Unmanned aerial vehicle flight path planning method and related apparatus

Abstract

The application discloses a method for planning a flight path of a UAV and related devices, comprising: determining grid nodes of a monitoring area and edges connecting adjacent nodes; extracting a monitoring point graph from the grid structure according to monitoring points and their adjacency relations; judging whether the monitoring point graph belongs to a first preset graph set, which corresponds to monitoring point graphs satisfying a right-angle Steiner minimum tree construction condition; if yes, obtaining a target connected monitoring point graph by using a first connected graph construction algorithm based on a right-angle Steiner minimum tree problem, otherwise, using a second connected graph construction algorithm based on a minimum spanning tree; then judging whether the target connected monitoring point graph belongs to a second preset graph set, which corresponds to connected graphs capable of determining a Hamilton path within a polynomial time; if yes, planning a flight path by using a first path planning algorithm based on a Hamilton path, otherwise, using a second path planning algorithm based on tree search. Thus, the timeliness of information collection can be ensured while the path planning efficiency is improved.

Description

Technical Field

[0001] This application relates to the field of unmanned aerial vehicle (UAV) flight control technology, and in particular to UAV flight path planning methods and related devices. Background Technology

[0002] Unmanned Aerial Vehicles (UAVs) play a crucial role in environmental monitoring, disaster response, and intelligent transportation. Currently, UAVs primarily collect real-time data to aid in decision-making, and the accuracy of these decisions largely depends on the freshness of the collected data. Age of Information (AoI) is a standard for measuring data freshness; AoI represents the time elapsed since the last data update. For UAVs, certain missions require periodically visiting the same monitoring point to ensure the collected data maintains a certain level of freshness. Therefore, when planning UAV flight paths, it is necessary to consider how to minimize AoI simultaneously.

[0003] Existing UAV trajectory planning technologies mostly focus on traditional performance metrics such as network transmission speed, latency, or energy consumption. However, these methods typically assume that each monitoring point only needs to be visited once to collect all data. In scenarios requiring continuous data updates, minimizing AoI (Aspect-Oriented Integrity) is more crucial. Therefore, to further optimize trajectories, some studies have employed heuristic techniques like deep reinforcement learning to find solutions. However, these heuristics fail to provide a clear standard; they cannot guarantee consistent performance on each run and cannot effectively control the range of information freshness under various real-world conditions. Furthermore, some theoretical studies attempt to provide theoretical guarantees for information freshness, but these studies often simplify practical problems, ideally assuming that monitoring points are regularly distributed and connected. This makes it difficult to handle the complexities of monitoring points scattered across multiple non-adjacent areas in real-world applications. When monitoring points are distributed in different isolated areas, the UAV not only needs to fly to the monitoring point itself but also needs to traverse other open areas to establish path connections with monitoring points in other areas. Existing trajectory planning algorithms often fail to provide effective path planning while simultaneously ensuring information freshness. Summary of the Invention

[0004] In view of the above problems, this application provides a method and related apparatus for UAV flight path planning, so as to adaptively select the connectivity graph construction strategy and path planning algorithm according to the structural characteristics of different monitoring point maps, and effectively traverse arbitrarily distributed monitoring points while ensuring information freshness. The specific solution is as follows:

[0005] The first aspect of this application provides a method for planning the flight path of an unmanned aerial vehicle (UAV), including:

[0006] Determine the grid structure corresponding to the monitoring area; the grid structure includes multiple grid nodes with two-dimensional coordinates and edges connecting adjacent grid nodes;

[0007] Based on multiple monitoring points distributed within the monitoring area and the adjacency relationships between these monitoring points, a monitoring point map is extracted from the grid structure; the monitoring point map includes the multiple monitoring points and the edges connecting adjacent monitoring points.

[0008] The algorithm determines whether the monitoring point map belongs to a first preset graph set. If the monitoring point map belongs to the first preset graph set, a first connected graph construction algorithm is used to obtain the target connected monitoring point map. If the monitoring point map does not belong to the first preset graph set, a second connected graph construction algorithm is used to obtain the target connected monitoring point map. The first preset graph set includes monitoring point maps that satisfy the construction conditions of Rectilinear Steiner Minimal Tree (RSMT). The first connected graph construction algorithm is a connected graph construction algorithm based on the Rectilinear Steiner Minimal Tree problem. The second connected graph construction algorithm is a connected graph construction algorithm based on Minimum Spanning Tree (MST).

[0009] The algorithm determines whether the target connectivity monitoring point graph belongs to a second preset graph set. If the target connectivity monitoring point graph belongs to the second preset graph set, a first path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connectivity monitoring point graph. If the target connectivity monitoring point graph does not belong to the second preset graph set, a second path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connectivity monitoring point graph. The second preset graph set includes connected graphs that can determine Hamiltonian paths (HP) in polynomial time. The first path planning algorithm is a Hamiltonian path-based algorithm (HPA). The second path planning algorithm is a tree-searching algorithm (TSA).

[0010] A second aspect of this application provides a drone flight path planning device, comprising:

[0011] A network structure determination unit is used to determine the grid structure corresponding to the monitoring area; the grid structure includes multiple grid nodes with two-dimensional coordinates and edges connecting adjacent grid nodes;

[0012] The monitoring point map construction unit is used to extract a monitoring point map from the grid structure based on multiple monitoring points distributed within the monitoring area and the adjacency relationships between the monitoring points; the monitoring point map includes the multiple monitoring points and the edges connecting adjacent monitoring points;

[0013] A connected graph construction unit is used to determine whether the monitoring point graph belongs to a first preset graph set; if the monitoring point graph belongs to the first preset graph set, a first connected graph construction algorithm is used to obtain a target connected monitoring point graph; if the monitoring point graph does not belong to the first preset graph set, a second connected graph construction algorithm is used to obtain a target connected monitoring point graph; the first preset graph set includes monitoring point graphs that satisfy the conditions for constructing a Cartesian Steiner minimum tree; the first connected graph construction algorithm is a connected graph construction algorithm based on the Cartesian Steiner minimum tree problem; the second connected graph construction algorithm is a connected graph construction algorithm based on a minimum spanning tree.

[0014] A path planning unit is used to determine whether the target connected monitoring point graph belongs to a second preset graph set. If the target connected monitoring point graph belongs to the second preset graph set, a first path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connected monitoring point graph. If the target connected monitoring point graph does not belong to the second preset graph set, a second path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connected monitoring point graph. The second preset graph set includes connected graphs that can determine Hamiltonian paths in polynomial time. The first path planning algorithm is a path planning algorithm based on Hamiltonian paths. The second path planning algorithm is a path planning algorithm based on tree search.

[0015] A third aspect of this application provides an electronic device, comprising at least one processor and a memory connected to the processor, wherein:

[0016] The memory is used to store computer programs;

[0017] The processor is used to execute the computer program so that the electronic device can implement the UAV flight path planning method of the first aspect or any implementation thereof.

[0018] The fourth aspect of this application provides a computer storage medium carrying one or more computer programs, which, when executed by an electronic device, enable the electronic device to perform the UAV flight path planning method described in the first aspect or any implementation thereof.

[0019] The fifth aspect of this application provides a computer program product including computer-readable instructions that, when executed on an electronic device, cause the electronic device to implement the UAV flight path planning method described in the first aspect or any implementation thereof.

[0020] Compared with existing technologies, this application first performs grid-based modeling of the monitoring area and then extracts the monitoring point map, thereby transforming the UAV flight path planning problem into a unified problem of connected graph construction and path planning on a graph structure. Furthermore, by determining whether the monitoring point map belongs to a first preset graph set, a connected graph construction algorithm based on the Cartesian Steiner minimum tree problem is used when the conditions for constructing a Cartesian Steiner minimum tree are met; otherwise, a connected graph construction algorithm based on minimum spanning trees is used. This allows for the adaptive generation of target connected monitoring point maps for monitoring point maps with different distribution patterns. Therefore, on the one hand, it can establish an effective connection structure even when monitoring points are scattered and the original monitoring point map is not connected, avoiding the inability to complete the overall path planning due to the lack of connectivity between monitoring points; on the other hand, it can minimize the introduction of intermediate connection nodes and the overall connection path length while ensuring the connectivity of the monitoring point map, thereby reducing the ineffective flight overhead during the subsequent UAV cruise.

[0021] After obtaining the target connected monitoring point graph, it is further determined whether it belongs to the second preset graph set, and accordingly, an adaptive selection is made between a path planning algorithm based on Hamiltonian paths and a path planning algorithm based on tree search. For target connected monitoring point graphs that meet the conditions for constructing Hamiltonian paths, each monitoring point can be traversed sequentially using Hamiltonian paths to improve path coverage efficiency; for target connected monitoring point graphs that do not meet the conditions, the access path can be gradually expanded through tree search, thereby ensuring that a flight path covering all monitoring points can still be formed under a more general graph structure. Therefore, this application is not only applicable to scenarios where the monitoring points are regularly distributed and traversal paths are easy to construct, but also applicable to scenarios where the monitoring points are complexly distributed, the original graph is not connected, or it is difficult to directly determine Hamiltonian paths, thus improving the applicability and robustness of the UAV flight path planning method. Attached Figure Description

[0022] Figure 1 This is a schematic flowchart of a UAV flight path planning method provided in an embodiment of this application;

[0023] Figure 2 This is a schematic flowchart of a UAV flight path planning method provided in an embodiment of this application;

[0024] Figure 3 This is a schematic flowchart of a UAV flight path planning method provided in an embodiment of this application;

[0025] Figure 4 A schematic diagram of a tree-search-based path planning algorithm provided in an embodiment of this application. Detailed Implementation

[0026] Reference Figure 1 , Figure 1 This is a flowchart illustrating a drone flight path planning method provided in an embodiment of this application, as shown below. Figure 1 As shown in the figure, the UAV flight path planning method provided in this application embodiment may include steps S110 to S140, which are described in detail below.

[0027] S110. Determine the grid structure corresponding to the monitoring area.

[0028] In this embodiment, the geographical or spatial region to be monitored can be discretized in a regularized manner, dividing the entire monitoring area into several equally spaced square grid structures. Each grid structure includes multiple grid nodes with two-dimensional coordinates and edges connecting adjacent grid nodes, thereby constructing a square grid map model. Specifically, the entire monitoring area is modeled as a region map. ,in This represents the set of nodes in the region graph. This represents the set of edges between nodes. Each node in the region graph... The coordinates of a grid node in the corresponding grid structure are represented as follows: ,in This represents the coordinate position of a node in a two-dimensional plane. There is a connecting edge between any two adjacent mesh nodes, and the edge is defined as follows: This means that two nodes are considered to have a connecting edge when they are adjacent in the horizontal or vertical direction. Each edge has a unit length, which can be regarded as the basic distance unit for the UAV to move between two adjacent grid nodes. In the above region graph model, let... Represents the set of all node indices in the region graph, where This represents the total number of nodes in the region graph.

[0029] S120. Based on the multiple monitoring points distributed within the monitoring area and the adjacency relationships between each monitoring point, extract the monitoring point map from the grid structure.

[0030] Based on multiple monitoring points distributed within the monitoring area and the adjacency relationships between them, a monitoring point map is extracted from the grid structure. The monitoring point map includes multiple monitoring points and edges connecting adjacent monitoring points. Specifically, the locations of all monitoring points requiring data collection or monitoring tasks within the monitoring area are first obtained, and each monitoring point is mapped to a corresponding grid node in the grid structure, using that grid node as the monitoring point. Assume there are a total of [number missing] monitoring points within the monitoring area. There are 10 Points of Interest (PoIs), which are also monitoring points. These monitoring points are randomly distributed across some nodes on the region map, and the drone needs to periodically visit these PoIs to collect fresh information. The set of PoI nodes is denoted as . and satisfy In the aforementioned area map Based on this, the monitoring point map can be further defined as a PoI map. A monitoring point map consists of multiple monitoring points and edges connecting adjacent monitoring points, represented as follows: In this context, edges represent reachable paths or adjacency relationships between two monitoring points. Adjacency relationships can be determined based on the spatial relationships of the monitoring points within the grid structure. For example, two monitoring points are considered to be adjacent if there is a traversable path between the corresponding grid nodes or if preset adjacency conditions are met within the grid structure. Specifically, the PoI graph... The set of nodes in Represents the set of all PoI nodes, and the set of edges. This indicates the connection relationship between adjacent PoI nodes.

[0031] In this graph model, a graph is defined as connected if and only if there exists a path between any two nodes, formed by sequentially connecting several edges, where a path refers to a sequence of edges connecting a series of different nodes; if there is no path between at least one pair of nodes, the graph is defined as disconnected. In the embodiments of this application, the region graph... A graph is always a connected graph, meaning that any two grid nodes in the region grid structure can be connected by several grid edges, whereas a PoI graph... The monitoring points may be connected or disconnected depending on their location. Therefore, in the subsequent path planning process, it is necessary to process and analyze the connected and disconnected PoI maps separately to achieve effective planning of the UAV flight path.

[0032] S130. Determine whether the monitoring point map belongs to the first preset map set; if the monitoring point map belongs to the first preset map set, then use the first connected graph construction algorithm to obtain the target connected monitoring point map; if the monitoring point map does not belong to the first preset map set, then use the second connected graph construction algorithm to obtain the target connected monitoring point map.

[0033] The first preset graph set includes monitoring point graphs that satisfy the conditions for constructing a Cartesian Steiner minimum tree. A Cartesian Steiner minimum tree is a tree structure in a Cartesian grid structure where, by introducing additional nodes at necessary locations, the total side length of the tree structure connecting all monitoring point nodes is minimized. If the monitoring point graph belongs to the first preset graph set, a first connected graph construction algorithm is used to construct the target connected monitoring point graph. This algorithm is based on the Cartesian Steiner minimum tree problem and introduces necessary intermediate nodes and establishes connecting edges in the grid structure, allowing all monitoring points to be connected through a tree structure with a smaller total side length, thus obtaining the target connected monitoring point graph.

[0034] If the monitoring point graph does not belong to the first preset graph set, a second connected graph construction algorithm is used to construct the target connected monitoring point graph. This second connected graph construction algorithm is based on a minimum spanning tree. It calculates the distances between monitoring points and establishes corresponding connecting edges, thereby constructing a spanning tree structure that connects all monitoring point nodes with relatively small overall edge weights, thus achieving connectivity processing of the monitoring point graph. Through this method, different connected graph construction methods can be adaptively selected based on the structural characteristics of the monitoring point graph, resulting in a target connected monitoring point graph for path planning.

[0035] S140. Determine whether the target connectivity monitoring point map belongs to the second preset map set; if the target connectivity monitoring point map belongs to the second preset map set, then use the first path planning algorithm to plan the flight path of the UAV in the monitoring area in the target connectivity monitoring point map; if the target connectivity monitoring point map does not belong to the second preset map set, then use the second path planning algorithm to plan the flight path of the UAV in the monitoring area in the target connectivity monitoring point map.

[0036] The second preset graph set includes connected graphs capable of determining Hamiltonian paths in polynomial time. A Hamiltonian path is a path in a graph structure that visits all nodes in the graph, with each node visited only once. When the target connected monitoring point graph belongs to the second preset graph set, it indicates that the connected graph structure satisfies the condition of efficiently determining Hamiltonian paths. In this case, the first path planning algorithm is used to plan the UAV's flight path in the monitoring area within the target connected monitoring point graph. The first path planning algorithm is a Hamiltonian path-based path planning algorithm, which forms the UAV's flight path by finding a path in the connected graph that sequentially visits all monitoring point nodes.

[0037] When the target connectivity monitoring point map does not belong to the second preset map set, the second path planning algorithm is used for path planning. The second path planning algorithm is a tree search-based path planning algorithm. The second path planning algorithm constructs a flight path that can cover all monitoring point nodes by progressively searching and expanding possible paths in the target connectivity monitoring point map.

[0038] In one feasible implementation, the coordinates of the grid nodes in the grid structure corresponding to the monitoring area are determined according to the size of the monitoring area and the preset grid spacing; the horizontal distance between adjacent grid nodes and the vertical distance between adjacent grid nodes are both preset grid spacings; the movement time between adjacent grid nodes is a time step; the time step is the time required for the UAV to move from one grid node to an adjacent grid node.

[0039] It is understandable that the monitoring area is typically the actual geographical area where data acquisition or environmental monitoring tasks need to be performed, and its size can be determined through pre-acquired regional boundary information or map data. After determining the monitoring area, the monitoring area is discretized according to rules, and then divided into grids according to a preset grid spacing to form multiple grid nodes. The two-dimensional coordinates of the grid nodes are used to represent the specific location of the node in the monitoring area, where the two-dimensional coordinates typically include two components: horizontal and vertical coordinates. The preset grid spacing is a fixed distance parameter between adjacent grid nodes during the grid division process. This grid spacing can be preset according to the UAV's flight accuracy requirements, the scale of the mission area, and the path planning accuracy requirements. By utilizing the size of the monitoring area and the preset grid spacing, the two-dimensional coordinates of all grid nodes within the entire monitoring area can be determined, thereby constructing the basic spatial grid structure for subsequent path planning calculations.

[0040] In this embodiment, both the horizontal distance and the vertical distance between adjacent grid nodes are set to a preset grid spacing. Adjacent grid nodes refer to two nodes that are directly adjacent in the horizontal or vertical direction within the grid structure. Since the entire monitoring area is divided using a regular grid, the distance between two adjacent grid nodes in the horizontal direction and the distance between two adjacent grid nodes in the vertical direction remain consistent, both equal to the preset grid spacing.

[0041] In this embodiment, the time required for a UAV to move from one grid node to an adjacent grid node is uniformly defined as a time step. In this embodiment, a time step is the basic unit of time used to describe the movement of a UAV within the grid structure, representing the time consumed by the UAV to complete one movement to an adjacent node. Specifically, when a UAV moves from its current grid node to an adjacent grid node in the horizontal or vertical direction, this movement process corresponds to one time step.

[0042] In one feasible implementation, after planning the UAV's flight path in the monitoring area in the target connectivity monitoring point graph, the method further includes: recording the node access status of the UAV in the target connectivity monitoring point graph at each time step, and updating the information age of each monitoring point at each time step; wherein, the information age of the monitoring point is the number of time steps elapsed since the UAV last visited the monitoring point; calculating the sum of the information ages of all monitoring points in the target connectivity monitoring point graph at each time step to obtain the total information age at each time step; averaging the total information ages of each time step within a preset time interval to obtain the average information age, and planning the UAV's flight path in the monitoring area with minimizing the average information age as the optimization objective.

[0043] To provide a unified model for the timeliness of UAV flight paths, this application discretizes time into time steps, denoted as . The algorithm assumes that the drone flies at a constant speed and altitude. Since the time consumed by a single data acquisition is negligible compared to the flight time of the drone moving from one node to an adjacent node in the grid structure, the constant time required for the drone to traverse an edge is defined as a time step. Based on this, the algorithm uses... Indicates time The location of the UAV in the target connectivity monitoring point map is used Indicates the end time (including time) The last time the drone visited the monitoring point The time step, among which Belongs to the set of monitoring points Based on the above definition, at each time step, the node access status of the UAV in the target connectivity monitoring point graph is recorded, and the information age of each monitoring point is updated at each time step. Specifically, the monitoring points... At any moment Information Age Defined as the current time step The time step of the drone's most recent visit to the monitoring point The difference between them, i.e. Therefore, it can be concluded that the information age of monitoring point p will continue to increase before the drone visits it; when the drone arrives at the monitoring point in the next time step, i.e. When the information age of a monitoring point is zero, its information age is reset to zero; otherwise, its information age at the next time step is incremented by one time step. Therefore, the dynamic update process of the information age of each monitoring point can be represented as: when... hour, ;when hour, ,in , Based on the above definition, the staleness of information at each monitoring point since its last visit can be continuously reflected on a discrete time scale, thereby enabling the evaluation of the timeliness of subsequent flight paths.

[0044] After updating the information age of each monitoring point, the sum of the information ages of all monitoring points in the target connected monitoring point graph can be calculated at each time step to obtain the total information age for that time step. Specifically, let... This represents a feasible flight path for a drone that repeatedly traverses all monitoring point nodes, where a feasible flight path is one that ensures the drone remains within the area map at all times. Within a given time step, and at each time step, the set of paths from the current node to its adjacent nodes; that is, if at time step... The drone is located at the node Then in the next time step At that time, the location of the drone Should meet and ,in Representation of the area map The set of nodes, Representation of the area map The set of edges. For a given flight path At any moment Below, the information age of each monitoring point can be expressed as: This vector represents the distribution of data freshness at each monitoring point in the entire monitoring network at the current moment. Based on this, the path... The total information age at time t is obtained by summing the information ages of all monitoring points. Total Information Age The mathematical form can be seen in the following expression: Therefore, the total information age calculated at each time step essentially represents the sum of the information age values ​​of all monitoring points in the monitoring network at the current moment. It is used to comprehensively reflect the freshness of the data of all monitoring points in the entire monitoring area at that moment. The smaller the total information age, the more timely the UAV flight path updates each monitoring point, and the higher the overall information collection timeliness.

[0045] After obtaining the total information age at each time step, the total information age at each time step can be averaged over a preset time interval to obtain the average information age. Specifically, let the preset time interval be from time step... Time to step Then in the flight path Below, from arrive The mathematical form of the average age over time can be found in the following expression: ;in, and These represent the start and end time steps of the preset time interval, respectively, and the denominator... This represents the total number of time steps counted. This averaging process eliminates the impact of random fluctuations at a single time step on the path evaluation results, allowing the average information age to more stably reflect the overall effectiveness of the UAV path in updating monitoring point information over a period of time. In this application, the preset time interval can be set according to the specific mission duration, cruise cycle, or evaluation window size, as long as it covers the continuous time steps used to evaluate the path's effectiveness. By averaging the total information age of each time step within the preset time interval, a timeliness index reflecting the long-term operational effectiveness of the path can be obtained, enabling comparisons of the merits of different flight paths on a unified time scale.

[0046] In this application, the average information age is not only used to describe the freshness of monitoring point information along the flight path, but also serves as an optimization objective for UAV flight path planning. Specifically, this application formalizes the UAV optimal trajectory planning problem into problem P1, which is the problem of planning the optimal trajectory across all feasible flight paths. Searching for a drone flight path This makes from Until any planned termination time step The average age of network information over time is the shortest. The mathematical form of problem P1 can be found in the following expression: Therefore, minimizing the average information age means ensuring that each monitoring point is visited as evenly and promptly as possible throughout the entire planning timeframe, thereby reducing the overall obsolescence of the monitoring data. Furthermore, to analyze the theoretical boundary of the optimization objective, this application combines the graph theory structures of Hamiltonian paths and Hamiltonian cycles (HC), where a Hamiltonian path is a path that visits each node in the graph exactly once, and a Hamiltonian cycle is a closed loop in the graph where each node is visited exactly once and the starting and ending nodes are adjacent. Based on this graph theory structure, the applicant found that for any... And any feasible flight path for problem P1 Total age of online information There exists a lower bound. Its mathematical form can also be referenced from the following expression: For any Furthermore, if and only if the monitoring point map When the circuit is connected and contains at least one Hamiltonian cycle, the lower bound is valid for any... Reachable. This indicates that the essence of flight path planning lies in rationally designing the node access order and repetition methods to make the time-averaged network information age as close as possible to the theoretical lower bound. Further analysis reveals that problem P1 is an NP-hard problem, therefore, it is generally difficult to directly obtain the exact optimal solution. Please refer to... Figure 2 This application first performs a first-stage judgment based on the extracted monitoring point map: determining whether the extracted monitoring point map is a connected graph; if the extracted monitoring point map is a connected graph, then a second-stage judgment can be performed: determining whether the extracted monitoring point map is a connected graph whose Hamiltonian path can be determined in polynomial time (that is, determining whether it belongs to the second preset graph set if it is determined to be a connected graph); if the extracted monitoring point map is a connected graph whose Hamiltonian path can be determined in polynomial time, then a first path planning algorithm (a path planning algorithm based on Hamiltonian path) is used to plan the UAV's flight path in the monitoring area in the target connected monitoring point map; if the extracted monitoring point map is not a connected graph whose Hamiltonian path can be determined in polynomial time, then a second path planning algorithm (a path planning algorithm based on tree search) is used to plan the UAV's flight path in the monitoring area in the target connected monitoring point map.

[0047] If the extracted monitoring point map is not a connected graph, the process proceeds to handle disconnected monitoring point maps. Specifically, the first stage of processing is performed on the disconnected monitoring point map, namely, constructing a connected graph. Before constructing the connected graph, it is necessary to determine the condition of the extracted monitoring point map. Does the extracted monitoring point map belong to scenario A, which can be solved in polynomial time? If it does, then the RSMT polynomial algorithm (i.e., a connected graph construction algorithm based on the Cartesian Steiner minimum tree problem, also known as the first connected graph construction algorithm) is used to solve the Cartesian Steiner minimum tree problem, thereby obtaining an accurate connected monitoring point map. (That is, the target connected monitoring point graph), which involves introducing necessary intermediate nodes into the region graph to connect previously disconnected monitoring point graphs while minimizing the total length of the connecting paths. If the extracted monitoring point graph does not belong to scenario A, the K-Approx approximation algorithm (i.e., the minimum spanning tree-based connected graph construction algorithm, also known as the second connected graph construction algorithm) is used to construct the connected structure, obtaining an approximate connected graph through the minimum spanning tree concept. This involves establishing connecting paths between monitoring points to ensure that there are reachable paths between all monitoring points, thereby obtaining a target connected monitoring point map.

[0048] After constructing the connected graph for the non-connected monitoring point graphs, the second stage of processing begins (i.e., planning the UAV flight trajectory on the obtained target connected monitoring point graph). Specifically, it is first determined whether the constructed connected graph belongs to scenario B. Scenario B is determined by whether the connected graph can determine the Hamiltonian path in polynomial time. If the constructed target connected monitoring point graph belongs to scenario B, the D-HPA series algorithm (i.e., the Hamiltonian path-based path planning algorithm, also known as the first path planning algorithm) is used to plan the trajectory on the connected graph. The first path planning algorithm obtains the UAV flight path by finding the Hamiltonian path in the connected graph and constructing a periodic traversal trajectory. If the connected graph does not belong to scenario B, the D-TSA series algorithm (i.e., the tree search-based path planning algorithm, also known as the second path planning algorithm) is used for path planning. The second path planning algorithm expands the access path step by step based on the tree search strategy, generating the UAV flight path while ensuring that all monitoring points can be accessed. Through the above two-stage processing, a feasible connected graph structure can be constructed even when the monitoring point graph is not originally connected. Furthermore, a drone flight path covering all monitoring points can be generated on this connected graph, thereby enabling the drone to periodically visit multiple monitoring points.

[0049] In summary, the embodiments of this application can construct a feasible connected graph structure even when the monitoring point map is originally disconnected, and further generate a UAV flight path covering all monitoring points on this connected graph, thereby obtaining the UAV flight path trajectory. Ultimately, this application can output the optimal or near-optimal UAV flight path trajectory. The application provides a corresponding theoretical performance guarantee, namely, the performance limit (approximation ratio) of the generated path relative to the optimal solution. This embodiment constructs UAV flight paths using path planning strategies under different graph structures, so that the resulting flight paths satisfy the optimization objective of minimizing the average information age as much as possible. This improves the timeliness of information collection within the monitoring area while also ensuring that the UAV flight paths have an analyzable theoretical performance boundary under the information age optimization objective.

[0050] In one feasible implementation, before determining whether the monitoring point map belongs to the first preset map set in step S130, the method of this application embodiment further includes: determining whether the monitoring point map is a connected graph; if the monitoring point map is a connected graph, then directly execute step S140, which is to determine whether the target connected monitoring point map belongs to the second preset map set; if the target connected monitoring point map belongs to the second preset map set, then use the first path planning algorithm to plan the flight path of the UAV in the monitoring area in the target connected monitoring point map; if the target connected monitoring point map does not belong to the second preset map set, then use the second path planning algorithm to plan the flight path of the UAV in the monitoring area in the target connected monitoring point map; wherein, the target connected monitoring point map is the monitoring point map itself. In one feasible implementation, determining whether a monitoring point graph is a connected graph specifically includes: selecting any monitoring point in the monitoring point graph as a starting node; traversing the monitoring point graph using a graph traversal algorithm and recording the monitoring points visited from the starting node during the traversal; if the number of visited monitoring points equals the total number of monitoring points in the monitoring point graph, then the monitoring point graph is determined to be a connected graph; otherwise, the monitoring point graph is determined to be a disconnected graph. Graph traversal algorithms include Depth-First Search (DFS) and Breadth-First Search (BFS).

[0051] Understandably, in applications where drones periodically visit multiple monitoring points, it's crucial to ensure all points can be visited sequentially via a feasible path. Therefore, analyzing the connectivity of the monitoring point map is typically necessary before path planning. Specifically, in some cases, the spatial distribution of monitoring points may result in the monitoring point map already possessing a connected structure, meaning there's a reachable path between any two points. In such cases, no additional connectivity construction is needed; path planning can be performed directly on the monitoring point map.

[0052] However, in actual monitoring areas, monitoring points are typically distributed in different locations, and some monitoring points may not be directly connected, resulting in a disconnected monitoring point map. If path planning is performed directly when the monitoring point map is disconnected, it may be impossible to access all monitoring points. Therefore, it is necessary to use a regional map... By introducing appropriate intermediate nodes, the original disconnected monitoring point map can be connected into a connected structure.

[0053] To address the aforementioned issues, this application will "use regional maps..." The question of "introducing appropriate intermediate nodes to enable the original disconnected monitoring point graph to form a connected structure" can be formalized into the following problem: In a region graph... A new image was found inside. By adding as few nodes as possible, the PoI graph can be optimized. This forms a connected graph; this problem is referred to as problem P2 in this application. The mathematical form of problem P2 can be found in the following expression: ;in, It is a connected graph; a connected PoI graph (C-PoI graph) is... , Is it a diagram The number of nodes required to connect. Let represent the optimal solution to problem P2. This indicates the minimum number of nodes that can be added.

[0054] Analysis reveals that problem P2 is NP-hard, making it difficult to obtain the optimal solution directly in polynomial time using exhaustive search. Therefore, the applicant further analyzed the graph structure characteristics of problem P2, discovering an equivalence relationship between problem P2 and the Cartesian Steiner Minimum Tree Problem. Specifically, the Cartesian Steiner Minimum Tree Problem refers to minimizing the total side length of the tree structure connecting all nodes in a Cartesian grid environment by introducing additional Steiner nodes at necessary locations. Therefore, it can be deduced that for any given PoI graph... The optimal solution to problem P2 is equivalent to the optimal solution to the RSMT problem, where the length of the Steiner tree is denoted as . Satisfying the relation ,in Indicates the number of monitoring points. This indicates the number of additional nodes that need to be introduced. Therefore, by solving the RSMT problem, the optimal or near-optimal solution to problem P2 can be obtained, thereby realizing the connectivity construction of the monitoring point graph.

[0055] In further research, the applicant also analyzed the theoretical limit of information age in the case of disconnected monitoring point graphs. Specifically, when the original PoI graph... When the graph is not connected and needs to be connected by adding intermediate nodes, even in the optimal connected graph... The above uses an arbitrary feasible path planning algorithm. Long-term (e.g. from) arrive The time-averaged information age still has an insurmountable theoretical lower bound. This lower bound is related not only to the number of monitoring points P, but also to the minimum number of nodes N required to connect the PoI graph. The specific mathematical form can be found in the following expression: ;in,

[0056] In other words, monitoring points Figure 1 If the graphs are not connected, the additional nodes and flight distances introduced by UAVs to establish path connections between different isolated areas will inevitably lead to a lower bound on the information age that is higher than the theoretical lower bound in the case of a connected graph. Therefore, the lower bound of the above expression reflects the basic limit that AoI optimization can achieve in a disconnected graph scenario, and also indicates that for a disconnected monitoring point graph, the number of nodes added to achieve connectivity should be minimized as much as possible to reduce the overall information age of subsequent path planning.

[0057] In further research, the applicant also discovered that although the RSMT problem is generally NP-hard, it can be solved in polynomial time on certain PoI graphs with specific structures. Specifically, when the PoI graph... It can be considered to belong to the RSMT polynomial atlas if one of the following two conditions is met. Therefore, the RSMT problem can be solved using a polynomial-time algorithm: First, the set of monitoring points Located on the outer boundary of a right-angled convex structure; secondly, the set of monitoring points. Located on a fixed number of parallel lines. Here, the right-angled convex outer boundary can be understood as the outer contour enclosed by horizontal and vertical sides, where the shortest path between any two points remains within the boundary; the fixed number of parallel lines refers to all monitoring point nodes being distributed only on a few pre-given, parallel straight lines. Based on the above analysis, it can be seen that when... When the right-angle Steiner minimum tree problem can be solved in polynomial time, then problem P2 can also be solved in polynomial time. This situation is also referred to as scenario A in the aforementioned embodiment. Therefore, scenario A essentially constrains the geometry of the PoI graph and determines whether the PoI graph is suitable for solving using a connected graph construction algorithm based on the right-angle Steiner minimum tree problem (i.e., the first connected graph construction algorithm), thereby constructing a connected graph based on the ability to solve problem P2. If it is not suitable, the second connected graph construction algorithm is used to construct the connectivity of the monitoring point graph. Specifically, when the PoI graph does not belong to the RSMT polynomial graph set... Since it is difficult to directly solve the Cartesian Steiner Minimum Tree Problem in polynomial time, we no longer attempt to obtain the optimal solution to problem P2 by precisely solving RSMT. Instead, we construct a connected structure based on the idea of ​​minimum spanning tree to obtain an approximate solution to problem P2. In this way, even if the PoI graph does not satisfy the polynomial solvability condition of RSMT, we can complete the connected construction of the monitoring point graph with low computational complexity, thereby providing a feasible connected graph structure for subsequent UAV flight path planning. For the specific construction process of the second connected graph construction algorithm, please refer to the following embodiments.

[0058] This paper introduces a feasible implementation method for constructing a connected graph using a first connected graph construction algorithm when the monitoring point graph belongs to the first preset graph set. Specifically, the process includes: using all monitoring points as endpoints, searching for the Steiner tree that minimizes the total side length in the grid structure corresponding to the monitoring area; determining all grid nodes on the Steiner tree as the node set of the first connected monitoring point graph; and connecting each adjacent grid node in the node set with edges to obtain the target connected monitoring point graph.

[0059] The first pre-defined graph set includes two special types of monitoring point graph structures: the first type has all monitoring points located on the boundary of a right-angled convex polygon, meaning the distribution of monitoring points exhibits a convex envelope characteristic, and each edge of the convex polygon is parallel or perpendicular to the grid coordinate axes; the second type has all monitoring points located on a predetermined number of parallel lines, meaning the ordinate or abscissa of the monitoring points takes only a finite number of discrete values, thus forming several straight lines parallel to the coordinate axes. Under these two special structural conditions, the right-angled Steiner minimum tree problem can be solved exactly in polynomial time.

[0060] All monitoring points As the set of terminal nodes in the RSMT problem, and the region graph The corresponding mesh structure serves as the solution space. Within this solution space, with the objective of connecting all terminal nodes and minimizing the total edge length, all candidate Steiner trees satisfying the Cartesian mesh connection constraints are searched and compared. A Steiner tree is a tree structure formed by allowing the introduction of additional mesh nodes as intermediate connection nodes during the process of connecting all monitoring point nodes; minimizing the total edge length means minimizing the sum of all edge lengths in all feasible Steiner trees. Since the monitoring point graph in this embodiment belongs to the RSMT polynomial atlas, the optimal Steiner tree can be accurately obtained in polynomial time, rather than through approximation.

[0061] Furthermore, when the monitoring point nodes are located on the boundary of a right-angled convex polygon, the RSMT polynomial solution process utilizes the ordered distribution of terminal nodes on the boundary to systematically search for feasible connection structures that satisfy the boundary geometric relationships. While maintaining connectivity among all terminal nodes, it determines the target Steiner tree with the minimum total side length. Since all terminal nodes are distributed on the right-angled convex outer boundary, and their relative positions are constrained by the boundary structure, the combination space of candidate connection structures can be effectively limited, allowing the determination of the optimal Steiner tree to be completed in polynomial time. When the monitoring point nodes are located on a fixed number of parallel lines, the RSMT polynomial solution process utilizes the ordered linear distribution of terminal nodes and the fixed number of parallel lines to solve for the optimal connection methods between different parallel lines, thereby determining the optimal Steiner tree connecting all terminal nodes. Since the number of parallel lines is fixed, the state scale during the solution process is effectively controlled, thus also allowing for an exact solution to be obtained in polynomial time.

[0062] After obtaining the optimal Steiner tree described above, this optimal Steiner tree is denoted as... .in, This represents the set of all nodes in the optimal Steiner tree, including both the original monitoring point nodes and the additional intermediate nodes introduced to achieve the shortest connection. This represents all connecting edges in the optimal Steiner tree. Since this tree is the minimum total edge length tree found within the mesh structure corresponding to the region graph, therefore... This is the exact optimal solution to problem P2. Further, let the original number of monitoring points be... The optimal number of nodes required to connect the original disconnected monitoring point graph is denoted as . It can be determined by the relationship between the number of nodes. Meanwhile, the length of the optimal Steiner tree is denoted as... Since the tree structure satisfies the condition that the number of edges equals the number of nodes minus one, therefore we have Therefore, by accurately solving the RSMT problem in scenario A, we can not only obtain the optimal connectivity structure connecting all monitoring points, but also... It can also simultaneously obtain the minimum number of nodes required to connect the monitoring point map. .

[0063] Obtaining the optimal Steiner tree and the optimal number of new nodes Next, all grid nodes on the optimal Steiner tree are determined as the set of nodes in the target connectivity monitoring point graph. Grid nodes satisfying the adjacency condition are then connected by edges to form the target connectivity monitoring point graph. Here, the adjacency condition means that two grid nodes are directly adjacent in the horizontal or vertical direction in the region graph, i.e., there is a connecting edge of unit length between the two nodes. In this way, the abstract optimal Steiner tree result obtained from the exact solution of RSMT can be transformed into a target connectivity monitoring point graph that can be directly used for subsequent UAV path planning. Since this target connectivity monitoring point graph originates from the optimal solution to problem P2, it achieves optimality in both the number of newly added nodes and the overall connection length, thus minimizing the additional path cost and information age cost introduced by disconnected structures in subsequent path planning.

[0064] When the monitoring point graph does not belong to the first preset graph set, i.e., when the monitoring point graph does not belong to the RSMT polynomial graph set, the computational complexity of directly solving the Cartesian Steiner minimum tree problem is high. The original monitoring point graph does not meet the structural condition that the exact optimal connected graph can be directly obtained through the RSMT polynomial solution method under scenario A. Therefore, another method is needed to construct the connected graph structure. In a feasible implementation, this application embodiment uses a second connected graph construction algorithm to construct the connected graph. The second connected graph construction algorithm adopts the K-Approx approximation construction process based on the Kruskal algorithm. Specifically, the connected graph construction process of the second connected graph construction algorithm includes: constructing a complete graph with all monitoring points as endpoints; the weight of each edge in the complete graph is the Manhattan distance between the corresponding two monitoring points; processing the complete graph using the minimum spanning tree algorithm to obtain the minimum spanning tree connecting all monitoring points, and using the edges contained in the minimum spanning tree as a virtual edge set; for each virtual edge in the virtual edge set, determining the Manhattan path connecting the two monitoring points at both ends of the virtual edge in the grid structure corresponding to the monitoring area, and adding each grid node passed through on the Manhattan path to a temporary node set; connecting adjacent grid nodes in the temporary node set with edges to obtain the target connected monitoring point graph.

[0065] Please refer to the algorithm pseudocode logic shown in Table 1 below. The input is a region map. and PoI node set Among them, the regional map This represents a grid diagram showing the entire monitoring area, with a set of nodes. Includes all grid nodes and edge sets within the monitoring area. Includes connecting edges between adjacent grid nodes; PoI node set This represents all monitoring point nodes in the original monitoring point graph. To implement the second connected graph construction process, initialization is first performed, letting... , , .in, Used to record the selected virtual edges in the subsequent minimum spanning tree. This is used to record the set of nodes in the target connectivity monitoring point graph, and its initial value is set to the original PoI node set. , Used to record the set of edges in the target connectivity monitoring point graph, with an initial value of an empty set.

[0066] In the first step of the second connected graph construction algorithm, a complete graph is constructed using all monitoring points as endpoints. Specifically, the complete image The node set is directly adopted from the original monitoring point set. And edge set It consists of virtual connection edges between any two different monitoring point nodes, that is, for any A virtual edge is constructed between the two. Thus obtain In this complete graph, the weight of each edge... Defined as the Manhattan distance between two corresponding monitoring points, i.e. ,in and They represent monitoring points respectively. and Two-dimensional coordinates in the region map. Manhattan distance is used to represent the shortest number of unit edges required to move from one monitoring point to another in a square grid structure along the horizontal and vertical directions, and thus can be used as the path cost connecting two monitoring points.

[0067] In the second step of the second connected graph construction algorithm, the complete graph is... The minimum spanning tree solution based on Kruskal's algorithm is executed to obtain the minimum spanning tree connecting all monitoring points, and the edges contained in this minimum spanning tree are used as a virtual edge set. Specifically, firstly, the complete graph... All edges in the array are arranged according to their corresponding weights. The edges are sorted in a monotonically increasing order to prioritize edges with smaller weights. Then, each edge is extracted sequentially according to the sorted order. And using the disjoint-set decision function FIND-SET With FIND-SET Determine whether the two endpoints belong to different connected components. If they do, it means that adding the edge will not create a cycle, and the edge is then added to the virtual edge set. and through UNION The operation merges the connected components to which the two edges belong; if they already belong to the same connected component, the edge is skipped. Through this iterative process, until all candidate edges have been traversed, the set of virtual edges corresponding to the minimum spanning tree connecting all monitoring points is obtained. During this process, Each edge in the graph represents an optimal connection between two monitoring points, but this connection is still an abstract virtual edge built on the complete graph, and therefore has not yet been reconstructed into the actual grid path of the region graph. It should be noted that the computational complexity of the second step mentioned above is mainly determined by the edge weight sorting process, with an overall complexity of approximately [missing information]. ,in This represents the number of monitoring point nodes. Since the number of edges in the complete graph is approximately... The sorting process becomes the main computational overhead of the entire algorithm due to its hierarchical structure.

[0068] In obtaining the virtual edge set The third step of the second connected graph construction algorithm is to construct the region graph. The process involves expanding the paths of each virtual edge in the set of virtual edges to construct the actual connected graph. Specifically, for Each virtual edge in Let the coordinates of its two endpoints be respectively and Then, a Manhattan path is determined in the grid structure corresponding to the region map, such that the path passes sequentially from... arrive The grid nodes between, and from arrive The grid nodes between them. In other words, in one implementation, the abstract virtual edge can be mapped to the actual polyline path in the grid by first moving horizontally and then vertically; each grid node traversed on this Manhattan path... Added to the set of nodes .because Since all original monitoring points were included during initialization, after sequentially expanding all virtual edges and performing a loop addition operation, This will include the original PoI nodes and all intermediate grid nodes introduced to achieve connectivity. This loop logic ensures that every abstract connection in the minimum spanning tree is transformed into an actual feasible path in the region graph.

[0069] After completing the path expansion of all virtual edges, it is necessary to construct the edge set of the target connectivity monitoring point graph based on the node set. Specifically, for Any two nodes If the two satisfy the adjacent condition in the region map, that is... Then, establish a connecting edge between the two and add the edge to the edge set. Thus obtain Therefore, the target connectivity monitoring point map can be constructed. Furthermore, the number of newly added nodes in the connected graph can be calculated. ,in Indicates the original number of monitoring points. Parameter The parameter is used to characterize the number of intermediate nodes required to connect the monitoring point graph using the second connected graph construction algorithm. The smaller the value, the lower the additional path overhead required for the drone to establish connections between different monitoring points.

[0070]

[0071] From a theoretical analysis perspective, the number of newly added nodes obtained through the above-described approximate connected graph construction process based on Kruskal's algorithm... With the optimal number of new nodes There is a clear quantitative relationship between them. Specifically, the number of new nodes introduced by the K-Approx algorithm... The following inequality relationship must be satisfied: ;in This represents the optimal number of new nodes required to connect the monitoring point graph. This inequality shows that although the second connected graph construction algorithm obtains an approximate connected graph, the upper bound is limited because the number of new nodes will not deviate infinitely from the optimal value. and the number of monitoring points The common constraints are always subject to theoretical bounds. Therefore, although the connected graph construction process yields an approximate connected structure, the number of intermediate nodes added is always kept within a controllable range, thus ensuring the structural efficiency of the constructed connected graph.

[0072] Furthermore, in the theoretical analysis of the UAV trajectory planning problem, it can be further proven that, under normal circumstances, the long-term average age of network information has a theoretical lower bound determined by both the number of monitoring points and the number of newly added nodes. Specifically, for any feasible algorithm for problem P1... The long-term average network AoI satisfies the following lower bound constraint:

[0073] ;

[0074] As can be seen from this expression, in the scenario of a general disconnected monitoring point graph, the theoretical lower bound of the network information age is not only related to the number of monitoring points. It is also related to the number of nodes introduced during the construction of the connected graph. This is relevant. As the number of new nodes increases, the path length required for the UAV to move between different monitoring areas increases, leading to a rise in the lower bound of the network's AoI. Therefore, by employing a performance-guaranteed K-Approx connected graph construction algorithm, the theoretical lower bound of the network's AoI can be reduced while controlling the number of new nodes, thus providing a theoretically performance-guaranteed connected graph foundation for subsequent UAV flight path planning.

[0075] In one feasible implementation, the path planning process of the first path planning algorithm includes: determining a starting node, which is any monitoring point in the target connected monitoring point graph, and there exists at least one Hamiltonian path from the starting node that passes through all monitoring points; taking the starting node as the current node, and repeating the following steps: searching for and selecting a Hamiltonian path in the target connected monitoring point graph; the Hamiltonian path takes the current node as the starting node, passes through all monitoring points in sequence, and each monitoring point appears only once in the Hamiltonian path; visiting each monitoring point on the Hamiltonian path in sequence until reaching the end node of the Hamiltonian path; taking the end node as the current node for the next round of path planning.

[0076] In one feasible implementation, the first path planning algorithm is applicable when a Hamiltonian path exists in the target connectivity monitoring point graph. Specifically, the target connectivity monitoring point graph can be represented as follows: ,in, Represents the set of all monitoring point nodes. Let P be the set of edges connecting the monitoring point nodes. A Hamiltonian path is a path in the target connected monitoring point graph that sequentially traverses all monitoring point nodes, with each monitoring point node appearing only once. The applicant's research found that when a UAV traverses along a Hamiltonian path, it can visit all P monitoring points exactly once within P-1 time steps. This represents the total number of monitoring points. Based on this Hamiltonian path structure, repeatedly visiting already visited monitoring points before other monitoring points have been updated can be avoided, thus reducing invalid flight processes. Simultaneously, a relatively balanced visit interval can be formed between monitoring points, reducing the linear accumulation of information age over time. Therefore, when the target connected monitoring point graph satisfies the Hamiltonian path existence condition, a path planning algorithm based on Hamiltonian paths can be used to plan the UAV flight path.

[0077] Please refer to the pseudocode logic of Algorithm 2 shown in Table 2 below. In this path planning process, the starting node needs to be determined first. Specifically, the starting node is any monitoring point node in the target connectivity monitoring point graph, denoted as [node name missing]. ,in Indicates the drone at time step The location of the monitoring point node. When selecting the starting node, there should be at least one Hamiltonian path from that node that passes through all monitoring points. In other words, the starting node belongs not only to the set of monitoring point nodes. Furthermore, it should be guaranteed that at least one feasible Hamiltonian path covering all monitoring points can be found starting from this node. To describe the periodic planning process of the algorithm, a time set can be further defined. ,in This indicates the time step when the drone reaches the end of the current Hamiltonian path and is ready to select the next Hamiltonian path. During the initialization phase, the following settings are configured: and initialize the round number to Therefore, the starting node It serves both as the initial position of the drone and as the... The current node in the round path planning.

[0078] After determining the starting node, the starting node is set as the current node, and the Hamiltonian path search and traversal process is repeated around this current node. Specifically, in the... In the round path planning, based on the current time The node where the drone is located is designated as the current node, denoted as . Then, search and select a Hamiltonian path starting from the current node in the target connectivity monitoring point graph, denoted as . ,in This is the starting node of the path in this round. This is the terminal node of the path in this round, and each node on the path belongs to the set of monitoring point nodes. Since this path is a Hamiltonian path, all monitoring point nodes along the path are pairwise distinct and precisely cover all monitoring points in the target connected monitoring point graph. This allows for the dynamic determination of a new Hamiltonian path based on the current node in each round, enabling subsequent path visits to be connected according to the UAV's current location, thus avoiding a disconnect between the path planning process and the UAV's current position.

[0079] After selecting the Hamiltonian path, the UAV sequentially visits each monitoring point along the path until it reaches the end node of the Hamiltonian path. Specifically, in the... In the cycle, for the time step The drone in time step The visited node can be represented as In other words, within the current round, the UAV moves and visits nodes sequentially according to the selected Hamiltonian path, until it reaches the final node of the Hamiltonian path in that round after the (P-1)th movement time step. Since each monitoring point on the Hamiltonian path appears only once, the drone can cover all monitoring points without repeatedly visiting already visited nodes during a single round of visits. This minimizes wasted flight paths by avoiding revisiting already visited nodes before other monitoring points have been updated. Furthermore, because all monitoring points are visited sequentially within a complete round, a more balanced update interval is achieved between monitoring points, thus reducing the overall information age of the system.

[0080]

[0081] Please refer to Figure 3 After the drone completes a full visit along the current Hamiltonian path, the terminating node will be used as the current node for the next round of path planning. Specifically, when the... When the round-route visit ends, the drone reaches the end node of the Hamiltonian path. This termination node also constitutes the starting position for the next round of path planning, i.e., it satisfies... Subsequently, this node was determined to be the [number]. The current node of the round path planning is used, and a new Hamiltonian path is searched and selected from that node, thus repeating the subsequent traversal process. Based on the round partitioning diagram, it can be seen that the... Wheel, First Wheel and the first The path planning process in each round follows the same logic: each round starts from the starting node of the current round, selects a Hamiltonian path that covers all monitoring points, completes the entire round of visits, and then uses the ending node as the starting node for the next round to continue planning. Thus, the entire first path planning algorithm forms a periodic path planning mechanism that continuously connects rounds, enabling the UAV to repeatedly traverse all monitoring points over a long period.

[0082] Based on the path planning mechanism described above, a special case can be further considered: if at any time... If the UAV always flies back and forth along the same Hamiltonian path, a specific strategy is obtained, denoted as HPA-S. In this strategy, the UAV traverses the same Hamiltonian path both forward and backward in each cycle. Analysis of different path selection strategies reveals that for any... The path planning algorithm based on Hamiltonian path performs well in the time interval. The average age of network information over time satisfies the following relationship: This relational expression indicates that among all possible Hamiltonian path traversal strategies, the strategy of fixedly flying back and forth along the same Hamiltonian path will produce the largest long-term average network information age. However, by reselecting the Hamiltonian path based on the current node in different rounds, the overall information age of the system can be reduced to some extent.

[0083] Further analysis reveals that when the number of monitoring points... At that time, the path planning algorithm based on Hamiltonian paths can achieve a stable performance limit under long-term operation. Its time-averaged network information age has a certain proportional relationship with the theoretical optimal value, which can be referred to as the following expression: ;in This represents the average age of network information over the time interval [0, T] achieved by the first path planning algorithm. This represents the average network information age over time corresponding to the theoretically optimal path planning strategy. The above inequality shows that, with a large number of monitoring points, the average network information age achieved by the path planning algorithm is at most 4 / 3 times the theoretical optimal value, thus demonstrating the algorithm's stable performance guarantee. The reason for this proportional relationship is that during the Hamiltonian path round-trip traversal, nodes in the middle of the path are typically visited twice in each round-trip cycle, while endpoint nodes are visited only once. Therefore, there is a certain difference in the visiting frequency between different nodes. Although this visiting pattern manifests as uneven visiting frequency, statistically speaking, intermediate nodes maintain a lower information age, thus helping to reduce the system's average information age.

[0084] Furthermore, from an algorithm complexity perspective, the computational complexity of the first path planning algorithm primarily depends on the process of finding a Hamiltonian path in the target connected monitoring point graph. This complexity arises when the monitoring point graph is a graph structure type capable of finding a Hamiltonian path in polynomial time. Belongs to HP polynomial atlas For example, with rectangular grid structures and grid structures with specific geometries (such as L-shaped, C-shaped, F-shaped, or E-shaped grid structures), Hamiltonian path search can be completed in polynomial time. Therefore, under the above graph structure conditions, the first path planning algorithm has polynomial time computation complexity, thus enabling it to efficiently complete UAV flight path planning tasks in practical applications.

[0085] In one feasible implementation, the path planning process of the second path planning algorithm includes: selecting any monitoring point in the target connectivity monitoring point graph as the starting node, and determining the starting node as the current node; initializing the visited node set and the traversed edge set; wherein, the visited node set contains only the current node, and the traversed edge set is an empty set; repeating the following node visiting steps in each traversal cycle until the visited node set contains all monitoring points in the target connectivity monitoring point graph: at the current time, obtaining the neighboring nodes adjacent to the current node in the target connectivity monitoring point graph, and determining the candidate node set from the neighboring nodes; wherein, the candidate node set includes nodes not included in the visited node set. The system identifies neighboring nodes, as well as neighboring nodes whose edges with the current node are recorded in the traversed edge set but are included in the visited node set. It calculates the information age of each candidate node in the candidate node set at the current moment and selects the candidate node with the largest information age as the next node. The system adds the next node to the visited node set and adds the connection edge between the current node and the next node to the traversed edge set. It updates the next node to the new current node. If the visited node set contains all monitoring points, the system ends the current traversal cycle, clears the traversed edge set, and resets the visited node set to contain only the current node at the current moment, thus starting the next traversal cycle.

[0086] Please refer to Table 3 below, which contains the pseudocode for the second path planning algorithm:

[0087]

[0088] The target connectivity monitoring point graph can be represented as follows: ,in, Represents the set of all monitoring point nodes. This represents the set of connecting edges between monitoring point nodes. Unlike path planning based on Hamiltonian paths, the second path planning algorithm uses a tree search strategy for flight path planning. In each step, it prioritizes moving to the neighboring node with the oldest current information age, thus updating the oldest information first. The applicant further discovered that if a simple greedy approach is used to move along the neighboring node with the highest AoI in a general connected graph, the presence of cycles in the graph may cause the UAV to repeatedly move in local loop regions, resulting in some unvisited monitoring points being ignored for a long time. To avoid this problem, the second path planning algorithm restricts the UAV's movement in each round of traversal, ensuring that the visited structure formed in the current round remains a tree structure, rather than a loop structure. Combined with... Figure 4As shown, the original target connectivity monitoring point graph can be a graph with loops. However, within one traversal cycle, by restricting candidate nodes and traversed edges, the final access trajectory corresponds to a tree, thereby preventing loops from causing some monitoring points to be ignored indefinitely.

[0089] In the second path planning algorithm, firstly, any monitoring point is selected as the starting node in the target connectivity monitoring point graph, and this starting node is determined as the current node. Let the UAV at time step... The location of the monitoring point node is denoted as During initialization, any option that satisfies this condition can be selected. The monitoring point node is used as the starting node. Unlike the first path planning algorithm, the second path planning algorithm does not require the existence of a Hamiltonian path starting from the starting node. Therefore, the selection condition for the starting node is more relaxed; it only needs to belong to the set of monitoring point nodes in the target connected monitoring point graph. During the initialization phase, a time set is also defined. ,in Indicates the first The starting time step of the round traversal cycle, and Indicates the first The earliest time step corresponding to the first complete visit of all monitoring points in a round-robin cycle. Further settings... and initialize the round number to Therefore, the starting node At the same time, as a drone in the The current node in the round-robin traversal cycle.

[0090] After determining the starting node, the set of visited nodes and the set of traversed edges are initialized to represent the node visit status and edge visit status within the current traversal cycle. Specifically, in the... During the round traversal cycle, record From the start time of this round The set of nodes that have been visited by drones since then, recorded From the start time of this round This is the set of edges that have been traversed by the drone. During initialization, let... That is, the set of visited nodes only contains the current node; at the same time, let This means that the set of traversed edges is empty. By introducing two sets, we can dynamically record the currently visited nodes and the edges traversed in each traversal cycle, thus providing constraints for determining the subsequent candidate node set. The purpose of this initialization step is to clarify the starting visit state of the current traversal cycle, so that the subsequent node expansion process always revolves around the newly generated tree structure in the current cycle, and will not be confused with the visit trajectory of the previous traversal cycle.

[0091] Within each traversal cycle, the second path planning algorithm repeatedly executes the node visiting step until the visited node set contains all the monitoring points in the target connectivity monitoring point graph. In this process, the first step is to determine the candidate node set based on the current node. Specifically, at the current time... Get all nodes related to the current node The neighboring nodes are selected, and a candidate node set is obtained from these neighboring nodes. .set up The index corresponding to a neighboring node of the current node can be used if and only if one of the following conditions is met. Add to the candidate node set, i.e. Firstly, the neighboring node Not yet included in the set of visited nodes in the current round In, that is Secondly, the neighboring node Although it is already included in the set of visited nodes, the connection edge between the current node and its neighboring node has been recorded in the set of traversed edges. In, that is This selection rule ensures that the drone prioritizes expanding towards unvisited new nodes in each traversal cycle, while allowing movement along edges already incorporated into the current tree structure when necessary, thus maintaining the connectivity and tree structure of the entire trajectory. Combined with... Figure 4 As shown in the diagram, the correspondence between the graph with loops, the tree, and the trajectory of one round of TSA indicates that although there may be loops in the original graph, through the above candidate node selection mechanism, the actual access trajectory formed by the UAV in the current round will not endlessly loop around the loop, but will gradually expand into a tree covering all nodes.

[0092] After obtaining the candidate node set, the second path planning algorithm calculates the information age of each candidate node in the set at the current time and selects the candidate node with the largest information age as the next node. Specifically, let... Indicates candidate nodes At the present moment If the information age is known, then the next node can be reached through the relationship. Confirmed. In other words, in each step of the current round, the drone always prioritizes visiting the candidate node with the oldest current information, ensuring that the information most in need of updating is collected first. This greedy strategy embodies the core idea of ​​the second path planning algorithm: in a general connected graph scenario, by locally selecting the neighboring node with the highest current AoI, the age level of the oldest information in the network is continuously reduced. Since the node with the highest AoI in the candidate node set is selected, this strategy can gradually generate an access trajectory that adapts to the current information age without pre-constructing the entire global path.

[0093] After determining the next node, add it to the set of visited nodes, add the connecting edge between the current node and the next node to the set of traversed edges, and update the next node to the new current node. Specifically, if the next node obtained according to the above greedy criterion is... Then update the set of visited nodes to And update the set of traversed edges to The step of adding connecting edges to the traversed edge set simultaneously in both directions is to uniformly record that an edge has been visited in the current iteration in the context of an undirected graph. Subsequently, the time step is updated to... And update the current node to the new position. Through this update process, the second path planning algorithm can maintain the node access status and edge access status in real time after each move, so that the subsequent candidate node selection and the next node selection are always based on the latest access information, thus forming a continuous and consistent path expansion process.

[0094] When the set of visited nodes contains all monitoring point nodes, it means that the UAV has visited all monitoring points in the target connected monitoring point graph at least once in the current traversal cycle. At this point, the current traversal cycle ends and the next traversal cycle begins. Specifically, when the following conditions are met... When the current round of coverage is complete, the set of traversed edges is cleared, i.e., let And reset the set of visited nodes to include only the current node at the current moment, that is, let At the same time, the current time step is recorded as the starting time step of the next traversal cycle, that is, let... and update the round number to In this way, at the start of the next traversal cycle, the UAV starts again from the node where it was at the end of the previous cycle, and expands the path again by generating a set of candidate nodes, selecting the next node with the largest AoI, and updating the access status. This allows the UAV to continuously build a tree-shaped access trajectory covering all monitoring points, thus enabling the UAV to continuously and periodically access all monitoring points.

[0095] Under the aforementioned path planning mechanism, since the drone can only select unvisited neighbors or return via already visited edges in each round of traversal, therefore, in the set... There is always only one path between any two nodes, meaning the drone will not loop during traversal. Therefore, from the time step... arrive The access trajectory always forms a tree containing A tree structure with nodes. Further analysis reveals that when the number of monitoring points satisfies... At that time, the long-term average network information age obtained by this algorithm satisfies the following relationship: ;in This represents the average age of network information over the time interval [0, T] for the second path planning algorithm, while This represents the average network information age over time corresponding to the theoretically optimal path planning strategy. The above inequality indicates that the average information age achieved by this algorithm in long-term operation is at most twice the theoretical optimal value. The reason for this proportional relationship is that, in the worst case, the drone needs to traverse each edge twice (once forward and once backward), while in the theoretically optimal path (such as a path based on a Hamiltonian cycle), each edge usually only needs to be traversed once.

[0096] Furthermore, from a computational complexity perspective, the second path planning algorithm only needs to calculate the information age in the neighbor set of the current node and select the node with the maximum value at each step. Therefore, its computational complexity is linearly related to the number of nodes, i.e., ... Since it does not require global path search or solving complex graph structures, this algorithm can complete UAV flight path planning tasks with low computational complexity in general connected monitoring point graph scenarios.

[0097] After completing the connected graph construction and path planning algorithm design, a unified analysis can be conducted on the average information age performance of different algorithm combinations under long-term operation. Specifically, when the number of monitoring points meets the requirements... At this time, an upper bound analysis can be performed on the relationship between the time-averaged network information age generated by different algorithm combinations within the time interval [0,T] and the theoretical optimal value. Here, let... This represents the average age of network information that the theoretically optimal flight strategy can achieve within the time interval [0,T]. , , and These represent the time-averaged network information age obtained under different combinations of connected graph construction algorithms and path planning algorithms. The four algorithm combinations mentioned above correspond to: constructing a connected graph using a Hamiltonian path-based path planning algorithm and Steiner tree (D-HPA-SMT); constructing a connected graph using a Hamiltonian path-based path planning algorithm and minimum spanning tree approximation (D-HPA-MST); constructing a connected graph using a tree search path planning algorithm and Steiner tree approximation (D-TSA-SMT); and constructing a connected graph using a tree search path planning algorithm and minimum spanning tree approximation (D-TSA-MST).

[0098] Under the above conditions, the upper bound of the long-term average network information age performance for each algorithm combination can be obtained. For the algorithm combination D-HPA-SMT, which is based on Hamiltonian paths and uses Steiner trees to construct connected graphs, its performance satisfies the following relationship: When the minimum spanning tree approximation algorithm is used to construct the connected graph and combined with Hamiltonian path planning (D-HPA-MST), its performance upper bound is: The two relationships above show that when path planning adopts the Hamiltonian path-based method, the upper bound of the system's time-averaged network information age is mainly determined by the performance ratio of the Hamiltonian path algorithm itself and the number of newly added nodes during the connected graph construction process.

[0099] Furthermore, when the tree search path planning algorithm is used in the path planning stage, the corresponding upper bound relationship for performance can also be obtained. For the case of using Steiner trees to construct connected graphs and combining them with the tree search path planning algorithm (D-TSA-SMT), its long-term average network information age satisfies: When the minimum spanning tree approximation algorithm is used to construct the connected graph and combined with the tree search path planning algorithm (D-TSA-MST), its performance upper bound satisfies: ;in, This is the optimal number of nodes to add to connect all PoIs; The number of nodes added is given by an approximation algorithm based on MST. The above relationship indicates that, when using a tree search path planning strategy, the upper bound of the system's time-averaged network information age is mainly affected by the performance ratio of the tree search path planning algorithm and the number of newly added nodes during the connected graph construction process.

[0100] Based on the above theoretical analysis, the applicant also verified the algorithm performance through numerical experiments. Experimental results show that in connected graph scenarios, the Hamiltonian path-based path planning algorithm (HPA) and the tree search-based path planning algorithm (TSA) both outperform the traditional age-based greedy algorithm (AA) and deep reinforcement learning (DRL) methods. Among them, HPA-S shows relatively stable performance across different network sizes, with its performance approaching the theoretical upper bound of 4 / 3. For example, when the network size is P=50, the performance ratio of the deep reinforcement learning method can reach 5.18, while the performance ratios of HPA and TSA remain near the theoretical upper bounds of approximately 4 / 3 and 2, respectively. This comparison demonstrates that the algorithm proposed in this application has a significant advantage in information age control. In non-connected graph scenarios, combining the connected graph construction algorithm with the path planning algorithm can further improve the overall system performance. For example, when using the D-HPA-MST algorithm combination, it maintains performance better than the theoretical upper bound across different network sizes. Experiments showed that the actual performance ratio gradually decreased from 5.63 at P=10 to 2.30 at P=50 as the network size increased. In contrast, the performance ratio of deep reinforcement learning methods remained consistently around 19 to 20. Therefore, the performance gap between D-HPA-MST and deep reinforcement learning methods widened from approximately 2.5 times at P=10 to approximately 7.4 times at P=50. Thus, the method proposed in this application has superior information age control capabilities in large-scale network scenarios.

[0101] In another feasible implementation, the method can be extended to multi-UAV collaborative scenarios. In this scenario, multiple UAVs collaborate to complete data acquisition tasks within the monitoring area. The system first obtains the current position and capability parameters of each UAV, which may include flight speed, battery capacity, communication range, payload capacity, etc. Based on the capability parameters of each UAV, the overall monitoring point set is divided into multiple subsets, and each subset is assigned to a different UAV to perform monitoring tasks. During the partitioning process, clustering results can be calculated based on the location distribution of each monitoring point, and combined with a preset number of UAVs, the clustering results are divided into a corresponding number of monitoring point subsets, while ensuring that the distribution of monitoring points in each subset meets the coverage capability of the corresponding UAV. Each UAV constructs a target connectivity monitoring point map within its assigned monitoring point subset, and selects either a first path planning algorithm or a second path planning algorithm based on whether the constructed map belongs to a second preset map set.

[0102] During multi-UAV operation, communication links can be established between the UAVs to periodically exchange location information and monitoring data, and the division of monitoring point subsets can be dynamically adjusted based on the flight status of each UAV. When a UAV malfunctions or runs out of power, its monitoring tasks can be reassigned to other UAVs. Collision avoidance measures can also be implemented during cooperative flight, namely, acquiring the real-time positions of each UAV, predicting potential collision risks based on their current positions and flight directions, and adjusting the flight path of at least one UAV when a collision risk is predicted to ensure the safe operation of the multi-UAV system.

[0103] For a multi-drone collaborative scenario, suppose there are K drones in the monitoring area, and the set of monitoring points that the k-th drone is responsible for is . ,satisfy And when hour Then the lower bound of the information age corresponding to the k-th drone satisfies: ;in, This indicates the number of monitoring points that the k-th drone is responsible for. Indicates to make The optimal number of nodes to add for connecting the corresponding monitoring point graph. The lower bound of the total information age of the entire system can be expressed as the weighted sum of the lower bounds of the information ages of each UAV: ;in, Let be the weight coefficient of the k-th UAV, which is related to the importance of the monitoring point. Furthermore, in the ideal case where the monitoring points are evenly distributed, the optimal task allocation satisfies... ≈P / K, at which point the lower bound of the total information age of the system is minimized; in real-world scenarios where monitoring points are not uniformly distributed, optimal task allocation also needs to comprehensively consider the number of monitoring points, spatial distribution, and differences in UAV capabilities. When the capabilities of each UAV are the same, the optimal allocation makes the lower bound of the information age of each subset as balanced as possible; when the capabilities of each UAV are different, UAVs with stronger capabilities can be allocated more monitoring points, and UAVs with weaker capabilities can be allocated fewer monitoring points.

[0104] In one feasible implementation, the method can also consider energy-constrained scenarios. Since the UAV's battery capacity is limited, the path planning process needs to ensure that the UAV can both complete the monitoring task and have sufficient power to return to the charging station. Therefore, after planning the UAV's flight path in the monitoring area in the target connectivity monitoring point map, the method in this embodiment further includes: obtaining the UAV's battery capacity. Energy consumption per unit distance and current remaining battery power ;

[0105] Simultaneously, the system acquires the location information of preset charging stations within the monitoring area. During path planning, the system calculates the estimated energy consumption of the drone from its current location to the next target monitoring point, and the estimated energy consumption from that next target monitoring point to the nearest charging station. When the estimated energy consumption exceeds the current remaining battery power, the flight path is adjusted to prioritize the drone's access to the nearest charging station. When the drone's battery power falls below a preset threshold, a flight path to the nearest charging station is planned, and the drone charges at the charging station until the preset requirements are met, then it continues to perform the remaining monitoring point access tasks. In multi-drone scenarios, task allocation can be dynamically adjusted based on the remaining battery power of each drone, prioritizing monitoring tasks for drones with more remaining battery power, thus ensuring that all drones can complete their tasks or return to the charging station before their battery power is depleted. Specifically, the set of feasible flight paths for drones can be set as follows: Based on the current remaining power and the minimum power required for the drone to return to the charging station. It can determine the set of feasible flight paths for drones. Then the set of paths that satisfy the energy constraints can be represented as: ;in, This indicates the minimum amount of electricity required for the drone to safely return to the charging station. Indicates the flight path of the drone. Indicates the drone at a certain time Flight speed, Indicates the end time of the path planning time interval. Indicates the start time of the path planning time interval; within the set of feasible flight paths. Above, the average age of online information over time To optimize the objective, an energy-constrained path optimization model is constructed; where the time-averaged network information age is used as the criterion. The optimization objective is expressed as: ;in, Indicates flight path In time interval The average age of network information over time; the energy-constrained path optimization model is expressed as: ;in, For Lagrange multipliers, Flight path Total energy consumption ; For available energy budget, Based on the path optimization model The candidate flight paths are solved to obtain the final flight path. This is achieved by adjusting... By doing so, a Pareto optimal solution can be obtained between information age and energy consumption, thus achieving the best balance between information age and energy consumption. The Pareto front is usually convex, indicating that increasing a small amount of energy in the low-energy-consumption region can significantly reduce the information age, while the improvement effect on information age decreases as energy continues to be increased in the high-energy-consumption region.

[0106] In another implementation, the method can also consider communication uncertainty scenarios. Since data transmission between the UAV and the monitoring point may involve random delays, communication delays can be incorporated into the information age calculation model during path planning. Specifically, the system acquires the probability distribution information of communication delays during data acquisition, including the average transmission time from the monitoring point to the UAV, the probability that the transmission time exceeds a preset threshold, and the communication quality differences between different monitoring point locations. Then, the average information age is calculated by averaging the total information age at each time step within a preset time interval. The flight path of the UAV in the monitoring area is planned with minimizing the average information age as the optimization objective. This specifically includes: acquiring the random variable of communication delays during data acquisition. The probability distribution information is obtained, and the time of each monitoring point is determined based on the probability distribution information. Data communication latency In the presence of communication delays, the monitoring points will be... At any moment Valid information: age Represented as: ;in, For monitoring points At any moment Physical information age; For monitoring points At any moment Corresponding data communication latency; based on age of valid information Determine the expected value of the average age of network information over time: ;in, Indicates flight path In time interval Average age of online information within a given timeframe. Represents a random variable for communication delay The expected value of the communication delay random variable. It can be obtained through statistical calculation of historical communication latency data, or through real-time measurement and updating of communication latency by the UAV during mission execution; based on the random variable of communication latency. The variance of the information age is used to determine its fluctuation range; a larger variance indicates higher uncertainty in the information age. Based on the expected value of the time-averaged network information age and its fluctuation range, the UAV flight path is adjusted. Furthermore, the variance of the communication delay can be used to characterize the fluctuation range of the information age; a larger variance indicates higher uncertainty in the information age. Based on this, the UAV flight path can be adjusted according to the expected value and fluctuation range. Furthermore, the probability distribution of the communication delay can be modeled using an exponential distribution, a log-normal distribution, or a mixed distribution. For example, for an exponential distribution model, the distribution function satisfies... ,in For the log-normal distribution model, [the parameter is missing in the original text] Follows a normal distribution ,in and These represent the mean and variance of the logarithmic delay, respectively. The distribution parameters can be determined based on actual measurement data using maximum likelihood estimation or moment estimation. Based on the communication delay model, the system can also record a data acquisition failure when the communication delay exceeds a preset tolerance threshold, and prioritize retransmitting data from the failed monitoring point in subsequent time steps, while dynamically adjusting the access priority based on the number of retransmissions. Furthermore, it can select the link with the best quality from multiple available communication links and automatically switch to a backup link when the quality of the primary link deteriorates, dynamically adjusting the data transmission rate based on link quality. Further, communication quality can be incorporated into the path planning objective function, performing a weighted trade-off between information age optimization and communication quality optimization to obtain a Pareto-optimal flight path.

[0107] In another feasible implementation, the method can also be extended to a weighted graph model scenario. In this scenario, the actual flight times for different flight paths may differ, making it difficult to accurately reflect the true flight cost using an unweighted graph. Therefore, in one possible implementation, a monitoring point graph is extracted from the grid structure based on multiple monitoring points distributed within the monitoring area and the adjacency relationships between these points. This includes: obtaining the edge weight information corresponding to each flight path within the monitoring area; wherein, nodes... and nodes The edge between The weight is denoted as This represents the actual time cost of the drone flying along the edge; based on the weights of each edge. Construct a weighted monitoring point graph and its adjacency matrix. , where, when node and nodes When there is no direct connection between them, Among them, in the weighted monitoring point map, monitoring points At any moment Information age is expressed as: ;in, The drone flies along the path and reaches the monitoring point. The last access time; based on edge weight information, determine the lower bound of the time-averaged network information age under the weighted graph model: ;in, Indicates the number of monitoring points. This represents the average weight of all edges in the weighted monitoring point graph. Furthermore, under the weighted graph model, the connected graph construction problem can be extended to the weighted Steiner tree problem, which involves finding a tree structure in the weighted graph that connects all monitoring points and has the minimum total weight. When the edge weights satisfy the triangle inequality, the performance ratio of the approximation algorithm for the weighted Steiner tree problem remains consistent with the unweighted case; when the edge weights do not satisfy the triangle inequality, virtual edges satisfying the triangle inequality can be added through preprocessing to ensure the approximation algorithm's approximation. The approximation algorithm based on the minimum spanning tree can still maintain a performance ratio of 2 under the weighted graph model, meaning the total weight of the newly added nodes does not exceed twice the optimal solution. During path planning in the weighted monitoring point graph, the weighted total travel time of each candidate path can be calculated, and the path with the minimum weighted total travel time can be selected as the optimal flight path, while ensuring that this flight path covers all monitoring points.

Claims

1. A method for planning flight paths of unmanned aerial vehicles (UAVs), characterized in that, include: Determine the grid structure corresponding to the monitoring area; the grid structure includes multiple grid nodes with two-dimensional coordinates and edges connecting adjacent grid nodes; Based on multiple monitoring points distributed within the monitoring area and the adjacency relationships between these monitoring points, a monitoring point map is extracted from the grid structure; the monitoring point map includes the multiple monitoring points and the edges connecting adjacent monitoring points. The algorithm determines whether the monitoring point map belongs to a first preset graph set. If the monitoring point map belongs to the first preset graph set, a first connected graph construction algorithm is used to obtain the target connected monitoring point map. If the monitoring point map does not belong to the first preset graph set, a second connected graph construction algorithm is used to obtain the target connected monitoring point map. The first preset graph set includes monitoring point maps that satisfy the conditions for constructing a Cartesian Steiner minimum tree. The first connected graph construction algorithm is a connected graph construction algorithm based on the Cartesian Steiner minimum tree problem. The second connected graph construction algorithm is a connected graph construction algorithm based on the minimum spanning tree problem. Determine whether the target connectivity monitoring point map belongs to the second preset map set; if the target connectivity monitoring point map belongs to the second preset map set, then use the first path planning algorithm to plan the flight path of the UAV in the monitoring area in the target connectivity monitoring point map; If the target connectivity monitoring point map does not belong to the second preset map set, the second path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connectivity monitoring point map; The second preset graph set includes a connected graph capable of determining Hamiltonian paths in polynomial time; The first path planning algorithm is a Hamiltonian path-based path planning algorithm; the second path planning algorithm is a tree search-based path planning algorithm.

2. The method according to claim 1, characterized in that, The first preset map set includes a map of monitoring points where each monitoring point is located on the boundary of a right-angled convex polygon and a map of monitoring points where each monitoring point is located on a preset number of parallel lines; The connected graph construction process of the first connected graph construction algorithm includes: Using all monitoring points as endpoints, search for the Steiner tree that minimizes the total side length in the grid structure corresponding to the monitoring area; All grid nodes on the Steiner tree are determined as the node set of the first connectivity monitoring point graph. Each adjacent grid node in the node set is connected by an edge to obtain the target connectivity monitoring point graph.

3. The method according to claim 1, characterized in that, The connected graph construction process of the second connected graph construction algorithm includes: A complete graph is constructed with all monitoring points as endpoints; the weight of each edge in the complete graph is the Manhattan distance between the corresponding two monitoring points. The complete graph is processed by the minimum spanning tree algorithm to obtain the minimum spanning tree connecting all monitoring points, and the edges contained in the minimum spanning tree are used as a set of virtual edges. For each virtual edge in the set of virtual edges, a Manhattan path connecting the two monitoring points of the virtual edge is determined in the grid structure corresponding to the monitoring area, and each grid node passed through on the Manhattan path is added to a temporary node set; Connecting adjacent grid nodes in the temporary node set with edges yields the target connectivity monitoring point map.

4. The method according to claim 1, characterized in that, The path planning process of the first path planning algorithm includes: Determine the starting node, which is any monitoring point in the target connectivity monitoring point graph, and there exists at least one Hamiltonian path from the starting node that passes through all monitoring points; Take the starting node as the current node and repeat the following steps: Search and select a Hamiltonian path in the target connectivity monitoring point map; the Hamiltonian path starts from the current node, passes through all monitoring points in sequence, and each monitoring point appears only once in the Hamiltonian path; Visit each monitoring point along the Hamiltonian path in sequence until the terminal node of the Hamiltonian path is reached; The termination node will be used as the current node for the next round of path planning.

5. The method according to claim 1, characterized in that, The path planning process of the second path planning algorithm includes: Select any monitoring point as the starting node in the target connectivity monitoring point map, and determine the starting node as the current node; Initialize the set of visited nodes and the set of traversed edges; wherein, the set of visited nodes contains only the current node, and the set of traversed edges is an empty set; The following node access steps are repeated in each traversal cycle until the set of visited nodes contains all the monitoring points in the target connectivity monitoring point graph: At the current moment, obtain the neighboring nodes adjacent to the current node in the target connectivity monitoring point graph, and determine a candidate node set from the neighboring nodes; wherein, the candidate node set includes neighboring nodes not included in the visited node set, and neighboring nodes included in the visited node set but whose edges with the current node are recorded in the traversed edge set; Calculate the information age of each candidate node in the candidate node set at the current time, and select the candidate node with the largest information age from the candidate node set as the next node; Add the next node to the set of visited nodes, and add the connection edge between the current node and the next node to the set of traversed edges; Update the next node to the new current node; If the set of visited nodes contains all monitoring points, end the current traversal cycle, clear the set of visited edges, and reset the set of visited nodes to contain only the current node at the current moment, so as to start the next traversal cycle.

6. The method according to claim 1, characterized in that, After planning the flight path of the UAV in the monitoring area in the target connectivity monitoring point map, the method further includes: At each time step, the node access status of the UAV in the target connectivity monitoring point graph is recorded, and the information age of each monitoring point is updated at each time step; wherein, the information age of the monitoring point is the number of time steps that have elapsed since the UAV last visited the monitoring point; At each time step, the sum of the information ages of all monitoring points in the target connectivity monitoring point graph is calculated to obtain the total information age at each time step; The average information age is calculated by averaging the total information age at each time step within a preset time interval, and the flight path of the UAV in the monitoring area is planned with minimizing the average information age as the optimization objective.

7. The method according to claim 1, characterized in that, Before determining whether the monitoring point map belongs to the first preset map set, the method further includes: Select any monitoring point from the monitoring point map as the starting node; The monitoring point graph is traversed using a graph traversal algorithm, and the monitoring points visited from the starting node during the traversal are recorded. If the number of accessed monitoring points is equal to the total number of monitoring points in the monitoring point graph, then the monitoring point graph is determined to be a connected graph; otherwise, the monitoring point graph is determined to be a disconnected graph. If the monitoring point map is a connected graph, then the step of determining whether the target connected monitoring point map belongs to the second preset map set is directly executed; if the target connected monitoring point map belongs to the second preset map set, then the first path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connected monitoring point map; if the target connected monitoring point map does not belong to the second preset map set, then the second path planning algorithm is used to plan the flight path of the UAV in the monitoring area in the target connected monitoring point map; wherein, the target connected monitoring point map is the monitoring point map itself.

8. The method according to claim 1, characterized in that, After planning the flight path of the UAV in the monitoring area in the target connectivity monitoring point map, the method further includes: Obtain the battery capacity of the drone. Energy consumption per unit distance and current remaining battery power ; Based on the current remaining power and the minimum power required for the drone to return to the charging station. Determine the set of feasible flight paths for the UAV. ,in, ； in, Indicates the flight path of the drone. Indicates the time when the drone is Flight speed, Indicates the end time of the path planning time interval. Indicates the start time of the path planning time interval; In the set of feasible flight paths Above, the average age of online information over time To optimize the objective, a path optimization model with energy constraints is constructed; wherein, the time-averaged network information age is used. The optimization objective is expressed as: ； in, Indicates flight path In time interval Average age of online information within a given timeframe; The energy-constrained path optimization model is expressed as follows: ； in, For Lagrange multipliers, Flight path Total energy consumption ; For available energy budget, ; According to the path optimization model The candidate flight paths are solved to obtain the actual flight path.

9. The method according to claim 6, characterized in that, The step of averaging the total information age at each time step within a preset time interval to obtain the average information age, and planning the flight path of the UAV in the monitoring area with minimizing the average information age as the optimization objective, includes: Obtain the communication delay random variable during the data acquisition process The probability distribution information is obtained, and the time of each monitoring point is determined based on the probability distribution information. Data communication latency ; In the presence of communication delays, the monitoring points At any moment Valid information: age Represented as: ； in, For monitoring points At any moment Physical information age; For monitoring points At any moment The corresponding data communication latency; Based on the aforementioned valid information, age Determine the expected value of the average age of network information over time: ； in, Indicates flight path In time interval Average age of online information within a given timeframe. Represents a random variable for communication delay The expected value of the communication delay random variable. It can be obtained by statistical calculation of historical communication latency data, or by real-time measurement and updating of communication latency by UAVs during mission execution; According to the communication delay random variable The variance is used to determine the range of fluctuation of the information age, wherein the larger the variance, the higher the uncertainty of the information age; The flight path of the UAV is adjusted based on the expected value of the average age of the network information over time and the fluctuation range of the information age.

10. The method according to claim 1, characterized in that, The step of extracting a monitoring point map from the grid structure based on multiple monitoring points distributed within the monitoring area and the adjacency relationships between these monitoring points includes: Obtain the edge weight information corresponding to each flight path in the monitoring area; wherein, nodes and nodes The edge between The weight is denoted as , representing the actual time cost of the drone flying along the edge; Based on the weights of each side Construct a weighted monitoring point graph and its adjacency matrix. , where, when node and nodes When there is no direct connection between them, ; In the weighted monitoring point diagram, the monitoring points At any moment Information age is expressed as: ； in, The drone flies along the path and reaches the monitoring point. The last access time.

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