Potential game distributed optimization method for unmanned aerial vehicle group area coverage

Abstract

The invention provides a potential game distributed optimization method for unmanned aerial vehicle group area coverage. The potential game distributed optimization method comprises the following steps: step 1, inputting and initializing; 2, calculating the regret value of each unmanned aerial vehicle; thirdly, each unmanned aerial vehicle judges whether the strategy needs to be updated or not according to the regret value; fourthly, each unmanned aerial vehicle judges whether the optimal response needs to be calculated in the next round of iteration or not; and 5, each unmanned aerial vehicle calculates the regret value according to the result of the step 4. According to the potential game distributed optimization method for unmanned aerial vehicle group area coverage, the coverage optimization can be effectively carried out aiming at the area optimal coverage problem of the unmanned aerial vehicle group, and the optimization effect close to that of a central method can be achieved only by carrying out local information interaction and distributed decision making by the unmanned aerial vehicle; and meanwhile, the time required for calculation is greatly reduced, and the problem of regional optimal coverage of the large-scale unmanned aerial vehicle group is effectively solved.

Description

Technical Field

[0001] This invention relates to a distributed optimization method for regional coverage of UAV swarms based on game theory. The method provides a game-theoretic framework for optimal coverage of UAV swarms and designs a distributed optimization method for regional coverage of UAV swarms, which is suitable for the efficient collaborative deployment of large-scale UAV swarms in dynamically changing environments. Background Technology

[0002] The optimal coverage problem is a typical optimization problem that aims to maximize or minimize coverage of a target under certain constraints, thereby improving the overall efficiency of the system. UAV swarm area coverage is a typical application scenario of the optimal coverage problem, with significant potential in disaster monitoring, urban security, and other fields. For example, when multiple UAVs collaboratively patrol a designated area, it is necessary to plan routes or hovering positions to minimize overlapping coverage areas while simultaneously satisfying full area coverage and endurance limitations.

[0003] Traditional methods for solving the optimal cover problem rely on a centralized approach, where the solution and computation are concentrated on a single node. Some related research can be found at: 1. Li Yaobing. Research on the Coverage Problem of Wireless Sensor Networks Based on Energy Optimization [D]. Beijing Institute of Technology, 2016. 2. Yoon Y, Kim Y H. An efficient genetic algorithm for maximum coverage deployment in wireless sensor networks [J]. ieee transactions oncybernetics, 2013, 43(5): 1473-1483. 3. Shi Tuo. Coverage problem of passive sensor networks [D]. Harbin Institute of Technology, 2021. As the scale of intelligent agent systems in reality continues to expand, centralized methods face significant challenges in terms of computational efficiency, communication burden, and fault tolerance, making it urgent to develop distributed decision-making methods suitable for large-scale multi-agent systems.

[0004] With the rapid development and increasing scale of multi-agent systems, distributed decision-making methods have become an important tool for solving the optimal coverage problem in large-scale multi-agent systems due to their advantages such as scalability, robustness, and efficiency. Existing distributed methods for optimal coverage problems can be mainly divided into three types: learning-based methods, heuristic-based methods, and game-theoretic methods. Learning-based methods (e.g., Cao Shuchen. Research on UAV Cooperative Area Coverage Strategy Based on Reinforcement Learning [D]. Harbin Institute of Technology, 2021.) can achieve adaptive optimization through data-driven approaches, avoiding the dependence on precise environmental modeling in traditional methods. Heuristic-based methods (e.g., Luo Xuan. Research on Multi-UAV Cooperative Task Decision and Planning Method Based on Ant Colony Algorithm in Unknown Environments [D]. University of Electronic Science and Technology of China, 2023.) include ant colony algorithms, virtual potential field methods, and genetic algorithms, which are relatively simple to implement and highly scalable, and have good results for many different problems. In game-theoretic methods, agents make independent decisions based on their own utility functions while also considering the strategies of other agents, which is highly compatible with the characteristics of multi-agent distributed decision-making and provides a rigorous mathematical framework for distributed optimization, attracting widespread attention. In particular, the potential game-based approach (e.g., Zhang Z, Jiang J, Zhang WA, et al. Distributed dynamic task allocation for unmanned aerial vehicle swarm systems: A networked evolutionary game-theoretic approach [J]. Chinese Journal of Aeronautics, 2024, 37(6): 182-204.) can guarantee the consistency between Nash equilibrium and the global optimal solution, while supporting distributed implementation that relies only on local information interaction.

[0005] The existing methods for optimizing UAV area coverage have the following limitations: 1. Centralized methods have high computational complexity and poor real-time performance when dealing with large-scale drone swarms.

[0006] 2. Learning-based methods lack theoretical convergence guarantees and require a large amount of training data, resulting in poor interpretability.

[0007] 3. Heuristic algorithms also lack theoretical convergence guarantees, the solutions are unstable, and their performance is sensitive to parameter selection. In practical applications, repeated parameter tuning is often required.

[0008] 4. Game-based methods are mostly limited to discrete strategy spaces or specific scenarios, and the theory of universality in continuous strategy spaces still needs to be developed.

[0009] To overcome the above limitations, this invention proposes a distributed optimization method for regional coverage of UAV swarms in a continuous policy space, which is a potential game-based approach to ensure that the agent's decision-making can converge to the equilibrium solution of the game with only local information interaction. Summary of the Invention

[0010] The technical problem solved by this invention is to address the problem of optimal regional coverage for UAV swarms. A distributed optimization method based on the potential game is proposed for regional coverage of UAV swarms. A global performance index that takes into account both coverage performance and energy consumption is constructed, and then a highly efficient distributed algorithm is designed to obtain global approximate optimal coverage.

[0011] The solution of this invention: For the problem of optimal regional coverage of UAV swarms, a distributed optimization method based on the potential game is proposed. This method can find the optimal solution of the problem of optimal regional coverage of UAV swarms through distributed information interaction and calculation without the need for a central node.

[0012] The specific steps proposed in this invention are explained below to address the problem. Consider the typical problem of maximizing the coverage area of ​​a two-dimensional target region by a drone swarm while minimizing energy consumption during the process. Assume there are a total of *k* drones, denoted as... For any , The strategy is ,represent The displacement between the desired deployment location and the initial deployment location. The feasible deployment location is a rectangular area near the initial location. ,Right now satisfy .

[0013] Assumption The coverage area of ​​the target is is a two-dimensional Lebesgue measurable set, and the coverage area (Lebesgue measure) is denoted as . .make This represents the combined strategy for all drones. The value space representing the combination strategy. Indicates except The combined strategy of all other agents. Let express Make a strategy The energy penalty function at that time.

[0014] Assuming the target area to be covered is In this scenario, The measure of target area coverage represents its coverage area and the area of ​​the overlapping portion of the target area. Furthermore, given a fixed initial deployment location, if... strategy If confirmed, then It will also be determined, therefore It is about The function, i.e. For a single drone In terms of its coverage area of ​​the target region It can be calculated using the following formula: (1) in, Represents the drone's position on a plane. represent The expression for the observation function of the target region is: (2) That is when Execution strategy It can then cover hour, ,otherwise To determine the coverage performance of multiple drones, a peak-shaving function is defined: (3) The overall coverage performance of so many drones can be calculated using the following formula: (4) in, Let represent the union of all drone coverage sets. The expression within the integral sign satisfies the condition that exists. It can cover points The value is 1 if it is true, and 0 otherwise. (Single drone) The local coverage performance can be calculated using the following formula: (5) in, Representing the l One drone The observation function; For the first k The set of neighbors of a drone is defined as the sum of the neighbors of the drones. There exists a set of drones with overlapping coverage; represent The union of all neighbor covers. The expression within the integral sign on the right-hand side of equation (5) satisfies the condition that only It can cover points It equals 1 when it is true and 0 otherwise, indicating that for The area that the neighbors can cover. Therefore, they tend to stop covering that area. Finally, the drone's energy consumption function is defined as: (6) in, This is the proportionality coefficient; The global performance metric is then calculated as follows: (7) The calculation method for local performance indicators is as follows: (8) The two indicators above illustrate that the optimization goal of drone swarms is to maximize the coverage of the target area while reducing the energy consumed during maneuvers.

[0015] Treating each drone as a rational player, the optimal coverage problem of a drone swarm is modeled as a game theory problem: (9) in, This represents the game between the drone swarm and local performance indicators; Indicates the first k If we consider the local performance metrics of each drone, then the optimal coverage distributed decision problem of a drone swarm can be expressed as: Each drone... By interacting with neighbors, the optimal strategy is sought to maximize the local performance index (8) while simultaneously maximizing the global performance index (7). It can be proven that when the local performance index is taken as (8) and the potential function as (7), then... This constitutes a potential game. At this point, the equilibrium solution of the game must be the local optimal solution of the potential function (7), and each agent improves its strategy unilaterally one by one, eventually converging to the equilibrium solution of the game.

[0016] Next, we will design a corresponding method to solve this problem. The specific steps are as follows: Step 1: Input and Initialization Input set of intelligent agents Convergence accuracy Total number of iterations P Initialize the initial policy , and number of iterations .

[0017] Step 2: Each drone Calculate your own regret value Each drone Calculate the first based on local information. p Regret value in the next iteration ,Right now (10) (11) in, Representing the p In the next iteration Obtain the strategy; Representing the In the next iteration, remove A combined strategy for all remaining drones; The representatives passed and Calculate the value of equation (8).

[0018] Step 3: Each drone determines whether it needs to update its strategy based on its regret value. Each drone Determine whether it satisfies the following two properties: 1. Among all its neighbors, It has the highest regret value and 2. Among all neighbors with the same regret value, It has the smallest index.

[0019] If so, keep Otherwise, let .

[0020] Step 4: Each drone determines whether it needs to calculate the optimal response in the next iteration. Each drone Determine whether the following properties are satisfied: Neighborhood set satisfy: (12) in, l Representing the l An index of drones, Representing the l The drone in the first p The regret value obtained in the round of iteration.

[0021] If yes, proceed to step 5 and execute case 1; otherwise, proceed to step 5 and execute case 2. Let... .

[0022] Step 5: Calculate the regret value for each drone based on the results of Step 4. Case 1: Calculate according to equations (10) and (11) and ; Scenario 2: Order , .

[0023] if Return to step 3; otherwise, end the loop and output the result. .

[0024] With an allowable error of Under the given conditions, following the steps described above, a locally optimal solution to the UAV area optimal coverage problem will eventually be output (maximizing the global performance index (7)), which is also a game theory problem. It is possible to find an equilibrium solution, and it can be proven that the method can always output the result in a finite number of steps.

[0025] The advantages of this invention compared to the prior art are: First, a potential game framework for optimal coverage of UAV swarms was established, which for the first time extended the potential game modeling of the optimal coverage problem of UAV swarms to the continuous policy space.

[0026] Second, a mechanism is proposed to determine whether to update the strategy based on the regret value through local interaction (the third step of the method), which enables the technology to achieve global optimization through fully distributed computing and accelerates the convergence speed of the technology.

[0027] Third, a local equilibrium judgment mechanism (step four of the method) is proposed, which enables UAVs to determine whether to perform policy update calculations based on local information, greatly reducing the consumption of computing resources and accelerating the convergence speed of this technology. Attached Figure Description Figure 1 This is a flowchart of a distributed optimization method for regional coverage by drone swarms based on potential game theory.

[0028] Figure 2 This is a schematic diagram of the initial scene of a drone swarm.

[0029] Figure 3 This is a distribution map of the drone swarm optimized using the method proposed in this invention.

[0030] Figure 4 This is a distribution map of drone swarms optimized using a traditional centralized method.

[0031] Figure 5 This is a computation time graph showing the methods proposed in this invention and the centralized method under different total numbers of drones.

[0032] Figure 6 The graph shows the performance indicators of the proposed method and the centralized method under different total numbers of drones.

[0033] Symbol explanation: : No. k One drone; : No.k A strategy for individual drones; : No. k The strategic space of each drone; :remove The combined strategy of all external agents; : A combined strategy for all drones; : The space for all drone strategy combinations; : No. k The coverage area of ​​the drone; : No. k Energy consumption of a drone maneuver; Global performance metrics of drone swarms; : No. k Local performance indicators of a drone; : No. k A collection of neighbors of a drone; The interplay between drone swarms and local performance metrics; Target coverage area; : No. k The observation function of a drone; Peak-shaving function; : Proportional coefficient; Convergence accuracy; Total number of algorithm iterations. Detailed Implementation The following simulation illustrates the specific implementation of the distributed optimization method for regional coverage using a drone swarm. First, the simulation scenario is introduced: in this simulation, there are 20 drones initially randomly deployed within the target coverage area, with a coverage radius of 60 meters. Figure 2 As shown, the small circle represents the deployment location of the drone, and the large circle with the small circle as its center represents the coverage area of ​​the drone.

[0034] In each iteration, the specific process for each drone is as follows: after interacting with its neighbors regarding the current strategy, it calculates its optimal response using Equation (8) as the optimization metric. And regret value The calculation method for equation (8) follows the formulas (1) to (6). This yields... Afterwards, exchange regret values ​​with your neighbors to determine if you have the highest regret value among your neighbors and if your regret value is greater than [a certain value]. If so, then according to Update the policy; otherwise, keep the policy the same as in the previous iteration. Then, for each drone... Determine whether expression (12) satisfies and let If not, it means that some neighbors are... The human-machine interface may still update its strategy in subsequent iterations, so The optimal response may change, so execute step 5, case 1; otherwise, execute step 5, case 2, then return to step 3 until the algorithm reaches its maximum number of iterations. .

[0035] According to the simulation scenario of the present invention, experiments were conducted for the following parameter values: convergence accuracy. Total number of iterations The proportionality coefficients in performance index equations (7) and (8) The target area is , In this scenario, using this technique and traditional centralized optimization (directly solving the global performance index (7)), the results are as follows: Figures 3 to 6 As shown.

[0036] Figure 3 and Figure 4 The images show the distribution of drone swarms after using this technology and centralized optimization. It can be seen that the results obtained by using the method given in this invention and the traditional centralized optimization method are quite similar. Both methods disperse the initially densely distributed drone swarms while maintaining good connectivity between the coverage areas of the drones.

[0037] Figure 5 The computation time is calculated using the method provided in this invention and the traditional centralized method for different total numbers of drones. Figure 6 Let's consider the values ​​of the global performance index (7) obtained by the two methods under different total numbers of drones. From... Figure 5 and Figure 6 As can be seen, the global performance metrics obtained by the method presented in this invention are very close to those of the centralized method. However, the method presented in this invention saves a lot of computation time, and the computation time of this method increases only slightly with the increase in the number of drones, while the computation time of the centralized method increases significantly.

[0038] In summary, the present invention proposes a distributed optimization method for regional coverage of UAV swarms, which can effectively optimize coverage by means of game theory. Moreover, it only requires UAVs to perform local information exchange and make decisions in a distributed manner, which can achieve optimization results close to those of centralized methods. At the same time, it greatly reduces the computation time required and effectively solves the regional optimal coverage problem of large-scale UAV swarms.

Claims

1. A distributed optimization method based on potential game theory for regional coverage by unmanned aerial vehicle (UAV) swarms, characterized in that: The method comprises the following steps: Step 1: input and initialization input drone set , convergence precision , and total iteration number P , initialize initial policy , , and iteration number ; Step 2: Calculate the regret value for each drone for each drone Each drone The regret value in the second iteration is calculated according to the local information p The regret value in the second iteration is calculated according to the local information That is (10) (11) wherein, representing the first p iteration get the policy; representing the first iteration, remove the combined policy of all remaining drones; Step 3: each UAV judges whether the UAV needs to update the strategy according to the regret value each drone determining whether two properties are satisfied Property 1, among all its neighbors, with the largest regret value and ; Property 2. Among all neighbors with the same regret value, with the smallest index; If yes, keep unchanged; otherwise, let ​ Step 4: each UAV judges whether the UAV needs to calculate the optimal response in the next round of iteration each drone determining whether the following property is satisfied: a neighbor set of satisfies: (12) wherein, l represents an index of the l drone, represents a regret value obtained by the l drone in the p round iteration, If yes, case 1 is performed in the fifth step, otherwise case 2 is performed in the fifth step; let ; Step 5: each UAV calculates the regret value according to the result of step 4 Case 1 : Calculate according to formula (10) and formula (11) and ; Case 2: Let , ; If , go to step 3; otherwise, end the loop and output . 2.The potential game distributed optimization method for regional coverage of UAV swarm according to claim 1, wherein: Let there be N drones in total, denoted as ; for any , strategy is , representing desired deployment location and the displacement between the initial deployment location, feasible deployment location is a rectangular area near the initial location , i.e. satisfies . 3.The potential game distributed optimization method for regional coverage of UAV swarm according to claim 1 or 2, characterized in that: Let The coverage of the target is is a two-dimensional Lebesgue measurable set, and the coverage area is denoted by Let denote the combined strategy of all UAVs, represent the value space of the combined strategy, represents the combined strategy of all drones except ; let represents the energy penalty function when making a strategy ​ 4. The potential game based distributed optimization method for regional coverage of UAV swarm according to claim 3, characterized in that: Let the target area to be covered be ; in this scenario, The measure of the target area coverage represents its coverage range and the area of the overlap with the target area; moreover, in the case of initial deployment position determination, if the strategy is determined, then will also be determined, therefore is a function of , i.e. ; for a single drone , it is the area of the target area coverage which is calculated by the following formula: (1) wherein, represents the position of the drone on the plane, represents an observation function of the target area, expressed as: (2) That is when Execute policy Post-override to , , otherwise .

5. The potential game based distributed optimization method for regional coverage of UAV swarm according to claim 4, characterized in that: For the coverage performance of multiple UAVs, a peak clipping function is defined as follows: (3) Then the overall coverage performance of multiple UAVs is calculated according to the following formula: (4) wherein, represents the union of all drone coverage sets; the expression inside the integral satisfies the existence covers a point is equal to 1, otherwise it is equal to 0. 6.The potential game distributed optimization method for regional coverage of UAV swarm according to claim 4, characterized in that: Single unmanned aerial vehicle The local coverage performance of the single unmanned aerial vehicle is calculated as follows: (5) in, Representing the l One drone The observation function; For the first k The set of neighbors of a drone is defined as the sum of the neighbors of the drones. There exists a set of drones with overlapping coverage; represent The union of all neighbor covers; the expression within the integral sign on the right-hand side of equation (5) satisfies when only Coverage Point The value is 1 if it is true and 0 otherwise, indicating that for The area covered by the neighbors, The tendency is to no longer cover that area; finally, the drone's energy consumption function is defined as: (6) wherein is a proportionality factor.

7. The potential game based distributed optimization method for regional coverage of UAV swarm according to claim 5 or 6, characterized in that: The calculation method of the global performance index is as follows: (7) The calculation method of the local performance index is as follows: (8) The above two indexes indicate that the optimization goal of the UAV group is to maximize the coverage range of the target area while reducing the energy consumption of the maneuvering process. 8.The potential game distributed optimization method for UAV swarm area coverage according to claim 7, wherein: Regarding each UAV as a rational player, the optimal coverage problem of the UAV group is modeled as a game problem: (9) wherein, represents a game composed of the UAV group and the local performance index; represents the local performance index of the i k th UAV. 9.The potential game distributed optimization method for UAV swarm area coverage according to claim 8, characterized in that: The optimal coverage distributed decision problem of UAV swarm is represented as: each UAV By interacting with neighbors, find the optimal strategy to maximize the local performance indicator formula (8), while also maximizing the global performance indicator formula (7); when the local performance indicator is taken as formula (8) and the potential function is taken as formula (7), then a potential game is formed, and the equilibrium solution of the game is the local optimal solution of the potential function formula (7), which will eventually converge to the equilibrium solution of the game.

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