A multi-machine space-time cooperative four-dimensional route parallel planning method based on time-varying cooperative range

Abstract

This invention provides a multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying cooperative flight paths. The method mainly includes: a multi-aircraft parallel planning model based on time-varying cooperative flight paths, a fast convergence model with a contraction factor and A* heuristic cost for time-coordination constraints, and a pre-collision-free expansion model of A* nodes with UAV performance constraints for spatial collaboration. Specifically, multiple UAVs perform spatiotemporal collaborative A* four-dimensional route parallel planning based on time-varying cooperative flight paths. This, combined with the A* heuristic cost with a contraction factor and time-coordination constraints, yields a fast-converging, accurate time-coordinated flight path. Furthermore, combined with the pre-collision-free expansion of A* nodes with UAV performance constraints for spatial collaboration, spatial collaboration is completed during the node expansion process of time collaboration. The method provided by this invention eliminates the need for multiple iterative planning and pre-planning of cooperative flight paths, effectively improving the accuracy of multi-UAV time-coordinated routes, reducing planning computation and time, and reliably ensuring the anti-collision capability of multi-UAV spatial collaboration. It achieves accurate time-coordinated arrival at the destination and reliable spatial collaboration for collision avoidance of multi-UAV flight paths.

Description

Technical Field

[0001] This invention belongs to the field of multi-aircraft spatiotemporal cooperative route planning technology, specifically involving a four-dimensional parallel route planning method based on time-varying cooperative flight path, with time-coordinated arrival of multiple UAVs and spatial cooperative collision avoidance. Background Technology

[0002] With the development of multi-UAV collaborative technology, especially in collaborative operation scenarios requiring high coordination consistency, the demands for time coordination performance in ensuring UAVs arrive at the target point simultaneously and spatial coordination capabilities for flight collision avoidance safety are becoming increasingly stringent. This has become a core technology for improving the efficiency and mission completion rate of multi-UAV collaborative operations. Common multi-UAV spatiotemporal collaborative route planning methods mainly fall into three categories: One type of approach involves using algorithms to plan multiple feasible routes for each UAV, determining a cooperative route that allows multiple UAVs to reach the target point simultaneously through iterative speed adjustments and collision detection. Because each UAV plans its own route, this method requires multiple re-plannings, speed adjustments, and collision detections during cooperative adjustments, resulting in long planning times and room for improvement in route optimality. Another type uses algorithms to first plan routes with the same range for each UAV, then combines cooperative range planning with multi-UAV route planning algorithms to perform a cooperative search for routes that satisfy both speed and collision-free conditions, allowing simultaneous arrival at the target point. The cooperativeness of the planned routes is related to the algorithm's performance and the size of the cooperative range, leading to long planning times and high computational difficulty. A third type is route search methods that integrate time and space constraints, often employing biomimetic genetic algorithms or other intelligent evolutionary algorithms. However, these algorithms face challenges in practical applications due to issues such as convergence speed, computational load, randomness, and local minima. The aforementioned multi-aircraft spatiotemporal collaborative route planning method can be effectively applied in non-highly complex scenarios and under certain time coordination requirements. However, for multi-UAV spatiotemporal collaborative scenarios with both strict performance requirements and high efficiency, the planning performance and route effectiveness need to be improved.

[0003] For collaborative flight scenarios involving multiple UAVs simultaneously arriving at a target point without collisions, the flight paths of these UAVs need to simultaneously meet both temporal and spatial coordination conditions. Existing temporal coordination technologies mostly rely on iterative speed adjustments or pre-planning of the shortest collaborative flight path. However, the heavy computational burden of multiple iterations and the complexity of finding the shortest collaborative flight path result in long planning times and high iterative computational complexity. Intelligent evolutionary algorithms also face challenges in practical applications due to issues such as convergence speed, randomness, and local minima. Spatiotemporal collaborative flight of multiple UAVs requires precise path planning that simultaneously reaches the target point and resolves spatial conflicts between UAVs; existing technologies are insufficient for solving this type of path planning problem. Summary of the Invention

[0004] This invention provides a multi-UAV spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying cooperative flight paths. By designing a fast-converging parallel planning method based on time-varying cooperative flight paths and A* heuristic costs for time-coordinated flight, it solves the problem of precise time coordination when multiple UAVs arrive at their destination simultaneously. Combined with a conflict-free expansion method for A* nodes with UAV performance constraints for spatial coordination, it solves the problem of reliable spatial coordination to avoid collisions during multi-UAV flight. Ultimately, it achieves high-precision four-dimensional route parallel planning with time-coordinated arrival at the destination and spatial coordination to avoid collisions.

[0005] This invention provides a multi-aircraft spatiotemporal cooperative four-dimensional route parallel planning method based on time-varying cooperative flight paths, comprising: a multi-aircraft parallel planning model based on time-varying cooperative flight paths, a fast convergence model with a contraction factor and a time-cooperation constraint A* heuristic cost, and a pre-conflict-free expansion model of A* nodes with UAV performance constraints for spatial cooperation. Specifically, multiple UAVs perform spatiotemporal cooperative A* four-dimensional route parallel planning based on time-varying cooperative flight paths. This, combined with the A* heuristic cost with a contraction factor and time-cooperation constraints, yields a fast-converging and accurate time-cooperation route. Furthermore, by combining this with the pre-conflict-free expansion of A* nodes with UAV performance constraints for spatial cooperation, spatial cooperation is completed during the node expansion process of time cooperation.

[0006] According to the present invention, a multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying collaborative range is provided. The multi-aircraft spatiotemporal collaborative four-dimensional route planning is carried out in a four-dimensional space composed of three-dimensional space and time. Based on the gridded sparse A* search method, time coordination is achieved by approximately ensuring that the range of each UAV is equal and that they fly at the same speed. At the same time, spatial coordination is achieved by not considering conflicting nodes when expanding the search of nodes.

[0007] According to the present invention, a multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying collaborative flight path is provided. The multi-aircraft parallel planning model based on time-varying collaborative flight path includes a process where each UAV simultaneously plans its route towards the target point in a step-by-step manner according to the number of route segments. The time-varying collaborative flight path is calculated during the parallel planning process by approximating the sum of the planned routes of each UAV within the same time period and the estimated route cost to reach the target point, and taking the route with the largest route cost as the current collaborative flight path. The multi-aircraft parallel planning process based on time-varying collaborative flight path involves obtaining the current collaborative flight path, continuing to plan routes for other UAVs that do not meet the current collaborative flight path until the cost tolerance requirement of the current collaborative flight path is met; when the current routes are equal and all are the current collaborative flight path, the collaborative flight path is updated step-by-step, and planning continues for UAVs that do not meet the current collaborative flight path until all UAVs reach the target point. The operating logic of the model includes: Step 1: Initialize the parameters in the algorithm, including the number of drones. The starting point, target point, open and closed lists of nodes searched by A*, and waypoint sequences for each UAV, along with the actual cost. Heuristic Cost Cooperative range cost tolerance contractile factor The starting point of each drone is taken as the current node. Step 2: Check each drone in turn to see if it has reached the target point. If the drone has reached the target point, backtrack to the parent node to build the route and end the route search for that drone. Step 3: Check if all drones have completed route construction. If they have, proceed to step 9; otherwise, proceed to step 4. Step 4: Calculate the collaborative flight path of multiple UAVs that have not reached the target point. If all UAVs meet the current collaborative flight path cost tolerance, then randomly select one UAV to extend the flight path. Otherwise, the flight path of the UAV that does not meet the current collaborative flight path cost tolerance is taken as the current flight path to be extended. Step 5: Expand the current node of the current route to be expanded in four dimensions by using the A* node pre-conflict-free expansion model with UAV performance constraints and spatial coordination. Step 6: Calculate the actual cost of expanding the node, and calculate the heuristic cost using a fast convergence model with a shrinkage factor and time co-constraint A* heuristic cost, and create successor child nodes; Step 7: Check the validity of subsequent child nodes to determine if they are conflict-free. If a node is already in the closed list, skip it. If a node is not in the open list or is in the open list but has a better cost, add it to the open list. Step 8: Remove the child node with the minimum total cost from the open list of the drone, use it as the waypoint for successful expansion, update the current travel cost, and go to step 2; Step 9: End multi-aircraft collaborative route planning and output the four-dimensional waypoint sequence planning results.

[0008] The present invention provides a multi-aircraft spatiotemporal cooperative four-dimensional route parallel planning method based on time-varying cooperative flight path. The fast convergence model with contraction factor and time cooperative constraint A* heuristic cost is implemented by introducing cooperative flight path constraints and contraction factor into the calculation of the A* heuristic cost. The calculation is as follows: in, The straight-line distance from the current node to the planned target point. For coefficients, To coordinate range constraints, Contraction factor. Cooperative range constraint. The calculation is as follows: in, For the current cooperative flight range of multiple drones, i.e. , , This represents the actual cost of the current drone, i.e., the cumulative distance traveled from the current node back to the starting point. It's evident that if the estimated range of the current drone is less than the cooperative range, the heuristic cost increases positively correlated with the difference between the cooperative range and the estimated range, allowing it to approach the cooperative range. (Shrinkage factor) The calculation is as follows: in, This is the straight-line distance from the starting point to the target point. This is a coefficient. It can be seen that... The smaller the value, the closer the current position is to the target; the smaller the value of the shrinkage factor, the lower the heuristic cost. The smaller the value, the smaller the value of the point that is closer to the target point, which can speed up the convergence to the target point.

[0009] According to the present invention, a multi-aircraft spatiotemporal cooperative four-dimensional route parallel planning method based on time-varying cooperative range is provided. The A* node pre-conflict-free expansion model with UAV performance constraints and spatial cooperation is based on the maximum climb angle of the UAV. Maximum dive angle and maximum turning angle Within the constraints, spatial cooperation is achieved during the search by performing a spatial collision-free pre-determination on the current nodes of the route to be expanded. The spatial cooperation constraint requires that a certain safe distance be maintained between UAVs during multi-UAV flight to avoid collisions. That is, for drones The current node to be expanded Consider drones of Other drones Is the distance greater than the safe distance? , Other drones It may not be in the current planning stage; it requires backtracking of waypoints and determining each node individually; drones should also be considered. A situation where the drone swaps positions with another drone. The current node to be expanded If a node's path takes one more step than some other drone tracks, it's necessary to estimate the possible locations of other drones' nodes to be expanded, and pre-process potential conflict locations to avoid collisions. By pre-judging the conflicts of nodes to be expanded during node search, nodes that do not meet the conditions are not considered, thus achieving spatial cooperation.

[0010] This invention provides a multi-UAV spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying collaborative flight paths. It employs a parallel planning strategy based on time-varying collaborative flight paths to perform spatiotemporal collaborative A* four-dimensional route planning for multiple UAVs. It designs a fast convergence heuristic cost with a contraction factor and time collaboration constraints, and combines it with pre-collision-free expansion of A* nodes with UAV performance constraints for spatial collaboration. This eliminates the need for multiple iterative planning and pre-planning of collaborative flight paths, effectively improving the route accuracy of multi-UAV time collaboration, reducing planning computation and time, and reliably ensuring the anti-collision capability of multi-UAV spatial collaboration. It achieves accurate time-coordinated arrival at the destination and reliable spatial collaboration for collision avoidance of multiple UAVs. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0012] Figure 1 This is the overall logical relationship diagram of the multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method provided by the present invention; Figure 2 This is a flowchart of the multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method provided by the present invention; Figure 3 This is a schematic diagram of the pre-conflict-free expansion of the multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method provided by the present invention. (a) Schematic diagram of multi-aircraft route backtracking node expansion (b) Schematic diagram of multi-aircraft route prediction node expansion. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0014] The following is combined with Figures 1-3This invention describes a multi-aircraft spatiotemporal collaborative four-dimensional parallel route planning method.

[0015] This invention provides a multi-UAV spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying cooperative flight path. This method addresses the time coordination of multiple UAVs to meet the collaborative mission requirements of multiple UAVs, ensuring that all UAVs depart from the starting point and arrive at the target point simultaneously. By employing a time-varying cooperative flight path calculation method and planning logic, time-coordinated planning with approximately equal flight paths is achieved. This invention uses the A* algorithm for route search, and spatial coordination is achieved by ignoring nodes that do not meet the conditions during node search, completing a pre-emptive conflict-free expansion. Simultaneously, to solve for time-coordinated and spatially coordinated routes, a four-dimensional flight path representation is used, that is, a sequence of waypoints composed of a series of coordinate points in a four-dimensional space with three-dimensional coordinate positions and times. The four-dimensional spatial coordinate points are represented as... ,in , , For three-dimensional spatial coordinates, The time coordinate is used. Multi-drone parallel planning is the process by which each UAV simultaneously plans its route from the starting point to the target point in a step-by-step manner according to the number of flight segments.

[0016] like Figure 1 As shown, the multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method provided by this invention includes: a multi-aircraft parallel planning model based on time-varying collaborative flight paths, a fast convergence model with a contraction factor and time collaborative constraints A* heuristic cost, and an A* node pre-conflict-free expansion model with UAV performance constraints and spatial collaboration. The overall operation logic of this method includes: Step 1: Initialization, start the multi-aircraft parallel planning model based on time-varying cooperative flight path; Step 2: Calculate the time-varying cooperative range of multiple aircraft; Step 3: Designate any UAV routes that do not meet the current cooperative range cost tolerance as routes to be expanded and initiate parallel expansion; Step 4: Calculate the heuristic cost with shrinkage factor and time co-constraint, and expand the nodes of the current route to be expanded using the A* heuristic search method; Step 5: Gradually perform time-varying collaborative range calculation and node expansion until each UAV reaches the target point, completing the parallel planning of multi-UAV time-coordination and spatial coordination; Step 6: Node backtracking to obtain multi-aircraft spatiotemporal collaborative four-dimensional flight path.

[0017] Understandably, the multi-drone parallel planning model 110 based on time-varying cooperative flight path calculates the current cooperative flight path of multiple UAVs that have not yet reached the target point. It then uses A* heuristic search to expand nodes for UAVs that do not meet the current cooperative flight path cost tolerance. If the current flight paths are equal and all are current cooperative flight paths, a UAV that has not yet reached the target point is randomly selected to update its cooperative flight path step by step. This process continues to expand nodes for UAVs that do not meet the current cooperative flight path cost tolerance until all UAVs reach the target point. The fast convergence model 120 with a contraction factor and time-cooperative constraint A* heuristic cost introduces cooperative flight path constraints into the heuristic cost calculation of the A* algorithm, making the flight path of the UAV to be expanded close to the cooperative flight path. A contraction factor is designed to enable fast convergence of the route search. Through modules 110 and 120, multiple UAVs complete time coordination during the step-by-step route planning process. The A* node pre-conflict-free expansion model 130 with UAV performance constraint spatial coordination determines UAV performance constraints and spatial collision conflicts during the A* node expansion process, ignoring nodes that do not meet the conditions, thus achieving spatial coordination among multiple UAVs.

[0018] like Figure 2 As shown, in an embodiment of the present invention, the overall operational logic of multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning can be realized through the multi-aircraft parallel planning process 210 based on time-varying cooperative flight path. The specific implementation process is as follows: Step 1: Initialize the parameters in the algorithm, including the number of drones. Starting points of each drone Target point A* search for open lists, closed lists, and waypoint sequences of nodes. Cooperative range cost tolerance contractile factor Wait, node Location of the drone ,time Actual cost Heuristic Costs Total cost Parent node , The starting point of each drone is taken as the current node.

[0019] Step 2: Sequentially determine whether the current node position of each UAV is consistent with the target point. If the UAV reaches the target point, backtrack the parent node to construct the UAV's route and end its route node search expansion to form the UAV's waypoint sequence.

[0020] Step 3: Check if all drones have completed route construction, i.e., the drone waypoint sequence is not empty. If all are completed, proceed to step 9; otherwise, proceed to step 4.

[0021] Step 4: Calculate the cooperative flight path of multiple UAVs that have not yet reached the target point. , , This represents the straight-line distance from the current node to the planned target point; assuming all drones meet the current cooperative flight cost tolerance... If the condition is met, a drone will be randomly selected to begin the expansion; otherwise, the drone route that does not meet the current cooperative range cost tolerance will be used as the current route to be expanded.

[0022] Step 5: Expand the current node of the current route to be expanded in four dimensions by using the A* node pre-conflict-free expansion model with UAV performance constraints and spatial coordination.

[0023] Step 6: Calculate the actual cost of expanding the node, and calculate the heuristic cost using a fast convergence model with a shrinkage factor and time co-constraint A* heuristic cost, and create the successor child node of the current route node to be expanded.

[0024] Step 7: Check the validity of subsequent child nodes without conflicts, including checking static obstacles and conflicts between drones; for static obstacles, the node is valid if its position is not the same as any static obstacle; for conflicts between drones, the node is valid if no node is in the same position at the same time and the positions of adjacent nodes are not swapped; if the node is valid, then determine: if the node is already in the closed list, skip it; if the node is not in the open list or its cost is better than its cost in the open list, add it to the open list.

[0025] Step 8: Select the drone with the lowest total cost from the open list of drones currently using routes to be expanded. The child nodes are used as waypoints for successful expansion, and the current journey cost is updated. Proceed to step 2.

[0026] Step 9: End multi-aircraft collaborative route planning and output the four-dimensional waypoint sequence planning results. .

[0027] In an embodiment of the present invention, a fast convergence model 220 with a contraction factor and a time-coordination constraint A* heuristic cost can be used to make the range of each UAV approach the cooperative range during the gradual expansion of the UAV's flight path, and accelerate the convergence speed of the flight path, ultimately achieving time coordination. The specific implementation process is as follows: In the calculation of A* heuristic cost, cooperative range constraints and a contraction factor are introduced, and the heuristic cost is... The calculation is as follows: in, The straight-line distance from the current node to the planned target point. For coefficients, To coordinate range constraints, Contraction factor. Cooperative range constraint. The calculation is as follows: in, For the current cooperative flight range of multiple drones, i.e. , , This represents the actual cost of the current drone, i.e., the cumulative distance traveled from the current node back to the starting point. It's evident that if the estimated range of the current drone is less than the cooperative range, the heuristic cost increases positively correlated with the difference between the cooperative range and the estimated range, allowing it to approach the cooperative range. (Shrinkage factor) The calculation is as follows: in, This is the straight-line distance from the starting point to the target point. This is a coefficient. It can be seen that... The smaller the value, the closer the current position is to the target; the smaller the value of the shrinkage factor, the lower the heuristic cost. The smaller the value, the smaller the value of the point that is closer to the target point, which can speed up the convergence to the target point.

[0028] like Figure 2 and Figure 3 As shown, in an embodiment of the present invention, by using the A* node pre-conflict-free expansion model 230 with UAV performance constraints for spatial collaboration, multi-UAV spatial collaboration can be achieved during the gradual node expansion process. The specific implementation process is as follows: During the process of expanding the current node of the current route to be expanded, from the first node... waypoints To the waypoints At that time, the maximum climb angle of the drone is satisfied. Maximum dive angle and maximum turning angle Within the constraints, i.e. in This represents the number of waypoints for the drone.

[0029] Spatial cooperative constraints are the requirement that a certain safe distance must be maintained between multiple drones during flight to avoid collisions. ,Right now .

[0030] like Figure 3 As shown in (a), blue represents a closed list and orange represents an open list. For drones... The current orange node to be expanded Consider drones of Other drones Is the distance greater than the safe distance? , Other drones It may not be in the current planning stage; it requires backtracking of waypoints and determining each node individually; drones should also be considered. of To exchange positions with other drones, i.e. and .like Figure 3 As shown in (b), if the drone The current node to be expanded The number of steps is higher than some other drone tracks To avoid potential collisions, it's necessary to estimate the possible locations of other drones currently being expanded into nodes, and pre-process potential conflict locations. By pre-judging the conflicts between nodes during node search, nodes that do not meet the criteria are not considered, thus achieving spatial collaboration.

[0031] In embodiments of the present invention, by executing multi-aircraft parallel planning logic based on time-varying cooperative flight paths, cooperative flight path constraints are introduced into the heuristic cost calculation of the A* algorithm to make the flight path of the UAV to be expanded close to the cooperative flight path. A shrinkage factor is designed to enable rapid convergence of the route search. Furthermore, during the expansion of A* nodes, a pre-conflict-free expansion method for A* nodes with UAV performance constraints and spatial coordination is designed, ultimately achieving multi-aircraft spatiotemporal cooperative route parallel planning.

[0032] The embodiments described above are merely illustrative. The models described may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the models can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0033] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms. Therefore, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a read-only memory, random access memory, magnetic disk, optical disk, etc., and includes several instructions and data calculations, causing a computer device (which may be a personal computer, server, or network device) to execute the methods described in each embodiment or a part of the embodiments.

[0034] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method based on time-varying cooperative flight path, characterized in that, include: A multi-aircraft parallel planning model based on time-varying cooperative flight path, a fast convergence model with shrinkage factor and time cooperative constraint A* heuristic cost, and an A* node pre-conflict-free expansion model with UAV performance constraint spatial cooperation. Among them, multiple UAVs perform spatiotemporal collaborative A* four-dimensional route parallel planning based on time-varying collaborative flight path. This, together with the A* heuristic cost with shrinkage factor and time collaboration constraint, obtains accurate time collaboration route with fast convergence. Then, combined with the pre-conflict-free expansion of A* nodes with UAV performance constraint spatial collaboration, spatial collaboration is completed in the process of time collaboration node expansion.

2. The multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method according to claim 1, characterized in that, The aforementioned multi-aircraft spatiotemporal collaborative four-dimensional route planning is based on a gridded sparse A* search method in a four-dimensional space composed of three-dimensional space and time. It achieves temporal collaboration by approximately ensuring that each UAV has the same range and flies at the same speed, while spatial collaboration is achieved by not considering conflicting nodes during node expansion search.

3. The multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method according to claims 1 and 2, characterized in that, The multi-drone parallel planning model based on time-varying cooperative flight path describes a process where each UAV simultaneously plans its route towards the target point in steps according to the number of flight segments. The time-varying cooperative flight path involves approximating the sum of the planned routes of each UAV within the same time frame and the estimated cost of reaching the target point, taking the route with the highest cost as the current cooperative flight path. The multi-drone parallel planning process based on time-varying cooperative flight path involves obtaining the current cooperative flight path and continuing to plan routes for other UAVs that do not meet the current cooperative flight path until the cost tolerance requirement of the current cooperative flight path is met. When the current flight paths are equal and all are the current cooperative flight path, the cooperative flight path is updated step by step, and planning continues for UAVs that do not meet the current cooperative flight path until all UAVs reach the target point. The operational logic of this model includes: Step 3-1: Initialize the parameters in the algorithm, including the number of drones. The starting point, target point, open and closed lists of nodes searched by A*, and waypoint sequences for each UAV, along with the actual cost. Heuristic Cost Cooperative range cost tolerance contractile factor The starting point of each drone is taken as the current node. Step 3-2: Check each drone in turn to see if it has reached the target point. If the drone has reached the target point, backtrack to the parent node to build the route and end the route search for that drone. Step 3-3: Check if all drones have completed route construction. If they have, proceed to step 3-9; otherwise, proceed to step 3-4. Steps 3-4: Calculate the collaborative flight path of multiple UAVs that have not reached the target point. If all UAVs meet the current collaborative flight path cost tolerance, then randomly select one UAV to extend the flight path. Otherwise, the flight path of the UAV that does not meet the current collaborative flight path cost tolerance is taken as the current flight path to be extended. Steps 3-5: Expand the current nodes of the current route to be expanded in four dimensions using the A* node pre-conflict-free expansion model with UAV performance constraints and spatial coordination. Steps 3-6: Calculate the actual cost of expanding the node, and calculate the heuristic cost using a fast convergence model with a shrinkage factor and time co-constraint A* heuristic cost, and create successor child nodes; Steps 3-7: Check the validity of subsequent child nodes to determine if they are conflict-free. If a node is already in the closed list, skip it. If a node is not in the open list or is in the open list but has a better cost, add it to the open list. Step 3-8: Remove the child node with the minimum total cost from the open list of the UAV, use it as the waypoint for successful expansion, update the current range cost, and go to step 3-2; Steps 3-9: End multi-aircraft collaborative route planning and output the four-dimensional waypoint sequence planning results.

4. The multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method according to claims 1 to 3, characterized in that, The fast convergence model with contraction factor and time-coordinated A* heuristic cost is implemented by introducing cooperative range constraints and contraction factor into the calculation of A* heuristic cost. The calculation is as follows: ； in, The straight-line distance from the current node to the planned target point. For coefficients, To coordinate range constraints, Contraction factor. Cooperative range constraint. The calculation is as follows: ； in, For the current cooperative flight range of multiple drones, i.e. , , This represents the actual cost of the current drone, i.e., the cumulative distance traveled from the current node back to the starting point. It's evident that if the estimated range of the current drone is less than the cooperative range, the heuristic cost increases positively correlated with the difference, allowing it to approach the cooperative range. (Shrinkage factor) The calculation is as follows: ； in, This is the straight-line distance from the starting point to the target point. This is a coefficient. It can be seen that... The smaller the value, the closer the current position is to the target; the smaller the value of the shrinkage factor, the lower the heuristic cost. The smaller the value, the smaller the value of the point that is closer to the target point, which can speed up the convergence to the target point.

5. The multi-aircraft spatiotemporal collaborative four-dimensional route parallel planning method according to claims 1 to 3, characterized in that, The A* node pre-conflict-free expansion model with UAV performance constraint spatial coordination is based on the UAV's maximum climb angle. Maximum dive angle and maximum turning angle Within the constraints, spatial cooperation is achieved during the search by performing a spatial collision-free pre-determination on the current nodes of the route to be expanded. The spatial cooperation constraint requires that a certain safe distance be maintained between UAVs during multi-UAV flight to avoid collisions. That is, for drones The current node to be expanded Consider drones of Other drones Is the distance greater than the safe distance? , Other drones It may not be in the current planning stage; it requires backtracking of waypoints and determining each node individually; drones should also be considered. A situation where the drone swaps positions with another drone. The current node to be expanded If a node's path takes one more step than some other drone tracks, it's necessary to estimate the possible locations of other drones' nodes to be expanded, and pre-process potential conflict locations to avoid collisions. By pre-judging the conflicts of nodes to be expanded during node search, nodes that do not meet the conditions are not considered, thus achieving spatial cooperation.

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