A multi-unmanned aerial vehicle game learning path optimization method for airspace congestion

Abstract

The application relates to a multi-unmanned aerial vehicle game learning path optimization method for airspace congestion, comprising the following steps: S1: structurally modeling a target airspace, depicting airspace congestion degree through a ratio of flow and capacity, so as to obtain a time-varying congestion state distribution; S2: based on historical flight flow data and the time-varying congestion state distribution, constructing a time series prediction model, and acquiring a continuous space-time congestion field; S3: for each unmanned aerial vehicle, combining a starting point, an ending point and the space-time congestion field, and generating a candidate path by using an improved heuristic search algorithm; S4: constructing a global path selection game model, and based on the candidate path, obtaining an initial optimal path distribution at a global level; S5: the unmanned aerial vehicle performs inspection based on the initial optimal path distribution at the global level, and a local collision avoidance game mechanism is introduced, so that the unmanned aerial vehicle avoids local conflicts while keeping the overall path trend. The application realizes the global coordination and local self-adaptation unification of multi-unmanned aerial vehicle path planning.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path optimization, and more particularly to a multi-UAV game-theoretic learning path optimization method for airspace congestion. Background Technology

[0002] With the opening of low-altitude airspace and the rapid growth of UAV applications, the high-density operation of multiple UAVs in limited airspace has made airspace congestion and flight conflicts increasingly prominent. Traditional path planning methods are mostly based on static environment or local information for decision-making, making it difficult to characterize the time-varying characteristics of airspace congestion and unable to effectively deal with the dynamic coupling relationship between multiple UAVs, which can easily lead to increased local congestion and decreased overall efficiency. At the same time, although centralized optimization methods can obtain better solutions, they have high computational complexity and poor scalability, making it difficult to meet the needs of large-scale real-time applications; while fully distributed methods lack global coordination and are prone to getting trapped in suboptimal solutions. Summary of the Invention

[0003] To address the aforementioned problems, the present invention aims to provide a multi-UAV game-theoretic learning path optimization method for airspace congestion. By constructing a spatiotemporal congestion field and introducing global path selection game and local collision avoidance game mechanisms, the method achieves a unified approach to global coordination and local adaptation in multi-UAV path planning.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: A multi-UAV game-theoretic learning path optimization method for airspace congestion includes the following steps: S1: Perform structured modeling of the target airspace, characterize the degree of airspace congestion by the ratio of flow to capacity, and thus obtain the time-varying congestion state distribution; S2: Based on historical flight traffic data and time-varying congestion status distribution, a time series prediction model is constructed to estimate the congestion level of each route in the future, forming a continuous spatiotemporal congestion field; S3: For each drone, candidate paths are generated using an improved heuristic search algorithm, taking into account its origin, destination, and spatiotemporal congestion field. S4: Construct a global path selection game model and obtain the initial optimal path distribution at the global level based on candidate paths; S5: The UAV performs inspections based on the initial optimal path distribution at the global level and introduces a local collision avoidance game mechanism to enable the UAV to avoid local conflicts while maintaining the overall path trend.

[0005] Furthermore, a structured model of the target airspace is performed, as follows: First, the continuous three-dimensional airspace is discretized into spatial cells with clear boundaries, forming a regular three-dimensional grid structure. Based on the flight characteristics of the UAV and air traffic rules, key spatial nodes are extracted as route intersections, turning points, and altitude change points, constructing a directed graph G=(V,E). Here, the node set V represents key spatial locations in the airspace, including take-off and landing points, waypoints, and temporary hovering areas. Each node has three-dimensional coordinate attributes (x,y,z) and a corresponding airspace type identifier. The edge set E represents the direct reachable paths between adjacent nodes. Each edge carries the flight constraints of the UAV at a specific altitude and direction, including the minimum flight distance, the allowed speed range, and the preconditions for entering the path segment. The original three-dimensional spatial nodes are expanded into four-dimensional spatiotemporal nodes, forming a spatiotemporal extended network G'=(V×T, E'). For each spatial node v∈V in the original network, sampling is performed on the continuous time axis according to the discrete time step Δt, generating a series of time-marked nodes (v,t), where t∈{0,Δt,2Δt,...,T}, and T is the planning time range; the spatiotemporal edge e'∈E' connects the spatial nodes at adjacent times, indicating that the UAV starts from position v i At time t, fly to position v j Feasible paths at time t+Δt.

[0006] Furthermore, the degree of airspace congestion is characterized by the ratio of flow to capacity, thereby obtaining the time-varying congestion state distribution, as detailed below: Define a capacity constraint C on each edge of the spatiotemporally extended network. e and dynamic flow variable f e (t), where the capacity C e This represents the maximum number of drones that can safely pass through this path segment per unit time; dynamic flow f e (t) represents the number of drones actually passing through this edge at time t: ; ; Among them, L e W is the length of the side. e H e These represent the width and height of the path cross-section, respectively; V safe The volume required for the safe use of a single drone; The function is an indicator function, which is 1 if the path of drone i at time t contains edge e, and 0 otherwise; Congestion level is obtained by calculating the ratio of traffic to capacity: ; Congestion costs : ; Where τ0 is the free-flow time; α and β are congestion parameters; and γ is the overload penalty coefficient. Global congestion state distribution : ; Overall airspace congestion index : .

[0007] Furthermore, based on historical flight traffic data and time-varying congestion status distribution, a time series prediction model is constructed to estimate the congestion level of each route in the future, forming a continuous spatiotemporal congestion field, as follows: Based on the time-varying congestion state ρ output in step S1 e (t), combined with historical flight traffic data, to construct a multi-dimensional time series input:

[0008] Where K is the number of extraction time steps; f e (tk) represents the flight flow data at time step tk; ρ is the time rate of change of congestion. e (tk) represents the time-varying congestion state at time step tk; Based on graph attention networks and the Transformer architecture, a prediction model that integrates temporal dependence and spatial coupling is constructed to obtain future congestion predictions. ; By integrating the predictions of all routes over multiple future time steps, a continuous spatiotemporal congestion field function is constructed, and the spatiotemporal congestion field is defined: ; in, For predicting the step size index; Continuous representation: ; Where φ(·) is the time kernel function; For the smoothed congestion estimate; Uncertainty modeling: ; in, The variance of the prediction error; For expectation operators; Risk-corrected congestion: ; in, This is the congestion level after risk correction; Final output predicts congested fields: .

[0009] Furthermore, based on graph attention networks and the Transformer architecture, a prediction model that integrates temporal dependence and spatial coupling is constructed, as follows: The original input is embedded into a high-dimensional feature space through a linear mapping: ; Among them, W emb For embedding the weight matrix, b emb For bias terms, This represents the initial feature representation; Spatial dependencies are modeled using a graph attention network, representing the entire route network as a graph structure. Each route edge is considered a graph node. If two edges are spatially adjacent or have a potential conflict, a connection is established. For any adjacent edges e and e′, their influence weights are dynamically calculated using an attention mechanism. ; Among them, h e and h e′ Let e ​​and e′ represent the feature vectors of edge e and edge e′ in the current layer, respectively. W is the linear transformation matrix, and a is the attention weight vector. This represents a vector concatenation operation; The attention coefficient was then normalized: ; in, Denote the set of adjacent edges of edge e; Finally, the updated spatial features are obtained through weighted aggregation: ; Where σ(·) is a nonlinear activation function; The temporal dependency is modeled using a Transformer structure, and the location encoding PE(t) is superimposed with spatial features: ; Then construct the query Q, key K, and value matrix V: ; Among them, W Q, W K W V It is a linear transformation matrix; Calculate time dependencies using a scaled dot product attention mechanism: ; Where, dk The dimension of the key vector; T represents the transpose; Further nonlinear features are extracted using a feedforward neural network. ; Among them, W 1, W2 is the weighting coefficient; b1 and b2 are the biases. The final feature representation after time modeling is obtained: ; Here, Transformer represents the Transformer module; The prediction layer is constructed to output the congestion values ​​for multiple future steps, and the value is taken at the last time step t. K Features are used as a global representation: ; The fully connected layer outputs the prediction results for the next HH time steps: ; in, W o To output the weight matrix, b o This is a bias term.

[0010] Furthermore, for each drone, candidate paths are generated using an improved heuristic search algorithm, taking into account its origin, destination, and spatiotemporal congestion field, as follows: After obtaining the spatiotemporal congestion field F(e,t) output in step S2, for each UAV i, its starting point s is considered. i End point d i Flight time windows and dynamic constraints are used to construct a unified input for the path search problem. A spatiotemporal extended network G′=(V×T,E′) is used as the search space, where each node represents the position and state of the UAV at a specific moment. A multi-factor fusion path cost function is defined, comprehensively considering factors such as flight distance, time consumption, current congestion, and predicted congestion. For any spatiotemporal edge e′=(v t →v t +Δt), the cost is defined as:

[0011] Among them, L e Let ρ be the side length. e (t) represents the current congestion level, ρ^e(t) represents the predicted congestion level, and w1, w2, w3, and w4 are weighting coefficients; Based on the cost function, an improved A algorithm is used for path search, incorporating congestion prediction information: ; Where d(n,d i ) represents the Euclidean distance from the current node to the target node; Accumulated congestion estimates for future paths; The weighting coefficients are used; through the improved A algorithm, multiple feasible paths are generated for each drone, forming a candidate path set. Each path is a sequence of nodes that satisfy spatiotemporal constraints: And it satisfies the time monotonically increasing and reachability constraints; Calculate the comprehensive cost for each candidate path: ; The output should be sorted by cost from low to high.

[0012] Furthermore, a global path selection game model is constructed, and based on the candidate paths, the initial optimal path distribution at the global level is obtained, as follows: Based on the candidate path set obtained for each drone in step S3, the multi-drone path selection problem is modeled as a non-cooperative congestion game. Let the drone set be U={1,2,…,i,…,N}, and for any drone i, its policy space is the candidate path set: ; Where K represents the number of candidate paths, and each path It consists of several spacetime edges; Define the cost function of the path, and for drone i, choose path P. i Its cost is defined as: ; Where, P -i This indicates the path selection for all drones except drone i; Let be the free flight time of edge e; g(·) be the congestion cost function; , These are the weighting coefficients of the cost function; The corresponding payoff function is: ; Since multiple drones share airspace resources, there are coupling relationships between their path choices. Therefore, a congestion game model is constructed, introducing a latent function to transform the problem into a potential game: ; Where P represents the path combination of all drones; f e Let C be the total flow on edge e; e Let the edge capacity be ; The latent function satisfies: ; A path selection mechanism based on a probabilistic strategy is used to solve the problem, defining the path selection for UAV i. The probability of selection is: ; in, For path The cost; θ is the temperature parameter; To obtain a stable path distribution, an iterative update mechanism is adopted. In each iteration, the edge traffic is calculated based on the current policy distribution of all drones. ; After updating the path cost, the strategy iterates as follows:

[0013] Where η is the learning rate or update step size; When the convergence condition is met, i.e., the policy change is less than the threshold, :

[0014] The system is then considered to have reached equilibrium. The final output is the global path distribution: ; Determine the deterministic path: .

[0015] Furthermore, the UAV performs inspections based on the initial optimal path distribution at the global level, and introduces a local collision avoidance game mechanism to ensure that the UAV maintains the overall path trend while avoiding local conflicts, as detailed below: After obtaining the initial optimal path distribution at the global level in step S4, each UAV follows its assigned optimal path. To carry out inspection tasks; During execution, the UAV updates its state in discrete time steps, and its ideal motion state is represented as: ; in, Reference trajectory state; To ensure flight stability and path tracking accuracy, path tracking control error is introduced: A local collision avoidance game mechanism is introduced to group nearby drones. As participants in the game, each drone selects a control strategy u in the continuous action space. i (t), including speed adjustment and heading offset, defines the relative distance between drones: ; Among them, p i (t), p j (t) represents the spatial positions of UAVs i and j, respectively; When d ij (t) is less than the preset safety distance This triggers a collision avoidance game. Constructing individual utility functions: ; Each drone selects the optimal action through Nash equilibrium to mitigate conflict.

[0016] A multi-UAV game-theoretic learning path optimization system for airspace congestion includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the multi-UAV game-theoretic learning path optimization method for airspace congestion as described above.

[0017] A computer storage medium, characterized in that the computer storage medium stores a plurality of instructions, the instructions being adapted to be loaded by a processor and executed as described above.

[0018] The present invention has the following beneficial effects: 1. This invention improves traditional path planning based on static or local information to future-oriented global perception optimization by constructing a time-varying congestion modeling and spatiotemporal prediction mechanism. By introducing a time series prediction model, it estimates the future congestion state in advance and forms a continuous spatiotemporal congestion field, enabling UAVs to avoid potentially high-congestion areas during the path planning stage, thereby effectively reducing congestion risk and delay probability. 2. This invention elevates the multi-UAV path planning problem from individual optimality to group collaborative optimality by generating candidate paths and modeling global path selection game theory. It constructs a game theory model using congestion coupling relationships and solves the global equilibrium through latent functions and probability policy distributions. This enables each UAV to adaptively coordinate path selection when sharing airspace resources, avoiding local overload problems caused by resource competition, significantly improving airspace resource utilization efficiency, and reducing systemic congestion caused by path conflicts. 3. This invention introduces a local collision avoidance game mechanism to achieve an organic integration of global path guidance and local dynamic adjustment. Under the premise of maintaining the overall path trend unchanged, the UAV can autonomously adjust its flight strategy according to the real-time neighborhood status, effectively avoiding local conflicts and potential collision risks. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: refer to Figure 1 In this embodiment, a multi-UAV game-theoretic learning path optimization method for airspace congestion is provided, including the following steps: S1: Perform structured modeling of the target airspace, characterize the degree of airspace congestion by the ratio of flow to capacity, and thus obtain the time-varying congestion state distribution; S2: Based on historical flight traffic data and time-varying congestion status distribution, a time series prediction model is constructed to estimate the congestion level of each route in the future, forming a continuous spatiotemporal congestion field; S3: For each drone, candidate paths are generated using an improved heuristic search algorithm, taking into account its origin, destination, and spatiotemporal congestion field. S4: Construct a global path selection game model and obtain the initial optimal path distribution at the global level based on candidate paths; S5: The UAV performs inspections based on the initial optimal path distribution at the global level and introduces a local collision avoidance game mechanism to enable the UAV to avoid local conflicts while maintaining the overall path trend.

[0021] In this embodiment, the target spatial domain is structurally modeled, as follows: First, the continuous three-dimensional airspace is discretized into spatial cells with clear boundaries, forming a regular three-dimensional grid structure. Based on the flight characteristics of UAVs and air traffic rules, key spatial nodes are extracted as route intersections, turning points, and altitude change points, constructing a directed graph G=(V,E). Here, the node set V represents key spatial locations in the airspace, including take-off and landing points, waypoints, and temporary hovering areas. Each node has three-dimensional coordinate attributes (x,y,z) and a corresponding airspace type identifier. The edge set E represents the direct reachable paths between adjacent nodes. Each edge carries the flight constraints of the UAV at a specific altitude and direction, including the minimum flight distance, the allowed speed range, and the preconditions for entering the path segment, thus forming a three-dimensional route network topology that conforms to actual flight rules. The original three-dimensional spatial nodes are expanded into four-dimensional spatiotemporal nodes, forming a spatiotemporal extended network G'=(V×T, E'). For each spatial node v∈V in the original network, sampling is performed on the continuous time axis according to the discrete time step Δt, generating a series of time-marked nodes (v,t), where t∈{0,Δt,2Δt,...,T}, and T is the planning time range; the spatiotemporal edge e'∈E' connects the spatial nodes at adjacent times, indicating that the UAV starts from position v i At time t, fly to position v jFeasible paths at time t+Δt; this spatiotemporal extension enables path planning to not only consider spatial connectivity, but also accurately describe the temporal evolution trajectory of UAVs, supporting accurate modeling of flight sequence, arrival time and path conflicts, and providing a complete spatiotemporal framework for subsequent dynamic congestion analysis and multi-UAV coordination.

[0022] In this embodiment, the airspace congestion level is characterized by the ratio of flow to capacity, thereby obtaining the time-varying congestion state distribution, as detailed below: Define a capacity constraint C on each edge of the spatiotemporally extended network. e and dynamic flow variable f e (t), where the capacity C e This represents the maximum number of drones that can safely pass through this path segment per unit time, constrained by airspace geometry, safety separation requirements, and air traffic control rules; dynamic flow f e (t) represents the number of drones actually passing through this edge at time t: ; ; Among them, L e W is the length of the side. e H e These represent the width and height of the path cross-section, respectively; V safe The volume required for the safe use of a single drone; The function is an indicator function, which is 1 if the path of drone i at time t contains edge e, and 0 otherwise; Congestion level is obtained by calculating the ratio of traffic to capacity: ; Congestion costs : ; Where τ0 is the free-flow time; α and β are congestion parameters; and γ is the overload penalty coefficient. Global congestion state distribution : ; Overall airspace congestion index : .

[0023] In this embodiment, a time series prediction model is constructed based on historical flight traffic data and time-varying congestion status distribution to estimate the congestion level of each route in the future, forming a continuous spatiotemporal congestion field, as detailed below: Based on the time-varying congestion state ρ output in step S1 e(t), combined with historical flight traffic data, to construct a multi-dimensional time series input:

[0024] Where K is the number of extraction time steps; f e (tk) represents the flight flow data at time step tk; ρ is the time rate of change of congestion. e (tk) represents the time-varying congestion state at time step tk; Based on graph attention networks and the Transformer architecture, a prediction model that integrates temporal dependence and spatial coupling is constructed to obtain future congestion predictions. ; The predictions of all routes at multiple future time steps are integrated to construct a continuous spatiotemporal congestion field function for subsequent path planning and game theory decision-making. The spatiotemporal congestion field is defined as follows: ; in, For predicting the step size index; Continuous representation: ; Where φ(·) is the time kernel function; For the smoothed congestion estimate; Uncertainty modeling (variance estimation): ; in, The variance of the prediction error; For expectation operators; Risk-corrected congestion: ; in, This is the congestion level after risk correction; Final output predicts congested fields: .

[0025] In this embodiment, a prediction model that integrates temporal dependence and spatial coupling is constructed based on graph attention networks and the Transformer architecture, as detailed below: The original input is embedded into a high-dimensional feature space through a linear mapping: ; Among them, W emb For embedding the weight matrix, b emb For bias terms, This represents the initial feature representation; Spatial dependencies are modeled using a graph attention network, representing the entire route network as a graph structure. Each route edge is considered a graph node. If two edges are spatially adjacent or have a potential conflict, a connection is established. For any adjacent edges e and e′, their influence weights are dynamically calculated using an attention mechanism. ; Among them, h e and h e′ Let e ​​and e′ represent the feature vectors of edge e and edge e′ in the current layer, respectively. W is the linear transformation matrix, and a is the attention weight vector. This represents a vector concatenation operation; The attention coefficient was then normalized: ; in, Denote the set of adjacent edges of edge e; Finally, the updated spatial features are obtained through weighted aggregation: ; Where σ(·) is a nonlinear activation function; The temporal dependency is modeled using a Transformer structure, and the location encoding PE(t) is superimposed with spatial features: ; Then construct the query Q, key K, and value matrix V: ; Among them, W Q, W K W V It is a linear transformation matrix; Calculate time dependencies using a scaled dot product attention mechanism: ; Where, d k The dimension of the key vector; T represents the transpose; Further nonlinear features are extracted using a feedforward neural network. ; Among them, W 1, W2 is the weighting coefficient; b1 and b2 are the biases. The final feature representation after time modeling is obtained: ; Here, Transformer represents the Transformer module; The prediction layer is constructed to output the congestion values ​​for multiple future steps, and the value is taken at the last time step t. KFeatures are used as a global representation: ; The fully connected layer outputs the prediction results for the next HH time steps: ; in, W o To output the weight matrix, b o This is a bias term.

[0026] In this embodiment, for each drone, a candidate path is generated using an improved heuristic search algorithm, taking into account its origin, destination, and spatiotemporal congestion field, as follows: After obtaining the spatiotemporal congestion field F(e,t) output in step S2, for each UAV i, its starting point s is considered. i End point d i Flight time windows and dynamic constraints are used to construct a unified input for the path search problem. A spatiotemporal extended network G′=(V×T,E′) is used as the search space, where each node represents the position and state of the UAV at a specific moment. A multi-factor fusion path cost function is defined, comprehensively considering factors such as flight distance, time consumption, current congestion, and predicted congestion. For any spatiotemporal edge e′=(v t →v t +Δt), the cost is defined as:

[0027] Among them, L e Let ρ be the side length. e (t) represents the current congestion level, ρ^e(t) represents the predicted congestion level, and w1, w2, w3, and w4 are weighting coefficients; Based on the cost function, an improved A algorithm is used for path search, incorporating congestion prediction information to reflect future path risks. ; Where d(n,d i ) represents the Euclidean distance from the current node to the target node; Accumulated congestion estimates for future paths; These are the weighting coefficients; using the improved A algorithm, multiple feasible paths are generated for each drone, forming a candidate path set. Each path is a sequence of nodes that satisfy spatiotemporal constraints: And it satisfies the time monotonically increasing and reachability constraints; Calculate the comprehensive cost for each candidate path: ; The output should be sorted by cost from low to high.

[0028] In this embodiment, a global path selection game model is constructed, and based on the candidate paths, the initial optimal path distribution at the global level is obtained, as follows: Based on the candidate path set obtained for each drone in step S3, the multi-drone path selection problem is modeled as a non-cooperative congestion game. Let the drone set be U={1,2,…,i,…,N}, and for any drone i, its policy space is the candidate path set: ; Where K represents the number of candidate paths, and each path It consists of several spacetime edges; Define the cost function of the path, and for drone i, choose path P. i Its cost is defined as: ; Where, P -i This indicates the path selection for all drones except drone i; Let be the free flight time of edge e; g(·) be the congestion cost function; , These are the weighting coefficients of the cost function; The corresponding payoff function is: ; Since multiple drones share airspace resources, there are coupling relationships between their path choices. Therefore, a congestion game model is constructed, introducing a latent function to transform the problem into a potential game: ; Where P represents the path combination of all drones; f e Let C be the total flow on edge e; e Let the edge capacity be ; The latent function satisfies: ; A path selection mechanism based on a probabilistic strategy is used to solve the problem, defining the path selection for UAV i. The probability of selection is: ; in, For path The cost; θ is the temperature parameter; To obtain a stable path distribution, an iterative update mechanism is adopted. In each iteration, the edge traffic is calculated based on the current policy distribution of all drones. ; After updating the path cost, the strategy iterates as follows:

[0029] Where η is the learning rate or update step size; When the convergence condition is met, i.e., the policy change is less than the threshold, :

[0030] The system is then considered to have reached equilibrium. The final output is the global path distribution: ; Determine the deterministic path: .

[0031] In this embodiment, the UAV performs inspections based on the initial optimal path distribution at the global level, and introduces a local collision avoidance game mechanism to enable the UAV to avoid local conflicts while maintaining the overall path trend, as detailed below: After obtaining the initial optimal path distribution at the global level in step S4, each UAV follows its assigned optimal path. To carry out inspection tasks; During execution, the UAV updates its state in discrete time steps, and its ideal motion state is represented as: ; in, Reference trajectory state; To ensure flight stability and path tracking accuracy, path tracking control error is introduced: ; The drone minimizes this error through closed-loop control (such as PID or model predictive control), thereby maintaining its position on the globally optimal path at the macro level and ensuring the orderly progress of the inspection task; a local collision avoidance game mechanism is introduced to group nearby drones. As participants in the game, each drone selects a control strategy u in the continuous action space. i (t), including speed adjustment and heading offset, defines the relative distance between drones: ; Among them, p i (t), p j (t) represents the spatial positions of UAVs i and j, respectively; When d ij (t) is less than the preset safety distance This triggers a collision avoidance game. Constructing individual utility functions: ; The first term represents the collision risk (the smaller the distance, the greater the penalty), the second term represents the cost of deviating from the original path, and the third term represents controlling energy consumption; Each drone selects the optimal action through Nash equilibrium to mitigate conflict.

[0032] A multi-UAV game-theoretic learning path optimization system for airspace congestion includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the multi-UAV game-theoretic learning path optimization method for airspace congestion as described above.

[0033] A computer storage medium storing a plurality of instructions adapted for loading by a processor and executing the method steps described above.

[0034] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0035] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0036] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0037] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0038] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A multi-UAV game-theoretic learning path optimization method for airspace congestion, characterized in that, Includes the following steps: S1: Perform structured modeling of the target airspace, characterize the degree of airspace congestion by the ratio of flow to capacity, and thus obtain the time-varying congestion state distribution; S2: Based on historical flight traffic data and time-varying congestion status distribution, a time series prediction model is constructed to estimate the congestion level of each route in the future, forming a continuous spatiotemporal congestion field; S3: For each drone, candidate paths are generated using an improved heuristic search algorithm, taking into account its origin, destination, and spatiotemporal congestion field. S4: Construct a global path selection game model and obtain the initial optimal path distribution at the global level based on candidate paths; S5: The UAV performs inspections based on the initial optimal path distribution at the global level and introduces a local collision avoidance game mechanism to enable the UAV to avoid local conflicts while maintaining the overall path trend.

2. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 1, characterized in that, The structured modeling of the target spatial domain is as follows: First, the continuous three-dimensional airspace is discretized into spatial cells with clear boundaries, forming a regular three-dimensional grid structure. Based on the flight characteristics of the UAV and air traffic rules, key spatial nodes are extracted as route intersections, turning points, and altitude change points, constructing a directed graph G=(V,E). Here, the node set V represents key spatial locations in the airspace, including take-off and landing points, waypoints, and temporary hovering areas. Each node has three-dimensional coordinate attributes (x,y,z) and a corresponding airspace type identifier. The edge set E represents the direct reachable paths between adjacent nodes. Each edge carries the flight constraints of the UAV at a specific altitude and direction, including the minimum flight distance, the allowed speed range, and the preconditions for entering that edge. The original three-dimensional spatial nodes are expanded into four-dimensional spatiotemporal nodes, forming a spatiotemporal extended network G'=(V×T, E'). For each spatial node v∈V in the original network, sampling is performed on the continuous time axis according to the discrete time step Δt, generating a series of time-marked nodes (v,t), where t∈{0,Δt,2Δt,...,T}, and T is the planning time range; the spatiotemporal edge e'∈E' connects the spatial nodes at adjacent times, indicating that the UAV starts from position v i At time t, fly to position v j Feasible paths at time t+Δt.

3. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 2, characterized in that, The spatial congestion level is characterized by the ratio of flow to capacity, thereby obtaining the time-varying congestion state distribution, as detailed below: Define a capacity constraint C on each edge of the spatiotemporally extended network. e and dynamic flow variable f e (t), where the capacity C e This represents the maximum number of drones that can safely pass through this path segment per unit time; dynamic flow f e (t) represents the number of drones actually passing through this edge at time t: ； ； Among them, L e W is the length of the side. e H e These represent the width and height of the path cross-section, respectively; V safe The volume required for the safe use of a single drone; The function is an indicator function, which is 1 if the path of drone i at time t contains edge e, and 0 otherwise; Congestion level is obtained by calculating the ratio of traffic to capacity: ； Congestion costs : ； Where τ0 is the free-flow time; α and β are congestion parameters; and γ is the overload penalty coefficient. Global congestion state distribution : ； Overall airspace congestion index : 。 4. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 1, characterized in that, Based on historical flight traffic data and time-varying congestion status distribution, a time series prediction model is constructed to estimate the congestion level of each route in the future, forming a continuous spatiotemporal congestion field, as detailed below: Based on the time-varying congestion state ρ output in step S1 e (t), combined with historical flight traffic data, to construct a multi-dimensional time series input: ； Where K is the number of extraction time steps; f e (tk) represents the flight flow data at time step tk; ρ is the time rate of change of congestion. e (tk) represents the time-varying congestion state at time step tk; Based on graph attention networks and the Transformer architecture, a prediction model that integrates temporal dependence and spatial coupling is constructed to obtain future congestion predictions. ; By integrating the predictions of all routes over multiple future time steps, a continuous spatiotemporal congestion field function is constructed, and the spatiotemporal congestion field is defined: ； in, For predicting the step size index; Continuous representation: ； Where φ(·) is the time kernel function; For the smoothed congestion estimate; Uncertainty modeling: ； in, The variance of the prediction error; For expectation operators; Risk-corrected congestion: ； in, This is the congestion level after risk correction; Final output predicts congested fields: 。 5. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 4, characterized in that, The prediction model, which integrates temporal dependence and spatial coupling, is constructed based on graph attention networks and Transformer structures, as follows: The original input is embedded into a high-dimensional feature space through a linear mapping: ； Among them, W emb For embedding the weight matrix, b emb For bias terms, This represents the initial feature representation; Spatial dependencies are modeled using a graph attention network, representing the entire route network as a graph structure. Each route edge is considered a graph node. If two edges are spatially adjacent or have a potential conflict, a connection is established. For any adjacent edges e and e′, their influence weights are dynamically calculated using an attention mechanism. ； Among them, h e and h e′ Let e ​​and e′ represent the feature vectors of edge e and edge e′ in the current layer, respectively. W is the linear transformation matrix, and a is the attention weight vector. This represents a vector concatenation operation; The attention coefficient was then normalized: ； in, Denote the set of adjacent edges of edge e; Finally, the updated spatial features are obtained through weighted aggregation: ； Where σ(·) is a nonlinear activation function; The temporal dependency is modeled using a Transformer structure, and the location encoding PE(t) is superimposed with spatial features: ； Then construct the query Q, key K, and value matrix V: ； Among them, W Q, W K W V It is a linear transformation matrix; Calculate time dependencies using a scaled dot product attention mechanism: ； Where, d k The dimension of the key vector; T represents the transpose; Further nonlinear features are extracted using a feedforward neural network. ； Among them, W 1, W2 is the weighting coefficient; b1 and b2 are the biases. The final feature representation after time modeling is obtained: ； Here, Transformer represents the Transformer module; The prediction layer is constructed to output the congestion values ​​for multiple future steps, and the value is taken at the last time step t. K Features are used as a global representation: ； The fully connected layer outputs the prediction results for the next HH time steps: ； in, W o To output the weight matrix, b o This is a bias term.

6. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 1, characterized in that, For each drone, a candidate path is generated using an improved heuristic search algorithm, taking into account its origin, destination, and spatiotemporal congestion field, as follows: After obtaining the spatiotemporal congestion field F(e,t) output in step S2, for each UAV i, its starting point s is considered. i End point d i Flight time windows and dynamic constraints are used to construct a unified input for the path search problem. A spatiotemporal extended network G′=(V×T,E′) is used as the search space, where each node represents the position and state of the UAV at a specific moment. A multi-factor fusion path cost function is defined, comprehensively considering factors such as flight distance, time consumption, current congestion, and predicted congestion. For any spatiotemporal edge e′=(v t →v t +Δt), the cost is defined as: ； Among them, L e Let ρ be the side length. e (t) represents the current congestion level, ρ^e(t) represents the predicted congestion level, and w1, w2, w3, and w4 are weighting coefficients; Based on the cost function, an improved A algorithm is used for path search, incorporating congestion prediction information: ； Where d(n,d i ) represents the Euclidean distance from the current node to the target node; Accumulated congestion estimates for future paths; These are the weighting coefficients; using the improved A algorithm, multiple feasible paths are generated for each drone, forming a candidate path set. Each path is a sequence of nodes that satisfy spatiotemporal constraints: And it satisfies the time monotonically increasing and reachability constraints; Calculate the comprehensive cost for each candidate path: ； The output should be sorted by cost from low to high.

7. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 6, characterized in that, The construction of the global path selection game model, based on candidate paths, yields the initial optimal path distribution at the global level, as detailed below: Based on the candidate path set obtained for each drone in step S3, the multi-drone path selection problem is modeled as a non-cooperative congestion game. Let the drone set be U={1,2,…,i,…,N}, and for any drone i, its policy space is the candidate path set: ; Where K represents the number of candidate paths, and each path It consists of several spacetime edges; Define the cost function of the path, and for drone i, choose path P. i Its cost is defined as: ; Where, P -i This indicates the path selection for all drones except drone i; Let be the free flight time of edge e; g(·) be the congestion cost function; , These are the weighting coefficients of the cost function; The corresponding payoff function is: ; Since multiple drones share airspace resources, there are coupling relationships between their path choices. Therefore, a congestion game model is constructed, introducing a latent function to transform the problem into a potential game: ; Where P represents the path combination of all drones; f e Let C be the total flow on edge e; e Let the edge capacity be ; The latent function satisfies: ； A path selection mechanism based on a probabilistic strategy is used to solve the problem, defining the path selection for UAV i. The probability of selection is: ； in, For path The cost; θ is the temperature parameter; To obtain a stable path distribution, an iterative update mechanism is adopted. In each iteration, the edge traffic is calculated based on the current policy distribution of all drones. ； After updating the path cost, the strategy iterates as follows: ； Where η is the learning rate or update step size; When the convergence condition is met, i.e., the policy change is less than the threshold, : ； The system is then considered to have reached equilibrium. The final output is the global path distribution: ; Determine the deterministic path: .

8. The multi-UAV game-theoretic learning path optimization method for airspace congestion according to claim 7, characterized in that, The UAV performs inspections based on an initial optimal path distribution at the global level and introduces a local collision avoidance game mechanism to ensure that the UAV maintains the overall path trend while avoiding local conflicts, as detailed below: After obtaining the initial optimal path distribution at the global level in step S4, each UAV follows its assigned optimal path. To carry out inspection tasks; During execution, the UAV updates its state in discrete time steps, and its ideal motion state is represented as: ； in, Reference trajectory state; To ensure flight stability and path tracking accuracy, path tracking control error is introduced: A local collision avoidance game mechanism is introduced to group nearby drones. As participants in the game; each drone selects a control strategy in the continuous action space. i (t), including speed adjustment and heading offset, defines the relative distance between drones: ； Among them, p i (t), p j (t) represents the spatial positions of UAVs i and j, respectively; When d ij (t) Triggers a collision avoidance game when the distance is less than the preset safety distance; Constructing individual utility functions: ; Each drone selects the optimal action through Nash equilibrium to mitigate conflict.

9. A multi-UAV game-theoretic learning path optimization system for airspace congestion, characterized in that, It includes a processor, a memory, and a computer program stored in the memory. When the processor executes the computer program, it specifically performs the steps in the multi-UAV game learning path optimization method for airspace congestion as described in any one of claims 1-8.

10. A computer storage medium, characterized in that, The computer storage medium stores a plurality of instructions adapted for loading by a processor and executing the method steps as claimed in any one of claims 1-8.

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