Stratosphere airship regional residence path planning method based on two-dimensional interval prediction search

Abstract

This invention discloses a method for planning a regional stationary flight path based on two-dimensional interval prediction. The method includes the following steps: establishing an energy consumption model for a stratospheric airship; expressing an optimization problem based on the airspeed and energy consumption of the stratospheric airship; referring to interval prediction algorithms and simulated annealing algorithms, solving the optimization problem based on the dynamics model and energy consumption model of the stratospheric airship to obtain the optimal airspeed and heading angle; and updating the current state variables of the airship and determining mission completion. In practical applications, the initial energy reserve, mission start point, target point, and other state variables of the flight mission are input into the controller, and the priority parameters of the flight mission optimization target are adjusted, thereby enabling the stratospheric airship to plan a route that meets the requirements to complete the mission. When applied to stratospheric airship regional stationary missions, this invention enables missions that enter the airspace from a target point outside the airspace and perform regional stationary operations.

Description

Technical Field

[0001] This invention provides a stratospheric airship regional dwell path planning method based on a two-dimensional interval prediction algorithm and a simulated annealing algorithm. It provides a stratospheric airship path planning method that considers airspace range, wind field conditions, target point location, and energy consumption, and belongs to the field of automatic control technology. Background Technology

[0002] A stratospheric airship is an aircraft capable of staying and performing missions in the stratosphere for extended periods. It combines the buoyancy of an airship with the propulsion of an aircraft, powered by solar cells or other energy sources. Due to the relatively stable atmospheric conditions and low wind speeds in the stratosphere, and its distance from various ground-based sources of interference, stratospheric airships can perform long-term monitoring, communication relay, and meteorological observation missions.

[0003] In recent years, with the development of materials science, energy storage, aerodynamics, and automatic control technologies, the design and manufacturing technologies of stratospheric airships have gradually matured, and stratospheric airships are gradually transitioning from the experimental stage to practical application. Nevertheless, stratospheric airships still face some technical challenges, such as energy supply and aircraft control. Regarding aircraft control, the flight control constraints of stratospheric airships mainly stem from control capability constraints caused by coupling with other systems and environmental constraints imposed by flight airspace and mission requirements. Simultaneously, to ensure mission reachability and extend the time spent in the region, under the constraints of energy storage batteries and the power system, stratospheric airships must select appropriate heading angles and airspeeds based on the wind field environment and target point orientation. On the other hand, as an aircraft that resides in the stratosphere for extended periods, its position needs to be maintained within a certain airspace range; therefore, a regional loiter path planning method that can balance the airspeed, energy consumption, and positional constraints of stratospheric airships is required. This invention, "A Method for Planning the Regional Stay Path of a Stratospheric Airship Based on a Two-Dimensional Interval Prediction Search Algorithm," takes the above-mentioned problem as its starting point and proposes a targeted solution to the problem of planning the regional stay path of a stratospheric airship based on wind field environment and airspace size. First, with the optimization objective of minimizing mission completion time and energy consumption, and considering airspace range and flight capability, an optimization problem model for the regional stay path planning of a stratospheric airship is established. Then, based on the idea of ​​two-dimensional interval prediction, the optimization problem is solved to obtain the heading angle and airspeed that can satisfy energy consumption and mission completion time. Finally, through simulation verification, it is proved that the involved control method can achieve the path planning task of a stratospheric airship in regional stay conditions with faster mission completion time and lower energy consumption, under the conditions of satisfying position constraints and energy constraints. Summary of the Invention

[0004] The purpose of this invention is to provide a path planning method for stratospheric airships in regional loitering situations based on a two-dimensional interval prediction algorithm. This method can provide a satisfactory flight trajectory while ensuring low energy consumption and rapid completion of the flight mission, based on the assessment of mission reachability. As a multi-objective task, airship path planning needs to consider both mission completion time and energy consumption. Control engineers can adjust parameters and prioritize optimization objectives during airship path planning according to actual application scenarios.

[0005] The technical solution adopted in this invention is a method for stratospheric airship regional dwell based on a two-dimensional interval prediction search algorithm. First, an energy consumption model of the stratospheric airship is established, and an optimization problem is expressed based on the airspeed and energy consumption of the stratospheric airship. Then, referring to the interval prediction algorithm and simulated annealing algorithm, the optimization problem is solved based on the dynamic model and energy consumption model of the stratospheric airship, yielding the optimal airspeed and heading angle. Next, the current state variables of the airship are updated, and a mission completion judgment is made. In practical applications, the initial energy reserve, mission starting point, target point, and other state variables of the flight mission are input into the controller, and the priority parameters of the flight mission optimization target are adjusted, thereby enabling the stratospheric airship to plan a route that meets the requirements to complete the mission.

[0006] The specific steps are as follows:

[0007] Step one: Based on the flight mission requirements, there are two optimization objectives. Weights are assigned to these two objectives to adjust their priority. An optimization objective function is constructed based on the two objectives of achieving higher airspeed and lower energy consumption.

[0008] Step two involves constructing a solver based on interval prediction and simulated annealing algorithms. Two-dimensional interval prediction is performed using the airspeed and heading angle of the stratospheric airship as two decision variables. Simulated annealing is employed, with probability retention of suboptimal solutions to improve algorithm reliability; the probability calculation references the Metropolis criterion. This forms the solver for the objective function, yielding the optimal airspeed and heading angle for the next step.

[0009] Step 3: Calculate various parameters of the airship after a one-time flight period based on the airspeed and heading angle output in Step 2, including airspeed, heading angle, remaining energy, and flight time. Update the airship's current state with the calculated parameters and determine mission completion. If the mission is not completed, return to Step 3 to continue iterating the airship state; if the mission is completed, output the planned path and relevant parameters for stratospheric airship flight.

[0010] In the optimization objective design described in step one, the optimization objective needs to be designed in two parts when achieving area stationary status. First, it is necessary to determine whether the starting position is within the airspace. If the starting position is outside the airspace, the aircraft needs to quickly fly into the airspace at the beginning of the area stationary task before continuing the task. If the starting position is within the airspace, the area stationary status can be directly achieved within that area. Therefore, the two optimization objectives are different.

[0011] (1) When the starting position is outside the region, the regional stationing target point needs to be set as the flight destination. Since the flight mission is to fly to the target point, the flight distance and energy consumption are optimization objectives that need to be considered. Therefore, the optimization objectives at this time consist of these two parts. Set the current stratospheric airship position to X now Y now This indicates that after a long period of time, the position of the stratospheric airship is X. next Y next This indicates that the target point's location is indicated by X. target Y target express.

[0012] The flight distance consists of two parts: one part is the flight distance D over a single step. step The other part is the distance D between the airship's position and the target point after a long time. end .

[0013] First is D step From the formula, we can obtain:

[0014]

[0015] Next is D target The distance is expressed as the lateral distance from the current point to the target point, which can be obtained from the formula:

[0016] D t =|X target -X now |+|Y target -Y now | (2)

[0017] D can be obtained from the above formula. step With D target Then, the flight distance was calculated:

[0018] D = D step +D target (3)

[0019] Regarding energy consumption, the energy consumption within a single time step is used as a reference. The remaining energy after a single time step of flight in the stratosphere is selected to express the energy consumption of the flight strategy. Therefore, it is necessary to calculate the remaining energy of the airship. The remaining energy is expressed as a percentage of remaining energy, and the calculation method is as follows:

[0020]

[0021] Among them, W b W represents the current remaining battery energy. bm This is the maximum capacity of the battery.

[0022] Calculate the remaining battery energy W b The method is as follows:

[0023]

[0024] Among them W b0 For the remaining battery energy a long time ago, P b δ represents the energy increase or consumption over a single step, where δ is the step duration in minutes.

[0025] Since the task has multiple optimization objectives, two coefficients, a1 and a2, were designed to represent the priority of distance and the priority of energy consumption in this path planning, respectively. From the above formula, the cost expression of the optimization function when the starting point is outside the airspace is derived as follows:

[0026] J1=a1D+a2N (6)

[0027] Therefore, the optimization objective in this design can be expressed as:

[0028] minJ1=a1D+a2N (7)

[0029] During flight, it is necessary to continuously check whether the current position is within the airspace. If the current position is within the airspace, the optimization target needs to be changed.

[0030] (2) When the airship is within the airspace, the optimization objective consists of two parts: the distance between the stratospheric airship and the airspace boundary and energy consumption.

[0031] First, the distance D between the airship and the airspace boundary. edge Since there are many airspace boundaries and the exact number of boundaries is uncertain, it is first necessary to determine the number of airspace boundaries. After determining the number of boundaries, each target point is checked for distances to these boundaries, and the minimum distance between each target point and all boundaries is taken as the boundary distance D corresponding to the target point. edge After obtaining the boundary distance D edgeThen, the negative of the minimum distance between the target point and all boundaries is taken as the distance-level optimization objective, thereby filtering out P points that are too close to the boundaries. n The effect.

[0032] The method for calculating the boundary distance is as follows: First, it is necessary to represent the current point P. n The foot of the perpendicular from the boundary line segment is P(X). p ,Y p The foot of the perpendicular P is represented as follows:

[0033]

[0034] And calculate P next The formula for calculating the distance D from P is as follows:

[0035]

[0036] Therefore, the distance-level optimization objective D can be obtained. e Expressed using the following formula:

[0037] D e =-D edge (11)

[0038] Regarding energy consumption, the energy consumption within a single time step is used as a reference. The remaining energy after a single time step of flight in the stratosphere is selected to express the energy consumption of the flight strategy. Therefore, it is necessary to calculate the remaining energy of the airship. The remaining energy is expressed as a percentage of the remaining energy, and the calculation method is the same as shown above:

[0039]

[0040] Among them, W b W represents the current remaining battery energy. bm This is the maximum capacity of the battery.

[0041] Calculate the remaining battery energy W b The method is as follows:

[0042]

[0043] Among them W b0 For the remaining battery energy a long time ago, P b δ represents the energy increase or consumption over a single step, where δ is the step duration in minutes.

[0044] Similarly, since the regional residency task still has multiple optimization objectives, it is also necessary to design optimization objective parameters to express the emphasis on the optimization objectives. Therefore, parameter a was designed. e1 a e2The two coefficients represent the priority of boundary distance and the priority of energy consumption in this path planning, respectively. Therefore, when the stratospheric airship is located within the airspace, the optimization function can be expressed as follows:

[0045] J2 = a e1 D e +a e2 N (14)

[0046] Therefore, the optimization objective is expressed as:

[0047] minJ2=a e1 D e +a e2 N (15)

[0048] The solver constructed in step two based on the two-dimensional interval prediction and simulated annealing algorithm is specifically solved as follows:

[0049] Step 1: Since the dimensions of the two-dimensional interval prediction are the airspeed and heading angle of the stratospheric airship, a two-dimensional coordinate system is constructed with the airspeed and heading angle as the coordinate axes. The heading angle is divided into m equal parts, and the distance between the maximum and minimum airspeeds is divided into n equal parts. Each division of the two coordinate axes is taken as one unit distance. The heading angle and airspeed intersect at every unit distance, resulting in a total of m×n intersection points. These discrete intersection points form the initial search range for the two-dimensional interval prediction, and subsequent two-dimensional interval predictions are performed.

[0050] Step 2: After obtaining the above m×n discrete coordinate points, select the corresponding objective function according to the current position of the stratospheric airship. If the airship is outside the airspace, substitute the airspeed and heading angle corresponding to the coordinate point into formula (6); if the airship is inside the airspace, substitute the airspeed and heading angle corresponding to the coordinate point into formula (14). In this way, the navigation cost corresponding to each coordinate point is obtained.

[0051] Step 4: Among the m×n discrete coordinate points mentioned above, select the coordinate point corresponding to the optimal cost according to the navigation mission requirements, and record this coordinate point in the set to be detected. The central idea of ​​this step is to use the coordinate point corresponding to the optimal cost to represent the midpoint of the interval, thereby predicting the interval where the optimal solution is located and narrowing the prediction range of airspeed and heading angle, so as to narrow the subsequent two-dimensional interval prediction range.

[0052] Step 5: Determine whether the regions enclosed by the top-left, top-right, bottom-left, and bottom-right points within the set to be tested contain portions exceeding the maximum airspeed and heading angle. If such portions exist, the regions outside the maximum range are considered non-existent; otherwise, the entire region is considered to exist. If a region exists, the unit airspeed and unit heading angle are equally divided and set as the new unit airspeed and unit heading angle. The cost of the points within the region is calculated, and the midpoints with costs better than the optimal coordinates are retained. Furthermore, since this design provides a set of solutions and searches for the optimal solution within that set, unlike the simulated annealing algorithm which adds perturbations to the solution to find a better one, but still aims to find the optimal solution while avoiding getting trapped in local optima, the approach of probabilistically retaining non-optimal solutions, similar to simulated annealing, is referenced. Following the Metropolis criterion, the midpoints of non-optimal coordinates are probabilistically retained, and these retained points are recorded in the set to be tested.

[0053] Referring to the Metropolis criterion, the retention probability P is calculated using the following formula, where J represents the cost corresponding to the current solution. best The cost of the current optimal solution:

[0054]

[0055] This allows us to achieve the effect of probabilistically preserving suboptimal solutions based on the cost of non-optimal solutions.

[0056] Step 6: Determine if a point to be detected exists within the detection set. If the detection set is empty, output the airspeed and heading angle corresponding to the optimal coordinate point. If the detection set is not empty, it means that the current optimal solution may not be the global optimal solution, and two-dimensional interval prediction is still needed to try to find a better solution. In this case, jump to step 5 and continue solving until the detection set is empty or the set number of iterations has been completed.

[0057] In step three, updating the stratospheric airship's state involves substituting the optimal heading angle and optimal airspeed, obtained from the solver built in step two, into the stratospheric airship's dynamic model. Based on the airship's current parameters, this yields parameters such as the airship's latitude and longitude, remaining energy, and total travel time after a certain period of flight at the optimal heading angle and optimal airspeed. After updating the stratospheric airship's state, its mission completion is assessed. If the airship successfully remains in the designated airspace for the set time, the mission is considered complete, and the loop exits. If it fails to remain for the set time, the process returns to step three, and the new stratospheric airship state is used to solve the problem in the solver built in step two. If environmental factors such as wind speed cause the airship to leave the designated area or run out of energy, the airship is considered unable to complete the assigned mission.

[0058] Technical breakthroughs and performance advantages of this invention:

[0059] This invention features high efficiency in interval search and accurate search results for optimal points. When applied to stratospheric airship regional stationing missions, it can enable missions that start from a target point outside the airspace and enter the airspace for regional stationing.

[0060] When this invention is applied to the regional stationing mission of stratospheric airships, it first determines whether the starting point is within the airspace. If it is, path planning is performed directly using the regional stationing mode. If the starting point is outside the airspace, entering the airspace is the first task, followed by the regional stationing mission. Since this invention is applied to the regional stationing mission of stratospheric airships, the two dimensions of the two-dimensional interval prediction correspond to the airspeed and heading angle of the stratospheric airship, which determine the path planning during regional stationing. Therefore, the two-dimensional interval prediction search algorithm can directly solve for the optimal airspeed and heading angle in the next time interval through the input of external parameters, improving path planning efficiency. Simultaneously, the interval prediction search method avoids the global search mode, improving the search efficiency for the optimal point. Finally, a simulated annealing algorithm is introduced to retain suboptimal solutions with a certain probability, preventing the two-dimensional interval prediction search algorithm from getting trapped in local optima and improving the search accuracy for the optimal point.

[0061] The symbols are explained as follows:

[0062] D step The distance traveled in a single step over a long period of time;

[0063] X now This represents the X-axis coordinate of the current position;

[0064] X next The X-axis coordinate of the next position;

[0065] Y now This is the Y-coordinate of the current position;

[0066] Y next The Y-coordinate of the next position;

[0067] D target The distance to the target point;

[0068] D end The distance between the airship and the target point after one long flight period;

[0069] X target The X-axis coordinate of the target point;

[0070] Y target The Y-coordinate of the target point;

[0071] m is a fraction representing the heading angle of a stratospheric airship;

[0072] n is a fraction of the airspeed of a stratospheric airship;

[0073] D represents the optimization objective in terms of distance;

[0074] N represents the optimization objective in terms of energy;

[0075] W b The remaining energy of the battery;

[0076] W bm To maximize battery energy storage;

[0077] W b0 The remaining energy in the battery at the previous moment;

[0078] P b For battery energy consumption / regeneration over a long period of time;

[0079] δ represents the time of one step;

[0080] J1 is the optimization target in navigation mode;

[0081] a1 is the distance target parameter in navigation mode;

[0082] a2 is the energy target parameter in navigation mode;

[0083] X p The vertical X-axis coordinates of the airship's position relative to the boundary position;

[0084] Y p The Y-axis coordinate is the perpendicular distance between the airship's position and the boundary position;

[0085] X1 is the boundary X-axis coordinate;

[0086] X2 is the boundary X-axis coordinate;

[0087] X3 is the X-axis coordinate of the airship's position;

[0088] Y1 is the boundary Y-axis coordinate;

[0089] Y2 is the boundary Y-axis coordinate;

[0090] Y3 is the Y-axis coordinate of the airship's position;

[0091] D edge The distance between the airship and the boundary;

[0092] D e Optimize the target for the airship and the boundary;

[0093] a e1For parameters related to boundary distance in the dwell mode;

[0094] a e2 These are parameters related to boundary energy consumption under the residency mode;

[0095] J2 represents the optimization objective under the residency mode;

[0096] J represents the cost corresponding to the current solution;

[0097] J best The cost of the current optimal solution;

[0098] P is the probability of retaining a non-optimal solution; Attached Figure Description

[0099] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0100] Figure 2 It is a speed line graph.

[0101] Figure 3 It is a line graph of the heading angle.

[0102] Figure 4 It is a trajectory planning diagram. Detailed Implementation

[0103] The design methods of each part of this invention will be further explained below:

[0104] The present invention, "A method for stratospheric airship regional dwelling based on a two-dimensional interval prediction search algorithm," comprises the following specific steps:

[0105] Step 1: Based on the airship's location, select the operating mode and construct the optimization objective function.

[0106] The airship's location may be within or outside the required airspace, necessitating a positional determination. If the airship is within the required airspace, it can directly perform an area-based stationary mission; if it is outside the required airspace, it must first fly into the required airspace before performing the stationary mission. Therefore, the first step of this invention is to determine the operating mode based on the stratospheric airship's initial position and construct a corresponding optimization objective function. Simultaneously, the optimization objective bias can be adjusted based on the externally input two-dimensional optimization objective weights, making the algorithm more inclined towards speed-first or energy-saving-first approaches.

[0107] If it is necessary to fly from outside the airspace to inside the airspace, the optimization objective can be set as follows:

[0108] minJ1=a1D+a2N

[0109] If the area is already within the airspace, the optimization objective can be set as follows:

[0110] minJ2=a e1 D e +a e2 N

[0111] Step 2: Construct an optimization objective function solver based on the two-dimensional interval prediction algorithm.

[0112] Using airspeed and heading angle as interval coordinate axes, an optimized objective function solver is designed based on the proposed two-dimensional interval prediction algorithm. Referring to the simulated annealing algorithm's approach of retaining non-optimal solutions, the range of the search solution set is slightly broadened to improve the reliability of the obtained solutions and avoid getting trapped in local optima. Based on this, interval prediction estimation is performed, gradually narrowing the prediction interval to find the interval containing the optimal solution, thereby finding the globally optimal airspeed and heading angle. After finding the optimal airspeed and heading angle, the obtained speed and heading angle are used as the next long-term flight speed and heading angle.

[0113] Step 3: Update the airship's real-time position based on the parameters obtained from the solver.

[0114] The airspeed and heading angle for the next long time period, obtained from step two, are substituted into the solver constructed in the second step. By continuously narrowing the prediction interval, the interval containing the optimal airspeed and heading angle is found, thus identifying the optimal airspeed and heading angle corresponding to that interval. The solved optimal airspeed and heading angle are then substituted into the execution layer to solve for various indicators of the airship at the next moment, including stratospheric airship speed, heading angle, position coordinates, and remaining energy. The mission completion is judged based on the airship's dwell time in the region. If the preset dwell time is successfully achieved, the loop ends; otherwise, the process returns to step two to continue predicting the next long interval.

[0115] The flowchart of this invention is as follows Figure 1 As shown:

[0116] Experimental charts and related data:

[0117] The reliability and feasibility of this invention have been verified through simulation. The invention will be further explained below using trajectory planning diagrams for regional dwelling, velocity planning line graphs, and heading angle planning line graphs.

[0118] Speed ​​line graph as shown Figure 2 As shown:

[0119] The heading angle broken line diagram is as follows Figure 3 As shown:

[0120] Trajectory planning diagram as follows Figure 4 As shown:

[0121] As can be seen from the line graph, when applied to the problem of stratospheric airship regional loitering, this invention can enable stratospheric airships to fly into the airspace and, based on environmental factors such as wind direction and wind speed and the established optimization objective function, find the most suitable heading angle and airspeed for regional loitering in the next time interval, and use this to plan the trajectory.

[0122] When applied to stratospheric airship loitering missions, this invention features the ability to flexibly set the maximum airspeed and heading angle. Simultaneously, it can also find the most suitable airspeed and heading angle for the next time interval with high accuracy and fast search speed, thereby guiding the airship in its flight mission.

Claims

1. A method for regional dwell flight path planning based on two-dimensional interval prediction, characterized in that, The specific steps are as follows: Step 1: Based on the flight mission requirements, there are two optimization objectives. Set corresponding weights for the two optimization objectives to adjust the priority of the flight mission optimization objectives. Based on the two optimization objectives of faster airspeed and less energy consumption, construct the optimization objective function. Step 2: Construct a solver based on the interval prediction algorithm and the simulated annealing algorithm; use the airspeed and heading angle of the stratospheric airship as two decision variables to perform two-dimensional interval prediction; adopt the simulated annealing algorithm to retain the suboptimal solution with probability, where the probability calculation adopts the Metropolis criterion; use this to form a solver to solve the objective function and obtain the next step of the long-optimal airspeed and heading angle. Step 3: Calculate various parameters of the airship after a one-time flight period based on the airspeed and heading angle output in Step 2, including airspeed, heading angle, remaining energy, and flight time. Update the airship's current state with the calculated parameters and determine mission completion. If the mission is not completed, proceed to Step 3 to continue iterating the airship's state. If the mission is completed, output the planned path and relevant parameters for stratospheric airship flight. The solver constructed in step two based on the two-dimensional interval prediction and simulated annealing algorithm is specifically solved as follows: Step 1: Since the dimensions of the two-dimensional interval prediction are the airspeed and heading angle of the stratospheric airship, a two-dimensional coordinate system is constructed with the airspeed and heading angle as the coordinate axes. The heading angle is divided into m equal parts, and the distance between the maximum and minimum airspeed is divided into n equal parts. Each division of the two coordinate axes is taken as one unit distance. The heading angle and airspeed intersect at every unit distance, resulting in a total of m×n intersection points. These discrete intersection points are used as the initial search range for the two-dimensional interval prediction, and subsequent two-dimensional interval predictions are performed. Step 2: After obtaining the above m×n discrete coordinate points, select the corresponding objective function according to the current position of the stratospheric airship. If the airship is outside the airspace at this time, substitute the airspeed and heading angle corresponding to the coordinate points into formula (6). If the airship is within the airspace at this time, substitute the airspeed and heading angle corresponding to the coordinate point into formula (14); thus obtain the navigation cost corresponding to each coordinate point; the cost expression of the optimization function is as follows: J1=a1D+a2N (6) J1 is the optimization target in navigation mode; a1 is the distance target parameter in navigation mode; a2 is the energy target parameter in navigation mode; D represents the optimization objective in terms of distance; N represents the optimization objective in terms of energy; When the stratospheric airship is located inside the airspace, the optimization function can be expressed in the following form: J2=a e1 D e +a e2 N (14) J2 represents the optimization objective under the residency mode; a e1 For parameters related to boundary distance in the dwell mode; a e2 These are parameters related to boundary energy consumption under the residency mode; D e Optimize the target for the airship and the boundary; Step 4: Among the above m×n discrete coordinate points, select the coordinate point corresponding to the optimal cost according to the requirements of the navigation mission, and record this coordinate point into the set to be detected; the central idea in this step is to use the coordinate point corresponding to the optimal cost to represent the midpoint of the interval, so as to predict the interval where the optimal solution is located, and narrow the prediction range of airspeed and heading angle, so as to narrow the prediction range of the subsequent two-dimensional interval. Step 5: Determine whether the regions enclosed by the top left, top right, bottom left, and bottom right points within the set to be tested contain portions exceeding the maximum airspeed and heading angle. If a portion exceeds the maximum value, the region is considered non-existent; otherwise, the entire region is considered to exist. If the region exists, the unit airspeed and unit heading angle are equally divided and set as the new unit airspeed and unit heading angle. The cost of the points in the region is calculated, and the midpoint with a cost better than the optimal coordinate point is retained. Referring to the Metropolis criterion, the retention probability P is calculated using the following formula, where J represents the cost corresponding to the current solution. best The cost of the current optimal solution: This achieves the goal of probabilistically preserving suboptimal solutions based on the cost of non-optimal solutions; Step 6: Determine whether there is a point to be detected in the set to be detected. If the set to be detected is empty, output the airspeed and heading angle corresponding to the optimal coordinate point. If the set to be detected is not empty, it means that the current optimal solution may not be the global optimal solution. Continue to perform two-dimensional interval prediction to find a better solution. Jump to step 5 and continue solving until the set to be tested is empty or the set number of loops has been completed.

2. The regional dwell flight path planning method based on two-dimensional interval prediction according to claim 1, characterized in that, Regarding the optimization target design described in step one, when achieving regional stationing, the optimization target needs to be designed in two parts. First, determine whether the starting position is within the airspace. If the starting position is outside the airspace, then at the beginning of the regional stationing mission, fly into the airspace and continue the regional stationing mission. If the starting position is within the airspace, then directly perform regional stationing within this range. (1) When the starting position is outside the area, the area's stationary target point needs to be set as the flight destination. Since the flight mission is to fly to the target point, flight distance and energy consumption are optimization objectives that need to be considered. At this time, the optimization objectives are flight distance and energy consumption; set the current stratospheric airship position to X now Y now This indicates that after a long period of time, the position of the stratospheric airship is X. next Y next This indicates that the target point's location is indicated by X. target Y target express; The flight distance consists of two parts: one part is the flight distance D over a single step. step The other part is the distance D between the airship's position and the target point after a long time. end ; First is D step From the formula, we get: Next is D target The distance is expressed as the lateral distance from the current point to the target point, which can be obtained from the formula: D t =|X target -X now |+|Y target -Y now | (2) D can be obtained from the above formula. step With D target Then, the flight distance was calculated: D=D step +D target (3) Regarding energy consumption, the energy consumption within a single time step is used as a reference. The remaining energy after a single time step of flight in the stratosphere is selected to express the energy consumption of the flight strategy. The remaining energy of the airship is calculated, and the remaining energy is expressed as a percentage of the remaining energy. The calculation method is as follows: Among them, W b W represents the current remaining battery energy. bm This is the maximum battery capacity; Calculate the remaining battery energy W b The method is as follows: Among them W b0 For the remaining battery energy a long time ago, P b δ represents the energy increase or consumption over a single time step, where δ is the time span of the step, expressed in minutes. Regarding the focus of the optimization objective, two coefficients, a1 and a2, are designed to represent the priority of distance and the priority of energy consumption in path planning, respectively. From the above formula, the cost expression of the optimization function when the starting point is outside the spatial domain is derived as follows: J1=a1D+a2N (6) Therefore, the optimization objective is expressed in the design as: minJ1=a1D+a2N (7) During flight, it is necessary to continuously check whether the current position is within the airspace. If the current position is within the airspace, the optimization target needs to be changed. (2) When the airship is within the airspace, the optimization objective consists of two parts: the distance between the stratospheric airship and the airspace boundary and energy consumption. First, the distance D between the airship and the airspace boundary. edge Since there are many airspace boundaries and the exact number of boundaries is uncertain, it is first necessary to determine the number of airspace boundaries. After determining the number of boundaries, each target point is checked for distances to these boundaries, and the minimum distance between each target point and all boundaries is taken as the boundary distance D corresponding to the target point. edge After obtaining the boundary distance D edge Then, the negative of the minimum distance between the target point and all boundaries is taken as the distance-level optimization objective, thereby filtering out P points that are too close to the boundaries. n The effect; The method for calculating the boundary distance is as follows: First, it is necessary to represent the current point P. n The foot of the perpendicular from the boundary line segment is P(X). p ,Y p The foot of the perpendicular P is represented as follows: And calculate P next The formula for calculating the distance D from P is as follows: Therefore, the distance-level optimization objective D is obtained. e Expressed using the following formula: D e =-D edge (11) Regarding energy consumption, the energy consumption within a single time step is used as a reference. The remaining energy after a single time step of flight in the stratosphere is selected to express the energy consumption of the flight strategy. Therefore, it is necessary to calculate the remaining energy of the airship. The remaining energy is expressed as a percentage of the remaining energy, and the calculation method is the same as shown above: Among them, W b W represents the current remaining battery energy. bm This is the maximum battery capacity; Calculate the remaining battery energy W b The method is as follows: Among them W b0 For the remaining battery energy a long time ago, P b δ represents the energy increase or consumption over a single step of time, where δ is the step time span in minutes. Since the regional residency mission still has multiple optimization objectives, optimization objective parameters are designed to express the emphasis on the optimization objectives. Based on this, a parameter is designed. e1 a e2 The two coefficients represent the priority of boundary distance and the priority of energy consumption in this path planning, respectively. When the stratospheric airship is located inside the airspace, the optimization function is expressed in the following form: J2=a e1 D e +a e2 N (14) The optimization objective is expressed as: minJ2=a e1 D e +a e2 N (15) D step The distance traveled in a single step over a long period of time; X now This represents the X-axis coordinate of the current position; X next The X-axis coordinate of the next position; Y now This is the Y-coordinate of the current position; Y next The Y-coordinate of the next position; D target The distance to the target point; D end The distance between the airship and the target point after one long flight period; X target The X-axis coordinate of the target point; Y target The Y-coordinate of the target point; m is a fraction representing the heading angle of a stratospheric airship; n is a fraction of the airspeed of a stratospheric airship; D represents the optimization objective in terms of distance; N represents the optimization objective in terms of energy; W b The remaining energy of the battery; W bm To maximize battery energy storage; W b0 The remaining energy in the battery at the previous moment; P b For battery energy consumption / regeneration over a long period of time; δ represents the time of one step; J1 is the optimization target in navigation mode; a1 is the distance target parameter in navigation mode; a2 is the energy target parameter in navigation mode; X p The vertical X-axis coordinates of the airship's position relative to the boundary position; Y p The Y-axis coordinate is the perpendicular distance between the airship's position and the boundary position; X1 is the boundary X-axis coordinate; X2 is the boundary X-axis coordinate; X3 is the X-axis coordinate of the airship's position; Y1 is the boundary Y-axis coordinate; Y2 is the boundary Y-axis coordinate; Y3 is the Y-axis coordinate of the airship's position; D edge The distance between the airship and the boundary; D e Optimize the target for the airship and the boundary; a e1 For parameters related to boundary distance in the dwell mode; a e2 These are parameters related to boundary energy consumption under the residency mode; J2 represents the optimization objective under the residency mode; J represents the cost corresponding to the current solution; J best The cost of the current optimal solution; P is the probability of retaining a non-optimal solution.

3. The regional dwell flight path planning method based on two-dimensional interval prediction according to claim 2, characterized in that, The step three update of the stratospheric airship state is achieved by substituting the optimal heading angle and optimal airspeed obtained by the solver constructed in the second step into the stratospheric airship dynamics model. Based on the airship's current relevant parameters, the latitude and longitude of the airship, the remaining energy of the airship, and the total travel time are obtained after traveling for a long time with the optimal heading angle and optimal airspeed. After updating the stratospheric airship's status, the mission completion of the stratospheric airship is judged. If the stratospheric airship successfully stays in the designated airspace for the set stay time, it is considered that the mission is completed and the loop is exited; if it does not stay for the set stay time, it returns to step three and substitutes the new stratospheric airship status into the solver constructed in step two to solve; if the airship leaves the stay area or runs out of energy due to wind speed and environmental factors, it is considered that the airship cannot complete the designated mission.

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