A game theory-based cooperative navigation scheduling method for marine unmanned ship cluster

Abstract

The application provides a game theory-based offshore unmanned ship cluster cooperative navigation scheduling method, which comprises the following steps: step 1, model establishment: the navigation tasks of all unmanned ships are independent of each other, and the navigation task of an unmanned ship can be decomposed into a series of subtasks, each of which contains one or more than two parts; the goal of the scheduling problem is to minimize the maximum navigation task completion time; step 2, two sub-games of the unmanned ship are established: the goal is to determine the optimal scheduling of each unmanned ship task through each sub-game; step 3, the perfect equilibrium solution of the two sub-games is calculated. The method of the application considers dynamic uncertain environment, task migration, multi-ship cooperation and emergency handling, can obtain a stable sub-game perfect Nash equilibrium solution under a double-layer game framework, and significantly improves the scheduling efficiency, robustness and economy of the unmanned ship cluster.

Description

Technical Field

[0001] This invention belongs to the field of intelligent ship control, unmanned system cluster scheduling and marine intelligent equipment technology, specifically involving a game theory-based method for collaborative navigation scheduling of unmanned marine vessel clusters. Background Technology

[0002] As tasks such as marine resource exploration, offshore wind power operation and maintenance, maritime search and rescue, environmental monitoring, and coastal defense patrols become increasingly complex, unmanned surface vessel (USV) swarm collaborative operations have become a core development direction for marine intelligent equipment. USVs possess advantages such as unmanned operation, high maneuverability, low cost, and swarm capability, enabling them to perform long-duration, large-scale missions in harsh sea conditions and dangerous areas, and are gradually being used in large numbers within the marine industry.

[0003] Current unmanned surface vessel (USV) navigation scheduling mostly adopts static pre-planning or single-vessel independent decision-making modes, which mainly have the following limitations:

[0004] The marine environment is highly dynamic and uncertain. Unexpected factors such as wind, waves, currents, channel constraints, and equipment failures frequently cause the original route to fail and the mission to be forced to relocate. Traditional ship scheduling methods cannot adapt to fuzzy and uncertain navigation migration decisions.

[0005] When multiple vessels operate in parallel, there are problems such as route conflicts and low coordination efficiency, and there is a lack of a balanced decision-making mechanism in the coordinated scheduling of unmanned navigation.

[0006] Existing technologies do not distinguish between independent and shared routes, resulting in low efficiency for multiple vessels on the same route and failing to achieve integrated scheduling functions such as route sharing, timing coordination, and energy consumption optimization.

[0007] In the face of emergencies such as equipment failure and communication interruption of unmanned vessels, there is a lack of a complete decision-making framework for task reassignment, navigation migration, and cluster rescheduling, resulting in insufficient robustness. Summary of the Invention

[0008] Purpose of the invention: This invention aims to address the shortcomings of existing unmanned vessel swarm cooperative navigation algorithms in dynamic marine environments, fuzzy and uncertain migrations, multi-vessel cooperative conflicts, and rescheduling in the event of emergencies.

[0009] This invention realizes Nash equilibrium in algorithmic game theory through decision tree optimization algorithm. This algorithm can smoothly cope with unexpected situations such as route conflicts, route failures, and forced mission relocation.

[0010] This invention specifically provides a game theory-based method for collaborative navigation scheduling of unmanned surface vessels (USVs) at sea. The method consists of a USV maritime task scheduling subgame and a maritime route navigation scheduling subgame. It comprehensively considers maritime task allocation and maritime navigation process, and improves transportation efficiency in the case of multiple USVs transporting on the same route by adopting a decision tree optimization algorithm that solves the constraint nonlinear programming problem.

[0011] This invention abstracts sudden events such as equipment failure, abrupt changes in sea state, and communication interruptions into service interruptions, and categorizes tasks into directly affected tasks and indirectly affected tasks. It uses a multi-stage impact classification method to hierarchically identify affected tasks and constructs two scheduling models: migration and non-migration. This is used to achieve stable operation of unmanned surface vessels (USVs) under fuzzy and uncertain routes.

[0012] The method includes the following steps:

[0013] Step 1: Model Establishment: The navigation tasks of all unmanned surface vessels (USVs) are independent of each other. The navigation task of the i-th USV is... This task It can be broken down into a series of subtasks Each of the subtasks Each contains one or more parts , where i represents the number of tasks, j represents the number of subtasks of each task, and k represents the number of unmanned vessels required to complete the task;

[0014] The goal of the scheduling problem is to minimize the maximum voyage completion time, which is expressed as:

[0015] ,

[0016] in The maximum time to complete the navigation mission. For maritime mission time. For sea voyage time;

[0017] Step 2: Establish two subgames for the unmanned vessels: a maritime mission scheduling subgame and a maritime route navigation scheduling subgame. These two subgames are played during the maritime missions and maritime route navigation of the unmanned vessel swarm. The purpose is to determine the optimal scheduling for each unmanned vessel mission through each subgame.

[0018] Step 3: Calculate the perfect equilibrium solution for the two subgames.

[0019] In step 1, the scheduling problem is divided into migration with a navigation mission and migration without a navigation mission;

[0020] In the event of a mission relocation, the duration of the maritime mission. Including task execution time and the delay time for interrupting tasks, defined as:

[0021] ,

[0022] in Indicates the time type of the task; A pattern representing a maritime mission; Indicating in task mode In the middle, time type The task execution time is as follows; This represents the summation of the three dimensions i, j, and k. This represents the number of unmanned vessels required for parallel task i and subtask j; The sum of the actual time required to use k unmanned vessels in the j-th sub-task of the i-th navigation mission, under the corresponding mission type and execution mode; This indicates the sequence number of the interrupted navigation mission; there are a total of B interrupted navigation missions. This indicates the duration of the b-th interrupted task; This means summing up all the extra delay time from non-navigation tasks to get the total system delay time;

[0023] Sea sailing time The calculation formula is:

[0024]

[0025]

[0026]

[0027]

[0028] ,

[0029] Where IDT represents independent flight time, and SLT represents time saved by shared flight time. Indicates the logical delay time. An identifier indicating the task; Indicates the processing speed of the task; Indicates from the task To the mission Switching costs; This represents the load of the entire unmanned vessel cluster when using k unmanned vessels in the j-th subtask of i navigation missions; The smoothing coefficient represents the smoothness of the unmanned surface vessel (USV) mission, i.e., when... The larger the coefficient, the closer it is to 1, and the greater the return. The smaller the time, the smaller the profit; Indicates from navigation mission To the next voyage mission The sum of switching costs is divided by the sum of the flight mission processing speeds to obtain the sum of switching loads per unit processing time. This indicates the sequence of tasks when the b-th voyage mission is interrupted; This indicates the order of subtasks when the b-th voyage mission is interrupted. This indicates the sequence of unmanned vessels when the b-th voyage mission was interrupted. This indicates the mission processing speed during the b-th mission interruption; This indicates that the mission was interrupted during the b-th voyage. The cost of mission switching when a flight mission is interrupted; This indicates the load status of the entire unmanned vessel cluster at the time of the interruption of the b-th navigation mission; This indicates a reduction in mission benefits resulting from mission balancing in the original navigation mission. This represents the sum of the switching costs between navigation tasks in the newly added navigation task sequence after the migration of navigation tasks, divided by the sum of the processing speeds of the navigation tasks, resulting in the sum of the initial switching load times. This indicates the reduced load benefit resulting from load balancing in the new navigation mission after migration.

[0030] In the absence of a navigation mission relocation, the formula for calculating the delay time of a maritime mission is as follows:

[0031] ,

[0032] in This represents the total system delay time obtained by summing up the termination times of all navigation missions.

[0033] Time at sea during migration without navigation mission Represented as:

[0034]

[0035]

[0036] ,

[0037] in Indicates from navigation mission To the next voyage mission The total switching cost is divided by the total processing speed of the navigation missions to obtain the total switching load per unit processing time.

[0038] This indicates a reduction in mission benefits resulting from mission balancing during the original navigation mission.

[0039] In step 2, the maritime mission scheduling subgame is defined by the following three elements:

[0040] ,

[0041] Where G is the set of maritime mission scheduling subgames. It is a set of sub-tasks required by maritime missions. The set; all unmanned surface vessels' navigation missions are independent of each other, and the navigation mission of the i-th unmanned surface vessel is... This task It can be broken down into a series of subtasks Each of the subtasks Each contains one or more parts Where i represents the number of tasks, j represents the number of subtasks per task, and k represents the number of unmanned vessels required to complete the task. ; It is the set of maritime mission services that unmanned vessels can provide, namely , For subtasks Assigned unmanned vessel maritime services; It is the overall payoff function of the maritime mission scheduling subgame, which is composed of each subgame. Decision, among which , For the task The payoff function.

[0042] In step 2, the maritime route navigation scheduling subgame is defined by the following three elements:

[0043] ,

[0044] in This represents the set of subgames for navigation scheduling on maritime routes. It is a set of maritime mission scheduling provided by the maritime mission scheduling subgame, in which This indicates the maritime mission scheduling using the k-th unmanned vessel under the j-th sub-task in mission i; ; It is a maritime navigation service provided by unmanned vessels. , This indicates that unmanned ships will perform maritime missions. Change to The operation, Indicates maritime navigation mission Change to Operation; It is the overall payoff function of the maritime navigation mission scheduling subgame. , For the task Change to The subsequent payoff function.

[0045] Step 3 includes: using a decision tree optimization model to form the optimal maritime mission scheduling. and maritime navigation scheduling The decision tree optimization model consists of nodes and branches, where each node represents a decision made by each unmanned surface vessel (USV), and each branch represents a set of actions that the USV may take.

[0046] Step 3 also includes:

[0047] In the case of no navigation mission migration: In the maritime mission scheduling subgame, the optimal equilibrium strategy for each maritime mission scheduling sub-task is:

[0048] ,

[0049] ,

[0050] The optimal equilibrium strategy for the maritime mission scheduling sub-task is expressed as follows: In an unmanned surface vessel (USV) maritime sub-mission, all other participants choose an equilibrium strategy. In the case of the first Participants in an unmanned surface vessel (USV) maritime sub-mission choose nonequilibrium strategies. The return at that time will not exceed that of choosing the equilibrium strategy. The benefits at that time;

[0051] in Represents the participant's payoff function; This indicates the nonequilibrium strategy chosen by the participants; This represents the equilibrium strategy chosen by the participants; This represents the set of strategies of all participants other than the participant. This represents the set of all participants except the participant who choose the equilibrium strategy. These are constraints; Indicates in subtask In addition to the participants In addition, the strategy combinations of all other participants; Let J represent the last element of the set of maritime mission scheduling strategies in the constraints, I represent the total number of mission stages in the entire mission scheduling problem, and J represent the total number of sub-tasks within stage I. This represents the total number of unmanned vessels under the above conditions.

[0052] Step 3 also includes:

[0053] In the maritime route scheduling subgame, the optimal equilibrium strategy for each maritime route scheduling subtask is:

[0054] ,

[0055] ,

[0056] The optimal equilibrium strategy for the maritime navigation scheduling sub-task represents the first equilibrium strategy in route scheduling. An unmanned vessel, when all other entities adopt a balanced navigation strategy At that time, the first The unmanned vessel chooses any non-equilibrium route. The gains obtained will not be higher than those from choosing the balanced route. The benefits at that time;

[0057] in The route revenue function for unmanned vessels; This indicates that the participant chose a non-optimal route; Indicates the optimal route for the participants; This represents the set of navigation strategies for all unmanned vessels other than the participants. This represents the set of strategies adopted by all entities other than the participants, which are based on a balanced flight path. At time t, in the current stage, the set of route strategies of all subjects is the portion after removing the kth subject; This represents the last element of the set of route scheduling strategies in the constraints.

[0058] Step 3 also includes:

[0059] Design a multi-stage impact classification method to define the affected tasks and solve the optimal scheduling problem, i.e., when maritime mission services are interrupted, the following constraints are applied:

[0060] ,

[0061] ,

[0062] in Indicates maritime mission The start time; This indicates the start time of the maritime mission after experiencing b failures; This indicates the duration of the b-th failure case;

[0063] The following algorithm is established:

[0064] ,

[0065] in Indicates the completion time of the preceding task, i.e., the maritime mission. The earliest time when execution can begin; Indicates current maritime mission The difference in workload between this task and the subsequent maritime mission m; Indicates maritime mission Processing speed; Indicates subsequent maritime missions The planned start time; For indicator functions, i.e., when subsequent tasks When task m is selected, the value is 1; otherwise, it is 0.

[0066]

[0067] ,

[0068] in Indicates subsequent tasks The planned start time, Indicates subsequent tasks The execution time; that is Indicates task The planned end time;

[0069] ,

[0070] in For the first The completion time of each preliminary maritime mission; For the indicator function, only the departure time after task p is completed. Earlier than the available start time for unmanned ships When the time condition is met, the value is 1; otherwise, it is 0. For the preceding tasks To the current task The quantified value of workload; For the speed of unmanned ships in navigation or task processing; For the subsequent task m to task The quantified value of workload; For the task The planned start time; For the task Execution time; For indicator functions, only when the task If it belongs to task flow l, the value is 1; otherwise, it is 0.

[0071] ,

[0072] in, For indicator functions, only when the task If it belongs to task flow l, the value is 1; otherwise, it is 0. For the task The planned start time; For the task Execution time; For the preceding tasks To the current task The quantified value of workload; For maritime missions Processing speed;

[0073] The unmanned vessel maritime mission scheduling subgame and maritime navigation scheduling subgame are defined by three elements in the following equation, as shown below:

[0074] ,

[0075] ,

[0076] in Subgame for maritime mission scheduling; This is a subgame for maritime navigation scheduling. A gathering of participants in maritime missions. A group of participants in maritime navigation missions; A set of task strategies; A collection of maritime routes and avoidance strategies;

[0077] First, address maritime missions directly affected by relocation without navigation tasks; then, process all maritime missions affected by delays or relocations in subsequent steps. In this game, for each subgame, participants formulate strategies based on the actions of the other unmanned vessels to minimize the payoff function. For each subtask within a maritime mission, each participating unmanned vessel has a nonequilibrium maritime mission strategy. Unbalanced route strategy All of them meet the following conditions:

[0078] ,

[0079] ,

[0080] in, Let μ be the payoff function of step μ in the maritime mission scheduling subgame; For step μ, the non-equilibrium task strategy selected in the task scheduling subgame; Let μ be the equilibrium task strategy selected in the task scheduling subgame in step μ. This represents the set of equilibrium strategies chosen by all other unmanned vessels in the subgame of maritime mission scheduling.

[0081] Let μ be the payoff function of step μ in the navigation scheduling subgame; For step μ, the non-equilibrium route strategy selected in the navigation scheduling subgame; The equilibrium route strategy selected in step μ within the navigation scheduling subgame; This is the set of equilibrium strategies chosen by all other unmanned vessels in the navigation scheduling subgame.

[0082] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0083] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0084] This invention's method takes into account dynamic and uncertain environments, task migration, multi-ship collaboration, and contingency handling. It can obtain stable subgame perfect Nash equilibrium solutions within a two-layer game framework, significantly improving the scheduling efficiency, robustness, and economy of unmanned surface vessel (USV) swarms. It has the following beneficial effects:

[0085] (1) It is adaptable to complex and dynamic marine environments and has strong resistance to uncertainty. When faced with sudden factors such as wind, waves and currents, channel constraints, equipment failures and communication packet loss, it can adapt to fuzzy and uncertain navigation migration, avoid route failure and mission interruption, and improve scheduling robustness and reliability.

[0086] (2) Two-layer game equilibrium scheduling to resolve multi-ship coordination conflicts. A two-layer sub-game model of task scheduling + navigation scheduling is constructed to distinguish between independent routes and shared routes; route conflicts are eliminated and the efficiency of timing coordination and path sharing is improved through perfect Nash equilibrium to achieve optimal scheduling of multiple ships in an integrated manner.

[0087] (3) Graded handling of emergencies, supporting task migration and rescheduling. Equipment failure, sudden changes in sea conditions, and communication interruption are abstracted as service interruptions, and a multi-stage impact classification method is used to distinguish between directly / indirectly affected tasks; three strategies are supported: full migration, partial migration, and no migration, to achieve smooth rescheduling under fault conditions.

[0088] (4) The equilibrium solution is stable, and no single unmanned vessel deviates from the equilibrium. Both layers of the game satisfy the subgame perfect Nash equilibrium, and any unmanned vessel changing its strategy (task allocation / route selection) will not increase its payoff.

[0089] The model is highly versatile and applicable to a wide range of scenarios. It can be used for collaborative operations of unmanned vessel swarms in offshore wind power maintenance, marine exploration, maritime search and rescue, environmental monitoring, and coastal defense patrols, providing efficient, reliable, and economical scheduling solutions for complex marine scenarios. Attached Figure Description

[0090] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0091] Figure 1 This describes the workflow of the decision tree optimization model used to form a perfect equilibrium solution in a two-level scheduling subgame.

[0092] Figure 2 The graph shows the task completion rate with and without a task migration algorithm in the event of a sudden malfunction and interruption of the unmanned vessel.

[0093] Figure 3 The graph shows the task latency with and without a task migration algorithm in the event of a sudden malfunction and interruption of the unmanned vessel. Detailed Implementation

[0094] This invention provides a game theory-based method for the coordinated navigation and scheduling of unmanned surface vessels (USVs) at sea, comprising the following steps:

[0095] 1. Establish a model

[0096] All unmanned surface vessel (USV) navigation missions are independent of each other. This task It can also be broken down into a series of sub-tasks. Each of the subtasks Each contains one or more parts , where i represents the number of tasks, j represents the number of subtasks of each task, and k represents the number of components.

[0097] Firstly, this invention identifies and handles unexpected events caused by unforeseen factors such as channel constraints, communication packet loss, and equipment failure encountered during unmanned navigation.

[0098] This invention discusses the two cases separately: those with navigation mission migration and those without. In the algorithm of this invention, the objective of the scheduling problem is to minimize the maximum navigation mission completion time. The maximum navigation mission completion time is expressed as:

[0099] ,

[0100] in The maximum time to complete the navigation mission. For maritime mission time. This refers to the time spent at sea.

[0101] (1) There is a navigation mission to relocate

[0102] In the event of a mission relocation, the duration of the maritime mission. Including task time and the delay time for interrupting tasks, defined as:

[0103] ,

[0104] in Indicates the base execution time; This indicates the time type of the task, which determines the baseline value of the time, such as the standard working hours for different maritime tasks; This can be represented as a pattern for maritime missions, such as the time scaling factor resulting from mission complexity. The overall meaning can be understood as the actual time required for the i, j, kth navigation tasks under the corresponding task type and execution mode. This indicates the situation where a navigation mission was interrupted; there were a total of B interrupted navigation missions. This indicates the duration of the b-th interrupted task, including additional time caused by waiting between tasks, device switching, etc. It can be understood as adding up all the extra delay time of all non-navigation tasks to get the total delay time of the system.

[0105] Sea sailing time The difference between the independent flight time (IDT) and the time saved by the shared flight time (SLT) is calculated. When the flight mission is relocated, the delayed logical time (DLT) must also be considered, as shown below:

[0106]

[0107]

[0108]

[0109]

[0110] ,

[0111] in An identifier indicating the task; Indicates the processing speed of the task; Indicates from the task To the mission Switching costs, such as vessel switchover time and resource allocation costs; This is expressed as the load level of the navigation mission, such as the number of missions currently being carried out by the unmanned vessel. Overall understanding is from the perspective of navigation mission To the next voyage mission The switching cost is divided by the processing speed of the navigation mission to obtain the switching load per unit processing time. The overall understanding is that in the original navigation mission, the reduced mission benefits are achieved through mission balancing (such as adjusting the mission order and allocating to unmanned vessels with fewer missions). The overall value is represented as the switching cost between navigation tasks in the newly added navigation task sequence after the migration navigation task, divided by the processing speed of the navigation task, to obtain the newly added initial switching load time. Overall, this means that in the new navigation mission after migration, the load reduction benefits are also achieved through load balancing.

[0112] (2) Migration without navigation mission

[0113] In the absence of a relocation of the navigation mission, a navigation mission terminated due to unforeseen circumstances does not require rescheduling. Therefore, the delay time of the maritime mission is equivalent to the termination time of the navigation mission, as shown below:

[0114] ,

[0115] in Same as the formula above; This can be understood as summing up the termination times of all navigation missions to obtain the total system termination time delay.

[0116] Since this voyage mission migration does not require mission reassignment, delay time is not considered in the voyage time; therefore, the sea voyage time is... Represented as:

[0117]

[0118]

[0119] ,

[0120] in Overall understanding is from the perspective of navigation mission To the next voyage mission The switching cost is divided by the processing speed of the navigation mission to obtain the switching load per unit processing time.

[0121] in This can be understood as reducing the rewards of missions in the original navigation mission by balancing missions (such as adjusting the mission order or allocating to unmanned vessels with fewer missions).

[0122] 2. Two-level scheduling algorithm

[0123] This invention divides the method into two sub-games: an unmanned vessel maritime mission scheduling sub-game and a maritime route navigation scheduling sub-game. The two sub-games are conducted separately during the maritime missions and maritime route navigation of the unmanned vessel swarm. The purpose is to determine the optimal scheduling of each unmanned vessel mission through each sub-game.

[0124] (1) Subgame of unmanned ship maritime mission scheduling

[0125] The maritime mission scheduling subgame in this method is defined by three elements:

[0126] ,

[0127] in It is a set of sub-tasks required by maritime missions. The set, i.e. ; It is the set of maritime mission services that unmanned vessels can provide, namely , For subtasks Assigned unmanned vessel maritime services; It is the overall payoff function of the subgame, which is composed of each subtask. Decision, among which , For the task The payoff function.

[0128] In this task scheduling subgame As participants in a game, they will make decisions based on their own strategies. Based on the corresponding task The strategy.

[0129] (2) Subgame of navigation scheduling on maritime routes

[0130] The navigation scheduling subgame in this method is also defined by three elements:

[0131] ,

[0132] in It is a set of maritime mission scheduling provided by the maritime mission scheduling subgame, in which . It is a maritime navigation service provided by unmanned vessels. , This indicates that unmanned ships will perform maritime missions. Change to The operation, Indicates maritime navigation mission Change to The operation. It is the overall payoff function of the subgame, determined by the corresponding task. Decision, among which , For the task Change to The subsequent payoff function.

[0133] (3) Perfect equilibrium solution of two-level subgame

[0134] Under the premise of the two subgames mentioned above, the optimal solution between the two is determined. This invention proposes a decision tree optimization model to form the optimal maritime mission scheduling. and maritime navigation scheduling The decision tree optimization model consists of nodes and branches, where each node represents a decision made by each unmanned surface vessel (USV), and each branch represents a set of possible actions the USV can take. A branch connects two nodes in one direction, indicated by an arrow. The workflow of the decision tree optimization model is as follows: Figure 1 As shown.

[0135] 3.1 Situation when there is no navigation mission during migration

[0136] In the unmanned vessel maritime mission scheduling subgame model of this invention, the optimal equilibrium strategy for each maritime mission scheduling sub-task is:

[0137] ,

[0138] ,

[0139] This expression represents the expression for the th In an unmanned surface vessel (USV) maritime sub-mission, all other participants choose an equilibrium strategy. In this situation, the participant chooses a nonequilibrium strategy. The return at that time will not exceed the return of the equilibrium strategy it chooses. The benefits at that time.

[0140] in Represents the participant's payoff function; This indicates the nonequilibrium strategy chosen by the participants; This represents the equilibrium strategy chosen by the participants; This represents the set of strategies of all participants other than the participant. This represents the set of all participants except the participant who choose the equilibrium strategy. "Constraint" is an abbreviation for "constraint condition". This constraint is defined The meaning of , which indicates in the subtask In addition to the participants In addition to the strategy combinations of all other participants.

[0141] Similarly, in the maritime route scheduling subgame, the optimal equilibrium strategy for each maritime route scheduling subtask is:

[0142] ,

[0143] ,

[0144] This expression represents the first... in route scheduling. An unmanned vessel, when all other entities adopt a balanced navigation strategy At that time, the subject chooses any non-equilibrium route. The gains obtained will not be higher than those obtained by choosing the balanced route. The benefits at that time.

[0145] in The route revenue function for a given unmanned vessel; This indicates that the participant chose a non-optimal route; Indicates the optimal route for the participants; This represents the set of navigation strategies for all unmanned vessels other than the participants. This represents the set of strategies adopted by all entities other than the participants, which are based on a balanced flight path. This constraint is clear. The meaning of is that at time t, in the current stage, the set of all subjects' route strategies is the part after removing the kth subject.

[0146] 3.2 Situation when there is a relocation of navigation missions

[0147] When unexpected events occur at sea, such as the interruption of maritime missions and navigation services, it is necessary to reorganize the task allocation, maritime mission pool, and maritime navigation service pool to reschedule unfinished unmanned vessel missions. This invention designs a multi-stage impact classification method to define affected tasks and solve the optimal scheduling problem. Specifically, when maritime mission services are interrupted, this definition is transformed into the following mathematical form:

[0148] ,

[0149] ,

[0150] in Indicates maritime mission The start time; This indicates the start time of the maritime mission after experiencing b failures; This indicates the duration of the b-th failure case.

[0151] In addition, there are some tasks that are affected by task migration or delay. The algorithm proposed in this invention is as follows:

[0152] ,

[0153] The core meaning of this formula is that in a balanced scheduling scheme for task migration, the completion time of the preceding task must not be earlier than the planned start time of the subsequent task. Indicates the completion time of the preceding task, i.e., the maritime mission. The earliest time when execution can begin; Indicates the available start time for the unmanned vessel; The function is the maximum of the two; Indicates current maritime mission The difference in workload between this task and the subsequent maritime mission m; Indicates maritime mission Processing speed; Indicates subsequent maritime missions The planned start time; For indicator functions, i.e., when subsequent tasks When task m is selected, the value is 1; otherwise, it is 0.

[0154]

[0155] ,

[0156] The core significance of this formula is that it applies to all maritime missions that are not directly followed by a direct sequel. Migration at sea The earliest possible end time must be earlier than the sea mission. The planned end time, i.e. when the migration task is completed, should not overlap with the execution time of other non-subsequent tasks to avoid resource conflicts or process chaos.

[0157] in Indicates subsequent tasks The planned start time, Indicates subsequent tasks The execution time; that is Indicates task The planned end time (start time + execution time).

[0158] ,

[0159] The core meaning of this formula is that the sum of the arrival times of all preceding tasks plus the total travel time of each segment must not be earlier than the end time of the subsequent task. For the first The completion time of each preliminary maritime mission; For the indicator function, only the departure time after task p is completed. Earlier than the available start time for unmanned ships When the time condition is met, the value is 1; otherwise, it is 0. For the speed of unmanned surface vessels' navigation / task processing; For subsequent task m to task The workload; For the task The planned start time; For the task Execution time; For indicator functions, only when the task If it belongs to task flow l, the value is 1; otherwise, it is 0.

[0160] ,

[0161] The core meaning of this formula is that in a balanced scheduling scheme for task migration, the earliest completion time of the current task flow l must be earlier than that of tasks in other task flows. The latest end time is determined to avoid overlapping and conflicting time intervals between different task flows. The explanation of the left-hand side of the equation is consistent with the above. For indicator functions, only when the task If it belongs to task flow l, the value is 1; otherwise, it is 0. For the task The planned start time; For the task Execution time; For the preceding task To the current task The workload; For maritime missions Processing speed.

[0162] In the two-layer scheduling scheme of this invention, the task migration strategy can be divided into three methods: full migration, partial migration, and no migration. Furthermore, the algorithm proposed in this invention provides the optimal solution for the task migration strategy of unmanned vessels.

[0163] 3.3 Perfect Equilibrium Solution in Two-Level Game

[0164] The unmanned vessel maritime mission scheduling subgame and maritime navigation scheduling subgame are defined by three elements in the following equation, as shown below:

[0165] ,

[0166] ,

[0167] in Subgame for scheduling unmanned surface vessel maritime missions; This is a subgame for maritime navigation scheduling. , The set of participants, that is, the set of unmanned vessels participating in the mission; A set of task strategies; It is a set of maritime routes and avoidance strategies.

[0168] The method of this invention first processes the maritime missions directly affected by the relocation of no navigation missions in section 3.1; after this stage, it processes all maritime missions affected by delays or relocations during this stage, in each subsequent step. In this game, for each subgame, participants formulate strategies based on the actions of the other unmanned vessels to minimize the payoff function. For each subtask within a maritime mission, each participating unmanned vessel has a nonequilibrium maritime mission strategy. Unbalanced route strategy All meet the following conditions:

[0169] ,

[0170] ,

[0171] In the first formula, Let μ be the payoff function of step μ in the maritime mission scheduling subgame; For step μ, the non-equilibrium task strategy selected in the task scheduling subgame; Let μ be the equilibrium task strategy selected in the task scheduling subgame in step μ. This represents the set of equilibrium strategies chosen by all other unmanned vessels in the subgame of maritime mission scheduling.

[0172] In the second formula, Let μ be the payoff function of step μ in the navigation scheduling subgame; For step μ, the non-equilibrium route strategy selected in the navigation scheduling subgame; The equilibrium route strategy selected in step μ within the navigation scheduling subgame; This is the set of equilibrium strategies chosen by all other unmanned vessels in the navigation scheduling subgame.

[0173] The method terminates only after it is determined whether all remaining tasks are affected and a perfect equilibrium solution for each stage is obtained. The final optimal solution is a combination of perfect equilibrium solutions for each stage.

[0174] The simulation involved six unmanned surface vessels (USV1 to USV6) conducting wind power operation and maintenance tasks. The six unmanned surface vessels were divided into two groups. USV1, USV2, and USV3 formed the operation and maintenance group, responsible for inspection, obstacle removal, and repair; USV4, USV5, and USV6 formed the support group, responsible for resupply, towing, and emergency response.

[0175] The overall task is broken down into the main task of offshore wind farm operation and maintenance. Sub-tasks include subordinate tasks such as inspection, obstacle clearing, maintenance, resupply, and emergency response. The specific execution modules under each subtask are: The core objective of this example is to minimize the maximum navigation mission completion time. It simultaneously satisfies the perfect Nash equilibrium of the two-layer subgame, enabling stable, efficient, and low-energy collaborative operation of unmanned vessel swarms.

[0176] A two-layer nested game model is constructed, with the upper layer being the unmanned vessel maritime mission scheduling subgame and the lower layer being the maritime route navigation scheduling subgame, achieving coordinated and balanced scheduling from the two dimensions of mission allocation and route planning respectively.

[0177] Subgame of unmanned vessel maritime mission scheduling:

[0178] ,

[0179] Participant Collection Includes all six unmanned ships Each unmanned vessel is an independent decision-making entity; a set of mission strategies. Record the available mission assignment, payload configuration, and operation sequence strategies for all unmanned surface vessels. ,in The specific task identifier assigned to the unmanned surface vessel; a set of revenue functions. , recorded as The higher the benefit, the better the scheduling scheme.

[0180] Subgame of navigation scheduling at sea:

[0181] ,

[0182] Participant Collection Consistent with the above, all are unmanned vessels; route strategy set Includes navigation avoidance, navigation path, and channel selection. ,in For navigation change operations, For path planning operations, the set of navigation revenue functions .

[0183] (1) Balanced scheduling during normal task migration

[0184] Calculation of Sea Mission Time (MST):

[0185] ,

[0186] in Basic assignment time, Indicates the time type of the task; This indicates the factor that amplifies or reduces the time required to complete a task, accurately quantifying the actual time spent on different tasks.

[0187] Actual time at sea (LT):

[0188] ,

[0189] For independent sailing time, To save time for shared routes.

[0190] The scheduling system uses a decision tree optimization algorithm. The maintenance group's unmanned surface vessels (USVs) employ a shared route + optimal speed strategy; the support group's USVs adopt a standby + nearest-source resupply strategy. All USVs meet the equilibrium condition and have no deviation motivation. The initial maximum completion time is... .

[0191] (2) Sudden failures and task migration scheduling

[0192] Midway through the operation, the USV2 unmanned surface vessel experienced a sudden propulsion failure and a brief communication interruption, triggering a scheduling mechanism that required relocation of navigation tasks. The scheduling system monitored the USV2 failure in real time. The tasks directly affected were the USV2's current maintenance tasks; those indirectly affected included subsequent underwater maintenance coordination, resupply timing, and passage along related routes. The scheduling system's time calculation model for switching to a navigation task relocation mechanism is as follows:

[0193] ,

[0194] New The sea voyage time is adjusted to account for the duration of the delay due to the malfunction. New To mitigate the logical time, the additional time spent on task reallocation and route adjustments is quantified.

[0195] The scheduling system re-solves the two-level game perfect Nash equilibrium, the upper-level maritime mission subgame: The unfinished marine life cleanup task was partially relocated to , , Shift to emergency support; Sub-game of lower-level routes: replanning , Flight routes, avoid In areas with malfunctions, optimize shared shipping lanes.

[0196] Perform load balancing verification:

[0197] ,

[0198] ,

[0199] , Rewards will not decrease after accepting a migration task. With stable support benefits, all unmanned vessels have no incentive to deviate from the equilibrium strategy, and the two-layer equilibrium is stably established. After fault migration scheduling, the unmanned vessel cluster successfully completed all maintenance tasks, with the maximum completion time TT shortened by approximately 18% compared to traditional static scheduling, resulting in reduced energy consumption and significantly improved operational efficiency.

[0200] This embodiment simulates three unmanned surface vessel (USV) swarm tasks under three different downtime durations: Br1 (1000-1500s), Br2 (3000-3500s), and Br3 (5000-5500s). The task completion rates with and without the task migration algorithm are shown in the graphs for sudden USV failures and downtime. Figure 2 As shown.

[0201] In the event of a sudden unmanned surface vessel (USV) malfunction and interruption, the task latency rates with and without a task migration algorithm are shown in the following graphs. Figure 3 As shown.

[0202] like Figure 2 It can be seen that the highest task completion rates occur at two different points, 0.32 and 0.5. This means that when tasks are broken down earlier, the distribution of task completion rates tends to be smaller, highlighting the importance of early detection and mitigation of unforeseen events for maintaining high task completion rates. Furthermore, for the same task duration, task migration leads to an increased task completion rate, indicating that task migration is an effective method for ensuring real-time scheduling and logistics allocation in dynamic environments in the event of unforeseen events.

[0203] like Figure 3 It can be seen that the algorithm proposed in this invention can effectively reduce the latency caused by service interruptions, with the task latency rate peaking at -0.2. The earlier the task is interrupted, the higher the task latency rate.

[0204] Depend on Figure 2 , Figure 3 It can be concluded that task migration can effectively mitigate the negative impact of unexpected events on task completion rate and task latency rate. Early detection of task interruptions and timely task migration are crucial for maintaining high task completion rate and minimizing task latency.

[0205] This invention provides a game theory-based method for the coordinated navigation and scheduling of unmanned surface vessels (USVs) at sea. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A game theory-based method for coordinated navigation scheduling of unmanned surface vessels (USVs) at sea, characterized in that, Includes the following steps: Step 1: Model Building: The navigation tasks of all unmanned surface vessels (USVs) are independent of each other. The navigation task of the i-th USV is... This task It can be broken down into a series of subtasks Each of the subtasks Each contains one or more parts , where i represents the number of tasks, j represents the number of subtasks of each task, and k represents the number of unmanned vessels required to complete the task; The goal of the scheduling problem is to minimize the maximum voyage completion time, which is expressed as: ， in The maximum time to complete the navigation mission. For maritime mission time. For sea voyage time; Step 2: Establish two subgames for the unmanned vessels: a maritime mission scheduling subgame and a maritime route navigation scheduling subgame. These two subgames are played during the maritime missions and maritime route navigation of the unmanned vessel swarm. The purpose is to determine the optimal scheduling for each unmanned vessel mission through each subgame. Step 3: Calculate the perfect equilibrium solution for the two subgames.

2. The method according to claim 1, characterized in that, In step 1, the scheduling problem is divided into migration with a navigation mission and migration without a navigation mission; In the event of a mission relocation, the duration of the maritime mission. Including task execution time and the delay time for interrupting tasks, defined as: ， in Indicates the time type of the task; A pattern representing a maritime mission; Indicating in task mode In the middle, time type The task execution time is as follows; This represents the summation of the three dimensions i, j, and k. This represents the number of unmanned vessels required for parallel task i and subtask j; The sum of the actual time required to use k unmanned vessels in the j-th sub-task of the i-th navigation mission, under the corresponding mission type and execution mode; This indicates the sequence number of the interrupted navigation mission; there are a total of B interrupted navigation missions. This indicates the duration of the b-th interrupted task; This means summing up all the extra delay time from non-navigation tasks to get the total system delay time; Sea sailing time The calculation formula is: ， Where IDT represents independent flight time, and SLT represents time saved by shared flight time. Indicates the logical delay time. An identifier indicating the task; Indicates the processing speed of the task; Indicates from the task To the mission Switching costs; This represents the load of the entire unmanned vessel cluster when using k unmanned vessels in the j-th subtask of i navigation missions; The smoothing coefficient represents the unmanned surface vessel (USV) mission. Indicates from navigation mission To the next voyage mission The sum of switching costs divided by the sum of flight mission processing speeds yields the sum of switching loads per unit processing time. This indicates the sequence of tasks when the b-th voyage mission is interrupted; This indicates the order of subtasks when the b-th voyage mission is interrupted. This indicates the sequence of unmanned vessels when the b-th voyage mission was interrupted. This indicates the mission processing speed during the b-th mission interruption; This indicates that the mission was interrupted during the b-th voyage. The cost of mission switching when a flight mission is interrupted; This indicates the load status of the entire unmanned vessel cluster at the time of the interruption of the b-th navigation mission; This indicates a reduction in mission benefits resulting from mission balancing in the original navigation mission. This represents the sum of the switching costs between navigation tasks in the newly added navigation task sequence after the migration of navigation tasks, divided by the sum of the processing speeds of the navigation tasks, resulting in the sum of the initial switching load times. This indicates the reduced load benefit resulting from load balancing in the new navigation mission after migration. In the absence of a navigation mission relocation, the formula for calculating the delay time of a maritime mission is as follows: ， in This represents the total system termination time delay, obtained by summing up the termination times of all navigation missions. Time at sea during migration without navigation mission Represented as: ， in Indicates from navigation mission To the next voyage mission The total switching cost is divided by the total processing speed of the navigation missions to obtain the total switching load per unit processing time. This indicates a reduction in mission benefits resulting from mission balancing during the original navigation mission.

3. The method according to claim 2, characterized in that, In step 2, the maritime mission scheduling subgame is defined by the following three elements: ， Where G is the set of maritime mission scheduling subgames. It is a set of sub-tasks required by maritime missions. The set; all unmanned surface vessels' navigation missions are independent of each other, and the navigation mission of the i-th unmanned surface vessel is... This task It can be broken down into a series of subtasks Each of the subtasks Each contains one or more parts Where i represents the number of tasks, j represents the number of subtasks per task, and k represents the number of unmanned vessels required to complete the task. ; It is the set of maritime mission services that unmanned vessels can provide, namely , For subtasks Assigned unmanned vessel maritime services; It is the overall payoff function of the maritime mission scheduling subgame, which is composed of each subgame. Decision, among which , For the task The payoff function.

4. The method according to claim 3, characterized in that, In step 2, the maritime route navigation scheduling subgame is defined by the following three elements: ， in This represents the set of subgames for navigation scheduling on maritime routes. It is a set of maritime mission scheduling provided by the maritime mission scheduling subgame, in which This indicates the maritime mission scheduling using the k-th unmanned vessel under the j-th sub-task in mission i; ; It is a maritime navigation service provided by unmanned vessels. , This indicates that unmanned ships will perform maritime missions. Change to The operation, Indicates maritime navigation mission Change to Operation; It is the overall payoff function of the maritime navigation mission scheduling subgame. , For the task Change to The subsequent payoff function.

5. The method according to claim 4, characterized in that, Step 3 includes: using a decision tree optimization model to form the optimal maritime mission scheduling. and maritime navigation scheduling The decision tree optimization model consists of nodes and branches, where each node represents a decision made by each unmanned surface vessel (USV), and each branch represents a set of actions that the USV may take.

6. The method according to claim 5, characterized in that, Step 3 also includes: In the case of no navigation mission migration: In the maritime mission scheduling subgame, the optimal equilibrium strategy for each maritime mission scheduling sub-task is: ， ， The optimal equilibrium strategy for the maritime mission scheduling sub-task is expressed as follows: for the first... In an unmanned surface vessel (USV) maritime sub-mission, all other participants choose an equilibrium strategy. In the case of the first Participants in an unmanned surface vessel (USV) maritime sub-mission choose nonequilibrium strategies. The payoff at that time will not exceed that of choosing the equilibrium strategy. The benefits at that time; in Represents the participant's payoff function; This indicates the nonequilibrium strategy chosen by the participants; This represents the equilibrium strategy chosen by the participants; This represents the set of strategies of all participants other than the participant. This represents the set of all participants except the participant who choose the equilibrium strategy. These are constraints; Indicates in subtask In addition to the participants In addition, the strategy combinations of all other participants; Let J represent the last element of the set of maritime mission scheduling strategies in the constraints, I represent the total number of mission stages in the entire mission scheduling problem, and J represent the total number of sub-tasks within stage I. This represents the total number of unmanned vessels under the above conditions.

7. The method according to claim 6, characterized in that, Step 3 also includes: In the maritime route scheduling subgame, the optimal equilibrium strategy for each maritime route scheduling subtask is: ， ， The optimal equilibrium strategy for the maritime navigation scheduling sub-task represents the first equilibrium strategy in route scheduling. An unmanned vessel, when all other entities adopt a balanced navigation strategy At that time, the first The unmanned vessel chooses any non-equilibrium route. The gains obtained will not be higher than those from choosing the balanced route. The benefits at that time; in The route revenue function for unmanned vessels; This indicates that the participant chose a non-optimal route; Indicates the optimal route for the participants; This represents the set of navigation strategies for all unmanned vessels other than the participants. This represents the set of strategies adopted by all entities other than the participants, which are based on a balanced flight path. At time t, in the current stage, the set of route strategies of all subjects is the portion after removing the kth subject; This represents the last element of the set of route scheduling strategies in the constraints.

8. The method according to claim 7, characterized in that, Step 3 also includes: Design a multi-stage impact classification method to define the affected tasks and solve the optimal scheduling problem, i.e., when maritime mission services are interrupted, the following constraints are applied: ， ， in Indicates maritime mission The start time; This indicates the start time of the maritime mission after experiencing b failures; This indicates the duration of the b-th failure case; The following algorithm is established: ， in Indicates the completion time of the preceding task, i.e., the maritime mission. The earliest time when execution can begin; Indicates current maritime mission The difference in workload between this task and the subsequent maritime mission m; Indicates maritime mission Processing speed; Indicates subsequent maritime missions The planned start time; For indicator functions, i.e., when subsequent tasks When task m is selected, the value is 1; otherwise, it is 0. ， in Indicates subsequent tasks The planned start time, Indicates subsequent tasks The execution time; that is Indicates task The planned end time; ， in For the first The completion time of each preliminary maritime mission; For the indicator function, only the departure time after task p is completed. Earlier than the available start time for unmanned ships When the time condition is met, the value is 1; otherwise, it is 0. For the preceding tasks To the current task The quantified value of workload; For the speed of unmanned ships in navigation or task processing; For the subsequent task m to task The quantified value of workload; For the task The planned start time; For the task Execution time; For indicator functions, only when the task If it belongs to task flow l, the value is 1; otherwise, it is 0. ， in, For indicator functions, only when the task If it belongs to task flow l, the value is 1; otherwise, it is 0. For the task The planned start time; For the task Execution time; For the preceding tasks To the current task The quantified value of workload; For maritime missions Processing speed; The unmanned vessel maritime mission scheduling subgame and maritime navigation scheduling subgame are defined by three elements in the following equation, as shown below: ， ， in Subgame for maritime mission scheduling; This is a subgame for maritime navigation scheduling. A gathering of participants in maritime missions. A group of participants in maritime navigation missions; A set of task strategies; A collection of maritime routes and avoidance strategies; First, address maritime missions directly affected by relocation without navigation tasks; then, process all maritime missions affected by delays or relocations in subsequent steps. In this game, for each subgame, participants formulate strategies based on the actions of the other unmanned vessels to minimize the payoff function. For each subtask within a maritime mission, each participating unmanned vessel has a nonequilibrium maritime mission strategy. Unbalanced route strategy All meet the following conditions: ， ， in, Let μ be the payoff function of step μ in the maritime mission scheduling subgame; For step μ, the non-equilibrium task strategy selected in the task scheduling subgame; Let μ be the equilibrium task strategy selected in the task scheduling subgame in step μ. The set of equilibrium strategies chosen by all other unmanned vessels in the maritime mission scheduling subgame; Let μ be the payoff function of step μ in the navigation scheduling subgame; For step μ, the non-equilibrium route strategy selected in the navigation scheduling subgame; The equilibrium route strategy selected in step μ within the navigation scheduling subgame; This is the set of equilibrium strategies chosen by all other unmanned vessels in the navigation scheduling subgame.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 8.

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