance between two USVs does not exceed the communication radius of the information connectivity domain. At that time, it was assumed that the two USVs could sense each other and freely exchange information; performance constraints: due to the structural limitations of the USVs themselves, there are upper limits on their speed, linear acceleration, and angular velocity during navigation, namely: in, 、 、 These represent the USV's maximum translational velocity, maximum acceleration, and maximum angular velocity, respectively; Workspace constraints: The USV searches for underwater targets within a two-dimensional bounded ocean area where underwater targets have been observed. In the formula, and They represent USV's Axis coordinates and Axis coordinates and These are the known sea areas in Minimum and maximum values ​​in the direction; and These are the known sea areas in Minimum and maximum values ​​for direction; USV collision avoidance constraints: To prevent collisions between USVs during the search process, the distance between any two USVs must be greater than the set safety distance. ： Where, in the formula, express The distance between any two USVs at any given time; and Indicates the first ships Horizontal coordinates and express The horizontal coordinates, where, ； This represents the safe distance between any two USVs.

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