CN113029150A - Intelligent aircraft track planning method under multi-constraint condition - Google Patents

Intelligent aircraft track planning method under multi-constraint condition Download PDF

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CN113029150A
CN113029150A CN202110258710.4A CN202110258710A CN113029150A CN 113029150 A CN113029150 A CN 113029150A CN 202110258710 A CN202110258710 A CN 202110258710A CN 113029150 A CN113029150 A CN 113029150A
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flight path
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CN113029150B (en
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郭羽含
丁文婧
刘永武
孙宁
姜彦吉
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Liaoning Technical University
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Abstract

The invention provides an intelligent aircraft flight path planning method under multiple constraint conditions, and relates to the technical field of flight path planning. Aiming at the problem of fast flight path planning of an intelligent aircraft under the limitation of system positioning accuracy, the method comprises the steps of preprocessing data according to a given limiting error in a constraint condition, removing invalid correction points which do not meet the constraint condition, establishing a multi-objective optimization model, meeting the requirements of small flight path length and few correction times as far as possible, then adopting a multi-objective optimization algorithm (NSGA2) to solve according to the specific requirements of each problem, obtaining effective correction points, and further obtaining the flight path of the aircraft. The method can effectively reduce the flight path length and the algorithm complexity of the aircraft, reduce the correction times, ensure the effectiveness of the algorithm and realize the rapid planning of the flight path of the intelligent aircraft under the multi-constraint condition.

Description

Intelligent aircraft track planning method under multi-constraint condition
Technical Field
The invention relates to the technical field of flight path planning, in particular to an intelligent aircraft flight path planning method under multiple constraint conditions.
Background
Route Planning (Route Planning) is a highly comprehensive cross-domain research topic. Since the 50 s of the last century, scholars in various fields at home and abroad propose various flight path planning methods according to respective subject backgrounds and professional fields. However, with the continuous proposition of new planning methods and new algorithms, troubles are brought to planning designers. Among the planning methods, selecting a method more suitable for the current needs requires grasping the essence of the flight path planning problem and having sufficient understanding and awareness of the various planning methods.
At present, a great deal of flight path planning under complex multi-constraint conditions focuses on the research of related mathematical problems, generally, a target weighting function is adopted to construct an evaluation index, a proper intelligent algorithm is selected, and the searched mathematical optimal points are utilized to construct the optimal flight path of the planning. With the progress of science and technology, the intelligent aircraft can play a great role in future military application, has different shapes, is more convenient to hide, can reconnoiter enemies, and can be applied in more fields in the future. Planning flight path and correcting flight path error are important links of intelligent flight development.
Therefore, whether the intelligent aircraft can rapidly plan the flight path in a complex environment becomes a crucial problem at present, and because a plurality of uncontrollable internal and external factors exist in the flight process, the positioning system of the existing aircraft cannot achieve the accuracy, and the error possibly causes accidents and further causes task failure.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art, and provides an intelligent aircraft track planning method under a multi-constraint condition to realize rapid planning of an aircraft track under complex and multi-constraint conditions.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: an intelligent aircraft track planning method under multiple constraint conditions is characterized in that according to a flight area of an aircraft, a departure place of the aircraft is set to be A, a destination of the aircraft is set to be B, and track constraints are as follows:
(1) the aircraft needs to be positioned in real time in the space flight process, and the positioning error comprises a vertical error a and a horizontal error b; each flying time of the aircraft is 1m, a and b are respectively increased by omega special units, when the aircraft reaches the terminal point, a is less than mu and b is less than mu, mu is another special unit, and when a is less than mu and b is less than mu, the aircraft can still fly according to the planned path;
(2) the aircraft needs to correct the positioning error in the flight process; setting a safety position for error correction in the flight area, namely a correction point, and when the aircraft reaches the correction point, performing error correction according to the error correction type of the position; if the vertical error a and the horizontal error b can be corrected within a specified time threshold, the aircraft flies according to a preset route, and finally arrives at a destination after error correction is carried out through a plurality of correction points;
(3) at origin a, the vertical error a is 0 and the horizontal error b is 0;
(4) after the vertical error correction is carried out on the aircraft at the vertical error correction point, the vertical error a is 0, and the horizontal error b is kept unchanged;
(5) after the horizontal error correction is carried out on the aircraft at the horizontal error correction point, the horizontal error b is 0, and the vertical error a is kept unchanged;
(6) setting alpha 1, alpha 2, beta 1 and beta 2 as four special units, and performing vertical error correction when a is less than or equal to alpha 1 and b is less than or equal to alpha 2;
(7) when a is less than or equal to beta 1 and b is less than or equal to beta 2, horizontal error correction can be carried out;
based on the constraint conditions, the aircraft track planning method specifically comprises the following steps:
step 1: model assumption;
1) converting the flight path planning of the intelligent aircraft into a path planning problem of the aircraft, performing space search based on geometry, and generating a flight path which is a static space curve unrelated to time without considering the kinematics and dynamics constraints of the aircraft; the flight path of the aircraft is a specific flight path of the intelligent aircraft, and the flight path of the aircraft is the sequence of the flight of the aircraft to each correction point;
2) the size of the aircraft is ignored, and the aircraft is simplified into particles;
3) ignoring situations where the distance between the aircraft origin a and destination B is too long and the aircraft is out of fuel;
4) the intelligent aircraft has the advantages that the intelligent aircraft is free of any damage when flying between the departure place A and the destination B, and the intelligent aircraft is not damaged due to faults, collision and external dangers from take-off to landing;
step 2: establishing a multi-target planning model for aircraft track planning;
abstracting the flight path planning problem of the aircraft into a path planning problem based on geometry, and defining the flight path planning problem of the aircraft into a multi-objective optimization problem with constraint conditions by adopting a rapid non-dominated multi-objective optimization algorithm with an elite reservation strategy, wherein the flight path planning problem comprises inequality constraints and equality constraints, and the following formula is shown as follows:
Figure BDA0002969023960000021
wherein, H (x) is an objective function set, and E is the number of objective functions; x is the number ofkAs decision variables, xk (W) and xk (S)Are respectively the kth decision variable xkM is the number of decision variables; p is a radical ofu(x) Is inequality constraint, U is the number of inequality constraint conditions; q. q.sr(x) For equality constraint, R is the number of equality constraint conditions;
and step 3: solving a multi-target planning model of the aircraft track planning by using an NSGA2 algorithm to obtain effective correction points, and connecting all the effective correction points to obtain the solved aircraft track;
step 3.1: aiming at a plurality of correction points for positioning error correction existing in the flight area, the vertical error correction can be carried out only when a is less than or equal to alpha 1 and b is less than or equal to alpha 2 through a constraint (6); constraining (7) to carry out horizontal error correction when a is not more than beta 1 and b is not more than beta 2, and obtaining that the distance from the next correction point to the current correction point is less than a limit value;
step 3.2: adding strategies to the initial solution generation process of each objective function, reducing invalid solutions, and selecting correction points which meet the constraint conditions; the initial solution for each objective function is described as:
Figure BDA0002969023960000031
wherein ,
Figure BDA0002969023960000032
indicating the position of the calibration point at which the aircraft is currently located,
Figure BDA0002969023960000033
indicating the position of the next correction point;
if the distance between the front correction node and the rear correction node exceeds a limited error, the initial solution is invalid; the error can be corrected only when the aircraft falls on the correction point, then the error of the next correction point is restrained by the current error margin, the X-axis correction point and the Y-axis correction point need to be restrained separately, the distance between the front and the rear correction points is mapped to the horizontal direction, namely the projection distance in the horizontal direction, and is mapped to the vertical direction, namely the projection distance in the vertical direction, the aircraft moves between the correction points to generate errors in the horizontal direction and the vertical direction, and then the flight error Err generated between the two correction points by the aircraft at the moment iiAs shown in the following equation:
Figure BDA0002969023960000034
wherein ,
Figure BDA0002969023960000035
representing the vertical distance between the front and the back correction points;
Figure BDA0002969023960000036
representing the horizontal distance between the front and back correction points;
when the flight error of the aircraft meets the constraint condition (7), horizontal correction can be carried out, the corrected horizontal error is 0, the vertical error is kept unchanged, if the flight error does not meet the constraint condition (7), the aircraft is considered to be failed to be corrected, the horizontal error failed to be corrected is smaller between the horizontal error before being corrected and 5, and the horizontal correction is defined as follows:
Figure BDA0002969023960000037
and when the flight error of the aircraft meets the constraint condition (6), performing vertical correction, wherein the corrected vertical error is 0, the horizontal error is kept unchanged, if the flight error does not meet the constraint condition (7), the aircraft is regarded as failed in correction, the vertical error which fails in correction is smaller between the vertical error before correction and 5, and the vertical correction is defined as follows:
Figure BDA0002969023960000038
if the next correction point of the aircraft is closer to the destination than the current correction point, selecting the next correction point and the correction points nearby to form a new correction point set, wherein the correction point selection is defined as follows:
if(Ind=NextToEnd<NowToEnd),NewId=Neigh(Ind) (6)
wherein, Ind and NextToEnd each represent the distance from the next correction point to the destination; NowToEnd represents the distance from the current calibration point of the aircraft to the destination; NewId represents the new set of correction points; neigh (ind) denotes the next correction point and its neighbor correction points;
meanwhile, each correction point can be selected only once, the neighbor correction points are ensured not to be selected when the neighbor correction points are selected, the vertical error and the horizontal error are both smaller than the residual error of the previous correction point, and the error distance between every two correction points is smaller than the limited error in the constraint condition, so the state of the new correction point is defined as follows:
NodeState(Nind)=1 (7)
wherein, NodeState represents the state of the correction point, and the value of 1 represents that the constraint condition is met; nind denotes the new correction point;
step 3.3: performing two basic operations of crossing and mutation on all new correction points meeting the conditions, setting seventy percent of probability for crossing, and performing mutation on thirty percent of probability; selecting two father individuals for mating, and finding out all effective correction points to obtain the flight path of the aircraft;
(A) and (3) cross action: obtaining two offspring individuals s by simulating binary crossing1u(n),s2u(n), as shown in the following equation:
Figure BDA0002969023960000041
Figure BDA0002969023960000042
wherein ,x1u(n) and x2u(n) represents a parent individual; delta is a custom parameter; v. ofuIs a [0,1 ]]Random numbers within the interval;
(B) variant behavior: obtaining effective correction points s by polynomial variation1u(n), as shown in the following equation:
s′1u(n)=s1u(n)+Δu (10)
Figure BDA0002969023960000043
and finally, connecting all the effective correction points to form the flight path of the aircraft.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the intelligent aircraft track planning method under the multi-constraint condition, preprocessing is performed before data processing, invalid solutions which do not influence results are eliminated, the algorithm efficiency is improved, the initial solution is generated through a proper strategy, optimization is performed from a proper position, the applicability is strong, a point which is close to a destination is consciously selected when a next node is selected, and the situation that the data are continuously repeated is avoided. In terms of complexity, the main complexity of the algorithm lies in the generation stage of an initial solution, and the segmented generation can reduce certain complexity. The method and the device ensure that the flight path of the intelligent aircraft is as small as possible under the limitation of the positioning accuracy of the system, and reduce the times of correction through a correction area.
Drawings
FIG. 1 is a flowchart of a method for planning a flight path of an intelligent aircraft under multiple constraints according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an aircraft trajectory planning region provided by an embodiment of the invention;
FIG. 3 is a flow chart of the NSGA2 algorithm provided by the embodiments of the present invention;
FIG. 4 is a schematic flow chart illustrating an initial solution strategy of the objective function according to the embodiment of the present invention;
FIG. 5 is a flow chart of a new solution strategy for an objective function provided by an embodiment of the present invention;
FIG. 6 is a schematic diagram of an aircraft trajectory planning corresponding to a first set of calibration point data provided in an embodiment of the present invention;
fig. 7 is a schematic view of an aircraft track planning obtained by corresponding to the first set of calibration point data according to the embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, as shown in fig. 1, according to a flight area of an aircraft, a departure place of the aircraft is set to be a, a destination of the aircraft is set to be B, and a track constraint is as follows:
(1) the aircraft needs to be positioned in real time in the space flight process, and the positioning error comprises a vertical error a and a horizontal error b; each flying time of the aircraft is 1m, a and b are respectively increased by omega special units, when the aircraft reaches the terminal point, a is less than mu and b is less than mu, mu is another special unit, and when a is less than mu and b is less than mu, the aircraft can still fly according to the planned path;
(2) the aircraft needs to correct the positioning error in the flight process; setting a safety position for error correction in the flight area, namely a correction point, and when the aircraft reaches the correction point, performing error correction according to the error correction type of the position; fig. 2 is a schematic diagram of a flight path, where the blue point is a correction point a, the yellow point is a correction point b, and the black curve represents a flight path. If the vertical error a and the horizontal error b can be corrected within a specified time threshold, the aircraft flies according to a preset route, and finally arrives at a destination after error correction is carried out through a plurality of correction points;
(3) at origin a, the vertical error a is 0 and the horizontal error b is 0;
(4) after the vertical error correction is carried out on the aircraft at the vertical error correction point, the vertical error a is 0, and the horizontal error b is kept unchanged;
(5) after the horizontal error correction is carried out on the aircraft at the horizontal error correction point, the horizontal error b is 0, and the vertical error a is kept unchanged;
(6) setting alpha 1, alpha 2, beta 1 and beta 2 as four special units, and performing vertical error correction when a is less than or equal to alpha 1 and b is less than or equal to alpha 2;
(7) when a is less than or equal to beta 1 and b is less than or equal to beta 2, horizontal error correction can be carried out;
based on the constraint conditions, the aircraft track planning method specifically comprises the following steps:
step 1: model assumption;
in order to better establish a model without affecting the meaning and the calculation accuracy of the model, the following assumptions are made:
1) converting the flight path planning of the intelligent aircraft into a path planning problem of the aircraft, performing space search based on geometry, and generating a flight path which is a static space curve unrelated to time without considering the kinematics and dynamics constraints of the aircraft; the flight path of the aircraft is a specific flight path of the intelligent aircraft, and the flight path of the aircraft is the sequence of the flight of the aircraft to each correction point;
2) the size of the aircraft is ignored, and the aircraft is simplified into particles;
3) ignoring situations where the distance between the aircraft origin a and destination B is too long and the aircraft is out of fuel;
4) the intelligent aircraft has the advantages that the intelligent aircraft is free of any damage when flying between the departure place A and the destination B, and the intelligent aircraft is not damaged due to faults, collision and external dangers from take-off to landing;
step 2: establishing a multi-target planning model for aircraft track planning;
the flight path planning problem of the aircraft is abstracted into a path planning problem based on geometry, the flight path length of the aircraft is ensured to be as small as possible, the correction times through a correction area are as small as possible, and the flight path planning problem and the path planning problem are not directly related. Aiming at the optimization problem of the complex constraint, a rapid non-dominated multi-objective optimization algorithm (a multi-objective optimization algorithm based on Pareto optimal solution, namely NSGA2 algorithm) with an elite reservation strategy is adopted. The flight path planning problem of the aircraft is defined as a multi-objective optimization problem with constraint conditions, which comprises inequality constraints and equality constraints, and the following formula is shown as follows:
Figure BDA0002969023960000061
wherein, H (x) is an objective function set, and E is the number of objective functions; x is the number ofkAs decision variables (also called control variables), xk (W) and xk (S)Are respectively the kth decision variable xkM is the number of decision variables; p is a radical ofu(x) Is inequality constraint, U is the number of inequality constraint conditions; q. q.sr(x) For equality constraint, R is the number of equality constraint conditions;
to solve such Constrained multi-objective optimization problem, a Constrained-dominance relationship (Constrained-dominance) is mainly used to process the Pareto dominance relationship based algorithm, and for the decomposition based algorithm, a new replacement strategy is used to update the solution. For a Solution x, if the constraint condition is satisfied, the Solution is called a Feasible Solution (Feasible Solution); if not, the Solution is called as infeasible Solution (unfeasable Solution); constraint violation value (Constraint utilization value) is typically used to process infeasible solutions and is used to quantify how much a solution violates a Constraint; for a solution x, the constraint violation value is expressed as:
Figure BDA0002969023960000071
wherein < λ > indicates that if λ ≦ 0, < λ > -0, otherwise < λ > - λ |; obviously, for a solution, the smaller the COV value, the better the solution is; meanwhile, if the solution is feasible, COV is 0, and if the solution is infeasible, COV > 0.
And step 3: solving a multi-target planning model of the aircraft track planning by using an NSGA2 algorithm to obtain effective correction points, and connecting all the effective correction points to obtain the solved aircraft track;
the basic idea of the NSGA2 algorithm is as follows: firstly, randomly generating an initial population with the scale of M, and obtaining a first generation filial population through three basic operations of selection, crossing and variation of a genetic algorithm after non-dominated sorting; secondly, from the second generation, merging the parent population and the offspring population, performing rapid non-dominant sorting, simultaneously performing crowding degree calculation on the individuals in each non-dominant layer, and selecting proper individuals according to the non-dominant relationship and the crowding degree of the individuals to form a new parent population; when the NSGA carries out non-dominant sorting, each individual in the population with the size of M is compared with M-1 individuals in the population according to E objective functions, and the complexity is O (EM), so that the complexity after the comparison of the M individuals in the population is O (EM)2) I.e. the time complexity of each Pareto grading performed is O (EM)2). In the worst case, each Pareto level only contains one individual, so that M grading is needed, and the time complexity is increased to O (EM)3). In view of this, a fast non-dominated sorting method is proposed, the time complexity of which is O (EM)2). The adoption of a congestion degree and congestion degree comparison operator not only overcomes the defect that sharing parameters need to be manually specified in NSGA, but also takes the NSGA as a comparison standard among individuals in a population, so that the standard Pa isIndividuals in the reto domain can uniformly extend to the whole Pareto domain, and the diversity of the population is ensured. In multi-objective planning, one solution is best on one objective and may be worse on other objectives, due to conflicts and incomparable phenomena between objectives. Pareto proposed the concept of a multi-objective solution-independent solution (Non-dominant set) in 1986. It is defined as: assuming that F1 is better than F2 for all targets for any two solutions F1 and F2, we call F1 dominates F2, and if the solution of F1 is not dominated by other solutions, then F1 calls a non-dominated solution (non-dominated solution), also called Pareto solution. The set of these non-dominant solutions is the so-called Pareto front. All solutions that fall within a Pareto front are not dominated by solutions outside the Pareto front (and other solutions within the Pareto front curve), so these non-dominated solutions have the least number of target conflicts than other solutions, providing the decision maker with a better choice space. Any objective function is necessarily attenuated while improving on the basis of some non-dominant solution, at least one other objective function. The algorithm needs to preserve two quantities:
(a) domination number mc: this quantity is the number of all individuals that can dominate the individual c in the feasible solution space.
(b) Set of dominated individuals Lc: this quantity is a set of all individuals in the feasible solution space that are dominated by individual c.
Finally, a new offspring population is generated through the basic operation of the genetic algorithm, and so on until the condition of program end is met. A flow chart of this algorithm is shown in fig. 3.
Step 3.1: aiming at a plurality of correction points for positioning error correction existing in the flight area, the vertical error correction can be carried out only when a is less than or equal to alpha 1 and b is less than or equal to alpha 2 through a constraint (6); constraining (7) to carry out horizontal error correction when a is not more than beta 1 and b is not more than beta 2, and obtaining that the distance from the next correction point to the current correction point is less than a limit value; in this embodiment, the data of the two sets of correction point data of the flight area are captured as shown in table 1 and table 2:
TABLE 1 first set of correction point data
Correction Point numbering X coordinate (unit: m) Y coordinate (unit: m) Z coordinate (unit: m) Correction point type
0 0.00 50000.00 5000.00 Point A
1 33070.83 2789.48 5163.52 0
2 54832.89 49179.22 1448.30 1
3 77991.55 63982.18 5945.82 0
4 16937.18 84714.34 5360.29 0
...... ...... ...... ...... ......
608 45789.20 21191.21 440.00 1
609 94917.73 82958.73 6169.66 0
610 14870.60 95939.17 8248.84 0
611 93009.57 4549.33 7882.61 1
612 100000.00 59652.34 5022.00 Point B
TABLE 2 second set of calibration Point data
Figure BDA0002969023960000081
Figure BDA0002969023960000091
Step 3.2: adding strategies to the initial solution generation process of each objective function, reducing some invalid solutions which do not accord with the constraint conditions, and selecting correction points which accord with the constraint conditions, as shown in fig. 4; the minimum value of the distance between the front correction point and the rear correction point is utilized to ensure that the initial solution satisfies that the track length is as small as possible, the minimum value of the number of the correction points satisfies that the correction times are as small as possible, and the initial solution of each objective function is described as follows:
Figure BDA0002969023960000092
wherein ,
Figure BDA0002969023960000093
indicating the position of the calibration point at which the aircraft is currently located,
Figure BDA0002969023960000094
indicating the position of the next correction point;
if the distance between the front correction node and the rear correction node exceeds a limited error, the initial solution is invalid; the error is corrected only when the aircraft is at the correction point, and the current error margin (i.e., the error that was not corrected at the previous correction point) is corrected downwardThe error of one correction point is restricted, and the X-axis correction point and the Y-axis correction point need to be separately restricted, the distance between the front and the rear correction points is mapped to the horizontal direction, namely the projection distance in the horizontal direction (also called horizontal error), and is mapped to the vertical direction, namely the projection distance in the vertical direction (also called vertical error), the movement of the aircraft between the correction points causes the errors in the horizontal and vertical directions, and then the flight error Err generated by the aircraft between the two correction points at the moment iiAs shown in the following equation:
Figure BDA0002969023960000101
wherein ,
Figure BDA0002969023960000102
representing the vertical distance between the front and the back correction points;
Figure BDA0002969023960000103
representing the horizontal distance between the front and back correction points;
when the flight error of the aircraft meets the constraint condition (7), horizontal correction can be carried out, the corrected horizontal error is 0, the vertical error is kept unchanged, if the flight error does not meet the constraint condition (7), the aircraft is considered to be failed to be corrected, the horizontal error failed to be corrected is smaller between the horizontal error before being corrected and 5, and the horizontal correction is defined as follows:
Figure BDA0002969023960000104
and when the flight error of the aircraft meets the constraint condition (6), performing vertical correction, wherein the corrected vertical error is 0, the horizontal error is kept unchanged, if the flight error does not meet the constraint condition (7), the aircraft is regarded as failed in correction, the vertical error which fails in correction is smaller between the vertical error before correction and 5, and the vertical correction is defined as follows:
Figure BDA0002969023960000105
the aircraft finally aims at flying from A to B, so that the probability of the correction point close to B can be intentionally amplified a little when the next correction point is selected, and the influence of repeated correction point selection on the selection efficiency is prevented. If the next correction point of the aircraft is closer to the destination than the current correction point, selecting the next correction point and the correction points nearby to form a new correction point set, wherein the correction point selection is defined as follows:
if(Ind=NextToEnd<NowToEnd),NewId=Neigh(Ind) (7)
wherein, Ind and NextToEnd each represent the distance from the next correction point to the destination; NowToEnd represents the distance from the current calibration point of the aircraft to the destination; NewId represents the new set of correction points; neigh (ind) denotes the next correction point and its neighbor correction points;
meanwhile, each correction point can be selected only once, the neighbor correction points are ensured not to be selected when the neighbor correction points are selected, the vertical error and the horizontal error are both smaller than the residual error of the previous correction point, and the error distance between every two correction points is smaller than the limited error in the constraint condition, so the state of the new correction point is defined as follows:
NodeState(Nind)=1 (8)
wherein, NodeState represents the state of the correction point, and the value of 1 represents that the constraint condition is met; nind denotes the new correction point;
step 3.3: performing two basic operations of crossing and mutation on all new correction points meeting the conditions, setting seventy percent of probability for crossing, and performing mutation on thirty percent of probability; selecting two father individuals for mating, and finding out all effective correction points to obtain the flight path of the aircraft;
(A) and (3) cross action: the process is still path planning essentially, and then the optimal intersection mode of the two path solutions is to take a correction point from the two paths respectively to divide the two paths into four paths, and then cross and combine every two paths to obtain 2 new paths, wherein the selection of the correction point is determined according to the distance;
obtaining two offspring individuals s by simulating binary crossing1u(n),s2u(n), as shown in the following equation:
Figure BDA0002969023960000111
Figure BDA0002969023960000112
wherein ,x1u(n) and x2u(n) represents a parent individual; delta is a self-defined parameter, and the larger the value of delta is, the higher the probability that the generated offspring individual approaches to the parent individual is; v. ofuIs a [0,1 ]]Random numbers within the interval;
(B) variant behavior: two optimization strategies are set according to the constraint conditions, wherein one strategy is to exchange two approximate correction points on the flight path of the aircraft, and the other strategy is to directly kick out one correction point; the new correction point generation flow is shown in fig. 5.
Obtaining effective correction point s 'through polynomial variation'1u(n), as shown in the following equation:
s′1u(n)=s1u(n)+Δu (11)
Figure BDA0002969023960000113
and finally, connecting all the effective correction points to form the flight path of the aircraft.
In this embodiment, the selection of the correction points and the flight path planning are respectively performed according to two given sets of correction point data, the aircraft flight path obtained by the first set of correction point data is shown in fig. 6, and 9 correction points are selected in total for correction; the aircraft track obtained by the second group of correction point data is shown in fig. 7, and 9 correction points are still selected for correction.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (3)

1. A method for planning a flight path of an intelligent aircraft under multiple constraint conditions is characterized by comprising the following steps: according to the flight area of the aircraft, setting the departure place of the aircraft as A and the destination as B, setting a track constraint condition, and planning the flight path of the aircraft according to the constraint condition, which specifically comprises the following steps:
step 1: model assumption;
1) converting the flight path planning of the intelligent aircraft into a path planning problem of the aircraft, performing space search based on geometry, and generating a flight path which is a static space curve unrelated to time without considering the kinematics and dynamics constraints of the aircraft; the flight path of the aircraft is a specific flight path of the intelligent aircraft, and the flight path of the aircraft is the sequence of the flight of the aircraft to each correction point;
2) the size of the aircraft is ignored, and the aircraft is simplified into particles;
3) ignoring situations where the distance between the aircraft origin a and destination B is too long and the aircraft is out of fuel;
4) the intelligent aircraft has the advantages that the intelligent aircraft is free of any damage when flying between the departure place A and the destination B, and the intelligent aircraft is not damaged due to faults, collision and external dangers from take-off to landing;
step 2: establishing a multi-target planning model for aircraft track planning;
abstracting the flight path planning problem of the aircraft into a path planning problem based on geometry, and defining the flight path planning problem of the aircraft into a multi-objective optimization problem with constraint conditions by adopting a rapid non-dominated multi-objective optimization algorithm with an elite reservation strategy, wherein the flight path planning problem comprises inequality constraints and equality constraints, and the following formula is shown as follows:
Figure FDA0002969023950000011
wherein, H (x) is an objective function set, and E is the number of objective functions; x is the number ofkAs decision variables, xk (W) and xk (S)Are respectively the kth decision variable xkM is the number of decision variables; p is a radical ofu(x) Is inequality constraint, U is the number of inequality constraint conditions; q. q.sr(x) For equality constraint, R is the number of equality constraint conditions;
and step 3: and solving the multi-target planning model of the aircraft track planning by using the NSGA2 algorithm to obtain effective correction points, and connecting all the effective correction points to obtain the solved aircraft track.
2. The method for planning the flight path of the intelligent aircraft under the multiple constraint conditions according to claim 1, wherein the method comprises the following steps: the set track constraint conditions are as follows:
(1) the aircraft needs to be positioned in real time in the space flight process, and the positioning error comprises a vertical error a and a horizontal error b; each flying time of the aircraft is 1m, a and b are respectively increased by omega special units, when the aircraft reaches the terminal point, a is less than mu and b is less than mu, mu is another special unit, and when a is less than mu and b is less than mu, the aircraft can still fly according to the planned path;
(2) the aircraft needs to correct the positioning error in the flight process; setting a safety position for error correction in the flight area, namely a correction point, and when the aircraft reaches the correction point, performing error correction according to the error correction type of the position; if the vertical error a and the horizontal error b can be corrected within a specified time threshold, the aircraft flies according to a preset route, and finally arrives at a destination after error correction is carried out through a plurality of correction points;
(3) at origin a, the vertical error a is 0 and the horizontal error b is 0;
(4) after the vertical error correction is carried out on the aircraft at the vertical error correction point, the vertical error a is 0, and the horizontal error b is kept unchanged;
(5) after the horizontal error correction is carried out on the aircraft at the horizontal error correction point, the horizontal error b is 0, and the vertical error a is kept unchanged;
(6) setting alpha 1, alpha 2, beta 1 and beta 2 as four special units, and performing vertical error correction when a is less than or equal to alpha 1 and b is less than or equal to alpha 2;
(7) the horizontal error correction can be performed when a is less than or equal to beta 1 and b is less than or equal to beta 2.
3. The method for planning the flight path of the intelligent aircraft under the multiple constraint conditions according to claim 2, wherein the method comprises the following steps: the specific method of the step 3 comprises the following steps:
step 3.1: aiming at a plurality of correction points for positioning error correction existing in the flight area, the vertical error correction can be carried out only when a is less than or equal to alpha 1 and b is less than or equal to alpha 2 through a constraint (6); constraining (7) to carry out horizontal error correction when a is not more than beta 1 and b is not more than beta 2, and obtaining that the distance from the next correction point to the current correction point is less than a limit value;
step 3.2: adding strategies to the initial solution generation process of each objective function, reducing invalid solutions, and selecting correction points which meet the constraint conditions; the initial solution for each objective function is described as:
Figure FDA0002969023950000021
wherein ,
Figure FDA0002969023950000022
indicating the position of the calibration point at which the aircraft is currently located,
Figure FDA0002969023950000023
indicating the position of the next correction point;
if the distance between the front correction node and the rear correction node exceeds a limited error, the initial solution is invalid; the error can only be corrected when the aircraft is at the correction point, so that the aircraft is currently in positionThe error margin can constrain the error of the next correction point, the X-axis correction point and the Y-axis correction point need to be separately constrained, the distance between the front correction point and the rear correction point is mapped to the projection distance in the horizontal direction and the projection distance in the vertical direction, the movement of the aircraft between the correction points causes the errors in the horizontal direction and the vertical direction, and then the flight error Err generated by the aircraft between the two correction points at the moment iiAs shown in the following equation:
Figure FDA0002969023950000031
wherein ,
Figure FDA0002969023950000032
representing the vertical distance between the front and the back correction points;
Figure FDA0002969023950000033
representing the horizontal distance between the front and back correction points;
when the flight error of the aircraft meets the constraint condition (7), horizontal correction can be carried out, the corrected horizontal error is 0, the vertical error is kept unchanged, if the flight error does not meet the constraint condition (7), the aircraft is considered to be failed to be corrected, the horizontal error failed to be corrected is smaller between the horizontal error before being corrected and 5, and the horizontal correction is defined as follows:
Figure FDA0002969023950000034
and when the flight error of the aircraft meets the constraint condition (6), performing vertical correction, wherein the corrected vertical error is 0, the horizontal error is kept unchanged, if the flight error does not meet the constraint condition (7), the aircraft is regarded as failed in correction, the vertical error which fails in correction is smaller between the vertical error before correction and 5, and the vertical correction is defined as follows:
Figure FDA0002969023950000035
if the next correction point of the aircraft is closer to the destination than the current correction point, selecting the next correction point and the correction points nearby to form a new correction point set, wherein the correction point selection is defined as follows:
if(Ind=NextToEnd<NowToEnd),NewId=Neigh(Ind) (6)
wherein, Ind and NextToEnd each represent the distance from the next correction point to the destination; NowToEnd represents the distance from the current calibration point of the aircraft to the destination; NewId represents the new set of correction points; neigh (ind) denotes the next correction point and its neighbor correction points;
meanwhile, each correction point can be selected only once, the neighbor correction points are ensured not to be selected when the neighbor correction points are selected, the vertical error and the horizontal error are both smaller than the residual error of the previous correction point, and the error distance between every two correction points is smaller than the limited error in the constraint condition, so the state of the new correction point is defined as follows:
NodeState(Nind)=1 (7)
wherein, NodeState represents the state of the correction point, and the value of 1 represents that the constraint condition is met; nind denotes the new correction point;
step 3.3: performing two basic operations of crossing and mutation on all new correction points meeting the conditions, setting seventy percent of probability for crossing, and performing mutation on thirty percent of probability; selecting two father individuals for mating, and finding out all effective correction points to obtain the flight path of the aircraft;
(A) and (3) cross action: obtaining two offspring individuals s by simulating binary crossing1u(n),s2u(n), as shown in the following equation:
Figure FDA0002969023950000041
Figure FDA0002969023950000042
wherein ,x1u(n) and x2u(n) represents a parent individual; delta is a custom parameter; v. ofuIs a [0,1 ]]Random numbers within the interval;
(B) variant behavior: obtaining effective correction point s 'through polynomial variation'1u(n), as shown in the following equation:
s′1u(n)=s1u(n)+Δu (10)
Figure FDA0002969023950000043
and finally, connecting all the effective correction points to form the flight path of the aircraft.
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