CN110986960A - Unmanned aerial vehicle track planning method based on improved clustering algorithm - Google Patents

Unmanned aerial vehicle track planning method based on improved clustering algorithm Download PDF

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CN110986960A
CN110986960A CN201911418899.8A CN201911418899A CN110986960A CN 110986960 A CN110986960 A CN 110986960A CN 201911418899 A CN201911418899 A CN 201911418899A CN 110986960 A CN110986960 A CN 110986960A
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path
track
path point
point
flight path
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CN110986960B (en
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宋申民
李欣
刘庭瑞
杨小艳
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
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    • G06F18/23—Clustering techniques
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    • G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
    • G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering

Abstract

The invention discloses an unmanned aerial vehicle track planning method based on an improved clustering algorithm, and relates to an unmanned aerial vehicle track planning method based on an improved clustering algorithm. The invention aims to solve the problems of low accuracy and large calculated amount caused by clustering each flight path in the conventional multi-target flight path planning method. The process is as follows: firstly, setting control parameters of a differential evolution operator; a maximum cluster number; a mating limit probability; generating an initial population and calculating a target value; establishing an external document; setting the iteration times as T times, and enabling T to be 1; thirdly, finding out the neighbor path point of each path point; setting the number of tracks, and enabling i to be 1; fifthly, generating a new flight path; sixthly, calculating a new flight path target value; seventhly, saving the optimal flight path in an external document; eight, let i become i +1, repeat four to eight until i become N; and ninthly, updating the population, and repeatedly executing two to nine until T is T + 1. The method is used for the field of unmanned aerial vehicle track planning.

Description

Unmanned aerial vehicle track planning method based on improved clustering algorithm
Technical Field
The invention relates to an unmanned aerial vehicle track planning method based on an improved clustering algorithm.
Background
To date, various flight path planning methods have been proposed by scholars, such as a-algorithm, D-Lite algorithm, two-layer planning algorithm, grid-based algorithm and intelligent computing method.
Although a number of methods have been proposed to solve the unmanned aerial vehicle trajectory planning problem, people generally represent the trajectory planning problem as a single-objective optimization problem and propose a single-objective optimization algorithm. However, the problem of planning the flight path usually has a plurality of mutually contradictory goals, such as the desire to obtain a minimum probability of being destroyed but at the same time the desire to have the shortest flight path. The existing approach to dealing with multiple conflicting objectives is to multiply each objective by a coefficient and then add the weighted objectives. In fact, the properties of these conflicting objects are different and cannot be simply weighted to sum them. And how to determine the appropriate weighting coefficients is a critical but not easy problem to solve. Furthermore, running a single-target optimization algorithm once based on a fixed set of weighting coefficients can only obtain an optimal flight path, and once the decision maker's preferences change, the algorithm needs to be run again to obtain a new optimal flight path. Considering that the multi-target evolution algorithm has strong global search capability and robustness, and diversified compromise flight paths can be provided for decision makers only by running once, the method for solving the unmanned aerial vehicle flight path planning problem by using the multi-target evolution algorithm is practical.
Some multi-target evolution algorithms for solving the unmanned aerial vehicle track planning problem are proposed in the existing documents. Mittal and Deb solve two flight path planning problems by using NSGA-II combined with a local search method, wherein one flight path planning problem does not consider other constraint conditions except unmanned aerial vehicle and terrain constraint, and the other planning problem defines a special point which an unmanned aerial vehicle must pass through. In planning a safe flight path for a drone, Sun et al use algorithms in the literature to find a compromise between drone navigation and bistatic SAR imaging in order to simultaneously obtain bistatic SAR imaging of the target of interest to the researcher. In addition, in order to solve the optimization problem, Sun et al also propose a constrained adaptive multi-objective differential evolution algorithm, which adaptively adjusts the control parameters of the differential evolution operator according to the entropy. In the literature, an NSGA-II is taken as a framework, several mutation operators are designed, the use probability of the operators is adaptively adjusted, and then the flight length, the flight altitude and the total threat index are optimized by using an improved algorithm. In addition, inspired by the a-algorithm, a reconstruction operator is also proposed to enable solution to escape from the restricted region. In order to better evolve the high-quality path points in the flight path, Yang et al propose to decompose the original flight path planning constraint condition and the objective function into a series of new subfunctions, and then to evolve and evaluate each path point independently. The optimization algorithm of the path point is a JADE algorithm combined with a multi-criterion processing method based on priority. To plan the trajectories of multiple drones, Besada-ports et al propose optimization criteria based on drone attributes, terrain and different priorities, and propose a multi-agent co-evolution algorithm that each drone uses one evolution algorithm and shares the optimal solution during evolution. Considering the changing environment and limited information in the flight path planning, Peng et al propose a dynamic multi-target evolution algorithm, which selects a historical Pareto solution set to construct a time sequence and uses a prediction method to speculate a new Pareto solution set.
In general, at present, methods for directly solving the problem of unmanned aerial vehicle multi-target track planning without weighting and summing targets are few, and further research is needed by students.
The unmanned aerial vehicle flight path planning problem is a type of optimization problem with multiple targets and constraints. Considering that multiple conflicting optimization targets exist in the unmanned aerial vehicle track planning problem, the optimization targets have different attributes, cannot be simply weighted and summed, and the weighting coefficient is difficult to determine, and the multiple targets for directly optimizing the unmanned aerial vehicle track planning by using the multi-target evolution algorithm are practical.
In the multi-target evolution algorithm, the distribution information of the solution can be extracted by utilizing a clustering algorithm to assist local search. In addition, in the track planning problem, one path is a solution, so that the clustering algorithm can find the neighboring track of the current track. However, the jth waypoint of the ith track may be far from the jth waypoint in the neighbor track of the ith track. Performing a reorganization operation using such physically far distributed path points does not ideally improve the local search capability of the algorithm.
Disclosure of Invention
The invention aims to solve the problems of low accuracy and large calculated amount caused by clustering each flight path in the conventional multi-target flight path planning method, and provides an unmanned aerial vehicle flight path planning method based on an improved clustering algorithm.
An unmanned aerial vehicle flight path planning method based on an improved clustering algorithm comprises the following specific processes:
step one, setting control parameters { F, CR } of a differential evolution operator, a maximum clustering number K, a mating limit probability β;
wherein F is a scaling factor and CR is a crossover factor;
generating an initial population P ═ x1,…,xNAnd calculating a P target value; establishing an external document A ═ P;
in the formula, x1For track 1, xNThe Nth track is obtained;
step two, setting the iteration times as T times, and enabling T to be 1 and T to be more than or equal to 1 and less than or equal to T;
step three, finding out a neighbor path point S of each path point by adopting a Clustering algorithm, wherein the S is the Clustering (P, w, K);
in the formula, w is the number of paths, and Clustering is Clustering;
setting the number of tracks to be N, setting i to be 1, and setting i to be not less than 1 and not more than N;
step five, recombining the path points to generate a new flight path np, np which is Reproduction (β, S, P, i, F, CR);
in the formula, Reproduction is recombination;
step six, calculating a new flight path target value;
step seven, saving the better flight path in the external document A, wherein A is Selection (A, np);
wherein, Selection is Selection;
step eight, making i equal to i +1, and repeatedly executing the step four to the step eight until i equal to N;
and step nine, updating the population P as A, making T as T +1, and repeatedly executing the steps two to nine until T as T.
The invention has the beneficial effects that:
the unmanned aerial vehicle flight path planning problem is a typical multi-objective optimization problem. Compared with a single-target evolution algorithm, the multi-target evolution algorithm can balance between contradictory targets, and find a series of tracks meeting different preferences. The decision maker can extract the relevant knowledge of the flight path optimization problem from the compromised flight paths, select the preference flight path from the plurality of flight paths, and solve the problem by using a multi-objective evolution algorithm.
In establishing the neighborhood relationship, each waypoint, rather than each flight path, should be clustered as a data point. The invention provides a multi-target evolution Algorithm (MFKC) for solving the unmanned aerial vehicle track planning problem aiming at the defects that path points of neighboring tracks are possibly distributed far and each track is clustered in the conventional multi-target track planning method. The MFKC finds the neighbor path point of each path point by using a K-means algorithm. And determining a parent generation source of each path point according to the mating limit probability of each path point, and controlling a pairing pool to be composed of the global path point or the neighbor path point of the current path point so as to respectively enhance exploration and exploitation. Followed by individual recombination and selection of execution environment
The main contributions of the present invention are as follows:
1) unmanned aerial vehicle flight path planning problem models under two scenes are provided.
2) And the K-means algorithm is utilized to search the neighbor path points for each path point, so that the accuracy is high and the calculated amount is small.
The problems of low accuracy and large calculated amount caused by clustering each flight path in the conventional multi-target flight path planning method are solved;
the invention controls the composition of the pairing pool based on the mating limit probability of each path point, and further controls the search range of the path points.
In order to test the performance of the MFKC in solving the unmanned aerial vehicle multi-target track planning problem, the MFKC and the NSGA-II are subjected to a comparison experiment under two scenes. The experimental result shows that the MFKC can not only find a feasible flight path and provide a diversified flight path for a decision maker, but also is superior to NSGA-II in terms of the average value of HV and the number of times of search failure.
Drawings
FIG. 1 is a middle point view on a track segment of the present invention;
FIG. 2 is a graph of the reason for clustering waypoints rather than tracks in accordance with the present invention;
FIG. 3a is a side view of the f1 flight path of the MFKC algorithm in scene 1;
FIG. 3b is a side view of the f2 flight path for the MFKC algorithm in scene 1;
FIG. 4a is a top view of the f1 flight path of the MFKC algorithm under scene 2;
FIG. 4b is a side view of the f1 flight path diagram for the MFKC algorithm in scene 2;
FIG. 4c is a top view of the f2 flight path for the MFKC algorithm under scene 2;
FIG. 4d is a side view of the f2 flight path diagram of the MFKC algorithm in scene 2.
Detailed Description
The first embodiment is as follows: the method for planning the flight path of the unmanned aerial vehicle based on the improved clustering algorithm comprises the following specific processes:
unmanned aerial vehicle track planning problem description
Unmanned aerial vehicles have demonstrated their advantages and potential in military and civilian areas. In order to realize unmanned aerial vehicle autonomous navigation, aspects such as modeling, flight path planning, control system design and the like must be considered. Among them, track planning is a type of important issue that has been widely studied.
Drone trajectory planning is the finding of an optimal or sub-optimal trajectory from a starting point to an end point, with a number of constraints (including drone attributes and terrain limitations) satisfied. The quality of the flight path is measured by the indexes of flight length, flight height, destroyed probability and the like. Thus, the trajectory planning problem can be described as a constrained multi-objective optimization problem. Specifically, based on a time domain, the unmanned aerial vehicle flight path planning problem can be divided into online optimization and offline optimization; based on the space domain, the unmanned aerial vehicle flight path planning problem is divided into an optimization problem under a 2-dimensional environment and a 3-dimensional environment. Because the online track planning problem can be regarded as an extension of the offline track planning problem, the most widely studied is the offline track planning problem. The flight path planning problem researched and mentioned by the invention is the problem of unmanned aerial vehicle off-line flight path planning in a 3-dimensional environment.
Track representation
The method for representing the unmanned aerial vehicle track based on the curve can make the track smooth, but needs large calculation cost[17]Therefore, the invention establishes a series of path points and connects the path points by line segments to form a flight path.
Some track planning methods transform the track coordinates to increase the search speed. For simplicity, the chromosomes of the evolutionary algorithm in the present invention are composed of coordinate values of a fixed number of path points in a cartesian coordinate system. There are w path points in a track, so a chromosome can be represented as (x)1,y1,z1,…,xj,yj,zj,…,xw,yw,zw)TWherein x isj,yj,zjIs the coordinate value of the jth path point, and j is the serial number of the path point in the flight path. The coordinates of the first and last point in the chromosome are the coordinates of the start and end points, respectively.
Objective function
In order to reduce fuel consumption and task completion time, the drone should have as short a flight path length as possible. In order to improve survival probability by using terrain shielding, the flying height of the unmanned aerial vehicle should be as low as possible. Thus, an optimization objective is established to minimize the total track length f1And a total flying height f2。
f1Representing the actual track length divided by the ideal track length. An ideal track is a line segment that directly connects the start and end points. f. of2Expressed as the average of the w-1 track segment heights. The existing method for measuring the flight altitude is to add the altitudes of all path points, but neglect the flight altitude between the path points, so the flight altitude is measured by adopting the altitude of a track section. Dividing line segments between adjacent track points into N by utilizing uniformly distributed intermediate pointsmEach line segment has a height of NmA middle point (including a path point) oppositeAverage height of the ground. The coordinate value of the mth middle point on the jth track segment is (px)j,m,pyj,m,pzj,m) As shown in fig. 1. Wherein, pzj,mCan be represented by the formula pzj,m＝zj-1+m/Nm×(zj-zj-1),m＝1,…,NmAnd (6) calculating. The objective function of the above-mentioned flight path planning problem is represented as follows:
Figure BDA0002351850240000051
wherein h isj,mIs a plane coordinate of (px)j,m,pyj,m) The height of the terrain.
Constraint function
Turning angle theta of flight path in consideration of operability of unmanned aerial vehiclejJ 2, …, w-1 should be smaller than the maximum turning angle θ of the dronemax. Otherwise, the violation function value for the constraint is set to be greater than 0. ThetajIs a vector (x)j-xj-1,yj-yj-1) And (x)j+1-xj,yj+1-yj) The included angle therebetween. The first constraint function is expressed as:
Figure BDA0002351850240000052
Figure BDA0002351850240000053
Figure BDA0002351850240000054
wherein the content of the first and second substances,
Figure BDA0002351850240000055
is the constraint violation for the jth turn angle. If the turning angle constraint is violated, thetajThe larger the size of the tube is,
Figure BDA0002351850240000056
the larger.
Figure BDA0002351850240000057
Is in the range of [0,1]]。
Similarly, limited by drone operability, there is a maximum climb/dive angle αmaxUsing slope α of track segmentjJ-2, …, w represents the climb/dive angle of the track, which should be less than αmax. The second constraint function is:
Figure BDA0002351850240000061
Figure BDA0002351850240000062
Figure BDA0002351850240000063
wherein the content of the first and second substances,
Figure BDA0002351850240000064
is the constraint violation for the jth ramp angle, the greater α in violation of the constraintjResult in being larger
Figure BDA0002351850240000065
Figure BDA00023518502400000614
In [0,1]]To change between.
Although a lower flying height can shield the unmanned aerial vehicle from the ground, in order to ensure the safety of the flight, the unmanned aerial vehicle must have a certain height from the ground during the flight. The lowest vertical height from the unmanned aerial vehicle to the ground is set to be hmin. The third constraint function can be expressed as:
Figure BDA0002351850240000066
Figure BDA0002351850240000067
wherein the content of the first and second substances,
Figure BDA0002351850240000068
is the constraint violation value of the height of the mth intermediate point in the jth track segment, and cn (j) is the number of the intermediate points violating the constraint in the jth track segment. Lower flying height pz in violation of constraintsj,mResulting in a larger constraint violation
Figure BDA0002351850240000069
Figure BDA00023518502400000615
Is also in [0,1]]To change between.
Because the unmanned aerial vehicle needs a certain time to adjust the attitude, the distance d between two adjacent path pointsj J 2, …, w should be greater than the minimum track segment length Lmin. The fourth constraint function is expressed as follows:
Figure BDA00023518502400000610
Figure BDA00023518502400000611
Figure BDA00023518502400000612
wherein the content of the first and second substances,
Figure BDA00023518502400000613
is a constraint violation for the jth track segment length. Shorter track length d in violation of constraintsjResult in the larger
Figure BDA0002351850240000071
Figure BDA0002351850240000077
In [0,1]]Within a range.
In addition to the track segment constraint, the total track length is defined to be less than a predefined length value L when planning the trackmax. The fifth constraint function is therefore:
Figure BDA0002351850240000072
the boundaries of the search space also need to be defined before planning the flight path. [ x ] ofa,xb]，[ya,yb]And [ z ]a,zb]Representing the lower and upper boundaries of the x, y and z coordinates, respectively. And processing the path points outside the search space by using a repair operator of an evolutionary algorithm, wherein a constraint function is not established.
To sum up, the unmanned aerial vehicle track planning problem can be expressed as:
Figure BDA0002351850240000073
further multiplying the constraint violation value by 106And then added to the target value, expressed in the form of equation (15). This approach allows the infeasible solution to have a very large target value, and the larger the constraint violation value, the larger the target value, and the earlier it is to be culled in the context selection. At this time, the constraint multi-objective optimization problem is converted into a multi-objective optimization problem only with box constraints, and can be solved by a general multi-objective evolution algorithm without considering a plurality of constraint conditions in environment selection.
Figure BDA0002351850240000074
Scene description
Specifying a search space range of [ xa,xb]＝[0,300]km,[ya,yb]＝[0,300]km,[za,zb]＝[0,1.5]km, and all location coordinate units are km. The invention provides an unmanned aerial vehicle track planning problem under two scenes.The scenario for unmanned aerial vehicle trajectory planning includes terrain and threats. The terrain consists of an initial terrain and a mountain terrain. The initial terrain is generated by the simulation of equation (16):
h1(x,y)＝sin(y/180+1.5×π)+0.1×sin(x/16)+0.9×cos(0.3×median)+0.01×sin(0.01×median)+0.3×cos(y/36) (16)
wherein h is1Is the initial terrain height of point (x, y),
Figure BDA0002351850240000075
the mountain terrain is simulated by equation (17):
Figure BDA0002351850240000076
wherein h is2Is the peak height of point (x, y). K represents the number of peaks. h (k) is the highest height of the kth mountain peak. (o)1(k),o2(k) Is the horizontal coordinate of the kth mountain center. L is1(k) And L2(k) Controlling the profile of the kth seat peak. 6 mountains exist in the setting environment, and the corresponding parameter values are h ═ 0.7,1.77,1.8,2.34,2.5 and 3.2; o1＝{50,160,70,130,100,100}；o2＝{60,100,30,20,160,100}；L1＝{140,170,170,160,280,150}；L2＝{20,230,150,190,220,280}。
Two air defense units of radar and missile are considered as threats to the flight path planning problem. Once the drone enters the maximum risk range of the air defense unit, it is likely to be discovered or attacked. Because the set maximum search range on the z-axis is much smaller than the maximum risk range of the air defense unit, the threat range of the air defense unit is simplified into a cylinder. The horizontal coordinate of the center point of the cylinder is consistent with the threat, the radius is the maximum risk distance of the threat, and the height is the maximum search range on the z-axis.
In the first scenario, two radar threats and two missile threats are considered, with center point horizontal coordinates of { [100,225], [240,150] } and { [100,100], [225,250] } respectively, and maximum risk distances of {50,50} and {25,25} respectively. In the second scenario, there are four radar threats and four missile threats, and the feasible range of the flight path is smaller than that in the first scenario. The center points of the threats are horizontally coordinated as { [120,240], [175,75], [50,175], [240,150] } and { [75,60], [225,250], [170,170], [100,125] }, with maximum risk distances of {50,50,35,35} and {25,25,25 }.
In addition, set N m10, and thus each track segment is divided into 10 areas when calculating physical quantities such as flight altitude and altitude constraint violation values. Maximum turning angle thetamaxAnd maximum climb/dive angle αmax60 deg. and 30 deg., respectively. The minimum flying height from the ground is hmin0.05km, length L of shortest track segmentmin2km, maximum track length of
Figure BDA0002351850240000081
Step one, setting control parameters { F, CR } of a differential evolution operator, a maximum clustering number K, a mating limit probability β;
wherein F is a scaling factor and CR is a crossover factor;
generating an initial population P ═ x1,…,xNAnd calculating a P target value; establishing an external document A ═ P;
in the formula, x1For track 1, xNThe Nth track is obtained;
step two, setting the iteration times as T times, and enabling T to be 1 and T to be more than or equal to 1 and less than or equal to T;
step three, finding out a neighbor path point S of each path point by adopting a Clustering algorithm, wherein the S is the Clustering (P, w, K);
in the formula, w is the number of paths, and Clustering is Clustering;
setting the number of tracks to be N, setting i to be 1, and setting i to be not less than 1 and not more than N;
step five, recombining the path points to generate a new flight path np, np which is Reproduction (β, S, P, i, F, CR);
in the formula, Reproduction is recombination;
step six, calculating a new flight path target value;
step seven, selecting according to the environment, and saving the better flight path in the external document A, wherein A is Selection (A, np);
wherein, Selection is Selection;
step eight, making i equal to i +1, and repeatedly executing the step four to the step eight until i equal to N;
step nine, updating the population P as A, making T as T +1, and repeatedly executing the steps two to nine until T as T;
the MFKC first finds its neighbor individuals for each waypoint (rather than each flight path) using the K-means clustering algorithm. And then according to the mating limit probability, selecting the neighbor path points or the global path points (all path points with the same sequence number as the current path point) of the path points as a pairing pool, thereby respectively enhancing the local search capability and the global search capability of the algorithm. And finally, selecting individuals with excellent quality through an environment selection operator to enter next generation evolution. The pseudo code for the MFKC is shown in algorithm 1. It should be noted that the path points clustered and evolved in the algorithm do not include a start point and an end point.
Figure BDA0002351850240000091
In Algorithm 1, N is the number of tracks. A is an external document for environment selection.
Figure BDA0002351850240000092
Is a neighborhood matrix, where K is the maximum cluster number,
Figure BDA0002351850240000093
and after all path points with the sequence number j are clustered, the path points are classified into k-th type path points. The MFKC first randomly generates an initial population P and calculates its target value, building a solution that the external document a performs well in the selection of storage environments (line 1). The N tracks are then evolved by T generations (lines 2-10). In each generation evolution process, path points with the same sequence number are first clustered by using a K-means algorithm, and a neighboring path point S of each path point is found (row 3). The reorganization operation and the environment selection operation are then run for each track (lines 4-8). Wherein, the MFKC evolves by recombination operatorNew w-2 waypoints, generating a new flight path np (line 5). The target value for the new track is then calculated (line 6). The new solution is then mixed with the external document for context selection, and if the new track quality is better, it is saved to the external document (line 7). At the end of each generation evolution, P is updated with A (line 9).
The second embodiment is as follows: the difference between this embodiment and the first embodiment is that the expression for calculating the P target value in the first step is as follows:
Figure BDA0002351850240000101
x＝(x1,y1,z1,…,xw,yw,zw)T
s.t.xj∈[xa,xb],yj∈[ya,yb],zj∈[za,zb],j＝1,…,w
wherein x is x1Or xN，f1(x) To minimize the total track length, f2(x) Total flying height, gkK is a clustering number for the constraint function; x is the number of1,y1,z1Is the coordinate value of the 1 st path point, xw,yw,zwIs the coordinate value of the w-th path point, and w is the number of paths in the flight path; x is the number ofj,yj,zjIs the coordinate value of the jth path point, j is the serial number of the path point in the flight path; [ x ] ofa,xb],[ya,yb]And [ z ]a,zb]Representing the lower and upper boundaries of the x, y and z coordinates, respectively.
The third concrete implementation mode: the difference between this embodiment and the first or second embodiment is that, in the third step, a Clustering algorithm is used to find the neighboring path point S, S-Clustering (P, w, K) of each path point; the specific process is as follows:
step three, setting a population P, the number w of path points and the maximum clustering number K;
let j equal 2;
step three and two, finding all track mediansPath point with number j, forming a global path point
Figure BDA0002351850240000102
In the formula (I), the compound is shown in the specification,
Figure BDA0002351850240000103
is the x coordinate value of the jth path point of the 1 st track,
Figure BDA0002351850240000104
is the x coordinate value of the jth path point of the Nth track,
Figure BDA0002351850240000105
is the y coordinate value of the jth path point of the 1 st track,
Figure BDA0002351850240000106
is the y coordinate value of the jth path point of the Nth track,
Figure BDA0002351850240000107
is the z-coordinate value of the jth path point of the 1 st track,
Figure BDA0002351850240000108
the z coordinate value of the jth path point of the Nth track is taken as the z coordinate value of the jth path point of the Nth track;
step three, using K-means algorithm to map the global path point SPjThe division into the K classes is done,
Figure BDA0002351850240000109
in the formula (I), the compound is shown in the specification,
Figure BDA00023518502400001010
is SPjThe class 1 of the video signal after the division,
Figure BDA00023518502400001011
is SPjThe K-th class after being divided;
step three and four, enabling j to be equal to j +1, and repeatedly executing the step three to the step three and four until j is equal to w-1;
step three and five, if only class 1 exists, the step is carried out
Figure BDA00023518502400001110
A path point is classified into
Figure BDA0002351850240000111
In (1), the other half of the path points are classified into
Figure BDA0002351850240000112
Performing the following steps; if only 1 type does not exist, ending;
step three and six, if
Figure BDA0002351850240000113
Only one path point in the path, the SPjOf randomly selected waypoints
Figure BDA0002351850240000114
Is added to
Figure BDA0002351850240000115
Performing the following steps; if it is not
Figure BDA0002351850240000116
If not, ending;
in the formula (I), the compound is shown in the specification,
Figure BDA0002351850240000117
is SPjAnd (5) dividing the kth class.
In consideration of low computational complexity and high clustering accuracy of the K-means algorithm, the MFKC clusters the path points by adopting the K-means algorithm. As can be seen from FIG. 2, points A and B can be regarded as neighboring waypoints of the jth waypoint of the ith track, but the i-1 track and the i-2 track where points A and B are located are not neighbors of the ith track. In contrast, point C is farther from the jth waypoint, but point C belongs to the (i + 1) th track, which is a neighbor of the ith track. Mating with point C with the jth waypoint of the ith track does not allow local searching as desired. In contrast, although point A and point B are not in the neighborhood of the ith track, using both points to mate with the jth waypoint facilitates a local search. Therefore, in order to further enhance the exploitation capacity of the algorithm, the MFKC utilizes the K-means algorithm to cluster all path points with the same serial number, and the K-means algorithm needs to be operated for w-2 times aiming at w-2 path points in the flight path. The clustering step in the MFKC is shown in algorithm 2.
Figure BDA0002351850240000118
In Algorithm 2, the K-means algorithm runs a total of w-2 times (lines 1-4). In each operation, path points with the same sequence number are collected to create global path points
Figure BDA0002351850240000119
(line 2) SP is divided by K-means algorithmjDivision into K classes
Figure BDA0002351850240000121
(line 3), the details of the K-means algorithm can be referred to. The clustering results are then examined (lines 5-6). If only class 1 exists after clustering, then it will be preceded
Figure BDA00023518502400001220
A path point is classified into
Figure BDA0002351850240000122
In (1), the other half of the path points are classified into
Figure BDA0002351850240000123
Middle (row 5). Classes with only one waypoint
Figure BDA0002351850240000124
Will be added with a slave SPjOf randomly selected waypoints
Figure BDA0002351850240000125
(line 6) of the first row of the second row of the third row,at this time, from
Figure BDA0002351850240000126
The parent individuals selected for recombination are sufficiently different to allow for changes in the waypoints.
Other steps and parameters are the same as those in the first or second embodiment.
Fourth embodiment, unlike the first to third embodiments, the fifth step recombines the path points to generate a new trajectory np, i, F, CR (β, S, P, i, F, CR), and the specific process is as follows:
fifthly, setting a mating limit probability β, a neighbor path point matrix S of each path point, a whole population P, a current evolution track number i, DE operator control parameters { F, CR };
let j equal 2;
step five and two, finding the current path point
Figure BDA0002351850240000127
Neighbor path point of
Figure BDA0002351850240000128
In the formula (I), the compound is shown in the specification,
Figure BDA0002351850240000129
is the x coordinate value of the jth path point of the ith track,
Figure BDA00023518502400001210
is the y coordinate value of the jth path point of the ith track,
Figure BDA00023518502400001211
the z coordinate value of the jth path point of the ith track is taken as the z coordinate value of the jth path point of the ith track;
step five and step three, establishing a pairing pool
Figure BDA00023518502400001212
Wherein rand1 is a random number in the range of [0,1 ];
step five and four, randomly selecting two points from M
Figure BDA00023518502400001213
And
Figure BDA00023518502400001214
as mating parents;
fifthly, evolving the current path point by using a differential evolution operator to obtain a trial solution;
Figure BDA00023518502400001215
Figure BDA00023518502400001216
Figure BDA00023518502400001217
wherein F is a difference coefficient and CR is a crossover probability; rand2, rand3, rand4 are random numbers in the range of [0,1 ];
step five and six, aiming at
Figure BDA00023518502400001218
Obtaining new path points by adopting polynomial mutation operators
Figure BDA00023518502400001219
During the recombination process, neighbor individuals of the current waypoint are selected as a pairing pool with a probability of β, and all global waypoints with the same sequence number are selected as parent sources with a probability of 1- β.
Figure BDA0002351850240000131
For in the ith trackThe jth path point finds its neighbor individuals
Figure BDA0002351850240000132
Thereafter (row 2), the neighbor waypoints are utilized according to the mating limit probability β
Figure BDA0002351850240000133
Or global path point SPjPairing pool M is established (line 3). Randomly choosing two parents from M
Figure BDA0002351850240000134
And
Figure BDA0002351850240000135
(line 4). The trial solution is then generated using a differential evolution operator
Figure BDA0002351850240000136
(line 5). In order to make a path point feasible, the value of a gene exceeding the search space is set as a boundary value (line 6). MFKC also employs evolution trial solutions of polynomial mutation operators with gene repair mechanisms (line 7). In Algorithm 3, SPjConsisting of waypoints having the same sequence number j. rand1, rand2, rand3, rand4 and rand5 are [0,1]]Random numbers within a range. In the DE operator at line 5, F is the difference coefficient and CR is the crossover probability. In addition, at the time of recombination, one gene (randomly selected) in the current pathway point is not mutated under the control of CR.
On the other hand, global waypoints with the same sequence number are generally distributed more widely in the search space, and the selection of the parent from such points is beneficial for exploration, β can control the composition of the paired pools, thus the proportion of exploitation and exploration can be controlled.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the seventh embodiment is different from the first to fourth embodiments in that, in the seventh step, a better track is saved in the external document a according to the environment Selection, where a is Selection (a, np); the specific process is as follows:
step seven, setting an external document A; a new track np;
performing fast non-dominated sorting on the population A ∪ np, if a solution dominated by other individuals exists in A ∪ np, executing step seven two, and if a solution dominated by other individuals does not exist in A ∪ np, executing step seven three;
seventhly, deleting the solution x dominated by the most individuals in the layer with the highest Pareto gradepE.g. A ∪ np, executing step seven and four;
seventhly, deleting the solution x with the minimum super-volume contribution degreepE.g. A ∪ np, executing step seven and four;
step seven and four, if xpNot equal to np; store np at the p-th position, x, in Ap＝np。
If xpNp; and (6) ending.
MFKC through environment selection[25]And ensuring that the high-quality solution enters the next generation evolution. The solution dominated by the most individuals on the worst leading edge converges the worst. When all solutions are mutually non-divergent, the solution diversity with the smallest degree of over-volume contribution is the worst. Based on Pareto dominance and the over-volume contribution, the environment selection in algorithm 4 can guarantee convergence and diversity of the solution.
Figure BDA0002351850240000141
To ensure convergence of the solution, it is necessary to delete the solution that is dominated by the most individuals on the worst leading edge (lines 1-2). If all solutions have the same Pareto rating, then the solution with the least contribution to the hyper-volume is deleted (lines 3-5). If the new flight path np is at least better than one solution in the external document A, the deleted solution xpIs located in a, at which time np is stored in the p-th location in a (lines 6-8).
Other steps and parameters are the same as in one of the first to fourth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the preparation method comprises the following steps:
experimental study of MFKC algorithm
To verify the performance of MFKC, NSGA-II was chosen[26]Is a comparative algorithm. For comparative fairness, the SBX operator in NSGA-II is replaced with the DE operator. In addition, the parameters of NSGA-II and MFKC were optimized based on the original literature and prior experiments. Specific parameter values are shown in table 1. The algorithm performance was evaluated using the hyper-volume index (HV). The reference point when the HV value is calculated is z ═ 1.5,1.5]T. The statistics of HV obtained with 31 independent runs of the algorithm in each scenario are listed in table 2. The number of times the algorithm failed the search is shown in parentheses.
The MFKC achieves the best HV average in both scenarios. In scenario 1, NSGA-II failed to find N feasible tracks 4 times. In contrast, MFKC found a feasible track in 31 runs. In scenario 2, since the number of the air defense units increases and the feasible space becomes smaller, the number of times of the NSGA-II and MFKC search failures becomes larger. However, the MFKC still had more success times and obtained a larger HV average than NSGA-II. From the above, the MFKC has better performance.
Table 1 parameter values of NSGA-II and MFKC algorithms for unmanned aerial vehicle flight path planning problem under two scenes
Figure BDA0002351850240000151
Table 2 statistical results obtained by NSGA-II and MFKC algorithms on unmanned aerial vehicle flight path optimization problem under two scenes
Figure BDA0002351850240000152
The path with the shortest path length and the path with the lowest flight height of the N paths when the MFKC is selected to obtain the maximum HV value in 31 runs are plotted in fig. 3a, 3b and fig. 4a, 4b, 4c, 4 d. The left and right hand figures are the same flight path, but the angles are plotted differently.
It can be found from fig. 3a, 3b and fig. 4a, 4b, 4c, 4d that the flight path searched by the MFKC is feasible. Comparing the flight paths of the upper and lower figures, it was found that the flight path flight height with the shortest flight length was higher, while the flight path flight length with the lowest flight height was longer. This phenomenon again illustrates that the goals of the drone trajectory planning problem are conflicting, with the raising of one target value resulting in the lowering of another. However, the MFKC can trade off both the overall flight path length and the flight height goals, finding a diverse range of feasible flight paths for decision makers to choose from.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (5)

1. An unmanned aerial vehicle flight path planning method based on an improved clustering algorithm is characterized in that: the method comprises the following specific processes:
step one, setting control parameters { F, CR } of a differential evolution operator, a maximum clustering number K, a mating limit probability β;
wherein F is a scaling factor and CR is a crossover factor;
generating an initial population P ═ x1,…,xNAnd calculating a P target value; establishing an external document A ═ P;
in the formula, x1For track 1, xNThe Nth track is obtained;
step two, setting the iteration times as T times, and enabling T to be 1 and T to be more than or equal to 1 and less than or equal to T;
step three, finding out a neighbor path point S of each path point by adopting a Clustering algorithm, wherein the S is the Clustering (P, w, K);
in the formula, w is the number of paths, and Clustering is Clustering;
setting the number of tracks to be N, setting i to be 1, and setting i to be not less than 1 and not more than N;
step five, recombining the path points to generate a new flight path np, np which is Reproduction (β, S, P, i, F, CR);
in the formula, Reproduction is recombination;
step six, calculating a new flight path target value;
step seven, saving the better flight path in the external document A, wherein A is Selection (A, np);
wherein, Selection is Selection;
step eight, making i equal to i +1, and repeatedly executing the step four to the step eight until i equal to N;
and step nine, updating the population P as A, making T as T +1, and repeatedly executing the steps two to nine until T as T.
2. The unmanned aerial vehicle track planning method based on the improved clustering algorithm is characterized in that: the expression for calculating the P target value in the first step is as follows:
Figure FDA0002351850230000011
x＝(x1,y1,z1,…,xw,yw,zw)T
s.t.xj∈[xa,xb],yj∈[ya,yb],zj∈[za,zb],j＝1,…,w
wherein x is x1Or xN，f1(x) To minimize the total track length, f2(x) Total flying height, gkK is a clustering number for the constraint function; x is the number of1,y1,z1Is the coordinate value of the 1 st path point, xw,yw,zwIs the coordinate value of the w-th path point, and w is the number of paths in the flight path; x is the number ofj,yj,zjIs the coordinate value of the jth path point, j is the serial number of the path point in the flight path; [ x ] ofa,xb],[ya,yb]And [ z ]a,zb]Representing the lower and upper boundaries of the x, y and z coordinates, respectively.
3. The unmanned aerial vehicle flight path planning method based on the improved clustering algorithm is characterized in that: in the third step, a Clustering algorithm is used for finding out a neighbor path point S of each path point, wherein S is the Clustering (P, w, K); the specific process is as follows:
step three, setting a population P, the number w of path points and the maximum clustering number K;
let j equal 2;
step three, finding path points with sequence number j in all tracks to form global path points
Figure FDA0002351850230000021
In the formula (I), the compound is shown in the specification,
Figure FDA0002351850230000022
is the x coordinate value of the jth path point of the 1 st track,
Figure FDA0002351850230000023
is the x coordinate value of the jth path point of the Nth track,
Figure FDA0002351850230000024
is the y coordinate value of the jth path point of the 1 st track,
Figure FDA0002351850230000025
is the y coordinate value of the jth path point of the Nth track,
Figure FDA0002351850230000026
is the z-coordinate value of the jth path point of the 1 st track,
Figure FDA0002351850230000027
the z coordinate value of the jth path point of the Nth track is taken as the z coordinate value of the jth path point of the Nth track;
step three, using K-means algorithm to map the global path point SPjThe division into the K classes is done,
Figure FDA0002351850230000028
in the formula (I), the compound is shown in the specification,
Figure FDA0002351850230000029
is SPjThe class 1 of the video signal after the division,
Figure FDA00023518502300000210
is SPjThe K-th class after being divided;
step three and four, enabling j to be equal to j +1, and repeatedly executing the step three to the step three and four until j is equal to w-1;
step three and five, if only class 1 exists, the step is carried out
Figure FDA00023518502300000211
A path point is classified into
Figure FDA00023518502300000212
In (1), the other half of the path points are classified into
Figure FDA00023518502300000213
Performing the following steps;
if only 1 type does not exist, ending;
step three and six, if
Figure FDA00023518502300000214
Only one path point in the path, the SPjOf randomly selected waypoints
Figure FDA00023518502300000215
Is added to
Figure FDA00023518502300000216
Performing the following steps;
if it is not
Figure FDA00023518502300000217
If not, ending;
in the formula (I), the compound is shown in the specification,
Figure FDA00023518502300000218
is SPjAnd (5) dividing the kth class.
4. The unmanned aerial vehicle flight path planning method based on the improved clustering algorithm is characterized in that in the fifth step, path points are recombined to generate a new flight path np, np which is Reproduction (β, S, P, i, F, CR), and the specific process is as follows:
fifthly, setting a mating limit probability β, a neighbor path point matrix S of each path point, a whole population P, a current evolution track number i, DE operator control parameters { F, CR };
let j equal 2;
step five and two, finding the current path point
Figure FDA0002351850230000031
Neighbor path point of
Figure FDA0002351850230000032
In the formula (I), the compound is shown in the specification,
Figure FDA0002351850230000033
is the x coordinate value of the jth path point of the ith track,
Figure FDA0002351850230000034
is the y coordinate value of the jth path point of the ith track,
Figure FDA0002351850230000035
the z coordinate value of the jth path point of the ith track is taken as the z coordinate value of the jth path point of the ith track;
step five and step three, establishing a pairing pool
Figure FDA0002351850230000036
Wherein rand1 is a random number in the range of [0,1 ];
step five and four, randomly selecting two points from M
Figure FDA0002351850230000037
And
Figure FDA0002351850230000038
as mating parents;
fifthly, evolving the current path point by using a differential evolution operator to obtain a trial solution;
Figure FDA0002351850230000039
Figure FDA00023518502300000310
Figure FDA00023518502300000311
wherein F is a difference coefficient and CR is a crossover probability; rand2, rand3, rand4 are random numbers in the range of [0,1 ];
step five and six, aiming at
Figure FDA00023518502300000312
Obtaining new path points by adopting polynomial mutation operators
Figure FDA00023518502300000313
5. The unmanned aerial vehicle track planning method based on the improved clustering algorithm as claimed in claim 4, wherein: in the seventh step, the better track is saved in the external document A, wherein A is Selection (A, np); the specific process is as follows:
step seven, setting an external document A; a new track np;
performing rapid non-dominated sorting on the population A ∪ np, and if the solution dominated by other individuals exists in the population A ∪ np, executing a step seven two;
if there are no solutions dominated by other individuals in A ∪ np, go to step seven and three;
seventhly, deleting the solution x dominated by the most individuals in the layer with the highest Pareto gradepE.g. A ∪ np, executing step seven and four;
seventhly, deleting the solution x with the minimum super-volume contribution degreepE.g. A ∪ np, executing step seven and four;
step seven and four, if xpNot equal to np; store np at the p-th position, x, in Ap＝np；
If xpNp; and (6) ending.
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