Multi-robot maritime patrol path planning method based on immune algorithm optimization

Abstract

The invention relates to a multi-robot maritime patrol path planning method based on immune algorithm optimization, and the method comprises the steps: S1, randomly initializing a binary coded population matrix, and calculating a corresponding target function value; s2, recombining each individual in the population matrix into a basis matrix; s3, iteration is carried out, and a random weight matrix, a query matrix and a key matrix are generated; s4, calculating an attention matrix, and obtaining an attention probability vector of each gene position of each individual; s5, calculating the Jaccard similarity coefficient and the Hamming similarity of each individual in the population matrix, and generating a similarity matrix; s6, the mutation probability is adjusted; s7, performing random flipping variation on each gene position of each individual; s8, combining the variation individuals with the current population matrix, and updating the population matrix; and S9, if iteration reaches the maximum number of iterations or a preset convergence condition, outputting a current population matrix, and generating a multi-robot patrol path planning scheme according to the population matrix. Compared with the prior art, the method is suitable for multi-robot path planning in a complex environment.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-robot maritime patrol path planning, and in particular to a multi-robot maritime patrol path planning method based on immune algorithm optimization. Background Art

[0002] As a heuristic optimization algorithm based on the biological immune system, the immune algorithm simulates the learning and memory functions of the immune system in organisms and possesses strong global search capabilities and adaptability. In the multi-robot maritime patrol problem, the immune algorithm also encounters many complex constraints due to the large-scale ship search and the need to consider a large number of conflicting objectives. Furthermore, in multi-robot scenarios, the number of robot groups also scales with the problem size, causing the optimization difficulty of the evolutionary algorithm to increase exponentially. Therefore, it is crucial to design an evolutionary algorithm that can simultaneously handle large-scale problems with conflicting decision variables and objective functions.

[0003] Currently, there are three main types of algorithms for large-scale multi-objective optimization problems: decomposition-based algorithms, dimensionality reduction-based algorithms, and deep learning-based algorithms. Decomposition-based algorithms typically break down large-scale problems into multiple small-scale sub-problems, but how to effectively transfer and integrate the optimization results of each sub-problem remains to be solved. Dimensionality reduction-based algorithms simplify the problem by reducing the dimensions of the decision variables or objective function, but the dimensionality reduction process often results in the loss of some important information, and the total amount lost is even higher in large-scale problems. Although deep learning-based algorithms improve the accuracy of evolution by learning population characteristics and then training, the large number of decision variables results in excessive training resources.

[0004] Chinese patent application CN118760172A discloses a multi-robot path planning method, device, and medium based on a multi-objective immune optimization algorithm. The method comprises: S1. Map modeling of the park scene, abstracting the exhibition hall area and inaccessible areas as convex polygonal obstacles, and initializing robot stations and patrol points; S2. Mathematically modeling the multi-robot patrol problem in the exhibition park, using the total patrol path length and the standard deviation of the path lengths between robots as objective functions; S3. Based on the map modeling information of the park scene, a PCM-VRAOA algorithm is used to calculate a path cost matrix; the path cost matrix stores the obstacle avoidance nodes and path lengths between all patrol points; S4. Optimizing the path cost matrix using a multi-objective immune algorithm, outputting the multi-robot patrol path planning results for the exhibition park. This invention aims to provide a robot patrol path planning method for the exhibition park with low computational complexity, capable of handling convex polygonal obstacles and dense human traffic. It is not suitable for offshore environments. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a multi-robot maritime patrol path planning method based on immune algorithm optimization.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A multi-robot maritime patrol path planning method based on immune algorithm optimization, the method comprising:

[0008] Step S1, randomly initializing a binary-coded population matrix and calculating the corresponding objective function value, where each row of the population matrix represents an individual, and the individual represents a multi-robot patrol path solution. The objective function includes the total length of the patrol path, energy consumption, and time urgency;

[0009] Step S2, reorganize each entity in the population matrix into a basis matrix;

[0010] Step S3, entering iteration, generating a random weight matrix, and constructing a query matrix and a key matrix based on the base matrix and the random weight matrix;

[0011] Step S4, calculating an attention matrix based on the query matrix and the key matrix, and averaging the attention matrix by column to obtain an attention probability vector for each gene position of each individual;

[0012] Step S5, calculating the Jaccard similarity coefficient and Hamming similarity of each individual in the population matrix to generate a similarity matrix;

[0013] Step S6, adjusting the mutation probability according to the confidence formula;

[0014] Step S7, performing random flip mutation on each gene position of each individual based on the adjusted mutation probability;

[0015] Step S8, merging the mutant individuals with the current population matrix, and updating the population matrix through non-dominated sorting and environmental selection;

[0016] Step S9: If the iteration does not reach the maximum number of iterations or the preset convergence condition, return to step S3; otherwise, output the current population matrix and generate a multi-robot patrol path planning scheme based on the population matrix.

[0017] Furthermore, in step S1, the objective function is:

[0018] min f=(f1,f2,f3)

[0019]

[0020]

[0021] Among them, f1 represents the total length of the patrol path, f2 represents the energy consumption, f3 represents the time urgency, m represents the number of robots, and n represents the number of patrol points. represents the path length of robot k from patrol point i to patrol point i+1, E k represents the total energy consumed, represents the actual time when robot k arrives at patrol point i;

[0022]

[0023] in, represents the movement energy consumption of robot k, represents the operating energy consumption of robot k, represents the standby energy consumption of robot k, a, β, and r are all energy consumption coefficients; v k represents the moving speed of robot k; L k represents the load of robot k; represents the time for robot k to perform tasks at patrol point i, p k is the power consumption of robot k; represents the time during which robot k does not perform tasks during patrol; p idle represents the standby power of robot k, represents the expected arrival time of patrol point i; w i Indicates the priority of each patrol point task.

[0024] Furthermore, the constraints of the objective function include:

[0025]

[0026] in, Indicates whether robot k visits patrol point i;

[0027]

[0028] in, Indicates whether robot k starts from the starting point; Indicates whether robot k returns to the starting point;

[0029]

[0030] Among them, D max Indicates the upper limit of the robot's moving distance;

[0031] E k ≤E max

[0032] T k ≤T max

[0033] L k ≤L max

[0034] Among them, E max 、T max 、L max They represent the upper limit of the robot's energy consumption, the upper limit of the key patrol points that can be visited within a certain period of time, and the maximum carrying capacity of each robot.

[0035]

[0036] Among them, p k (t) represents the position of robot k at time t; d safe Indicates the minimum safe distance between robots;

[0037]

[0038] Among them, δ represents the balance tolerance of task allocation.

[0039] Furthermore, in step S2, the base matrix is constructed by converting the individual codes into a two-dimensional matrix, where each row of the two-dimensional matrix represents the genetic information corresponding to a robot, including the patrol point sequence, path angle, and load parameters.

[0040] Furthermore, in step S3, the dimension of the weight matrix matches the base matrix, and the weight values in the weight matrix are randomly generated.

[0041] Furthermore, in step S4, the calculation expression of the attention matrix is:

[0042]

[0043] Among them, Q i is the query matrix, K i is the key matrix, d i Represents the dimension of the matrix;

[0044]

[0045] Among them, b P，V Represents the P gene position of the V ship, A random value representing the weight.

[0046] Furthermore, in step S3, the calculation expression of the attention probability vector is:

[0047]

[0048] Among them, A i (s,t) is the attention matrix A i The value in the sth row and tth column of , where P is the number of individuals in the population.

[0049] Furthermore, in step S5, the expression of the Jaccard similarity coefficient is:

[0050]

[0051] The expression of Hamming similarity is:

[0052]

[0053] Among them, x and y are individual codes, and n is the gene length.

[0054] Furthermore, in step S6, the confidence formula is:

[0055] C(x,y)=γ*J(x,y)+(1-γ)*H(x,y)

[0056] Among them, γ is a weight parameter used to balance the influence of Jaccard similarity coefficient and Hamming similarity, x and y are individual codes, H(x,y) is the Hamming similarity, and J(x,y) is the Jaccard similarity coefficient.

[0057] Furthermore, in step S6, the expression of mutation probability is:

[0058]

[0059] Among them, C(x,y) is the confidence level, is the attention probability vector.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 1. This invention dynamically calculates the importance weights of gene positions through a self-attention mechanism, assigning higher mutation probabilities to key gene positions, enabling the algorithm to quickly focus on optimizing key areas, thereby significantly accelerating the convergence process. At the same time, by combining the Jaccard similarity coefficient and Hamming similarity, the confidence of the mutation probability is dynamically adjusted to balance the similarities and differences between individuals within the population. This collaborative strategy avoids the premature convergence caused by excessive similarity in traditional immune algorithms and prevents the dispersion of search directions caused by random mutations, thereby achieving a dual improvement in convergence speed and solution quality in multi-objective optimization problems. Experiments show that compared with traditional algorithms based on decomposition or dimensionality reduction, this invention can improve the Pareto front coverage by approximately 30% under the same number of iterations, and improve the distribution uniformity of the solution set by more than 25%;

[0062] 2. Through a non-dominated sorting and environment selection mechanism, the algorithm prioritizes non-dominated solutions under conflicting objectives during iterations, and combines this with a crowding comparison strategy to select evenly distributed individuals. Furthermore, a balanced task allocation constraint ensures a relatively balanced load across robots, preventing excessively long paths or excessive energy consumption for individual robots. This design enables the algorithm to consistently output a diverse set of Pareto solutions in complex search spaces, adapting to dynamic environmental changes.

[0063] 3. Compared to deep learning algorithms that rely on large-scale data training, this invention is based on the immune algorithm framework and requires only binary-coded population initialization and lightweight matrix operations. It does not require high-performance hardware support such as GPUs. By introducing a random weight matrix, the algorithm can still effectively explore the search space under limited computing resources. It is suitable for edge computing devices or resource-constrained offshore platforms.

[0064] 4. This invention enhances task execution safety and collaborative efficiency by implementing real-time constraints on the minimum safe distance between robots to avoid collision risks caused by path intersections. By incorporating priority weights into time-criticality objectives, path planning strategies can be dynamically adjusted based on task urgency. For example, in disaster emergency scenarios, delayed visits to high-priority patrol points will be significantly penalized, driving robots to respond quickly.

[0065] 5. The algorithm framework of this invention is highly modular. Users can adjust optimization objectives or modify constraint thresholds according to specific scenarios. The objective function and constraints are customizable, and the weight parameters support dynamic adjustment to balance the contribution ratio of Jaccard and Hamming similarity to adapt to the needs of populations of different sizes. This feature makes it scalable to multi-robot collaborative tasks in warehousing and logistics, environmental monitoring, and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flow chart of the method of the present invention;

[0067] Figure 2 A schematic diagram of the coding structure of the present invention;

[0068] Figure 3 FIG. 1 is a diagram showing the path planning results for a scenario with ten ships according to an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0070] Example 1

[0071] This embodiment intends to disclose a multi-robot maritime patrol path planning method based on immune algorithm optimization. Figure 1 As shown, the specific method steps include:

[0072] S1, randomly initialize the binary-coded population matrix and calculate the corresponding objective function value. Each row of the population matrix represents an individual, and the individual represents a multi-robot patrol path plan. The objective function includes the total length of the patrol path, energy consumption, and time urgency;

[0073] S2, reorganize each individual in the population matrix into a basis matrix;

[0074] S3, enters the iteration, generates a random weight matrix, and constructs the query matrix and key matrix based on the base matrix and the random weight matrix;

[0075] S4, calculate the attention matrix based on the query matrix and the key matrix, and average the attention matrix column by column to obtain the attention probability vector of each gene position of each individual;

[0076] S5, calculating the Jaccard similarity coefficient and Hamming similarity of each individual in the population matrix to generate a similarity matrix;

[0077] S6, adjust the mutation probability according to the confidence formula;

[0078] S7, random flip mutation is performed on each gene position of each individual based on the adjusted mutation probability;

[0079] S8, merge the mutant individuals with the current population matrix, and update the population matrix through non-dominated sorting and environmental selection;

[0080] S9: If the iteration does not reach the maximum number of iterations or the preset convergence condition, return to S3; otherwise, output the current population matrix and generate a multi-robot patrol path planning scheme based on the population matrix.

[0081] In the multi-robot maritime patrol path planning problem, the total patrol path length (f1), energy consumption (f2) and time urgency (f3) constitute a multi-objective optimization problem. In S1, the objective function is:

[0082] min f=(f1,f2,f3)

[0083]

[0084] Among them, f1 represents the total length of the patrol path, f2 represents the energy consumption, f3 represents the time urgency, m represents the number of robots, and n represents the number of patrol points. represents the path length of robot k from patrol point i to patrol point i+1, E k represents the total energy consumed, represents the actual time when robot k arrives at patrol point i;

[0085]

[0086]

[0087] in, represents the movement energy consumption of robot k, represents the operating energy consumption of robot k, represents the standby energy consumption of robot k, a, β, and r are all energy consumption coefficients; v k represents the moving speed of robot k; L k represents the load of robot k; represents the time for robot k to perform tasks at patrol point i, p k is the power consumption of robot k; represents the time during which robot k does not perform tasks during patrol; p idle represents the standby power of robot k, represents the expected arrival time of patrol point i; w i Indicates the priority of each patrol point task.

[0088] Since multiple robots are subject to a series of restrictions such as the robot group itself and the environment when patrolling at sea, some constraints need to be imposed, including ensuring that each patrol point is visited by at least one robot (c1), ensuring that the patrol path of each robot is closed (c2), ensuring that the length of the path searched by each robot does not exceed the upper limit of the robot's movement distance (c3), energy consumption (c4), ensuring that collisions between robots are avoided (c5), and ensuring that the task distribution of each robot is relatively balanced (c6).

[0089] Therefore, the constraints of the objective function include:

[0090] (1) Ensure that each patrol point is visited by at least one robot:

[0091]

[0092] in, Indicates whether robot k visits patrol point i;

[0093] (2) Ensure that each robot's patrol path is closed, that is, the robot starts from the starting point and returns to the starting point:

[0094]

[0095] in, Indicates whether robot k starts from the starting point; Indicates whether robot k returns to the starting point;

[0096] (3) Ensure that the length of the path each robot searches does not exceed the upper limit of the robot's movement distance:

[0097]

[0098] Among them, D max Indicates the upper limit of the robot's moving distance;

[0099] (4) Energy consumption, time urgency and robot load limitations:

[0100] E k ≤E max

[0101] T k ≤T max

[0102] L k ≤L max

[0103] Among them, E max 、T max 、L max They represent the upper limit of the robot's energy consumption, the upper limit of the key patrol points that can be visited within a certain period of time, and the maximum carrying capacity of each robot.

[0104] (5) Ensure that robots avoid collisions:

[0105]

[0106] Among them, p k (t) represents the position of robot k at time t; d safe Indicates the minimum safe distance between robots;

[0107] (6) Ensure that the tasks of each robot are distributed relatively evenly to avoid some robots being overloaded and patrolling overly long paths:

[0108]

[0109] Among them, δ represents the balance tolerance of task allocation.

[0110] The above are the three goals and six constraints in the entire multi-robot maritime patrol path planning.

[0111] In this embodiment, S1 first sets the maximum number of iterations, and then randomly initializes the real number coded population matrix, wherein the specific encoding method is as follows: Figure 2 As shown in the figure, the encoding string of each individual is composed of a sequence variable representing the order of patrol nodes, a numerical variable representing the distance between the patrol node and the ship and the angle formed by the ship, the node and the path, and a categorical variable representing the number of robots used by the robot group to complete the patrol. The maximum number of iterations is set to Iter_max = 100, and the dominant population size N is set to d =100, the size of the clone population N c =50, number of robots m = 5, number of patrol points n = 20, safety distance d safe =10, energy consumption coefficient a=0.8, β=1.2, r=0.5. Antibody population B0, randomly generates ship positions, transmission ranges and storm positions, and sets the dominant antibody population D0, active antibody population A0 and cloned antibody population C0 to be empty. Specific scenario examples are as follows Figure 3 As shown in the figure, the orange nodes are patrolled nodes and the arrows are the patrol routes of the robots. The objective function values f1 (total path length), f2 (total energy consumption), and f3 (time urgency) of each individual are calculated according to the formula.

[0112] In S2, the base matrix is constructed by converting the individual code into a two-dimensional matrix. Each row of the two-dimensional matrix represents the genetic information corresponding to a robot, including the patrol point sequence, path angle, and load parameters. The base matrix is expressed as:

[0113]

[0114] Among them, b P，V Represents the P locus position of the V vessel.

[0115] In S3, the dimension of the weight matrix matches the base matrix, and the weight values in the weight matrix are randomly generated.

[0116] Generate a random weight matrix W i The expression is:

[0117]

[0118] in, A random value representing the weight, d i Represents the dimensions of the matrix.

[0119] Compute the query matrix Q by matrix multiplicationi and the key matrix K i The generation of query matrix and key matrix is based on the basis matrix B i and the random weight matrix W i The product of , we get the query matrix Q of the corresponding population i With the key matrix K i , which can be expressed as follows:

[0120]

[0121] In S4, by calculating the attention matrix A i And average by column to get the attention probability vector p for each gene position i ; According to the attention probability vector p i Dynamically adjust the mutation probability to focus on key gene positions.

[0122] The calculation expression of the attention matrix is:

[0123]

[0124] Among them, Q i is the query matrix, K i is the key matrix, d i represents the dimension of the matrix, is a scaling factor used to stabilize the attention score, while the softmax function normalizes the attention score to a probability distribution

[0125] The calculation expression of the attention probability vector at each genetic position is:

[0126]

[0127] Among them, A i (s,t) is the attention matrix A i The value in the sth row and tth column of , where P is the number of individuals in the population.

[0128] Attention probability vector Each element in represents the importance of each gene position in the population. A higher probability value indicates that the gene position has a greater impact on the optimization target. In this way, It is used to dynamically adjust the mutation probability P(x) of each gene position, so that the algorithm can focus more on key gene positions.

[0129] In S5, the attention probability vector Each element in represents the importance of each gene position in the population. A higher probability value indicates that the gene position has a greater impact on the optimization target. In this way, It is used to dynamically adjust the mutation probability P(x) of each gene position, so that the algorithm can focus more on key gene positions.

[0130] The expression of Jaccard similarity coefficient is:

[0131]

[0132] The expression of Hamming similarity is:

[0133]

[0134] Among them, x and y are individual codes, and n is the gene length.

[0135] For each individual in the population, the Jaccard similarity coefficient and Hamming similarity are calculated with respect to all other individuals, forming two similarity matrices: J(x,y) and H(x,y). Based on the Jaccard and Hamming values, the confidence level of the mutation probability for a particular individual can be determined.

[0136] In S6, the confidence formula is:

[0137] C(x,y)=γ*J(x,y)+(1-γ)*H(x,y)

[0138] Among them, γ is a weight parameter used to balance the influence of Jaccard similarity coefficient and Hamming similarity, x and y are individual codes, H(x,y) is the Hamming similarity, and J(x,y) is the Jaccard similarity coefficient.

[0139] In S6, to ensure that individuals contribute more to population diversity, J and H are each considered as part of the confidence factor. When J and H are inversely proportional, indicating that individuals share many genes, the probability of mutation at different loci is increased, while the probability of mutation at the same loci is maintained. Conversely, the probability of mutation at different loci is decreased, while the probability of mutation at different loci is maintained. For ease of calculation, the confidence factor represents the above properties. Depending on the confidence factor, the expression for the mutation probability is:

[0140]

[0141] Among them, C(x,y) is the confidence level, is the attention probability vector.

[0142] In S7, according to the obtained mutation probability, including the attention probability vector calculated by the self-attention mechanism The mutation probability based on the Jaccard similarity coefficient and the Hamming similarity is randomly mutated, and the mutation is performed in the form of gene bit flipping with the probability of P(x).

[0143] In S8, the algorithm compares the fitness values of individuals in the current population with those of the previous generation to determine whether to retain individuals in the current population. A non-dominated sort is performed on the combined population. Non-dominated sorting divides individuals in the population into multiple strata, with individuals in each stratum having similar fitness across multiple objectives. Based on the results of the non-dominated sorting, the top half of individuals with the highest fitness are selected and retained in the next generation.

[0144] In step S9, if the set number of iterations has been reached, the population is output and the path of the complete robot group is obtained based on the patrol points obtained by each individual. Otherwise, the process returns to step S3 for iteration.

[0145] Example 2

[0146] Based on Example 1, this embodiment provides an electronic device, including: one or more processors and a memory, wherein the memory stores one or more programs, and the one or more programs include instructions for executing the multi-robot maritime patrol path planning method based on immune algorithm optimization as described above.

[0147] At the hardware level, the electronic device includes a processor, an internal bus, a network interface, memory, and non-volatile storage, and may also include other hardware required for its operations. The processor reads the corresponding computer program from the non-volatile storage into the internal memory and then runs it to implement the aforementioned multi-robot maritime patrol path planning method based on immune algorithm optimization. Of course, in addition to software implementation, the present invention does not exclude other implementation methods, such as logic devices or a combination of software and hardware. In other words, the execution of the following processing flow is not limited to individual logic units and can also be hardware or logic devices.

[0148] Memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. Memory is an example of a computer-readable medium.

[0149] Computer-readable media includes permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0150] 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 technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A multi-robot maritime patrol path planning method based on immune algorithm optimization, characterized in that: The method comprises: Step S1, randomly initializing a binary-coded population matrix and calculating the corresponding objective function value, where each row of the population matrix represents an individual, and the individual represents a multi-robot patrol path solution. The objective function includes the total length of the patrol path, energy consumption, and time urgency; Step S2, reorganize each entity in the population matrix into a basis matrix; Step S3, entering iteration, generating a random weight matrix, and constructing a query matrix and a key matrix based on the base matrix and the random weight matrix; Step S4, calculating an attention matrix based on the query matrix and the key matrix, and averaging the attention matrix by column to obtain an attention probability vector for each gene position of each individual; Step S5, calculating the Jaccard similarity coefficient and Hamming similarity of each individual in the population matrix to generate a similarity matrix; Step S6, adjusting the mutation probability according to the confidence formula; Step S7, performing random flip mutation on each gene position of each individual based on the adjusted mutation probability; Step S8, merging the mutant individuals with the current population matrix, and updating the population matrix through non-dominated sorting and environmental selection; Step S9: If the iteration does not reach the maximum number of iterations or the preset convergence condition, return to step S3; otherwise, output the current population matrix and generate a multi-robot patrol path planning scheme based on the population matrix.

2. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S1, the objective function is: min f=(f1,f2,f3) Among them, f1 represents the total length of the patrol path, f2 represents the energy consumption, f3 represents the time urgency, m represents the number of robots, and n represents the number of patrol points. represents the path length of robot k from patrol point i to patrol point i+1, E k represents the total energy consumed, represents the actual time when robot k arrives at patrol point i; in, represents the movement energy consumption of robot k, represents the operating energy consumption of robot k, represents the standby energy consumption of robot k, a, β, and r are all energy consumption coefficients; v k represents the moving speed of robot k; L k represents the load of robot k; represents the time for robot k to perform tasks at patrol point i, p k is the power consumption of robot k; represents the time during which robot k does not perform tasks during patrol; p idle represents the standby power of robot k, represents the expected arrival time of patrol point i; w i Indicates the priority of each patrol point task.

3. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 2 is characterized in that: The constraints of the objective function include: in, Indicates whether robot k visits patrol point i; in, Indicates whether robot k starts from the starting point; Indicates whether robot k returns to the starting point; Among them, D max Indicates the upper limit of the robot's moving distance; AND k ≤E max T k ≤T max L k ≤L max Among them, E max 、T max 、L max They represent the upper limit of the robot's energy consumption, the upper limit of the key patrol points that can be visited within a certain period of time, and the maximum carrying capacity of each robot. Among them, p k (t) represents the position of robot k at time t; d safe Indicates the minimum safe distance between robots; Among them, δ represents the balance tolerance of task allocation.

4. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S2, the base matrix is constructed by converting the individual codes into a two-dimensional matrix, where each row of the two-dimensional matrix represents the genetic information corresponding to a robot, including patrol point sequence, path angle, and load parameters.

5. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S3, the dimension of the weight matrix matches the base matrix, and the weight values in the weight matrix are randomly generated.

6. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S4, the calculation expression of the attention matrix is: Among them, Q i is the query matrix, K i is the key matrix, d i Represents the dimension of the matrix; Among them, b P，V Represents the P gene position of the V ship, A random value representing the weight.

7. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S3, the calculation expression of the attention probability vector is: Among them, A i (s,t) is the attention matrix A i The value in the sth row and tth column of , where P is the number of individuals in the population.

8. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S5, the expression of the Jaccard similarity coefficient is: The expression of Hamming similarity is: Among them, x and y are individual codes, and n is the gene length.

9. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S6, the confidence formula is: C(x,y)=γ*J(x,y)+(1-γ)*H(x,y) Among them, γ is a weight parameter used to balance the influence of Jaccard similarity coefficient and Hamming similarity, x and y are individual codes, H(x,y) is the Hamming similarity, and J(x,y) is the Jaccard similarity coefficient.

10. The multi-robot maritime patrol path planning method based on immune algorithm optimization according to claim 1 is characterized in that: In step S6, the expression of mutation probability is: Among them, C(x,y) is the confidence level, is the attention probability vector.

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