A multi-constrained trajectory planning method for aircraft considering positioning error correction

Abstract

The present invention proposes an aircraft trajectory planning method considering positioning error correction under multiple constraints. The method first solves a general solution that satisfies the constraints through a greedy algorithm, then traverses the search space, and uses the general solution of the greedy algorithm as a benchmark to accurately prune unnecessary search space using the precise pruning-enumeration method, thereby quickly finding an optimal solution. After analysis, the algorithm can ensure that the track length reaches the theoretical optimum, the number of corrections is also small, and the solution speed is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft trajectory planning, and in particular relates to an aircraft trajectory planning method considering positioning error correction under multiple constraints. Background Art

[0002] When performing a mission, an aircraft needs to rely on the positioning signal provided by the navigation system to accurately reach the predetermined position. However, due to the limitations of its system structure, the aircraft cannot accurately position itself. During long-distance flight, as the positioning error gradually accumulates, it may deviate from the original track and cause the mission to fail. Therefore, correcting the positioning error during flight is an important task in aircraft trajectory planning. On the other hand, trajectory planning requires seeking the optimal flight path based on various constraints in a complex environment. Therefore, the trajectory planning of the aircraft must not only meet its unique constraints, but also be combined with the correction of positioning errors. At the same time, the two goals of the number of corrections and the track length must be minimized and optimized, which greatly increases the difficulty of problem solving.

[0003] In recent years, this topic has attracted many research teams to study it, and due to the existence of public data sets, various studies can be easily compared fairly. "Application of Floyd Algorithm in Rapid Aircraft Trajectory Planning under Multi-Constraint Conditions" solves the problem based on the Floyd algorithm, and verifies that the Floyd algorithm is superior to the A-star algorithm and the minimum deviation angle search algorithm. The length of the solved trajectory is 104,066 meters, and it has been corrected 9 times. "A Dijkstra-based Intelligent Aircraft Trajectory Planning Algorithm under Multi-Constraint Conditions" improves the Dijkstra algorithm by calculating the residual error and the constrained flight distance, and applies it to the problem. The solution result is a trajectory with a length of 144,288 meters and 18 corrections. Subsequently, based on the "An Algorithm for Intelligent Aircraft Trajectory Planning under Multiple Constraints Based on Dijkstra", "UAV Trajectory Planning under Multiple Constraints" added correction strategy optimization and correction scheme optimization, and improved the processing method of the adjacency matrix, reducing the computational complexity and improving the solution results. It was verified that the improved algorithm is superior to the traditional Dijkstra algorithm and genetic algorithm. The length of the solution trajectory is 105,581 meters, and it has been corrected 10 times. "Error Correction Method for Intelligent Aircraft Trajectory Planning under Multiple Constraints" established two dynamic programming models. After mutual comparison, the superiority of one of them was verified. The optimal solution corresponds to a trajectory length of 105,100 meters and the number of corrections is 8 times. In addition, evolutionary algorithms have also been applied to the solution of this problem. "Aircraft Trajectory Planning Considering Multiple Constraints" uses the NSGA-II algorithm in evolutionary computing to establish a global optimization cooperative control algorithm for this problem, and compares it with the traditional genetic algorithm. Its advantages are verified through experiments. The length of the solution trajectory is 114,591 meters, and it has been corrected 11 times. However, the algorithms introduced above cannot guarantee the optimality of the solution, and some algorithms have poor solution stability. Summary of the invention

[0004] In order to solve the above problem, the present invention first obtains a general solution that satisfies the constraints through a greedy algorithm, then traverses the search space, and uses the general solution as a benchmark to accurately delete unnecessary search space, thereby quickly finding a set of tracks whose track lengths are better than the greedy algorithm solution, and finally performs a Pareto sort on the set, and saves the track at the first frontier as the output of the algorithm. The algorithm obtains two tracks, one with the smallest theoretical length and the other with fewer correction times.

[0005] The technical solution adopted by the present invention is: a method for aircraft trajectory planning considering positioning error correction under multiple constraints, comprising the following steps:

[0006] Step 1: Given the spatial distribution of vertical error and horizontal error correction points, and setting the flight conditions and positioning error constraints of the aircraft;

[0007] Step 2: It is defined that the flight of the aircraft from one calibration point to the next calibration point is a "step". The greedy algorithm is used to solve the problem that the aircraft searches for calibration points that can fly normally and perform horizontal or vertical calibration step by step from the starting point, and preferentially selects the calibration point closest to the end point as the next step, and then continues searching until it reaches the end point.

[0008] Step 3, based on the result of the greedy algorithm, the precise pruning-enumeration method is used to calculate the difference between the track length and the length of the straight line between the starting point; then, starting from the starting point, all feasible tracks are gradually exhaustively searched, and during the search process, the difference between the track length and the length of the straight line between the starting point is used to accurately prune the branches corresponding to the inferior solutions, thereby ensuring the speed of solution and ultimately finding the optimal solution.

[0009] Furthermore, the flight conditions of the aircraft include:

[0010] The vertical error and horizontal error of the aircraft at the starting point are both 0;

[0011] The distance between the starting point and the end point is large, and several corrections must be made along the way before reaching the end point smoothly;

[0012] The aircraft can fly in a straight line between any two calibration points;

[0013] When the aircraft is turning, the turning radius is not considered;

[0014] The aircraft has sufficient power and will not malfunction;

[0015] Furthermore, the positioning error constraint includes:

[0016] Without any correction, the vertical error and horizontal error increase by δ units for every meter the aircraft flies;

[0017] When both the vertical error and the horizontal error are less than θ units, the aircraft can fly normally; otherwise, the trajectory planning task fails;

[0018] At the vertical correction point, if the vertical error of the aircraft is less than α1 units and the horizontal error is less than α2 units, the vertical error is set to zero and the horizontal error remains unchanged;

[0019] At the horizontal correction point, if the vertical error of the aircraft is less than β1 units and the horizontal error is less than β2 units, the horizontal error is set to zero and the vertical error remains unchanged.

[0020] Further, in step 2, the greedy algorithm includes the following steps:

[0021] Initialization: g1=0, g2=0, P={H,V}, start, end, PATH={start}.

[0022] Where: H is the horizontal correction point set, V is the vertical correction point set, g1 is the current vertical error of the aircraft, g2 is the current horizontal error of the aircraft, is the set of error increase, L is the set of Euclidean distances, P is the set of feasible points for the next step, PATH is the set of paths in the search process, start is the starting point coordinate, and end is the end point coordinate.

[0023] Step 201: In order to prevent the aircraft from flying back and forth, the correction points in PATH are deleted from P, P = P\PATH.

[0024] Step 202: Count the Euclidean distance L between the current position of the aircraft and all the correction points in P, and calculate the error increase

[0025] Step 203: Delete the calibration points in P that cannot be reached normally due to large errors; for each calibration point i in P, if or Then delete the calibration point.

[0026] Step 204: Delete the correction points in P that cannot be corrected; for each correction point i in P, if i∈V, and Then vertical correction can be performed; if i∈H, and For the correction points that can neither be corrected vertically nor horizontally, delete them from P.

[0027] Step 205: Assume that the aircraft flies to the correction point in P and then flies straight to end. The distance between the position of the aircraft when the error reaches θ and end is used as the evaluation index. For each correction point i in P, calculate the distance L1: the Euclidean distance between the correction point and end; calculate the distance L2: the maximum flight distance of the aircraft at this correction point without correction. Assuming that the current track is {start,1}, L1 and L2 corresponding to the correction point i are as follows: Figure 3 As shown; if L1≤L2, the trajectory planning ends; otherwise, L1-L2 is used as the evaluation index.

[0028] Step 206: Select the correction point corresponding to the minimum value of the evaluation index as the next step of the track and update the PATH.

[0029] Step 207 : looping steps 201 - 206 until the loop stops in step 205 .

[0030] Further, the steps of the precise pruning-enumeration method in step 3 are:

[0031] Initialization: P = {H, V}, start, end, PATH output by the greedy algorithm.

[0032] Step 301, calculate the offset, that is

[0033] Step 302: Count the Euclidean distance L between the current position of the aircraft and all the correction points in P, and calculate the error increase

[0034] Step 303: Delete the calibration points in P that cannot be reached normally due to large errors; for each calibration point i in P, if or Then delete the calibration point.

[0035] Step 304: Delete the correction points in P that cannot be corrected; for each correction point i in P, if i∈V, and Then vertical correction can be performed; if i∈H, and For the correction points that can neither be corrected vertically nor horizontally, delete them from P.

[0036] Step 305, delete the correction point corresponding to the inferior solution; for each correction point i in P, calculate the length of flying from the starting point to i according to the planned trajectory, and calculate the distance from i to the end, i.e. L i-end , with the two and L start-end The difference between Do a comparison, if it is greater than Then delete the calibration point.

[0037] Step 306, for each correction point i in P, determine whether the aircraft can fly directly to the end after the new correction; if it can fly to the end, save the track; otherwise, loop steps 302-303 until there are no more correction points in P.

[0038] Step 307, perform Pareto sorting on all the saved tracks based on track length and number of corrections, and select the track corresponding to the Pareto first preface as output.

[0039] The beneficial effect of the present invention is that the present invention adopts a new algorithm of precise pruning-enumeration method, so that the aircraft can correct the positioning error in the long-distance flight track planning, thereby achieving the purpose of minimizing the number of corrections and the track length. The algorithm first solves the general solution that satisfies the constraints through a greedy algorithm, then traverses the search space, and accurately deletes the unnecessary search space based on the general solution, so as to quickly find the optimal solution. After analysis, the algorithm can ensure that the track length reaches the theoretical optimum, the number of corrections is also small, and the solution speed is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A schematic diagram of the route planning;

[0041] Figure 2 This is a schematic diagram of the precise pruning-enumeration algorithm;

[0042] Figure 3 is a schematic diagram of step 205 in the greedy algorithm;

[0043] Figure 4 This is a schematic diagram of the flight path;

[0044] Figure 5 It is a schematic diagram of step 303 in the precise pruning-enumeration algorithm;

[0045] Figure 6 is the spatial distribution map of the correction points;

[0046] Figure 7 PATH a Visual graphics;

[0047] Figure 8 PATH b Visual graphics;

[0048] Fig. 9 Output target values ​​of the track for the six algorithms. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with the accompanying drawings.

[0050] The present invention is a method for aircraft trajectory planning considering positioning error correction under multiple constraints. First, given the spatial distribution of vertical error and horizontal error correction points, a trajectory from the starting point to the end point is planned for the aircraft under the condition of satisfying the positioning error constraints, such as Figure 1 As shown, it is required to minimize the track length and the number of corrections.

[0051] The relevant information of positioning error includes: (1) When no correction is performed, the vertical error and horizontal error increase by δ units for every meter the aircraft flies; (2) When the vertical error and horizontal error are both less than θ units, the aircraft can fly normally. Otherwise, the trajectory planning task fails; (3) At the vertical correction point, if the vertical error of the aircraft is less than α1 units and the horizontal error is less than α2 units, its vertical error is set to zero and the horizontal error remains unchanged; (4) At the horizontal correction point, if the vertical error of the aircraft is less than β1 units and the horizontal error is less than β2 units, its horizontal error is set to zero and the vertical error remains unchanged.

[0052] The assumptions include: (1) the vertical error and horizontal error of the aircraft at the starting point are both 0; (2) the distance between the starting point and the end point is large, and the aircraft must undergo several corrections along the way before it can successfully reach the end point; (3) the aircraft can fly in a straight line between any two correction points; (4) the aircraft does not consider the turning radius when turning; (5) the aircraft has sufficient power and will not malfunction.

[0053] like Figure 2 As shown in the figure, the precise pruning-enumeration method first solves a general solution that satisfies the constraints based on the greedy algorithm. Then it traverses the search space and uses the solution as a benchmark to accurately prune the unnecessary search space.

[0054] Since the distance between the starting point and the end point is large, several corrections must be performed during the flight, and the aircraft flies in a straight line, so the track is represented by the set of correction point numbers that the aircraft passes during the flight. In addition, it is defined that the flight of the aircraft from one correction point to the next correction point is called a "step". For example: the track {1,3,5,7} means that the aircraft flies through four correction points numbered 1, 3, 5, and 7 in order, and the flight from correction point 1 to correction point 3 is a step.

[0055] The overall idea of ​​the greedy algorithm solution is to start from the starting point and search step by step for a correction point that can fly normally, that is, the vertical error and horizontal error are both less than θ units, and can perform horizontal correction or vertical correction, and give priority to the correction point closest to the end point as the next step, and then continue searching until reaching the end point. The specific solution steps are:

[0056] Initialization: g1=0, g2=0, p={H, V}, start, end, PATH={start};

[0057] Where: H is the horizontal correction point set, V is the vertical correction point set, g1 is the current vertical error of the aircraft, g2 is the current horizontal error of the aircraft, is the set of error increase, L is the set of Euclidean distances, P is the set of feasible points for the next step, PATH is the set of paths in the search process, start is the starting point coordinate, and end is the end point coordinate.

[0058] Step 201: In order to prevent the aircraft from flying back and forth, the correction points in PATH are deleted from P, P = P\PATH.

[0059] Step 202: Count the Euclidean distance L between the current position of the aircraft and all the correction points in P, and calculate the error increase

[0060] Step 203: Delete the calibration points in P that cannot be reached normally due to large errors. For each calibration point i in P, if or Then delete the calibration point.

[0061] Step 204: Delete the correction points in P that cannot be corrected. For each correction point i in P, if i∈V, and Then vertical correction can be performed; if i∈H, and For the correction points that cannot be corrected vertically or horizontally, they are deleted from P.

[0062] Step 205: Assume that the aircraft flies to the calibration point in P and then flies straight to the end. The distance between the position of the aircraft when the error reaches θ and the end is used as the evaluation index. For each calibration point i in P, calculate the distance L1: the Euclidean distance between the calibration point and the end; calculate the distance L2: the maximum flight distance of the aircraft at this calibration point without calibration, for example: i∈V, after calibration, g1=0, The maximum flight distance without correction is (θ-g2) ÷ δ meters. Assuming the current track is {start, 1}, the L1 and L2 corresponding to the correction point i are as follows: Figure 3 If L1≤L2, the trajectory planning ends; otherwise, L1-L2 is used as the evaluation index.

[0063] Step 206: Select the correction point corresponding to the minimum value of the evaluation index as the next step of the track and update the PATH.

[0064] Step 207 : looping steps 201 - 206 until the loop stops in step 205 .

[0065] In actual operation, if the greedy algorithm only searches for one track, it may happen that all the next steps in the middle of the search are not feasible, resulting in track planning failure. In order to avoid this situation, the method of searching multiple routes simultaneously is adopted, that is, in step 6, not only the correction point with the minimum value of the evaluation index is selected, but the first x smallest correction points are selected. When the value of x is larger, the probability of generating a feasible solution is higher, and the quality of the solution also increases within a certain range. In this paper, the value of x is 50 to ensure that a better feasible solution can be generated under the current data set. Since the overall algorithm of this paper can guarantee the optimality of the solution, the value of x has no effect on the quality of the final solution, but only has a slight effect on the running speed of the algorithm, so this paper does not discuss the value of the x parameter in detail.

[0066] All the tracks output by the greedy algorithm are sorted by length, and the track with the smallest length is selected as the input for the next step.

[0067] Let the distance from calibration point a to calibration point b be L a-b , the length of the track PATH is L PATH .like Figure 4 As shown, a trajectory is simulated, where PATH = {start, 1, 3, 5, end}, L PATH =L start-1 +L 1-3 +L3-5+L5-end. Definition L PATH With L start-end The difference is the offset Right now

[0068] The exact pruning-enumeration method is to first calculate the general solution output by the greedy algorithm. Then, starting from the starting point, all feasible paths are gradually exhausted. This process is similar to a tree that continuously grows new branches, and uses Accurately prune the branches corresponding to the inferior solution to ensure the speed of solution and eventually find the optimal solution. The specific solution steps are as follows:

[0069] Initialization: P = {H, V}, start, end, PATH output by the greedy algorithm.

[0070] Step 301: Calculate the offset, i.e.

[0071] Step 302: Find all feasible next steps, which is equivalent to steps 202-204.

[0072] Step 303: Delete the correction points corresponding to the inferior solution. For each correction point i in P, calculate the length from the starting point to i according to the planned trajectory (e.g. Figure 5 As shown in the figure, assuming that the current planned track is {start,1}, i is the optional next correction point, then the length from the starting point to i according to the planned track is L start-1 +L 1-i ), and calculate the distance from i to end, i.e. L i-end , the sum of the two (in this example, L start-1 +L 1-i +L i-end ) and L start-end The difference (L in this example) start-1 +L 1-i +L i-end -L start-end )and Do a comparison, if it is greater than Then delete the calibration point.

[0073] Step 304: For each calibration point i in P, determine whether the aircraft can fly directly to the end after the new calibration, that is, the case where distance 1 is less than or equal to distance 2 in step 205, which will not be repeated here. If it can fly to the end, save the track; otherwise, loop steps 302-303 until there are no more calibration points in P.

[0074] Step 305: Perform Pareto sorting on all saved tracks based on track length and number of corrections, and select the track corresponding to the Pareto first preamble as output.

[0075] The precise pruning-enumeration method can obtain all tracks whose track length is better than the track output by the greedy algorithm, and due to the accuracy of pruning, the algorithm runs at a high speed.

[0076] Since the present invention solves a dual-objective optimization problem, namely minimizing the number of corrections and minimizing the track length, the method proposed in this paper analyzes the optimization effects that can be achieved by the two optimization objectives.

[0077] First, for the number of corrections, this method can obtain a better solution. The greedy algorithm outputs a general solution, while the exact pruning-enumeration method can output a track that is obtained by Pareto sorting from all tracks whose lengths are shorter than the general solution. Although the number of corrections is not directly related to the track length, since the optimal value of the number of corrections is selected from a large number of tracks with shorter lengths, it can also achieve a better optimization effect.

[0078] In addition, for the track length, this method can obtain the theoretical minimum length track. Here is a brief proof: Let the minimum length track be PATH min, the corresponding offset is First, because PATH min is the minimum length of the track, then It is also the smallest offset among all feasible trajectories. Therefore, in the pruning process of the precise pruning-enumeration method, the offset used as the pruning standard must be greater than or equal to Because, the offset of the minimum length track corresponding to the mid-course track must be less than or equal to Therefore, according to the pruning rule, the intermediate track corresponding to the minimum length track will not be pruned in the middle, that is, the track corresponding to the minimum length will be saved and continuously extended until the entire track planning is completed. Therefore, the track output by the method proposed in this paper must contain the track with the minimum length in theory.

[0079] This paper uses a public data set to verify the algorithm and compares it with five studies in the same direction. In addition to the fixed starting point and end point, the data set has a total of 611 correction points, including 305 vertical error correction points and 306 horizontal error correction points, distributed as follows: Figure 6 As shown. The positioning error related parameters are set the same as those in the comparison algorithm: α1 = 25, α2 = 15, β1 = 20, β2 = 25, θ = 20, δ = 0.001. The computing hardware configuration is: Processor: Intel(R) Xeon(R) CPU E5-2650 v3@2.30GHz 2.30GHz, memory: 16.0GB. The running software is: MATLAB 2021a.

[0080] The output of the proposed algorithm for this data set is two tracks with independent target values, named PATH a and PATH b .PATH a ={504,295,92,608,541,251,341,278}. As shown in Table 1, this trajectory does not violate any constraints and is a feasible solution. a The corresponding number of corrections is 8, and the track length is 104861 meters. Figure 7 PATH b ={504,201,81,238,171,279,370,215,398}. As shown in Table 2, this track is also a feasible solution. b The corresponding number of corrections is 9, and the track length is 103517 meters. Figure 8 shown.

[0081] Table 1 PATH a Details of trajectory planning results

[0082]

[0083] Table 2 PATH b Details of trajectory planning results

[0084]

[0085] For the convenience of drawing, the target values ​​of the two tracks are Fig. 9 The icon in the figure is named "0", and the icons corresponding to the five target values ​​are named "1", "2", "3", "4", and "5" respectively. The comparison results are as follows Fig. 9 Except for the algorithm in this paper which outputs two tracks, the other five comparison algorithms output only one track. a The number of corrections with "4" is the smallest in the comparison results, but PATH a The track length of PATH (104,861 meters) is better than that of PATH 4 (105,100 meters). b The number of corrections for "1" is 9, but PATH b The track length of "1" (103517 meters) is better than the track length of "1" (104066 meters), and is better than the lengths of all other tracks. For this data set, the theoretical minimum track length that meets the constraints is 103517 meters, and the corresponding track is PATH b In addition, the running time of our algorithm is 15.5 seconds (the average time of ten runs).

Claims

1. A method for aircraft trajectory planning considering positioning error correction under multiple constraints, characterized in that: The following steps are involved: Step 1: Given the spatial distribution of vertical error and horizontal error correction points, and setting the flight conditions and positioning error constraints of the aircraft; Step 2: It is defined that the flight of the aircraft from one calibration point to the next calibration point is called a "step". The greedy algorithm is used to solve the problem that the aircraft searches for calibration points that can fly normally and perform horizontal or vertical calibration step by step from the starting point, and preferentially selects the calibration point closest to the end point as the next step, and then continues searching until it reaches the end point. The greedy algorithm includes the following steps: Initialization: g1=0, g2=0, P={H,V}, start, end, PATH={start}; Where: H is the horizontal correction point set, V is the vertical correction point set, g1 is the current vertical error of the aircraft, g2 is the current horizontal error of the aircraft, is the error increase, L is the Euclidean distance set, P is the set of feasible points for the next step, PATH is the path set in the search process, start is the starting point coordinate, and end is the end point coordinate; Step 201: In order to prevent the aircraft from flying back and forth, the correction points in PATH are deleted from P, P = P\PATH; Step 202: Count the Euclidean distance L between the current position of the aircraft and all the correction points in P, and calculate the error increase Step 203: Delete the calibration points in P that cannot be reached normally due to large errors; for each calibration point i in P, if or Then delete the calibration point; Step 204: Delete the correction points in P that cannot be corrected; for each correction point i in P, if i∈V, and Then vertical correction can be performed; if i∈H, and Then horizontal correction can be performed; for the correction points that can neither be corrected vertically nor horizontally, delete them from P; Step 205: Assume that the aircraft flies to the correction point in P and then flies straight to the end. The distance between the position of the aircraft when the error reaches θ and the end is used as the evaluation index. For each correction point i in P, calculate the distance L1: the Euclidean distance between the correction point and the end. Calculate the distance L2: the maximum flight distance of the aircraft at this correction point without correction. If L1≤L2, the trajectory planning ends. Otherwise, L1-L2 is used as the evaluation index. Step 206: Select the correction point corresponding to the minimum value of the evaluation index as the next step of the track and update the PATH; Step 207: looping steps 201-206 until the loop stops in step 205; Step 3, based on the result of the greedy algorithm, the exact pruning-enumeration method is used to calculate the difference between the track length and the straight line length between the starting point; Then, starting from the starting point, all feasible tracks are exhaustively searched step by step. During the search process, the difference between the track length and the straight line length between the starting point is used to accurately prune the branches corresponding to the inferior solutions, thereby ensuring the speed of solution and ultimately finding the optimal solution. The steps of the precise pruning-enumeration method are as follows: Initialization: P = {H, V}, start, end, PATH output by the greedy algorithm; Step 301, calculate the offset, that is Step 302: Count the Euclidean distance L between the current position of the aircraft and all the correction points in P, and calculate the error increase Step 303: Delete the calibration points in P that cannot be reached normally due to large errors; for each calibration point i in P, if or Then delete the calibration point; Step 304: Delete the correction points in P that cannot be corrected; for each correction point i in P, if i∈V, and Then vertical correction can be performed; if i∈H, and Then horizontal correction can be performed; for the correction points that can neither be corrected vertically nor horizontally, delete them from P; Step 305, delete the correction point corresponding to the inferior solution; for each correction point i in P, calculate the length of flying from the starting point to i according to the planned trajectory, and calculate the distance from i to the end, i.e. L i-end , the sum of the two and L start-end The difference between Do a comparison, if it is greater than Then delete the calibration point; Step 306, for each calibration point i in P, determine whether the aircraft can fly directly to the end after the new calibration; if it can fly to the end, save the track; Otherwise, loop steps 302-303 until there are no more calibration points in P; Step 307, perform Pareto sorting on all the saved tracks based on track length and number of corrections, and select the track corresponding to the Pareto first preface as output.

2. The method for aircraft trajectory planning considering positioning error correction under multiple constraints according to claim 1, characterized in that: The flight conditions of the aircraft include: The vertical error and horizontal error of the aircraft at the starting point are both 0; The distance between the starting point and the end point is large, and several corrections must be made along the way before reaching the end point smoothly; The aircraft can fly in a straight line between any two calibration points; When the aircraft is turning, the turning radius is not considered; The aircraft has sufficient power and will not malfunction.

3. The method for aircraft trajectory planning considering positioning error correction under multiple constraints according to claim 1, characterized in that: The positioning error constraints include: Without any correction, the vertical error and horizontal error increase by δ units for every meter the aircraft flies; When both the vertical error and the horizontal error are less than θ units, the aircraft can fly normally; otherwise, the trajectory planning task fails; At the vertical correction point, if the vertical error of the aircraft is less than α1 units and the horizontal error is less than α2 units, the vertical error is set to zero and the horizontal error remains unchanged; At the horizontal correction point, if the vertical error of the aircraft is less than β1 units and the horizontal error is less than β2 units, the horizontal error is set to zero and the vertical error remains unchanged.

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