Air refueling planning method, system, equipment and medium

Abstract

The invention relates to an air refueling planning method, system, equipment and medium, and the air refueling planning method comprises the steps: planning a refueling leg of an oil receiver according to the information of the oil receiver and the airspace information; according to the planned navigation condition of the oil receiver, the refueling time is sequenced; and the refueling machines which can arrive on time are screened, and the task sequence and the round-trip route of the refueling machines are planned based on set rule constraints. A multi-machine refueling planning problem can be split into two independent and associated sub-problems, and the solving complexity is reduced.

Description

Technical Field

[0001] This invention relates to the field of aerial refueling mission planning, and more particularly to an aerial refueling planning method, system, equipment, and medium. Background Technology

[0002] Aerial refueling is a core means to overcome aircraft range limitations and enhance systemic application capabilities. However, existing planning methods face multiple challenges in dynamic adversarial environments: traditional algorithms struggle to handle the strong spatiotemporal coupling constraints of multiple receiver aircraft and multiple refueling aircraft, easily leading to imbalances in refueling aircraft resource allocation and insufficient spatiotemporal matching accuracy between receiver aircraft and refueling aircraft. In complex scenarios, the solution space has high dimensionality; rule-based methods (such as nearest neighbor) are prone to getting trapped in local optima, while mathematical programming methods (such as mixed integer programming) have high computational complexity, failing to meet the needs of large-scale real-time planning. Receiver aircraft route planning and refueling aircraft scheduling are performed independently, lacking joint optimization and information sharing, resulting in low system resource utilization and poor overall efficiency. Existing platforms struggle to support multi-scenario generation, dynamic visualization and simulation, and quantitative evaluation of algorithm performance, failing to provide comprehensive verification support for complex planning algorithms. To address these issues, there is an urgent need to construct a simplified method for solving multi-aircraft collaborative refueling planning. Summary of the Invention

[0003] The purpose of this invention is to propose an aerial refueling planning method, system, equipment, and medium to solve the problem of high computational complexity in traditional aerial refueling planning methods.

[0004] The aerial refueling planning method of the present invention includes: Based on the receiver aircraft information and airspace information, the refueling route of the receiver aircraft is planned; Based on the planned flight schedule of the receiving aircraft, the refueling times are scheduled. Select refueling aircraft that can arrive on time, and plan the mission sequence and round-trip routes of the refueling aircraft based on the set rule constraints.

[0005] Optionally, the planning of the refueling segment for the receiver aircraft includes: With the goal of minimizing total fuel consumption, a genetic algorithm is used to plan the refueling starting point for each receiving aircraft.

[0006] Optionally, the step of planning the refueling starting point for each receiving aircraft using a genetic algorithm includes: The coordinates of the refueling start point for each receiving aircraft on its outbound / inbound journey are encoded as a binary chromosome. The total fuel consumption is used as the fitness function, and an initial population is generated by combining preset expert rules. Multiple iterations are then performed to find the optimal population.

[0007] Optional, preset expert rules include: The starting point for refueling on the outbound journey is selected from 1 / 4 to 1 / 2 of the total route length, and the starting point for refueling on the return journey is selected from 1 / 3 to 1 / 2 of the total route length. After the initial population is generated, the search space is reduced to 1 / 8 to 1 / 5 of the original space.

[0008] Optionally, the planning of the refueling segment for the receiver aircraft also includes: After the refueling starting point of each receiving aircraft is determined, the refueling endpoint of each receiving aircraft is determined by a binary search method, with the constraint that the amount of fuel in the receiving aircraft when it changes its path to the endpoint of this refueling meets the target value of this mission.

[0009] Optionally, determining the refueling endpoint for each receiver aircraft using the binary search method includes: Within the refueling airspace search range, the midpoint is iteratively selected, and fuel consumption is calculated in segments according to the order of path change start point, refueling start point, refueling end point and path change end point; The remaining oil quantity meets the target value when the receiving unit reaches the end point of the path change in the adjusted interval.

[0010] Optionally, the step of calculating segmented fuel consumption according to the order of route change starting point, refueling starting point, refueling ending point, and route change ending point includes: Fuel consumption is calculated using a modified Breguet formula between the refueling start and end points, while fuel consumption is calculated using the classic Breguet formula for the remaining segments. The modified Breguet formula is: ,in, For distance (m). Vacuum velocity (m / s) For specific fuel consumption (kg / (N·s)), The acceleration due to gravity (m / s²) The lift-to-drag ratio is dimensionless. These are the initial and final weights (N), and the dynamic equilibrium weight. This refers to the refueling rate.

[0011] On the other hand, the present invention also provides an aerial refueling planning system, comprising: The flight segment planning unit is configured to plan the refueling flight segment of the receiver aircraft based on receiver aircraft information and airspace information; The time sorting unit is configured to sort the refueling times according to the planned flight status of the receiving aircraft; The collaborative allocation unit is configured to select refueling aircraft that can arrive on time and plan the mission sequence and round-trip routes of the refueling aircraft based on the set rule constraints.

[0012] On the other hand, the present invention also provides an aerial refueling planning device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the steps of the aerial refueling planning method as described above.

[0013] On the other hand, the present invention also provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the steps of the aerial refueling planning method as described above.

[0014] The aerial refueling planning method of the present invention can be applied to the planning of multi-aircraft refueling and can decompose the multi-aircraft refueling planning problem into two independent and related sub-problems (i.e., the segment optimization problem of the receiving aircraft and the cooperative allocation problem of the refueling aircraft), thereby reducing the solution complexity. Attached Figure Description

[0015] Figure 1 A basic flowchart of the aerial refueling planning method provided for the embodiments; Figure 2 This is a schematic diagram of the refueling segment planning for a single receiver aircraft in the simulation verification platform provided in the embodiment. Figure 3 A schematic diagram of the system architecture of the simulation verification platform provided in this embodiment; Figure 4 A schematic diagram of the visualization interface of the simulation system provided for the embodiment; Figure 5 A flowchart illustrating the refueling task planning process provided for this embodiment; Figure 6 A schematic diagram illustrating the process of optimizing the refueling starting point using a genetic algorithm, provided for an embodiment. Figure 7 A schematic diagram of the binary search method for finding the refueling destination provided in the embodiment; Figure 8 A schematic diagram of the aerial refueling planning system provided in the embodiment; Figure 9 A schematic diagram of the structure of an aerial refueling planning device provided for an embodiment. Detailed Implementation

[0016] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0017] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0018] Example 1: This embodiment provides an aerial refueling planning method, such as... Figure 1 As shown, it includes, but is not limited to, the following steps: S101. Based on the receiver aircraft information and airspace information, plan the refueling segment for the receiver aircraft; In this embodiment, the receiver aircraft information includes, but is not limited to, at least one of the following: empty weight, cruising speed, and refueling rate. Airspace information includes, but is not limited to, at least one of the following: airport / target / threat zone location, and refueling airspace range.

[0019] The refueling segment mainly includes the route change origin (WCS), route change destination (WCE), refueling origin (RS), and refueling destination (RE). The route change origin and destination refer to the starting and ending points of the route that are altered from the receiver aircraft's original planned route for the purpose of aerial refueling. In step S101, segments where a single receiver aircraft deviates from its original route to the refueling airspace can be planned or further optimized.

[0020] S102. Based on the planned flight status of the receiving aircraft, sort the refueling times. S103. Select refueling aircraft that can arrive on time, and plan the mission sequence and round-trip routes of the refueling aircraft based on the set rule constraints. The above step S103 may specifically include task pairing between the refueling machine and the receiving machine, route planning for the refueling machine rendezvous point (RVP), and fuel consumption calculation for the refueling machine, to ensure that the refueling machine meets the rules and constraints such as time and space constraints and fuel quantity safety.

[0021] The aerial refueling planning method in this embodiment is applicable to the planning of multi-aircraft refueling and can decompose the multi-aircraft refueling planning problem into two independent and related sub-problems (i.e., the segment optimization problem of the receiver aircraft and the cooperative allocation problem of the tanker aircraft), thereby reducing the solution complexity.

[0022] In some implementations, planning the refueling segment for the receiver aircraft includes: using a genetic algorithm to plan the refueling starting point for each receiver aircraft with the goal of minimizing total fuel consumption.

[0023] The refueling starting point for each receiver aircraft is planned using a genetic algorithm, including: The coordinates of the refueling start point for each receiving aircraft on its outbound / inbound journey are encoded as a binary chromosome. The total fuel consumption is used as the fitness function, and an initial population is generated by combining preset expert rules. Multiple iterations are then performed to find the optimal population.

[0024] For example, the iterative optimization process includes selection (tournament / roulette), crossover (simulated binary crossover SBX), mutation (polynomial mutation) operations, etc.

[0025] In some implementations, the preset expert rules include: selecting a refueling point on the outbound journey that is 1 / 4 to 1 / 2 of the total route length, and selecting a refueling point on the return journey that is 1 / 3 to 1 / 2 of the total route length. After the initial population is generated, the search space is reduced to 1 / 8 to 1 / 5 of the original space. Multiple iterations of optimization combined with the preset expert rules can generate a high-quality initial population and reduce the search space.

[0026] In addition, the route planning in this embodiment also includes the planning of the refueling destination. In some implementations, the planning of the refueling route for the receiver aircraft also includes: After the refueling starting point of each receiver aircraft is determined, the refueling endpoint of each receiver aircraft is determined by a binary search method, with the constraint that the amount of fuel in the receiver aircraft when it changes its path to the endpoint of this refueling meets the target value of this mission.

[0027] In some implementations, determining the refueling endpoint for each receiver aircraft using a dichotomy method includes: Within the refueling airspace search range, the midpoint is iteratively selected, and fuel consumption is calculated in segments according to the order of path change start point, refueling start point, refueling end point and path change end point; The remaining oil quantity meets the target value when the receiving unit reaches the end point of the path change in the adjusted interval.

[0028] In this embodiment, the refueling airspace search interval is [RS.x, zone.right], where RS.x represents the x-coordinate of the refueling starting point, and zone.right represents the right boundary coordinate of the preset refueling airspace (i.e., the maximum allowable value in the x-direction). Segmented fuel consumption can be calculated using the Breguet formula. In some implementations, both the classic Breguet formula and the modified Breguet formula can be used, employing different formulas for different flight segments to achieve more accurate calculations.

[0029] In some embodiments of this example, calculating segmented fuel consumption according to the order of route change start point, refueling start point, refueling end point, and route change end point includes: Fuel consumption between the refueling start and end points is calculated using a modified Breguet formula, while fuel consumption for the remaining segments is calculated using the classic Breguet formula.

[0030] In this embodiment, the Breguet formula is modified to Equation 1 below, where, For distance (m). Vacuum velocity (m / s) For specific fuel consumption (kg / (N·s)), The acceleration due to gravity (m / s²) The lift-to-drag ratio is dimensionless. Initial and final weights (N), dynamic equilibrium weight This refers to the refueling rate.

[0031] Formula 1: In practical applications, the above-mentioned aerial refueling planning method can be implemented in a simulation system. Based on the simulation platform, a technical route of "layered decoupling - hybrid optimization - simulation verification" can be achieved. The following section provides a further explanation based on the actual simulation planning process.

[0032] In this example, the layered decoupling process, also known as the dynamic decoupling strategy, refers to breaking down the multi-aircraft refueling planning problem into two independent but related sub-problems: optimizing the refueling segment for the receiving aircraft and coordinating the allocation of refueling aircraft, thereby reducing the solution complexity.

[0033] The purpose of optimizing the refueling segment for receiver aircraft is to determine the starting point and ending point of the path change, the starting point and the ending point of refueling, and to optimize the segment where a single receiver aircraft deviates from its original route to the refueling airspace.

[0034] The purpose of tanker collaborative allocation is to complete the task pairing of tanker and receiver aircraft, the route planning of the tanker rendezvous point (RVP), and the fuel consumption calculation of the tanker, ensuring that the tanker meets the time and space constraints and fuel quantity safety. It can be understood that, in the example of this embodiment, tanker collaborative allocation is a further matching plan based on the already planned receiver aircraft refueling segment.

[0035] In this example, the algorithmic framework for hybrid optimization is as follows: Global optimization of refueling starting point (genetic algorithm): With the goal of "minimizing total fuel consumption", the coordinates of the outbound / inbound refueling starting point of each receiving aircraft are encoded as binary chromosomes. The chromosomes are iteratively evolved through selection (e.g., tournament / roulette), crossover (e.g., simulated binary crossover, SBX), and mutation (e.g., polynomial mutation). At the same time, expert rules are introduced to generate a high-quality initial population (in this example, the expert rules are configured to select the 1 / 4-1 / 2 segment of the route for the outbound RS and the 1 / 3-1 / 2 segment for the inbound refueling starting point) to reduce the search space.

[0036] Fast refueling destination search (binary search): After the refueling starting point is determined, the midpoint is iteratively selected within the refueling airspace search interval, with the constraint that "the remaining fuel quantity meets the target value when the receiver arrives at WCE". The interval is adjusted by segmented fuel consumption calculation (classic Breguet formula + modified Breguet formula) to quickly locate the optimal refueling destination.

[0037] Tanker Cooperative Allocation (Expert Rules): Based on spatiotemporal constraints (tankers must arrive at RVP within the receiver's RS time window), load balancing (prioritizing the allocation of the nearest available tanker), and range limitations (ensuring tankers have sufficient fuel for return), a rule base is built to dynamically generate tanker mission sequences and round-trip routes.

[0038] In this example, planning is based on a high-precision simulation verification platform. An integrated platform is built, encompassing scenario generation, path planning, refueling management, simulation execution, and visualization. This platform supports random A* path generation, multi-scenario parameter configuration (number of aircraft, threat zone, refueling airspace), and dynamic simulation, providing support for algorithm performance verification.

[0039] like Figure 2 The diagram shown is a schematic diagram of the refueling segment planning for a single receiver aircraft in the simulation verification platform. It illustrates the positional relationship between the receiver aircraft's original path, path change start point (WCS), path change end point (WCE), refueling start point (RS), and refueling end point (RE), and marks the current time and the receiver aircraft's fuel quantity, intuitively presenting the insertion logic of the refueling segment.

[0040] Figure 3 The system architecture diagram of the simulation verification platform is shown, presenting the core process of scene generation, task planning, and simulation execution. It includes the collaborative relationship of modules such as the main program, simulator, simulation context, path generator, refueling manager, and visualization, and clarifies the data interaction and functional boundaries of each module.

[0041] Figure 4The simulation system's visualization interface is shown: using latitude and longitude as coordinates, it displays the real-time positions of the refueling aircraft and the receiving aircraft, and marks the refueling airspace, threat zone, airport, target point, and original path. It supports dynamic viewing of refueling events and fuel quantity changes, providing an intuitive display of simulation results.

[0042] See Figure 5 The diagram illustrates the refueling task planning process in this example, describing the complete process from input (refueling airspace, waypoints, threat zone) to output (receiver / tanker route, total fuel consumption). It includes key steps such as original path planning, determination of refueling start / end point, tanker route planning, and fuel consumption update, reflecting the core logic of dynamic decoupling and hybrid optimization.

[0043] In this example, the scenario is first initialized by inputting the parameters of the receiver / refueling aircraft (empty weight, cruising speed, refueling rate, etc.), the location of the airport / target / threat zone, and the refueling airspace range. The simulator then generates the initial path and mission constraints.

[0044] After initialization, the refueling segment for the receiver aircraft is planned, including two parts: refueling start point optimization and refueling destination search. The refueling start point optimization process includes: starting a genetic algorithm, encoding the coordinates of the outbound / return refueling start point, calculating the individual fitness (total fuel consumption), performing selection / crossover / mutation, iterating to the maximum number of generations, and outputting the optimal RS (Refueling Range). The refueling destination search process includes: initializing a bipartite interval, calculating the midpoint RE (Refueling Execution), calculating fuel consumption segment by segment, comparing the final fuel quantity with the target value, adjusting the interval, and outputting the optimal RE. See also... Figure 6 This example illustrates a process for optimizing the refueling starting point using a genetic algorithm. See also: Figure 7 This example demonstrates a binary search process for finding the refueling destination.

[0045] In this example, the strategy for calculating fuel consumption in segments is as follows: the classic Breguet formula is used from WCS to RS; the modified Breguet formula is used from RS to RE; and the classic Breguet formula is used from RE to WCE. That is, fuel consumption is calculated using the modified Breguet formula between the refueling start and end points, and the classic Breguet formula is used for the remaining segments.

[0046] After optimizing the receiver aircraft's flight segment, the refueling aircraft are coordinated and allocated. The process includes: collecting refueling tasks and sorting them by time, selecting refueling aircraft that can arrive on time, allocating tasks based on expert rules, and planning the refueling aircraft's RVP route and return path.

[0047] The planning results can be further simulated and analyzed through a simulation verification platform. The simulation verification platform can update the aircraft status in real time, record indicators such as total fuel consumption and mission completion rate, and visualize the flight path and refueling process.

[0048] This example uses the following experimental configuration: Scenario parameters: Small scale (4 receiver aircraft, 2 airfields, 4 threat areas), large scale (40-60 receiver aircraft, 10-20 airfields); Aircraft parameters: receiver aircraft empty weight 12,973 kg, cruising speed 900 km / h; tanker aircraft empty weight 98,000 kg, refueling rate 15 kg / s; Algorithm parameters: Genetic algorithm population size 100, number of iterations 100, binary search maximum number of iterations 50.

[0049] As shown in Table 1 below, in the simulated planning process of an example, the method in this example can reduce the total fuel consumption to a certain extent, resulting in a significant improvement in collaborative efficiency. In small-scale scenarios (such as 4 receiving aircraft), the total fuel consumption is reduced by 20.6%, and in large-scale scenarios (40-60 receiving aircraft), it is reduced by 9.9%, with the refueling aircraft resource utilization rate increasing by more than 40%. Furthermore, the method in this example enhances the global optimization capability: the genetic algorithm combined with expert rules improves the convergence speed by 21.2% compared to the standard genetic algorithm, avoiding local optima; the binary search method shortens the RE search time by more than 17 times, meeting the requirements of real-time planning.

[0050] Table 1 Planning Methods Small-scale reduction in total fuel consumption Large-scale reduction in total fuel consumption RE search speedup This example method 20.6% 9.9% 17.23 times Expert rule algorithm 8.4% 3.8% - Random Algorithm 0% 0% - In addition, this example supports dynamic threat adjustment and task priority change, maintaining stable performance in large-scale scenarios and demonstrating strong robustness. Furthermore, the verification system is complete, with the simulation platform capable of generating 100+ independent scenarios, supporting visualization and multi-dimensional performance evaluation (fuel consumption, time, task completion rate), providing a reliable basis for algorithm iteration.

[0051] This embodiment also provides an aerial refueling planning system 100, see [link / reference] Figure 8 It includes a flight segment planning unit 101, a time sequencing unit 102, and a collaborative allocation unit 103.

[0052] The route planning unit 101 is configured to plan the refueling route of the receiver aircraft based on the receiver aircraft information and airspace information.

[0053] The time sorting unit 102 is configured to sort the refueling times according to the planned flight status of the receiving aircraft.

[0054] The collaborative allocation unit 103 is configured to select tanker aircraft that can arrive on time and plan the mission sequence and round-trip routes of the tanker aircraft based on the set rule constraints.

[0055] This embodiment also provides an aerial refueling planning device, see [link / reference] Figure 9 ,include: Processor 91; Memory 92 is used to store executable instructions of processor 91; The processor 91 is configured to invoke instructions stored in the memory 92 to execute the steps of the aerial refueling planning method as described above.

[0056] This embodiment also provides a computer-readable storage medium storing computer program instructions thereon, which, when executed by a processor, implement the steps of the aerial refueling planning method as described above.

[0057] Furthermore, although exemplary embodiments have been described herein, their scope includes any and all embodiments based on this disclosure that have equivalents, modifications, omissions, combinations (e.g., schemes involving intersections of various embodiments), adaptations, or changes. They are not limited to the examples described in this specification or during the implementation of this application, and such examples are to be interpreted as non-exclusive.

[0058] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more of them) can be used in combination with each other. Other embodiments can be used by those skilled in the art when reading the above description.

[0059] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, various modifications and variations of the embodiments of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An aerial refueling planning method, characterized in that, include: Based on the receiver aircraft information and airspace information, the refueling route of the receiver aircraft is planned; Based on the planned flight path of the receiving aircraft, the refueling times are scheduled. Select refueling aircraft that can arrive on time, and plan the mission sequence and round-trip routes of the refueling aircraft based on the set rule constraints.

2. The aerial refueling planning method as described in claim 1, characterized in that, The planning of the refueling segment for the receiver aircraft includes: With the goal of minimizing total fuel consumption, a genetic algorithm is used to plan the refueling starting point for each receiving aircraft.

3. The aerial refueling planning method as described in claim 2, characterized in that, The planning of the refueling starting point for each receiving aircraft using a genetic algorithm includes: The coordinates of the refueling start point for each receiving aircraft on its outbound / inbound journey are encoded as a binary chromosome. The total fuel consumption is used as the fitness function, and an initial population is generated by combining preset expert rules. Multiple iterations are then performed to find the optimal population.

4. The aerial refueling planning method as described in claim 3, characterized in that, The preset expert rules include: The starting point for refueling on the outbound journey is selected from 1 / 4 to 1 / 2 of the total route length, and the starting point for refueling on the return journey is selected from 1 / 3 to 1 / 2 of the total route length. After the initial population is generated, the search space is reduced to 1 / 8 to 1 / 5 of the original space.

5. The aerial refueling planning method as described in claim 2, characterized in that, The planning of the refueling segment for the receiving aircraft also includes: After the refueling starting point of each receiving aircraft is determined, the refueling endpoint of each receiving aircraft is determined by a binary search method, with the constraint that the amount of fuel in the receiving aircraft when it changes its path to the endpoint of this refueling meets the target value of this mission.

6. The aerial refueling planning method as described in claim 5, characterized in that, The determination of the refueling endpoint for each receiving aircraft using the binary search method includes: Within the refueling airspace search range, the midpoint is iteratively selected, and fuel consumption is calculated in segments according to the order of path change start point, refueling start point, refueling end point and path change end point; The remaining oil quantity meets the target value when the receiving unit reaches the end point of the path change in the adjusted interval.

7. The aerial refueling planning method as described in claim 6, characterized in that, The calculation of segmented fuel consumption according to the order of route change start point, refueling start point, refueling end point, and route change end point includes: Fuel consumption is calculated using a modified Breguet formula between the refueling start and end points, while fuel consumption is calculated using the classic Breguet formula for the remaining segments. The modified Breguet formula is: ,in, : represents the range (m). Vacuum velocity (m / s) For specific fuel consumption (kg / (N·s)), The acceleration due to gravity (m / s²) The lift-to-drag ratio is dimensionless. These are the initial and final weights (N), and the dynamic equilibrium weight. This refers to the refueling rate.

8. An aerial refueling planning system, characterized in that, include: The flight segment planning unit is configured to plan the refueling flight segment of the receiver aircraft based on receiver aircraft information and airspace information; The time sorting unit is configured to sort the refueling times according to the planned flight status of the receiving aircraft; The collaborative allocation unit is configured to select refueling aircraft that can arrive on time and plan the mission sequence and round-trip routes of the refueling aircraft based on the set rule constraints.

9. An aerial refueling planning device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the steps of the aerial refueling planning method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores computer program instructions, which, when executed by a processor, implement the steps of the aerial refueling planning method according to any one of claims 1-7.

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