Marine attack and defense game task allocation method for underactuated unmanned surface vehicle

Abstract

The invention relates to an underactuated unmanned ship maritime attack and defense game task allocation method. Comprising the following steps: respectively constructing a total cost function under an attack and defense game task of a single defense unmanned ship to a single attack unmanned ship, an attack and defense game task of a plurality of defense unmanned ships with a limited number to the single attack unmanned ship, and an attack and defense game task of a plurality of defense unmanned ships with an infinite number to the single attack unmanned ship; and a consistent auction algorithm is adopted, a target point is autonomously selected for auction according to comprehensive factors of the distance, the speed and the endurance time between the defense unmanned ship and the attack unmanned ship, the maritime unmanned ship attack and defense game target distribution model is solved, and attack and defense game task distribution of the defense unmanned ship and the attack unmanned ship is realized. According to the method, fine distribution is realized by adopting a clustering algorithm, and the distance is considered as auction cost, so that the configuration of defense resources is more scientific and reasonable, and the efficiency of the whole defense strategy is improved.

Description

Technical Field

[0001] The present invention relates to the field of target allocation for unmanned surface vehicle (USV) maritime attack and defense games, and particularly to a method for task allocation of underactuated USV maritime attack and defense games. Background Art

[0002] In recent years, with the rapid development of unmanned technology and intelligent algorithms, the application of USVs in maritime military operations has become increasingly widespread. As an intelligent device with autonomous navigation and task execution capabilities, USVs have shown great potential in tasks such as maritime reconnaissance, surveillance, anti-submarine warfare, and attack and defense operations. Especially in the scenario of maritime attack and defense games, USVs have become an indispensable part of modern maritime warfare due to their high efficiency, flexibility, and low cost. However, due to the complexity of the marine environment and the underactuated characteristics of USVs themselves, how to effectively allocate tasks to USVs in a dynamic and uncertain environment has become a major challenge in current research. In maritime attack and defense game tasks, the effective allocation of tasks not only needs to fully consider the kinematic constraints of USVs and the dynamic changes of the maritime environment, but also must comprehensively evaluate the strategies of the opposing parties and the optimal utilization of its own resources. At the same time, the requirement for multi-USV cooperative operations has increased the complexity of task allocation, which requires researchers to incorporate more intelligence and adaptability into task allocation strategies to cope with the uncertain marine environment and hostile forces.

[0003] Research on the multi-robot task allocation (MRTA) problem for multi-agent systems has achieved many relevant research results both at home and abroad. E. Schneider adopted a market auction mechanism for the problem of unmanned aerial vehicle task allocation, that is, the "tendering-bidding-winning" process, and carried out task allocation based on the contract net auction algorithm. Li Yan proposed an improved auction algorithm based on the benefits and cost attributes of ships for multi-agent maritime search task allocation. Nunes proposed to use sequential single auctions for allocation for each robot that can maintain its own independent local time network, effectively reducing communication costs. Song Shibing applied the auction algorithm to the problem of joint operation equipment maintenance support task allocation and compared it with the genetic algorithm, proving that the auction algorithm has better convergence. Ye proposed an extended CBBA with task coupling constraints for the multi-task allocation problem with task coupling constraints in heterogeneous multi-unmanned aerial vehicle systems. Chen proposed a local replanning algorithm based on CBBA for how to achieve task reallocation in a dynamic environment. Gao Cheng proposed to extend the task package construction and conflict resolution rules in the extended consistency packet algorithm to eliminate deadlocks for the deadlock problem in the execution of distributed tasks. Choi H L relaxed the limit on the number of robots for each task based on the auction algorithm for tasks that require robot cooperation, added cooperation constraints for robots, and proposed a new scoring mechanism. These algorithms are crucial for target allocation in the process of maritime attack and defense games. However, the existing unmanned boat target allocation methods still have the following deficiencies:

[0004] First, the computational burden and communication overhead of the centralized system are huge, which easily leads to a delay in the system's response time and reduces the efficiency of task execution. Secondly, when facing emergencies, the centralized system lacks sufficient flexibility and robustness, and is prone to problems such as command failure or improper task allocation. In addition, the centralized method responds slowly to the dynamic changes in the environment, which is likely to have an adverse impact on the system.

[0005] Second, in most cases, the existing unmanned boats use the straight-line path distance for fully actuated unmanned boats during the task allocation process, and do not fully consider the kinematic constraint problems caused by the characteristics of underactuated unmanned boats.

[0006] Third, when using the consistency auction algorithm for the existing distributed task allocation strategy, it usually only focuses on the return value of a single defensive unmanned boat and a single attacking unmanned boat, while ignoring the potential interaction between defensive unmanned boats. In a 1-on-1 attack and defense game, this method can be effectively applied, but in a complex multi-on-1 game, defensive unmanned boats need to coordinate their actions to achieve the best defense, and the existing algorithms fail to effectively handle this cooperation, which may lead to the inability to fully utilize the collective potential of defensive unmanned boats. Summary of the Invention

[0007] To solve the above problems, the technical solution adopted by the present invention is as follows: A method for task allocation in the offensive and defensive game of underactuated unmanned boats at sea, comprising the following steps:

[0008] Obtain the quantities and position information of the defensive unmanned boats and the attacking unmanned boats;

[0009] Construct an offensive and defensive game target allocation model for unmanned boats at sea;

[0010] Respectively construct total cost functions for the offensive and defensive game tasks of a single defensive unmanned boat against a single attacking unmanned boat, multiple limited-number defensive unmanned boats against a single attacking unmanned boat, and multiple infinite-number defensive unmanned boats against a single attacking unmanned boat;

[0011] In the case of the offensive and defensive game task of a single defensive unmanned boat against a single attacking unmanned boat, adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defensive unmanned boat and the attacking unmanned boat, and solve the offensive and defensive game target allocation model for unmanned boats at sea to achieve the offensive and defensive game task allocation for the defensive unmanned boats and the attacking unmanned boats;

[0012] In the case of the offensive and defensive game tasks of multiple limited-number defensive unmanned boats against a single attacking unmanned boat and multiple infinite-number defensive unmanned boats against a single attacking unmanned boat,

[0013] When dealing with the offensive and defensive game task of multiple limited-number defensive unmanned boats against a single attacking unmanned boat, taking the target protection area as the center, divide the defender area, the attacker area near zone, and the attacker area far zone;

[0014] In the attacker area far zone, allocate 2 defensive unmanned boats to each detected attacking unmanned boat, and in the attacker area near zone, allocate 3 defensive unmanned boats to each detected attacking unmanned boat, and adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defensive unmanned boat and the attacking unmanned boat to achieve the offensive and defensive game task allocation for the defensive unmanned boats and the attacking unmanned boats;

[0015] When dealing with the offensive and defensive game task of multiple infinite-number defensive unmanned boats against a single attacking unmanned boat, apply the nearest neighbor clustering algorithm based on the greedy strategy to the offensive and defensive game task of unmanned boats at sea, classify adjacent defensive unmanned boats into one category, and based on the clustering center, adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defensive unmanned boat and the attacking unmanned boat to achieve the offensive and defensive game task allocation for the defensive unmanned boats and the attacking unmanned boats.

[0016] Furthermore, the general mathematical model of the offensive and defensive game target allocation model for the unmanned surface vehicle is as shown in Equations (1)-(4):

[0017]

[0018] Define the index set as and In Equation (1), x ij ∈{0,1} is the decision vector. When x ij = 1, it means that the attacking unmanned surface vehicle β j is allocated to the defensive unmanned surface vehicle α i ; when x ij = 0, it means that the attacking unmanned surface vehicle β j is not allocated to the unmanned surface vehicle α i ; represents the task sequence executed by the defensive unmanned surface vehicle α i . If the k-th task executed by the defensive unmanned surface vehicle α i is β j , then the k-th element of p i is j. If the defensive unmanned surface vehicle α i has no task to execute, then the ordered task set is In Equation (1), the benefit function c ij (x i , p i ) is a non-negative function of the decision vector x ij and the task sequence p i . It is the benefit obtained by the defensive unmanned surface vehicle α i bidding for the attacking unmanned surface vehicle β i according to p j . When x ij = 0, c ij (x i , p i ) = 0; the summation term in the parentheses represents the local reward of the defensive unmanned surface vehicle α i .

[0019] Furthermore, when the number of defensive unmanned surface vehicles is equal to the number of attacking unmanned surface vehicles, the total cost function of the offensive and defensive game target allocation model for the unmanned surface vehicle includes a voyage cost function and a performance cost function. The weight of the voyage cost function is 0.3, and the performance cost function is 0.7.

[0020] Furthermore, for the offensive and defensive game tasks of multiple limited defensive unmanned surface vehicles against a single attacking unmanned surface vehicle and multiple infinite defensive unmanned surface vehicles against a single attacking unmanned surface vehicle, the total cost function adopts the voyage cost function. The construction process of the voyage cost function is as follows:

[0021] For the mission assignment of each unmanned boat, the initial position coordinates and heading angle of the defensive unmanned boat are A(x A , y A , θ1); the position coordinates of the attacking unmanned boat are D(x D , y D , θ2), and the minimum turning radius of the unmanned boat is R min . For a given initial pose, the unmanned boat can turn and sail clockwise or counterclockwise, thus obtaining two trajectories. Therefore, it is necessary to select the shorter one as the shortest Dubins path. The center O2 of the turning circle of the unmanned boat is obtained from the initial pose and the minimum turning radius of the unmanned boat:

[0022]

[0023] The coordinates of the tangent points B and C are:

[0024]

[0025] The optimal trajectory between the defensive unmanned boat and the attacking unmanned boat consists of the circular arc AB, the straight line BC, and the circular arc CD, and the length is:

[0026]

[0027] The length of the chord l corresponding to the central angle ε is:

[0028]

[0029] Then the position coordinates D(x D , y D ) of the attacking unmanned boat are:

[0030]

[0031] The heading angle θ2 of the unmanned boat to reach the first target point is:

[0032]

[0033] Furthermore: The performance cost function includes:

[0034] 4) Performance calculation of the defensive unmanned boat:

[0035] Performance of the defensive unmanned boat: Set the speed of the defensive unmanned boat as v d and the endurance time as t d , and calculate the comprehensive performance of the defensive unmanned boat as:

[0036]

[0037] 5) Performance calculation of the attacking unmanned boat:

[0038] Performance of the attacking unmanned boat: Set the speed of the attacking unmanned boat as v a and the endurance time as t a , and calculate the comprehensive performance of the attacking unmanned boat as:

[0039]

[0040] 6) Comprehensive performance index:

[0041] The comprehensive performance of the defense mission is defined based on the ratio of the comprehensive performance of the defense unmanned boat and the attacking unmanned boat, and the specific calculation is as follows.

[0042]

[0043] Furthermore: The nearest neighbor clustering algorithm based on the greedy strategy is applied to the unmanned boat's maritime attack and defense game mission. The process of classifying adjacent defense unmanned boats into one category is as follows:

[0044] First, statistics and initialization are performed on the characteristics of the initial position, speed, direction, etc. of the defense unmanned boats. The position of each defense unmanned boat will be used as the input sample point of the clustering algorithm;

[0045] Set the number of attacking unmanned boats as N, then select K = N sample points as the initial clustering cluster center points, denoted as Each cluster point will be responsible for intercepting the attacking unmanned boat closest to it, thus forming a targeted defense unit;

[0046] Define a distance cost function to evaluate the distance between the defense unmanned boat and the clustering center, as shown in Equation (16), and divide each defense unmanned boat into the area formed by the clustering center closest to it by Formula (17). Thus, the clustering center and the data around it form the initial temporary cluster;

[0047]

[0048] where a is the sample object; c i is the center of the i-th clustering result; M is the overall dimension of the sample object;

[0049]

[0050] Then recalculate the average value of each cluster, continuously change the position of the clustering center, and adjust the samples within the cluster;

[0051] Set the iteration number \(t = 0\), and gradually adjust the clustering results of the defensive unmanned boats until the clustering of all defensive unmanned boats is completed and converges. In each iteration, the cost function will be re-evaluated based on the current clustering results, and the allocation and deployment of the defensive unmanned boats will be optimized to ensure that the configuration of each clustering unit best meets the actual interception requirements. Finally, when the clustering of all defensive unmanned boats reaches a stable state, that is, the cost function converges, the deployment strategy is in the best state;

[0052] For the defensive unmanned boats belonging to the same sub-cluster, according to the new positions and dynamic postures of the attacking unmanned boats, they are adjusted to new cluster centers by Equation (18). The defensive unmanned boats can be more effectively concentrated near the attacking unmanned boats to form a strong defensive front.

[0053]

[0054] Furthermore: The consistency auction algorithm is divided into two stages: the auction stage and the consistency stage. In the auction stage, each defensive unmanned boat first determines whether the attacking unmanned boat target needs to be allocated. If allocation is required, calculate the revenue of the target and bid for the target with the highest revenue; in the consistency stage, a consistency conflict-free rule is established, and the defensive unmanned boats communicate with each other to transfer bidding information, and according to the consistency conflict-free rule, solve the allocation conflict problem between the targets;

[0055] In the auction stage, the defensive unmanned boat determines whether the target needs to be allocated, and defines the variable where \(y\) ij represents the revenue of the defensive unmanned boat \(R\) bidding for the attacking unmanned boat target \(B\), that is, \(y\) ij \(= c\) ij ; is an indicator function, which is true when the equation in the parentheses holds, that is, \(h\) ij \(= 1\), otherwise \(0\). The defensive unmanned boat \(R\) needs to calculate the revenue of all attacking unmanned boat targets \(B\) as \(r\) ij \(= c\) ij \(\cdot h_{ij}\), and select the target \(j\) * as:

[0056] \(j\) * \(= \arg\max c\) ij \((j)\cdot h\) ij (19)

[0057] At this time, \(j\) * is the target with the highest revenue among all the attacking unmanned boats \(B\) bid by the defensive unmanned boat. The revenue of the defensive unmanned boat bidding for the target \(B\) is Therefore, the bidding information of the defensive unmanned boat \(R\) is established as:

[0058] \(z\) ij \(= 1\) (20)

[0059]

[0060] In the consistency stage, after the defensive unmanned boats establish the bidding information, they need to communicate with each other to solve the problem of target allocation conflicts for the defensive unmanned boats. By using the consistency principle, the bidding information of all unmanned boats converges to a unified allocation decision information.

[0061] A method for task allocation in the offensive and defensive game of underactuated unmanned boats on the sea provided by the present invention fully considers the urgency of the offensive and defensive game tasks of unmanned boats on the sea and the challenges of dynamic environmental changes, and deeply explores the target allocation problem. First, considering the actual kinematic characteristics of the underactuated unmanned boats, a cost function based on the Dubins curve is designed to quantitatively describe the distance cost between the defensive unmanned boats and the attacking unmanned boats, and solves the kinematic constraint problem ignored by the cost function based on a straight line. On this basis, the idea of the market auction mechanism is applied to the target allocation problem in the offensive and defensive game tasks of unmanned boats, and a distributed cooperative auction allocation algorithm without a communication center is designed. The defensive unmanned boats independently select target points for bidding according to comprehensive factors such as the distance, speed, and endurance time from the attacking unmanned boats, and complete the allocation by updating information through local communication with neighboring unmanned boats. This method not only reduces the communication bandwidth but also improves the system robustness. In addition, considering the problem of coordinating multiple defensive unmanned boats to protect the target area and prevent the intrusion of a single attacking unmanned boat, based on the traditional distributed cooperative auction allocation algorithm, the nearest neighbor clustering algorithm based on the greedy strategy is applied to the offensive and defensive game tasks of unmanned boats on the sea. The adjacent defensive unmanned boats are grouped into one category, reducing the complexity of target allocation, which can effectively reduce redundancy and conflicts in the allocation process, improve the efficiency of task allocation and the overall performance of the system. The present application has the following advantages:

[0062] First, in the face of the centralized communication method widely adopted by the current unmanned boat formation, the present invention proposes an innovative distributed communication strategy. This strategy abandons the dependence on centralized planning and unified operation communication nodes, reduces the consumption of hardware resources, and improves the accuracy and flexibility of formation control. Under this strategy, each defensive unmanned boat serves as an independent communication node, and through intelligent algorithms, it realizes information interaction and cooperative operation with other unmanned boats to ensure the efficiency and stability of the formation operation.

[0063] Second, compared with the existing unmanned boat task allocation methods, the allocation method designed by the present invention fully considers the kinematic constraint problem caused by the underactuated characteristics of the unmanned boats, making the allocation result closer to the path distance from the unmanned boats to the target points, thereby improving the executability.

[0064] Third, compared with the application of the existing auction algorithm CBAA in the task allocation problem of the unmanned surface vehicle (USV) cluster's maritime attack and defense game, the present invention designs different algorithms for the 1-on-1 and multi-on-1 attack and defense game scenarios respectively. In the 1-on-1 attack and defense game, by comprehensively considering distance and performance as the auction cost, the present invention enhances the resource utilization efficiency, realizes more accurate and efficient task allocation, thereby improving the success rate of single attack and defense confrontation and reducing resource waste. For the complex multi-on-1 game, when the number of defensive USVs is limited, the present invention divides the potential attack area into multiple sub-areas and reasonably allocates defensive resources according to distance and performance, enhancing the coordination ability and collective defense effect of the defensive USVs, reducing the pressure on a single defensive USV, and ensuring the effective interception of multiple attacking USVs. In addition, for the theoretically infinite number of defensive USVs, the present invention uses a clustering algorithm to achieve refined allocation and considers distance as the auction cost, making the configuration of defensive resources more scientific and reasonable and enhancing the effectiveness of the overall defense strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0066] Figure 1 It is a communication topology diagram of the centralized and distributed allocation methods.

[0067] Figure 2 It is a schematic diagram of the Dubins curve path model. (a) is RSL, (b) is LSR, (c) is RSR, (d) is LSR, (e) is RLR, (d) is LRL;

[0068] Figure 3 It is a schematic diagram of the optimal Dubins path.

[0069] Figure 4 It is a result diagram of the K-means clustering algorithm.

[0070] Figure 5 It is a schematic diagram of the attack and defense game task scenario of a single defensive USV against a single attacking USV.

[0071] Figure 6 It is a simulation result diagram of the attack and defense game task of a single defensive USV against a single attacking USV.

[0072] (a) 10 defense unmanned boats vs. 10 attack unmanned boats, (b) 20 defense unmanned boats vs. 20 attack unmanned boats, (c) 30 defense unmanned boats vs. 30 attack unmanned boats;

[0073] Figure 7 It is a schematic diagram of the attack and defense game task scenario of multiple defense unmanned boats against a single attack unmanned boat (the number of defense unmanned boats is limited).

[0074] Figure 8 It is a simulation result diagram of the attack and defense game task of multiple defense unmanned boats against a single attack unmanned boat (the number of defense unmanned boats is limited), (a) 10 defense unmanned boats vs. 4 attack unmanned boats, (b) 20 defense unmanned boats vs. 8 attack unmanned boats, (c) 30 defense unmanned boats vs. 11 attack unmanned boats.

[0075] Figure 9 It is a schematic diagram of the attack and defense game task scenario of multiple defense unmanned boats against a single attack unmanned boat (the number of defense unmanned boats is unlimited).

[0076] Figure 10 It is a simulation result diagram of the attack and defense game task of multiple defense unmanned boats against a single attack unmanned boat (the number of defense unmanned boats is unlimited), (a) 15 defense unmanned boats vs. 4 attack unmanned boats, (b) 21 defense unmanned boats vs. 8 attack unmanned boats, (c) 28 defense unmanned boats vs. 12 attack unmanned boats. Specific implementation manner

[0077] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and in combination with the embodiments.

[0078] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way limits the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0079] An underactuated unmanned boat maritime attack and defense game task allocation method includes the following steps:

[0080] S1: Obtain the number and position information of defense unmanned boats and attack unmanned boats;

[0081] S2: Construct an attack-defense game target allocation model for unmanned surface vessels;

[0082] S3: Respectively construct the total cost functions under the attack-defense game tasks of a single defense unmanned surface vessel against a single attack unmanned surface vessel, multiple limited-number defense unmanned surface vessels against a single attack unmanned surface vessel, and multiple infinite-number defense unmanned surface vessels against a single attack unmanned surface vessel;

[0083] S4: Under the attack-defense game task of a single defense unmanned surface vessel against a single attack unmanned surface vessel, adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defense unmanned surface vessel and the attack unmanned surface vessel, and solve the attack-defense game target allocation model for unmanned surface vessels to achieve the attack-defense game task allocation for the defense unmanned surface vessel and the attack unmanned surface vessel;

[0084] S5: Under the attack-defense game tasks of multiple limited-number defense unmanned surface vessels against a single attack unmanned surface vessel and multiple infinite-number defense unmanned surface vessels against a single attack unmanned surface vessel,

[0085] S6: When it comes to the attack-defense game task of multiple limited-number defense unmanned surface vessels against a single attack unmanned surface vessel, with the target protection area as the center, divide the defender area, the near attacker area, and the far attacker area;

[0086] In the far attacker area, allocate 2 defense unmanned surface vessels to each detected attack unmanned surface vessel, and in the near attacker area, allocate 3 defense unmanned surface vessels to each detected attack unmanned surface vessel, and adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defense unmanned surface vessel and the attack unmanned surface vessel to achieve the attack-defense game task allocation for the defense unmanned surface vessel and the attack unmanned surface vessel;

[0087] S7: When it comes to the attack-defense game task of multiple infinite-number defense unmanned surface vessels against a single attack unmanned surface vessel, apply the nearest neighbor clustering algorithm based on the greedy strategy to the attack-defense game task of unmanned surface vessels at sea, group adjacent defense unmanned surface vessels into one category, and based on the clustering center, adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defense unmanned surface vessel and the attack unmanned surface vessel to achieve the attack-defense game task allocation for the defense unmanned surface vessel and the attack unmanned surface vessel.

[0088] The construction of the attack-defense game target for unmanned surface vessels is as follows:

[0089] This application sets the main body executing the task as a group of N uA set A = {ai|i = 1, 2…Nu} consisting of Nu defense unmanned boats, and a set T = {βj|j = 1, 2…Nt} consisting of Nt attack unmanned boats. The decision-making objective of the allocation is to optimize the task allocation between multiple defense unmanned boats and attack unmanned boats through a distributed consensus auction algorithm, ensuring that each defense unmanned boat can effectively respond to the threat of a specific attack unmanned boat and achieve comprehensive protection of the target area. At the same time, the algorithm should effectively coordinate the resource usage of defense unmanned boats, avoid duplicate resource allocation or idleness, maximize the defense effect, and improve the overall defense efficiency. The general mathematical model constructed is as shown in equations (1)-(4):

[0090]

[0091] Define the index set as and In equation (1), x ij ∈{0, 1} is the decision vector. When x ij = 1, it means that the attack unmanned boat β j is allocated to the defense unmanned boat α i ; when x ij = 0, it means that the attack unmanned boat β j is not allocated to the unmanned boat α i ; represents the task sequence executed by the defense unmanned boat α i . If the k-th task executed by the defense unmanned boat α i is β j , then the k-th element of p i is j. If the defense unmanned boat α i has no task to execute, then the ordered task set is In equation (1), the revenue function c ij (x i , p i ) is a non-negative function of the decision vector x ij and the task sequence p i . It is the benefit obtained by the defense unmanned boat α i bidding for the attack unmanned boat β i according to p j . When x ij = 0, c ij (x i , p i ) = 0; the summation term in the parentheses represents the local reward of the defense unmanned boat α i .

[0092] When the number of defense unmanned boats is equal to the number of attack unmanned boats, the total cost function of the offensive and defensive game target allocation model of maritime unmanned boats includes a voyage cost function and a performance cost function; the weight of the voyage cost function is 0.3, and the performance cost function is 0.7.

[0093] For the offensive and defensive game tasks of multiple limited defense unmanned boats against a single attacking unmanned boat and multiple infinite defense unmanned boats against a single attacking unmanned boat, the total cost function adopts the voyage cost function;

[0094] For the offensive and defensive game tasks of multiple limited defense unmanned boats against a single attacking unmanned boat and multiple infinite defense unmanned boats against a single attacking unmanned boat, the total cost function adopts the voyage cost function. The construction process of the voyage cost function (the cost function of the Dubins curve) is as follows:

[0095] In the offensive and defensive game of unmanned boats at sea, the defense unmanned boat needs to effectively defend against the attacking unmanned boat and protect the target area. Therefore, the impact of the sailing distance on the target allocation result should be considered first. During the target allocation process, the path distance from the initial position of the defense unmanned boat to the position of the attacking unmanned boat can be regarded as the cost. The shorter the path distance, the smaller the cost. For the task assignment of each unmanned boat, the initial position coordinates and the heading angle of the defense unmanned boat are A(x A , y A , θ1); the position coordinates of the attacking unmanned boat are D(x D , y D , θ2). The minimum turning radius of the unmanned boat is R min . For a given initial pose, the unmanned boat can turn and sail clockwise or counterclockwise, so two trajectories can be obtained. Therefore, the shorter one needs to be selected as the shortest Dubins path. The center O2 of the turning circle of the unmanned boat can be obtained from the initial pose and the minimum turning radius of the unmanned boat:

[0096]

[0097] The coordinates of the tangent points B and C are:

[0098]

[0099] The optimal trajectory between the defense unmanned boat and the attacking unmanned boat consists of the arc AB, the straight line BC, and the arc CD, and the length is:

[0100]

[0101] The length of the chord l corresponding to the central angle ε is:

[0102]

[0103] Then the position coordinates D(x D , y D ) of the attacking unmanned boat are:

[0104]

[0105] The heading angle θ2 of the unmanned boat reaching the first target point is:

[0106]

[0107] The construction of the performance cost function is specifically as follows:

[0108] In the attack and defense game of unmanned boats at sea, the defensive unmanned boat needs to effectively defend against the attacking unmanned boat and protect the target area. To optimize the target allocation, the speed and endurance time can be comprehensively used as the cost function to evaluate the performance of the defensive unmanned boat and the attacking unmanned boat. The following is the design idea:

[0109] 1) Performance calculation of the defensive unmanned boat:

[0110] Performance of the defensive unmanned boat: Set the speed of the defensive unmanned boat as v d (range 1 - 5 m / s) and the endurance time as t d (range 1800 - 3000 s). Calculate the comprehensive performance of the defensive unmanned boat as:

[0111]

[0112] 2) Performance calculation of the attacking unmanned boat:

[0113] Performance of the attacking unmanned boat: Set the speed of the attacking unmanned boat as v a (range 1 - 5 m / s) and the endurance time as t a (range 1800 - 3000 s). Calculate the comprehensive performance of the attacking unmanned boat as:

[0114]

[0115] 3) Comprehensive performance index

[0116] The comprehensive performance of the defense mission is defined based on the ratio of the comprehensive performance of the defensive unmanned boat and the attacking unmanned boat. The specific calculation is as follows:

[0117]

[0118] When the number of defensive unmanned boats and attacking unmanned boats is equal, the overall cost function of the attack and defense game target allocation model of unmanned boats at sea is as follows:

[0119] To effectively balance the mobility and overall combat performance of the unmanned boat, the cost function combines the Dubins distance with the comprehensive performance index. Specifically, the cost function can be defined as:

[0120]

[0121] Among them: Dubins_path_weight = 0.3;

[0122] Performance_weight = l - Dubins_path_weight = 0.7

[0123] B. Offensive and defensive game tasks of multiple defense unmanned boats against a single attacking unmanned boat

[0124] (1) Maritime offensive and defensive game scenario 1

[0125] When the number of defense unmanned boats is limited, to ensure the effective protection of the target area, we need to divide the potential attack area into multiple sub - areas according to the distance and reasonably allocate defense resources to ensure effective interception and protection of the target area.

[0126] a) Attacker area division:

[0127] Attacker area 1 (near area): The dangerous area adjacent to the target protection area, which is the first key area for the attacking unmanned boat to approach the target.

[0128] Attacker area 2 (far area): The early - warning area far from the target area, which is the starting area where the attacking unmanned boat may launch an attack.

[0129] The target protection area is a circle with the center at coordinates (25, 25) and a radius of 10. The defender area is a ring with the center at coordinates (25, 25) and a radius of 30. The attacker near - area is a ring with the center at coordinates (25, 25) and a radius of 40, and the attacker far - area is composed of a ring with the center at coordinates (25, 25) and a radius of 50;

[0130] Because the entire sea area of this setting is, for example, 50 meters by 50 meters, so according to the position of the protection area, the defender area, as well as the attacker near - area and attacker far - area are set one by one;

[0131] b) Defense strategy:

[0132] Step1: Set a defense area centered on the attacking unmanned boat for deploying defense unmanned boats.

[0133] Step2: In attacker area 1, allocate 2 defense unmanned boats to each detected attacking unmanned boat. These defense unmanned boats will be deployed on the circumference of the defense area centered on the attacking unmanned boat to form a preliminary defense line. According to the Dubins distance (considering the movement limitations of the unmanned boat) and comprehensive performance evaluation, ensure that the selected positions can achieve effective interception in the shortest time.

[0134] Step 3: In the attacker area 2, allocate 3 defense unmanned boats to each attacking unmanned boat. Similarly, these defense unmanned boats will be deployed on the circumference of the defense area to form a denser defense network. This strategy aims to increase the interception success rate and create multiple deterrents against the attacking unmanned boats.

[0135] (2) Maritime attack and defense game scenario 2

[0136] When the number of defense unmanned boats is theoretically infinite, we can adopt a more precise strategy to ensure the effective protection of the target area. To this end, we can use a clustering algorithm to optimize the allocation of defense unmanned boats.

[0137] Applying the nearest neighbor clustering algorithm based on the greedy strategy to the maritime attack and defense game task of unmanned boats, the process of grouping adjacent defense unmanned boats into one class is as follows:

[0138] First, statistically analyze and initialize the characteristics of the defense unmanned boats, such as their initial positions, speeds, and directions. The position of each defense unmanned boat will be used as an input sample point for the clustering algorithm to determine its subsequent deployment and action strategies.

[0139] Set the number of attacking unmanned boats as N, then select K = N sample points as the initial clustering center points. Denote them as Each cluster point will be responsible for intercepting the attacking unmanned boat closest to it, thus forming a targeted defense unit.

[0140] Define a distance cost function to evaluate the distance between the defense unmanned boat and the clustering center, as shown in Equation (16), and use Equation (17) to divide each defense unmanned boat into the area formed by the clustering center closest to it. Thus, the clustering center and the data around it form the initial temporary cluster.

[0141]

[0142] Among them, a is the sample object; c i is the center of the i-th clustering result; M is the overall dimension of the sample object.

[0143]

[0144] Then recalculate the average value of each cluster, continuously change the position of the clustering center, and adjust the samples within the cluster.

[0145] Set the iteration count \(t = 0\), and gradually adjust the clustering results of the defensive unmanned boats until the clustering of all defensive unmanned boats is completed and converges. In each iteration, the system will re-evaluate the cost function based on the current clustering results and optimize the allocation and deployment of the defensive unmanned boats to ensure that the configuration of each clustering unit best meets the actual interception requirements. Finally, when the clustering of all defensive unmanned boats reaches a stable state, i.e., the cost function converges, the deployment strategy of the defense system is in the optimal state to adapt to the changes in the battlefield situation and ensure the comprehensive defense of the target area.

[0146] Through the optimization of the cost function, each defensive unmanned boat is assigned to the sub-cluster of the attacking unmanned boat closest to it. This process clusters the defensive unmanned boats around the closest attackers according to their geographical locations to form initial defense units, ensuring that the defensive unmanned boats can approach and intercept the attacking unmanned boats in the shortest time and maximizing the defense efficiency.

[0147] For the defensive unmanned boats belonging to the same sub-cluster, according to the new positions and dynamic situations of the attacking unmanned boats, they are adjusted to new cluster centers by Equation (18). In this way, the defensive unmanned boats can be more effectively concentrated near the attacking unmanned boats to form a strong defense front.

[0148]

[0149] 1) Design of the maritime attack and defense game scenario

[0150] In the maritime defensive unmanned boat system, when facing a single intruder, the goal of task allocation is to ensure that the defensive unmanned boats can effectively intercept and defend against the intruder and protect the target area. The following is a detailed supplementary description of the schematic diagram of the attack and defense game scenario:

[0151] Target area: This area may include important marine facilities, ships, or other strategic assets. It is marked with specific identifiers or colors in the figure for clear display.

[0152] Positions of the defensive unmanned boats: The starting positions of the defensive unmanned boats are usually set on the periphery or surrounding areas of the target area. The initial positions of the defensive unmanned boats are marked in the figure, and the defense areas they can cover are shown. According to the strategy, the defensive unmanned boats may form a defense circle around the target area or be distributed at multiple key positions to increase the interception success rate.

[0153] Positions of the attacking unmanned boats: The attacking unmanned boats should start their actions in areas outside the defense circle of the defensive unmanned boats to avoid being detected immediately. This position should be in the blind spot of the defensive unmanned boats' coverage or far from their main defense areas. It may include open waters or hidden waters far from the target area.

[0154] 2) Consensus auction algorithm

[0155] The consistency auction algorithm is divided into two stages: the auction stage and the consistency stage. In the auction stage, each defensive unmanned boat first determines whether the target of the attacking unmanned boat needs to be allocated. If allocation is required, it calculates the benefit of the target and bids for the target with the highest benefit. In the consistency stage, a consistency conflict-free rule is established. The defensive unmanned boats communicate with each other to transfer bidding information and solve the allocation conflict problem between the targets according to the consistency conflict-free rule.

[0156] In the auction stage, the defensive unmanned boat determines whether the target needs to be allocated and defines a variable where y ij represents the benefit of the defensive unmanned boat R bidding for the target B of the attacking unmanned boat, that is, y ij = c ij ; is an indicator function, which is true when the equation in the parentheses holds, that is, h ij = 1, otherwise 0. The defensive unmanned boat R needs to calculate the benefit of all targets B of the attacking unmanned boat as r ij = c ij hij, and select the target j with the maximum benefit * as:

[0157] j * = argmaxc ij (j)·h ij (19)

[0158] At this time, j * is the target with the maximum benefit among all the targets B bid by the defensive unmanned boat. The benefit of the defensive unmanned boat bidding for the target B is Therefore, the bidding information of the defensive unmanned boat R is established as:

[0159] z ij = 1 (20)

[0160]

[0161] In the consistency stage, after the defensive unmanned boats establish the bidding information, they need to communicate with each other to solve the target allocation conflict problem of the defensive unmanned boats. Using the consistency principle, the bidding information of all unmanned boats converges to a unified allocation decision information.

[0162] Figure 1 shows the communication topology diagram of the unmanned boat cluster. By comparing the centralized and distributed communication topologies, it shows that the distributed communication topology reduces the dependence on the communication center, thus improving the robustness of the formation system to a certain extent.

[0163] Figure 2Shows the schematic diagram of the path model of Dubins curves. Given the minimum turning radius, the shortest path between two states may be of the type circle - straight - circle or circle - circle - circle. The circle refers to the circle with the minimum turning radius of the unmanned boat, and the straight line refers to the tangent of the arc. These two types of paths include six path patterns, {RSL, LSR, RSR, LSL, RLR, LRL} (L represents a left - turning circle, R represents a right - turning circle, S represents a straight line). (a) is RSL, (b) is LSR, (c) is RSR, (d) is LSR, (e) is RLR, (d) is LRL;

[0164] Figure 3 Describes the analytical diagram of the optimal Dubins path of the unmanned boat, clearly revealing the motion characteristics of the under - actuated unmanned boat and making it closer to the path distance between the defensive unmanned boat and the attacking unmanned boat.

[0165] Figure 4 Shows the result diagram of the K - means clustering algorithm. Through clustering analysis, the defensive unmanned boats can be clustered according to the number of attacking unmanned boats. If the number of attacking unmanned boats is K, the defensive unmanned boats will be divided into K clusters. This classification method helps to improve the defense efficiency, enabling each cluster of defensive unmanned boats to optimize the deployment and adjust the defense strategy for specific attacking unmanned boats.

[0166] Figure 5 Shows the schematic diagram of the attack - defense game task scenario of a single defensive unmanned boat against a single attacking unmanned boat. The following are the scenario settings and parameter settings:

[0167] Size of the target protection area: The target protection area is set as a circular area with the center at the coordinate (25, 25) and a radius of 10 meters. This means that the center of the target area is at the point (25, 25) on the two - dimensional plane, and the farthest distance from the center point to the boundary of the circular area is 10 meters.

[0168] Defender area: To effectively protect the target area, the defender area is set as an annular area with the same center as the target area. Specifically, the defender area is an annular area with the center at the coordinate (25, 25), an inner radius of 10 meters, and an outer radius of 30 meters. In this way, the defender can deploy defenses within a 30 - meter range outside the target area, forming an effective protection zone for the target area while avoiding directly entering the interior of the target area.

[0169] Attacker area: To simulate the attacking route of the attacker, the attacker area is set as the area between two concentric circles. The attacker area is set as an annular area with an inner radius of 50 meters and an outer radius of 100 meters. The center of the attacker area is also at the coordinate (25, 25). Within this area, the attacking unmanned boat will launch attacks from a range of 50 meters to 100 meters away from the target area.

[0170] Turning radius: Set the turning radii of the defensive unmanned boat and the attacking unmanned boat to 3 meters.

[0171] Through these settings, a clear operating range can be provided for the defenders and attackers, thereby better evaluating the protection effect of the target area and the effectiveness of the attack strategy.

[0172] Figure 6 Shows the allocation results of the auction algorithm under different scale confrontation scenarios, (a) 10 defensive unmanned boats vs. 10 attacking unmanned boats, (b) 20 defensive unmanned boats vs. 20 attacking unmanned boats,

[0173] (c) 30 defensive unmanned boats vs. 30 attacking unmanned boats;

[0174] To more comprehensively analyze the attack and defense game behaviors under different scales, the following three scenarios are set:

[0175] 10 defensive unmanned boats against 10 attacking unmanned boats. This scenario is used to simulate small-scale confrontation and observe the basic strategy selection and execution effects.

[0176] 20 defensive unmanned boats against 20 attacking unmanned boats. This scenario is used to simulate medium-scale confrontation and analyze the strategy cooperation effect during cluster operations.

[0177] 30 defensive unmanned boats against 30 attacking unmanned boats. This scenario is used to simulate large-scale confrontation and evaluate the complexity and effectiveness of the cluster strategy.

[0178] From Figure 6 It can be seen that by minimizing the Dubins distance, it can be ensured that the defensive unmanned boat responds to the attack with the shortest path and the fastest time, improving the system reaction speed and combat efficiency. Secondly, the comprehensive performance index considers the sailing speed, communication efficiency and endurance time, ensuring that the unmanned boat not only considers mobility but also the overall combat performance during task allocation, thereby enhancing the combat ability of the defense system.

[0179] Figure 7 Shows a schematic diagram of the attack and defense game task scenario of multiple defensive unmanned boats against a single attacking unmanned boat when the number of defensive unmanned boats is limited. The following are the scenario and parameter settings:

[0180] 1. Attacker area design:

[0181] Attacker area 1 (near area): 30 meters away from the target protection area.

[0182] Description: This area is considered a high-risk area. Once the attacking unmanned boat enters this area, the threat level is extremely high. Therefore, a defensive strategy that requires quick response is needed for interception.

[0183] Attacker Area 2 (Far Area): 40 meters away from the target protection area.

[0184] Description: This area is the early warning area. The defense strategy should focus on prevention and early intervention to ensure interception before the attacking unmanned boats enter the near area.

[0185] 2. To analyze the attack and defense game behavior under different scales more comprehensively, the following three scenarios are set:

[0186] 1) When the total number of randomly set attacking unmanned boats is 4, these unmanned boats will be assigned to different attack areas. In Attacker Area 1, 2 attacking unmanned boats launch attacks. For effective defense, 2×3 = 6 defense unmanned boats are required in this area. At the same time, in Attacker Area 2, there are also 2 attacking unmanned boats, so 2×2 = 4 defense unmanned boats are required in this area to deal with potential threats. Therefore, to comprehensively defend against the threat of 4 attacking unmanned boats, a total of 6 (Area 1) + 4 (Area 2) = 10 defense unmanned boats are required.

[0187] 2) When the total number of randomly set attacking unmanned boats is 8, in Attacker Area 1, 4 attacking unmanned boats launch attacks. For effective defense, 4×3 = 12 defense unmanned boats are required in this area. At the same time, in Attacker Area 2, there are 4 attacking unmanned boats, so 4×2 = 8 defense unmanned boats are required in this area to deal with potential threats. Therefore, a total of 12 (Area 1) + 8 (Area 2) = 20 defense unmanned boats are required.

[0188] 3) When the total number of randomly set attacking unmanned boats is 11, in Attacker Area 1, 8 attacking unmanned boats launch attacks. For effective defense, 8×3 = 24 defense unmanned boats are required in this area. At the same time, in Attacker Area 2, there are 3 attacking unmanned boats, so 3×2 = 6 defense unmanned boats are required in this area to deal with potential threats. Therefore, a total of 24 (Area 1) + 6 (Area 2) = 30 defense unmanned boats are required.

[0189] According to the above parameter settings, Figure 8 Shows the distribution results of the attack and defense game under different orders of magnitude, (a) 10 defense unmanned boats vs. 4 attacking unmanned boats, (b) 20 defense unmanned boats vs. 8 attacking unmanned boats, (c) 30 defense unmanned boats vs. 11 attacking unmanned boats.

[0190] Figure 9 Shows the schematic diagram of the attack and defense game task scenario of multiple defense unmanned boats against a single attacking unmanned boat when the number of defense unmanned boats is theoretically infinite. The following are the parameter settings:

[0191] First, randomly set the number of attacking unmanned boats as 4, 6, and 9. Set the initial number of cluster centers K according to the number of attacking unmanned boats, that is, K = 4, 6, 9. Each cluster center will correspond to an attacking unmanned boat and be responsible for the defense tasks in its vicinity.

[0192] After completing the preliminary clustering, use the auction algorithm to allocate defense unmanned boats according to the distance between each cluster center and the corresponding attacking unmanned boat. The auction algorithm will preferentially allocate those defense unmanned boats that are closest to the attacker to ensure that they can approach and intercept the attacker most effectively in the shortest time.

[0193] Set the communication frequency to 0.5 Hz, that is, update the clustering results every 2 seconds to ensure that the defense system can respond to the dynamic changes of the attacking unmanned boats in real time.

[0194] Set the speed range of the defense unmanned boats to 3 m / s. This speed can not only ensure the efficient interception ability of the defense unmanned boats but also adapt to the flexible adjustment in the dynamic environment.

[0195] Figure 10 It is the simulation result diagram of the attack and defense game task of multiple defense unmanned boats against a single attacking unmanned boat (the number of defense unmanned boats is infinite). (a) 15 defense unmanned boats vs. 4 attacking unmanned boats, (b) 21 defense unmanned boats vs. 8 attacking unmanned boats, (c) 28 defense unmanned boats vs. 12 attacking unmanned boats.

[0196] The present invention is not limited to this embodiment. Any equivalent concept or change within the technical scope disclosed by the present invention shall be included in the protection scope of the present invention.

[0197] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An underactuated unmanned surface vehicle's maritime attack and defense game task allocation method, characterized in that: It includes the following steps: Obtain the quantity and position information of defense unmanned boats and attack unmanned boats; Construct an offensive and defensive game target allocation model for unmanned boats at sea; Respectively construct the total cost functions under the offensive and defensive game tasks of a single defense unmanned boat against a single attack unmanned boat, multiple defense unmanned boats with limited quantity against a single attack unmanned boat, and multiple defense unmanned boats with unlimited quantity against a single attack unmanned boat; Under the offensive and defensive game task of a single defense unmanned boat against a single attack unmanned boat, adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defense unmanned boat and the attack unmanned boat, and solve the offensive and defensive game target allocation model for unmanned boats at sea to achieve the offensive and defensive game task allocation for defense unmanned boats and attack unmanned boats; Under the offensive and defensive game tasks of multiple defense unmanned boats with limited quantity against a single attack unmanned boat and multiple defense unmanned boats with unlimited quantity against a single attack unmanned boat, When it comes to the offensive and defensive game task situation of multiple defense unmanned boats with limited quantity against a single attack unmanned boat, with the target protection area as the center, divide the defender area, the near attacker area, and the far attacker area; In the far attacker area, allocate 2 defense unmanned boats to each detected attack unmanned boat. In the near attacker area, allocate 3 defense unmanned boats to each detected attack unmanned boat, and adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defense unmanned boat and the attack unmanned boat to achieve the offensive and defensive game task allocation for defense unmanned boats and attack unmanned boats; When it comes to the offensive and defensive game task situation of multiple defense unmanned boats with unlimited quantity against a single attack unmanned boat, apply the nearest neighbor clustering algorithm based on the greedy strategy to the offensive and defensive game task of unmanned boats at sea, classify adjacent defense unmanned boats into one category, and based on the clustering center, adopt the consistent auction algorithm, and autonomously select target points for bidding according to the comprehensive factors of the distance, speed, and endurance time between the defense unmanned boat and the attack unmanned boat to achieve the offensive and defensive game task allocation for defense unmanned boats and attack unmanned boats.

2. The method for allocating the maritime offense and defense game tasks of an underactuated unmanned boat according to claim 1, wherein: The general mathematical model of the offensive and defensive game target allocation model for unmanned boats at sea is as shown in formulas (1)-(4): Define the index set as and In formula (1), x ij ∈ {0, 1} is a decision vector. When x ij = 1, it means that the attacking unmanned boat β j is assigned to the defensive unmanned boat α i ; when x ij = 0, it means that the attacking unmanned boat β j is not assigned to the unmanned boat α i ; represents the task sequence executed by the defensive unmanned boat α i . If the k-th task executed by the defensive unmanned boat α i is β j , then the k-th element of p i is j. If the defensive unmanned boat α i has no task to execute, then the ordered task set is The benefit function c ij (x i , p i ) in formula (1) is a non-negative function of the decision vector x ij and the task sequence p i . It is the benefit obtained by the defensive unmanned boat α i bidding for the attacking unmanned boat β i according to p j . When x ij = 0, c ij (x i , p i ) = 0; the summation term in the parentheses represents the local reward of the defensive unmanned boat α i .

3. A method for allocating the sea offensive and defensive game tasks of an underactuated unmanned boat according to claim 1, characterized in that: When the quantities of defense unmanned boats and attack unmanned boats are equal, the total cost function of the offensive and defensive game target allocation model for unmanned boats at sea includes a voyage cost function and a performance cost function. The weight of the voyage cost function is 0.3, and the performance cost function is 0.

7.

4. A method for task allocation of an underactuated unmanned surface vehicle in a maritime attack and defense game according to claim 1, characterized in that: The total cost function under the offensive and defensive game tasks of multiple defense unmanned boats with limited quantity against a single attack unmanned boat and multiple defense unmanned boats with unlimited quantity against a single attack unmanned boat adopts the voyage cost function. The construction process of the voyage cost function is as follows: For the mission assignment of each unmanned boat, the initial position coordinates and heading angle of the defense unmanned boat are A(x A , y A , θ1); the position coordinates of the attack unmanned boat are D(x D , y D , θ2), and the minimum turning radius of the unmanned boat is R min . For a given initial pose, the unmanned boat can turn and navigate clockwise or counterclockwise, thus obtaining two trajectories. Therefore, it is necessary to select the shorter one as the shortest Dubins path. The center O2 of the turning circle of the unmanned boat is obtained from the initial pose and the minimum turning radius of the unmanned boat: The coordinates of the tangent points B and C are: The optimal track between the defense unmanned boat and the attack unmanned boat consists of the arc AB, the straight line BC, and the arc CD, and the length is: The length of the chord l corresponding to the central angle ε is: Then the position coordinates D(x D , y D ) of the attacking unmanned boat are as follows: The course angle θ2 of the unmanned boat reaching the first target point is:

5. A method for task allocation of an underactuated unmanned surface vehicle in a maritime attack and defense game according to claim 1, characterized in that: The performance cost function includes: 1) Performance calculation of the defense unmanned boat: Performance of the defensive unmanned boat: Set the speed of the defensive unmanned boat to v d and the endurance time to t d , and calculate the comprehensive performance of the defensive unmanned boat as: 2) Performance calculation of the attack unmanned boat: Performance of the attack unmanned boat: Set the speed of the attack unmanned boat as v a and the endurance time as t a , and calculate the comprehensive performance of the attack unmanned boat as: 3) Comprehensive performance index: The comprehensive performance of the defense mission is defined based on the ratio of the comprehensive performance of the defense unmanned boat and the attack unmanned boat, and the specific calculation is as follows.

6. The method for allocating the sea attack and defense game tasks of an underactuated unmanned boat according to claim 1, wherein: The above-mentioned nearest neighbor clustering algorithm based on the greedy strategy is applied to the sea attack and defense game mission of unmanned boats. The process of classifying adjacent defense unmanned boats into one category is as follows: First, the characteristics such as the initial position, speed, and direction of the defense unmanned boats are statistically analyzed and initialized. The position of each defense unmanned boat will be used as the input sample point of the clustering algorithm; Set the number of attacking unmanned boats to be N, then select K = N sample points as the initial clustering cluster center points, denoted as Each cluster point will be responsible for intercepting the attacking unmanned boat closest to it, thus forming a targeted defense unit; Define a distance cost function to evaluate the distance between the defense unmanned boat and the clustering center, as shown in Equation (16), and use Equation (17) to divide each defense unmanned boat into the area formed by the clustering center closest to it. Thus, the clustering center and the data around it form the initial temporary cluster; Among them, a is the sample object; c i is the center of the i-th clustering result; M is the overall dimension of the sample object; Then recalculate the average value of each cluster, continuously change the position of the clustering center, and adjust the samples within the cluster; Set the number of iterations t = 0, and gradually adjust the clustering results of the defense unmanned boats until the clustering of all defense unmanned boats is completed and converges. In each iteration, the cost function will be re-evaluated according to the current clustering results, and the allocation and deployment of the defense unmanned boats will be optimized to ensure that the configuration of each clustering unit best meets the actual interception requirements. Finally, when the clustering of all defense unmanned boats reaches a stable state, that is, the cost function converges, the deployment strategy is in the best state; For the defense unmanned boats belonging to the same sub-cluster, according to the new position and dynamic situation of the attack unmanned boat, they are adjusted to a new cluster center by Equation (18). The defense unmanned boats can be more effectively concentrated near the attack unmanned boat to form a strong defense front line.

7. A method for allocating the maritime attack and defense game tasks of an underactuated unmanned surface vehicle according to claim 1, characterized in that: The above-mentioned consensus auction algorithm is divided into two stages: the auction stage and the consensus stage. In the auction stage, each defense unmanned boat first judges whether the attack unmanned boat target needs to be allocated. If it needs to be allocated, calculate the revenue of the target and bid for the target with the highest revenue; In the consensus stage, a consensus conflict-free rule is established. The defense unmanned boats communicate with each other to transmit bid information. According to the consensus conflict-free rule, the allocation conflict problem between the targets is solved; In the auction stage, the defensive unmanned boat determines whether the target needs to be allocated and defines variables where y ij represents the payoff of the defensive unmanned boat R bidding for the target B of the attacking unmanned boat, that is, y ij = c ij ; is an indicator function, which is true when the equation in the parentheses holds, that is, h ij = 1, otherwise 0. The defensive unmanned boat R needs to calculate the payoff for all attacking unmanned boat targets B as r ij = c ij hij, and select the target j with the maximum payoff * as: j * = argmaxc ij (j)·h ij (19) At this time, j * To defend against all attacks on the unmanned boat B and target the most profitable objective among them, the profit of the defensive unmanned boat competing for target B is Therefore, the bidding information for the defensive unmanned boat R is established as follows: z ij ＝1 (20) In the consensus stage, after the defense unmanned boats establish bid information, they need to communicate with each other to solve the target allocation conflict problem of the defense unmanned boats. Using the consensus principle, the bid information of all unmanned boats converges to a unified allocation decision information.

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