CN111580556A - Multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint - Google Patents

Multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint Download PDF

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CN111580556A
CN111580556A CN202010441326.3A CN202010441326A CN111580556A CN 111580556 A CN111580556 A CN 111580556A CN 202010441326 A CN202010441326 A CN 202010441326A CN 111580556 A CN111580556 A CN 111580556A
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unmanned aerial
aerial vehicle
target point
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CN111580556B (en
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王玉杰
陈清阳
侯中喜
鲁亚飞
贾高伟
朱柄杰
辛宏博
唐钟南
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National University of Defense Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention provides a multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint, which comprises the steps of obtaining current position information of an unmanned aerial vehicle and a target point, and establishing a flight plane coordinate system where an unmanned aerial vehicle cluster and the target point are located; determining a threat area in a flight plane coordinate system according to the target point projection coordinate, calculating a scheme data packet of a mapping relation formed by the unmanned aerial vehicle cluster and the virtual target point, and calculating a flight track of the unmanned aerial vehicle from the unmanned aerial vehicle projection coordinate to the virtual target point according to the scheme data packet; optimizing to obtain an optimal flight track corresponding to each unmanned aerial vehicle, and performing middle-stage flight guidance; and the unmanned aerial vehicle group arriving at the virtual target point carries out the tail-segment flight guidance. According to the unmanned aerial vehicle collaborative striking method, the unmanned aerial vehicle group collaborative striking process is divided into the middle-stage flight guidance and the end-stage flight guidance, so that the problem is reduced in dimension, the calculation complexity is reduced, the optimal path from the current position of the unmanned aerial vehicle to the target position can be calculated quickly, and the requirement of striking the end-stage real-time flight path planning can be met.

Description

Multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint
Technical Field
The invention relates to the technical field of unmanned aerial vehicle flight path planning, in particular to a multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint.
Background
In a battlefield, high-value targets such as a radar station and a command department generally have a complete defense system and are not easy to be broken. In active equipment, hypersonic weapons or ballistic missiles can effectively defend, but the development and use costs are extremely high, and the hypersonic weapons or ballistic missiles cannot be affordable at every point of interest. How to achieve the same or better striking effect in a low-cost mode becomes a problem to be solved urgently, and is a research hotspot in the field of military affairs at present.
The advent of suicide drones has renewed the awareness of people about penetration weapons. Compared with the traditional guided missile, the suicide unmanned aerial vehicle has the characteristics of both the unmanned aerial vehicle and the guided missile and has higher flexibility. Therefore, the mode of cooperative combat by using a large number of cheap suicide unmanned aerial vehicles is more and more emphasized, and the research on the cooperative strategy is also promoted.
At present, many unmanned aerial vehicle flight path planning and collaborative strategy methods developed based on various intelligent algorithms exist. The core of this algorithm is to search for an optimal path between the starting position and the target position under the constraint of some performance indexes. In practical application, the intelligent algorithm is difficult to search for a large space, solve at a low speed, and fail to ensure the optimality of the solution. Meanwhile, due to the limitation of the computing power of the onboard computer, real-time flight path planning is difficult to perform. For the suicide unmanned aerial vehicle, after an attack target is determined, a hitting track must be rapidly planned and maneuvering is implemented, so that timeliness of a hitting process can be guaranteed. Therefore, based on the factors, the collaborative strike problem is decomposed and dimension reduced, and it is essential to find a rapid target strike track planning method at the tail end of the aircraft, which can meet the track optimality requirement and the real-time calculation requirement.
Disclosure of Invention
The invention aims to provide a multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint so as to solve the technical problems in the prior art.
In order to achieve the purpose, the invention provides a multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint, which comprises the following steps:
establishing a flight plane coordinate system, acquiring current position information of an unmanned aerial vehicle cluster and a target point, and projecting the current position information of the unmanned aerial vehicle cluster and the current position information of the target point to the flight plane coordinate system to obtain a projection coordinate of the unmanned aerial vehicle cluster and a projection coordinate of the target point;
determining a threat area in the flight plane coordinate system according to the projection coordinate of the target point, and calculating a scheme data packet of a mapping relation formed by the unmanned aerial vehicle cluster and the virtual target point; the threat area is a circular area with the projection coordinate of the target point as the center, the edge of the threat area is set as a threat circle, and the point on the threat circle is set as a virtual target point;
calculating the flight track of the projection coordinate of the unmanned aerial vehicle group to reach the virtual target point according to the scheme data packet;
optimizing the flight tracks to obtain optimal flight tracks corresponding to the unmanned aerial vehicles, and performing middle-stage flight guidance in a three-dimensional space according to the optimal flight tracks;
and when the unmanned aerial vehicle group reaches the virtual target point through the middle-stage flight guidance, performing the tail-stage flight guidance.
Further, acquiring initial state parameters of the unmanned aerial vehicle cluster and a target point from the unmanned aerial vehicle control equipment, and determining current position information of the unmanned aerial vehicle cluster and the target point according to the initial state parameters;
initial state parameter p of unmanned aerial vehicle groupiComprises the following steps:
Figure BDA0002504249730000021
wherein, PiRepresenting the initial position of the unmanned aerial vehicle cluster, wherein the number of the unmanned aerial vehicles is n; thetaiRepresents a heading angle; r isiRepresents the minimum turning radius of each drone;
the parameters T of the target points are: t ═ xT，yTR) in which (x)T，yT) And R is the projection coordinate of the target point in a flight plane coordinate system, and is the radius of the threat circle.
Further, the acquisition of the initial state parameters of the unmanned aerial vehicle cluster and the target point is specifically acquired from a satellite positioning system, an onboard sensor device and an onboard computer.
Further, setting a virtual target point on the threat circle as a destination of path planning of the unmanned aerial vehicle cluster in the middle-stage flight guidance process, and calculating a scheme data packet of a mapping relation formed by the unmanned aerial vehicle cluster and the virtual target point;
all the single machines with the virtual target points being the unmanned aerial vehicle cluster reach corresponding positions t on the threat circle under the constraint of the path planning strategyiExpressed as:
Figure BDA0002504249730000022
wherein, { Tj(j ═ 1,2 …, n) } refers to the position of the virtual target point of the unmanned aerial vehicle on the threat circle, and is also the end point position of the path plan of the middle-stage flight guidance process; { β; (j;)j(j ═ 1,2 …, n) } is the expected impact angle of the drone at the virtual target point on the threat circle;
Figure BDA0002504249730000031
relative to TjThe center angle of (d);
Figure BDA0002504249730000032
is set as
Figure BDA0002504249730000033
The number of unmanned planes is n, then
Figure BDA0002504249730000034
Is estimated as
Figure BDA0002504249730000035
Wherein
Figure BDA0002504249730000036
The estimated value of the number of the mapping relation groups between the unmanned aerial vehicle group and the virtual target point is
Figure BDA0002504249730000037
Further, the speed direction of the drone needs to be directed to the target point when passing through the threat circle, which is expressed as:
Figure BDA0002504249730000038
and the virtual target points are evenly distributed on the threat circle, represented as:
Figure BDA0002504249730000039
Figure BDA00025042497300000310
it is determined that all of the remaining virtual target points are also determined accordingly.
Further, according to the scheme data packet, calculating a flight trajectory of the projection coordinate of the unmanned aerial vehicle cluster to the virtual target point, including:
calculating two terminal points of a Dubins track determined by a minimum circle of the initial left or right turn of the unmanned aerial vehicle and a common tangent of a threat circle, and setting the two terminal points as characteristic points;
dividing a visible area and a blind area planned by the path by using the characteristic points;
and determining a track calculation method adopted by any unmanned aerial vehicle to reach the corresponding virtual target point by taking whether the virtual target point falls in the blind area as a judgment condition.
Further, for the case that the virtual target point falls within the visual area, the flight trajectory of the unmanned aerial vehicle cluster to reach the virtual target point is calculated by using the classic Dubins algorithm.
Further, for the situation that the virtual target point falls in the blind area, a section of circular arc on the threat circle is added to be used as a part of the path, the path is calculated in a segmented mode by the classical Dubins method, and finally the flight path of the unmanned aerial vehicle cluster from the projection coordinate to the virtual target point is obtained.
Further, optimizing the flight trajectory to obtain an optimal flight trajectory corresponding to each unmanned aerial vehicle, specifically, performing global search on a pattern data packet based on a weighting function of two distribution strategies of time optimal cooperation and deviation optimal cooperation, and calculating to obtain an optimal distribution mode and a corresponding path group.
Further, the terminal flight guidance specifically adopts a time coordinated guidance law to perform coordinated guidance on the unmanned aerial vehicle group reaching the respective virtual target point.
The invention has the following beneficial effects:
the invention provides a multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint. The method specifically comprises the following steps: in the middle-stage flight guidance process, current position information of the unmanned aerial vehicle and a target point is determined according to a satellite positioning system, airborne sensor equipment and an airborne computer, a plane coordinate system is established under specific assumption, a scheme data packet which is mapped by the unmanned aerial vehicle group and the virtual target point one by one is calculated, then concepts of the feature points are provided, related parameters of the feature points are calculated to serve as judgment conditions of different path calculation methods, and an optimal distribution scheme and a corresponding path group are calculated based on comprehensive collaborative strategy function global search. In the tail-segment flight guidance process, a method for calculating a guidance instruction according to a preset time cooperative guidance law is provided, and the unmanned aerial vehicle group is guided to simultaneously launch a dive attack to a target at the maximum speed. Compared with the prior art, the method has the advantages that the cluster attack problem is divided into two stages of middle-stage flight guidance and end-stage flight guidance by introducing the concept of a threat circle, and the cooperation problem is simplified into the problem of path planning and adjustment; an improved Dunbins method is provided for calculating a target path with threat circle blind zone constraint, and can adapt to various initial conditions; meanwhile, a comprehensive cooperation strategy formed by a weighting function based on two distribution strategies of time optimal cooperation and deviation optimal cooperation is used for path optimization, so that the solving speed and quality can be ensured, and the requirement of real-time flight path planning in a strike section can be met. By adopting the method, the calculation complexity is greatly reduced, the optimal path from the current position of the unmanned aerial vehicle to the target position can be quickly calculated, and the requirement of real-time track planning at the end of the strike can be met.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a general procedural flow diagram of the present invention;
FIG. 2 is a schematic view of the flight modeling of the present invention;
FIG. 3 is a schematic diagram of feature points of the present invention illustrating a right turn of the UAV;
FIG. 4 is a schematic diagram of feature triangle calculation in the present invention;
FIG. 5 is a schematic view of a feature triangle rotation process of the present invention;
FIG. 6 is a schematic representation of the Dubins method "L-S-L" of the present invention;
FIG. 7 is a schematic representation of the Dubins method "L-S-R" of the present invention;
FIG. 8 is a schematic representation of the Dubins method "R-S-L" of the present invention;
FIG. 9 is a schematic representation of the Dubins method "R-S-R" of the present invention;
FIG. 10 is a schematic diagram of the improved Dubins method path planning of the present invention;
FIG. 11 is a diagram illustrating an optimal path group obtained after a global search in the present invention;
FIG. 12 is a schematic diagram of the simulation of the whole process of target striking in the present invention.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
The invention provides a multi-unmanned aerial vehicle cooperative target path planning and guidance method under space-time constraint, which specifically comprises the following steps:
the method comprises the steps of firstly, establishing a flight plane coordinate system, obtaining current position information of an unmanned aerial vehicle cluster and a target point, projecting the current position information of the unmanned aerial vehicle cluster and the current position information of the target point to the flight plane coordinate system, and obtaining a projection coordinate of the unmanned aerial vehicle cluster and a projection coordinate of the target point.
Specifically, the current position information of the unmanned aerial vehicle cluster and the target point is determined according to a satellite positioning system, an airborne sensor device and an airborne computer.
Under the condition of introducing a specific hypothesis, establishing a flight plane coordinate system Oxy where the unmanned aerial vehicle cluster is located, and projecting the target point into the plane.
Specific assumptions are specifically: (1) two-dimensional plane assumption: the path planning only considers a two-dimensional plane, and vertical motion and height change of the unmanned aerial vehicle are ignored. (2) The kinematic assumption is that: the performance parameters of the unmanned aerial vehicle can be simplified into the minimum turning radius and the adjustable flight speed of the range. (3) Wind field assumption: ignoring the variation of the wind field and its effects, the drone can fly according to the expected trajectory. (4) Threat hypothesis: the threat zone, which encompasses the perimeter of the target's defense system, can be reduced to a circular area centered on the target, with the edges called the threat circle. Outside the circle, the impact or interference of the defense system is negligible.
Secondly, determining a threat area in the flight plane coordinate system according to the projection coordinates of the target point, and calculating a scheme data packet of a mapping relation formed by the unmanned aerial vehicle cluster and the virtual target point; the threat zone is a circular zone taking the projection coordinate of the target point as the center, the edge of the threat zone is set as a threat circle, and the point on the threat circle is set as a virtual target point.
The virtual target point is the corresponding position of all the single machines of the unmanned aerial vehicle cluster on the threat circle under the constraint of the path planning strategy, and is also the destination position of the path planning of the unmanned aerial vehicle cluster in the middle-stage flight guidance process.
Wherein, the initial state parameter p of the unmanned aerial vehicle groupiExpressed as:
Figure BDA0002504249730000061
wherein, PiRepresenting the initial position of the unmanned aerial vehicle cluster, wherein the number of the unmanned aerial vehicles is n; thetaiRepresents a heading angle; r isiRepresents the minimum turning radius of each drone;
the parameters T of the target points are: t ═ xT，yTR) in which (x)T，yT) And R is the projection coordinate of the target point in a flight plane coordinate system, and is the radius of the threat circle.
All the single machines with the virtual target points being the unmanned aerial vehicle cluster reach corresponding positions t on the threat circle under the constraint of the path planning strategyiExpressed as:
Figure BDA0002504249730000062
wherein, { Tj(j ═ 1,2 …, n) } refers to the position of the virtual target point of the unmanned aerial vehicle on the threat circle, and is also the end point position of the path plan of the middle-stage flight guidance process; { β; (j;)j(j ═ 1,2 …, n) } is the expected impact angle of the drone at the virtual target point on the threat circle;
Figure BDA0002504249730000063
relative to TjThe center angle of (d);
Figure BDA0002504249730000064
is set as
Figure BDA0002504249730000065
The number of unmanned planes is n, then
Figure BDA0002504249730000066
Is estimated as
Figure BDA0002504249730000067
Wherein
Figure BDA0002504249730000068
The estimated value of the number of the mapping relation groups between the unmanned aerial vehicle group and the virtual target point is
Figure BDA0002504249730000069
In order to realize the embracing strike, the speed direction of the unmanned aerial vehicle is required to be directed to a target point when passing through a threat circle, and is represented as follows:
Figure BDA00025042497300000610
and the virtual target points are evenly distributed on the threat circle, represented as:
Figure BDA0002504249730000071
Figure BDA0002504249730000072
it is determined that all of the remaining virtual target points are also determined accordingly.
And thirdly, calculating the flight track of the projection coordinate of the unmanned aerial vehicle cluster to the virtual target point on the threat circle according to the scheme data packet.
Specifically, two end points of a Dubins trajectory determined by a minimum circle of the initial left turn or right turn of the unmanned aerial vehicle and a common tangent of a threat circle are calculated, the two end points are set as feature points, a visual area and a blind area of a path plan are divided by using the feature points, and a trajectory calculation method adopted by any unmanned aerial vehicle to a corresponding virtual target point is determined by taking whether the virtual target point falls in the blind area as a judgment condition. For the case that the virtual target point falls within the visual area, the flight trajectory of the unmanned aerial vehicle cluster to the virtual target point is calculated by using the classic Dubins algorithm. For the situation that a blind area exists and the virtual target point is located in the blind area, an improved Dubins algorithm is utilized, namely, a section of circular arc along a threat circle is added to be used as a part of a path, then the path is calculated in a segmented mode through a classical Dubins method, and finally the flight path of the unmanned aerial vehicle cluster from the projection coordinate to the virtual target point is obtained. The starting point of the circular arc is a common tangent point with the threat circle, and the radius of the circular arc is equal to that of the threat circle.
And fourthly, optimizing the flight tracks to obtain the optimal flight track corresponding to each unmanned aerial vehicle, and performing middle-section flight guidance in a three-dimensional space according to the optimal flight track.
Specifically, the pattern data packet is globally searched based on a weighting function of two distribution strategies, namely time-optimal cooperation and deviation-optimal cooperation, and an optimal distribution mode and a corresponding path group are obtained through calculation.
And fifthly, performing final-stage flight guidance after the unmanned aerial vehicle group reaches the virtual target point through the intermediate-stage flight guidance.
Specifically, in order to ensure that all unmanned aerial vehicles hit a target at the same time, after all unmanned aerial vehicles reach corresponding virtual target points according to the searched paths, a cluster starts a terminal guidance process, information interaction is performed through a cluster data chain, and a dive attack is launched to the target at the maximum speed under guidance of a preset time coordinated guidance law.
Considering the existence of an actual navigation guidance error, the parameters of the unmanned aerial vehicle group are not required to be strictly converged to the parameters at the virtual target point, and whether the unmanned aerial vehicle enters the target threat circle is taken as a condition for judging whether the terminal guidance process is started or not.
Example 1:
as shown in fig. 1, a method for planning and guiding cooperative strike paths of multiple unmanned aerial vehicles under space-time constraint includes the following steps:
s1, establishing a flight plane coordinate system, acquiring current position information of the unmanned aerial vehicle cluster and the target point, and projecting the current position information of the unmanned aerial vehicle cluster and the current position information of the target point to the flight plane coordinate system to obtain a projection coordinate of the unmanned aerial vehicle cluster and a projection coordinate of the target point.
As shown in fig. 2, the current position information of the unmanned aerial vehicle cluster and the target point is determined according to the satellite positioning system, the onboard sensor equipment and the onboard computer. In this embodiment, the unmanned aerial vehicle cluster has 4 unmanned aerial vehicles in total, the initial position and the heading angle are (0, 0, pi/6), (800m, -100m, -3 pi/4), (-100m, 300m, 0), (400m, -100m, pi/2), the minimum turning radius is 50m, the coordinates of the target point are (500m, 400m), and the radius of the threat circle is 200 m. Under the condition of introducing a specific hypothesis, establishing a flight plane coordinate system Oxy where the unmanned aerial vehicle cluster is located, and projecting the target point into the plane.
S2, determining a threat area in the flight plane coordinate system according to the projection coordinates of the target points, and calculating a scheme data packet of a mapping relation formed by the unmanned aerial vehicle cluster and the virtual target points; the threat zone is a circular zone taking the projection coordinate of the target point as the center, the edge of the threat zone is set as a threat circle, and the point on the threat circle is set as a virtual target point.
Defining a series of virtual target points on the threat circle as the end points of path planning of the unmanned aerial vehicle group in the middle-section flight guidance process, and calculating the schemes and the number of scheme groups for one-to-one mapping of the unmanned aerial vehicle group and the virtual target points. The method comprises the following specific steps:
and S21, defining a virtual target point. As shown in FIG. 2, the virtual target point refers to a corresponding position t on a threat circle reached by all the singlets of the unmanned aerial vehicle cluster under the constraint of the path planning strategyiExpressed as:
Figure BDA0002504249730000081
wherein, { Tj(j ═ 1,2 …, n) } refers to the position of the virtual target point of the unmanned aerial vehicle on the threat circle, and is also the end point position of the path plan of the middle-stage flight guidance process; { β; (j;)j(j ═ 1,2 …, n) } is the expected impact angle of the drone at the virtual target point on the threat circle;
Figure BDA0002504249730000082
relative to TjThe central angle of (c). Obviously, to achieve a contained strike, the direction of the drone's speed is to point exactly to the target point when passing through the threat circle, expressed as:
Figure BDA0002504249730000083
and the virtual target points are evenly distributed on the threat circle, represented as:
Figure BDA0002504249730000084
Figure BDA0002504249730000085
once determined, all of the remaining virtual target points are determined accordingly.
And S22, calculating a scheme data packet of the mapping relation formed by the unmanned aerial vehicle cluster and the virtual target point. In practice, considering factors such as system error, measurement accuracy and environmental interference,
Figure BDA0002504249730000091
given as an embodiment of the invention a fluctuation range of (-5 °,5 °) and a number of drones of n-4, there is a fluctuation, then
Figure BDA0002504249730000092
Possible values are
Figure BDA0002504249730000093
Figure BDA0002504249730000094
The one-to-one mapping relation between the unmanned aerial vehicle cluster and the virtual target point has the value of all possible groups
Figure BDA0002504249730000095
And S3, calculating the flight path of the unmanned aerial vehicle cluster to the virtual target point according to the scheme data packet.
Calculating two end points of a Dubins track determined by the smallest circle of the initial left turn or right turn of the unmanned aerial vehicle and the common tangent of the threat circles, regarding the two end points as feature points, dividing a visual area and a blind area of path planning by using the feature points, and determining a track calculation method taken from any unmanned aerial vehicle to a corresponding virtual target point by taking whether the virtual target point falls in the blind area as a judgment condition. The method comprises the following specific steps:
and S31, calculating the coordinates of the feature points. As shown in fig. 3, taking the initial right turn case of the drone (similar to the left turn case), the feature point may be defined as a virtual target point for which the path calculated by the drone according to classical Dubins theory to the feature point is exactly tangent to the threat circle. The calculation steps are as follows:
according to the geometric relationship and symmetry in the figure
Figure BDA0002504249730000096
Wherein
Figure BDA0002504249730000097
Can be determined according to the common tangent angle
Figure BDA0002504249730000098
According to the relative geometric relationship of the two circles, the common tangent angle can be determined as
Figure BDA0002504249730000099
Wherein
Figure BDA0002504249730000101
In summary, the coordinates (x, y) of the feature points are
Figure BDA0002504249730000102
Figure BDA0002504249730000103
And S32, calculating parameters related to the characteristic points. According to the geometrical relationship shown in FIG. 4, the tangent point T2,T4Subsequent trajectory T2C1And T4C2About tangent point T2,T4Perpendicular bisector of the connecting line TC0Symmetrical, simultaneous TC0Is also the symmetry axis of the whole pattern, has
Figure BDA0002504249730000104
Wherein
Figure BDA0002504249730000105
Figure BDA0002504249730000106
Figure BDA0002504249730000107
To this end, the compound C is obtained0,C1,C2The formed figure is called a characteristic triangle. T is Δ C0C1C2The outer heart of (1).
S33、And judging whether a blind area exists or not. Two regions, namely a visual region and a blind region, can be further defined through the feature points, wherein the blind region means a set of virtual target points which pass through a threat circle by utilizing a path generated by the classical Dubins theory, and when the target points are positioned in the blind region, the classical Dubins algorithm can not be adopted for calculation. The existence of the blind area is related to the relative position of the unmanned aerial vehicle and the target and the minimum turning radius. When the calculation result shows that the two feature points are overlapped or staggered, the blind area can be judged not to exist. Due to the arbitrary initial position of the unmanned aerial vehicle, therefore
Figure BDA0002504249730000108
Can be arbitrarily changed when
Figure BDA0002504249730000109
There is no uniform size criterion because when
Figure BDA00025042497300001010
While changing, point C1,C2Either on both sides or on the same side in the positive direction of the x-axis, and it can be determined that the feature point C is the only feature point1,C2Must relate to TC0Therefore, this feature can be used to rotate the feature triangle around point T counterclockwise α degrees, as shown in fig. 5.
Figure BDA0002504249730000111
Make TC0Pointing in the negative x-axis direction, in which case C1,C2The angle is distributed at both sides (or coincided) of the positive direction of the x axis, and the judgment standard of the angle size is unique, namely when the angle is distributed at both sides (or coincided) of the positive direction of the x axis
Figure BDA0002504249730000112
There is a blind zone.
And S34, judging the area of the virtual target point. When in use
Figure BDA0002504249730000113
In the process, no blind area exists, and the virtual target points are all in the visible area; when in use
Figure BDA0002504249730000114
And is
Figure BDA0002504249730000115
In time, there is a "blind zone", but the virtual target point is in the "visible zone"; when in use
Figure BDA0002504249730000116
And is
Figure BDA0002504249730000117
Or
Figure BDA0002504249730000118
And the virtual target is positioned in the blind area.
And S4, optimizing the flight tracks to obtain the optimal flight track corresponding to each unmanned aerial vehicle, and performing middle-section flight guidance in a three-dimensional space according to the optimal flight track.
And carrying out global search on the pattern data packet based on the weighting functions of the two distribution strategies of time optimal cooperation and deviation optimal cooperation, and calculating to obtain an optimal distribution mode and a corresponding path group. The method comprises the following specific steps:
s41, calculating the optimal path of the virtual target points in the 'visible area'. For the condition without the blind zone, the track lengths under four typical conditions of L-S-L, L-S-R, R-S-L, R-S-R (R represents right turn, L represents left turn, and S represents flight along straight line) can be calculated by using the classical Dubins algorithm, and the shortest path scheme can be selected by comparing the four Dubins track lengths. The specific calculation process is as follows:
1)L-S-L
"L-S-L" is denoted as "Left-Straight-Left", i.e., the beginning and end arcs are all counterclockwise as shown in FIG. 6. Wherein the angle is defined as: rotating counterclockwise to positive along the positive x-axis.
Wherein the calculation of the central angle can be performed by an angle function F (theta)s,θeAnd d) represents, i.e
Figure BDA0002504249730000119
In function, θs,θeThe angles corresponding to the start and end positions of the arc are respectively indicated, d indicates the rotation direction of the arc, d-1 indicates the counterclockwise rotation of the arc, and d-2 indicates the clockwise rotation of the arc.
To realize the function of the angle function, the input quantity of the function needs to be further calculated
Figure BDA00025042497300001110
Is easy to obtain according to the starting and ending states
Figure BDA00025042497300001111
Figure BDA0002504249730000121
The calculation of (A) involves the common tangent of the two circles, which can be obtained from the geometrical relationship in the figure
Figure BDA0002504249730000122
Wherein the content of the first and second substances,
Figure BDA0002504249730000123
calculating the coordinates of the centers of the beginning and end circular arcs and the distance between the centers of the two circular arcs
Figure BDA0002504249730000124
Figure BDA0002504249730000125
Figure BDA0002504249730000126
Finally, the length of the straight line segment, namely the length of the common tangent line, is calculated according to the Pythagorean theorem
Figure BDA0002504249730000127
At this point, the calculation of the "L-S-L" track length is completed, and the calculation ideas of the remaining three track lengths are similar to that, and the following description focuses on the differences.
2)L-S-R
"Left-Stright-Right" as shown in FIG. 7. The initial segment of the arc is counter-clockwise, thus
Figure BDA0002504249730000128
The calculation of (A) is the same as that of 'L-S-L'; the end arc is rotated clockwise, therefore
Figure BDA0002504249730000129
Become into
Figure BDA00025042497300001210
The common tangent on the same side is changed into the common tangent on the different side, so the calculation of the tangent point angle is also changed,
Figure BDA00025042497300001211
according to geometric relationship have
Figure BDA00025042497300001212
Figure BDA0002504249730000131
Figure BDA0002504249730000132
3)R-S-L
"Right-Straight-Left" as shown in FIG. 8. This case is exactly symmetrical to "L-S-R",
Figure BDA0002504249730000133
the calculation of (a) is the same as "L-S-L",
Figure BDA0002504249730000134
become into
Figure BDA0002504249730000135
Angle of tangent point of
Figure BDA0002504249730000136
Figure BDA0002504249730000137
4)R-S-R
"Right-Straight-Right" is shown in FIG. 9. This case is exactly symmetrical to "L-S-L", and there are
Figure BDA0002504249730000138
Figure BDA0002504249730000139
In summary, the shortest path solution can be selected by comparing the lengths of the four Dubins trajectories.
And S42, calculating the optimal path of the virtual target points in the dead zone. For the case where there is a "blind area" and the virtual target point is located in the "blind area", the modified Dubins algorithm is used, that is, the path is calculated in segments by using the classical Dubins method by adding a circular arc on a threat circle with the starting point of the circle C1 and a common tangent point of the circle C2 and the radius equal to the threat radius bypassing the threat area as a part of the path, and finally the modified shortest path is obtained, as shown in fig. 10.
S43, carrying out global search solution on the N schemes, wherein the strategy for evaluating the quality of the schemes is as follows:
(1) time optimal collaboration:
the flight path length sequence of the overhead unmanned aerial vehicle in a certain scheme is calculated by the methods given by S41 and S42 as follows:
Lm＝{Lm1,Lm2,Lm3,…,Lmn}
the time-of-flight sequence is
Figure BDA0002504249730000141
Expected arrival time is
Figure BDA0002504249730000142
For each drone, the expected path length is available (matching needs to be done by path extension methods):
Figure BDA0002504249730000143
for all schemes, the corresponding expected arrival time can be calculated according to the same method, and the global optimal solution is
Figure BDA0002504249730000144
(2) Deviation optimal cooperation: the index function is the mean square error of the time sequence of each drone arriving at the virtual target point, as follows
Figure BDA0002504249730000145
Wherein
Figure BDA0002504249730000146
The optimal solution is given by the following equation
Figure BDA0002504249730000147
In practical application, a comprehensive cooperative strategy is adopted, and a weighting index function is taken
Figure BDA0002504249730000148
The scheme with the minimum value of the cyclic calculation searching weighting function is the optimal solution of the embodiment.
For the present example, the optimal path group of the mid-flight guidance obtained by the global search calculation is shown in fig. 11.
And S5, when the unmanned aerial vehicle group reaches the virtual target point through the middle-stage flight guidance, calculating a guidance instruction by adopting a terminal guidance law, and performing terminal-stage flight guidance (namely a terminal guidance stage).
Specifically, after all unmanned aerial vehicles reach corresponding virtual target points according to the searched paths, a cluster starts an end guidance process, information interaction is performed through a cluster data chain, and a dive attack is launched to a target at the maximum speed under guidance of a preset time coordinated guidance law.
Expression of acceleration command
a＝ap+aξ
Wherein a ispAcceleration command being proportional guidance law
Figure BDA0002504249730000151
N is the pilot coefficient, V is the current speed,
Figure BDA0002504249730000152
is the line-of-sight angular variability.
aξFor adding a time control item, the specific expression is
Figure BDA0002504249730000153
Figure BDA0002504249730000154
Wherein T is the predicted time (a given value) for the unmanned aerial vehicle to reach the target from the virtual target point, r (T) is the distance from the current position to the target,
Figure BDA0002504249730000155
and predicting the residual time of the current unmanned aerial vehicle when the unmanned aerial vehicle reaches the target point, wherein a coefficient k represents the influence degree of time constraint.
As shown in fig. 12, after the unmanned aerial vehicle group reaches the predetermined virtual target point, the guidance process is switched to, and the target is hit under the guidance of the time-coordinated guidance law.
The above example fully verifies the feasibility and effectiveness of the overall calculation method through simulation of the whole process of striking. When the number of the unmanned aerial vehicles is small, the method is low in calculation complexity, the optimal path from the current position of the unmanned aerial vehicle to the target position can be calculated quickly, and the requirement of real-time flight path planning of the attack section can be met. The invention can be applied to flight path planning of combat unmanned aerial vehicles, cruise missiles and the like.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A multi-unmanned aerial vehicle collaborative path planning and guidance method under space-time constraint is characterized by comprising the following steps:
establishing a flight plane coordinate system, acquiring current position information of an unmanned aerial vehicle cluster and a target point, and projecting the current position information of the unmanned aerial vehicle cluster and the current position information of the target point to the flight plane coordinate system to obtain a projection coordinate of the unmanned aerial vehicle cluster and a projection coordinate of the target point;
determining a threat area in the flight plane coordinate system according to the projection coordinate of the target point, and calculating a scheme data packet of a mapping relation formed by the unmanned aerial vehicle cluster and the virtual target point; the threat area is a circular area with the projection coordinate of the target point as the center, the edge of the threat area is set as a threat circle, and the point on the threat circle is set as a virtual target point;
calculating the flight track of the projection coordinate of the unmanned aerial vehicle group to reach the virtual target point according to the scheme data packet;
optimizing the flight tracks to obtain optimal flight tracks corresponding to the unmanned aerial vehicles, and performing middle-stage flight guidance in a three-dimensional space according to the optimal flight tracks;
and when the unmanned aerial vehicle group reaches the virtual target point through the middle-stage flight guidance, performing the tail-stage flight guidance.
2. The method for planning and guidance of the collaborative path of the multiple unmanned aerial vehicles under the space-time constraint is characterized in that initial state parameters of an unmanned aerial vehicle cluster and a target point are obtained from an unmanned aerial vehicle control device, and current position information of the unmanned aerial vehicle cluster and the target point is determined according to the initial state parameters;
initial state parameter p of unmanned aerial vehicle groupiComprises the following steps:
Figure FDA0002504249720000011
wherein, PiRepresenting the initial position of the unmanned aerial vehicle cluster, wherein the number of the unmanned aerial vehicles is n; thetaiRepresents a heading angle; r isiRepresents the minimum turning radius of each drone;
the parameters T of the target points are: t ═ xT，yTR) in which (x)T，yT) And R is the projection coordinate of the target point in a flight plane coordinate system, and is the radius of the threat circle.
3. The method for planning and guidance of cooperative paths of multiple unmanned aerial vehicles under space-time constraint according to claim 2, wherein the initial state parameters of the unmanned aerial vehicle cluster and the target point are obtained from a satellite positioning system, an onboard sensor device and an onboard computer.
4. The method for planning and guidance of the collaborative path of multiple unmanned aerial vehicles under space-time constraint according to claim 1, characterized in that a virtual target point on a threat circle is set as a destination of path planning of an unmanned aerial vehicle cluster in the middle-stage flight guidance process, and a scheme data packet of a mapping relationship formed by the unmanned aerial vehicle cluster and the virtual target point is calculated;
all the single machines with the virtual target points being the unmanned aerial vehicle cluster reach corresponding positions t on the threat circle under the constraint of the path planning strategyiExpressed as:
Figure FDA0002504249720000021
wherein, { Tj(j ═ 1,2 …, n) } refers to the position of the virtual target point of the unmanned aerial vehicle on the threat circle, and is also the end point position of the path plan of the middle-stage flight guidance process; { β; (j;)j(j ═ 1,2 …, n) } is the expected impact angle of the drone at the virtual target point on the threat circle;
Figure FDA0002504249720000022
relative to TjThe center angle of (d);
Figure FDA0002504249720000023
is set as
Figure FDA0002504249720000024
The number of unmanned planes is n, then
Figure FDA0002504249720000025
Is estimated as
Figure FDA0002504249720000026
Wherein
Figure FDA0002504249720000027
The estimated value of the number of the mapping relation groups between the unmanned aerial vehicle group and the virtual target point is
Figure FDA0002504249720000028
5. The method for planning and guidance of the collaborative path of the multiple unmanned aerial vehicles under the space-time constraint is characterized in that the speed direction of the unmanned aerial vehicle points to a target point when passing through a threat circle, and is represented as follows:
Figure FDA0002504249720000029
and the virtual target points are evenly distributed on the threat circle, represented as:
Figure FDA00025042497200000210
Figure FDA00025042497200000211
it is determined that all of the remaining virtual target points are also determined accordingly.
6. The method for planning and guidance of the collaborative path of multiple unmanned aerial vehicles under space-time constraint according to claim 1, wherein calculating the flight trajectory of the projection coordinates of the unmanned aerial vehicle cluster to the virtual target point according to the scheme data packet comprises:
calculating two terminal points of a Dubins track determined by a minimum circle of the initial left or right turn of the unmanned aerial vehicle and a common tangent of a threat circle, and setting the two terminal points as characteristic points;
dividing a visible area and a blind area planned by the path by using the characteristic points;
and determining a track calculation method adopted by any unmanned aerial vehicle to reach the corresponding virtual target point by taking whether the virtual target point falls in the blind area as a judgment condition.
7. The method for planning and guidance of the collaborative path of multiple unmanned aerial vehicles under space-time constraint according to claim 6, wherein for the case that the virtual target point falls within the visible area, the flight trajectory of the unmanned aerial vehicle fleet to reach the virtual target point is calculated by using the classical Dubins algorithm.
8. The method for planning and guidance of the collaborative path of multiple unmanned aerial vehicles under space-time constraint according to claim 6, characterized in that, for the case that the virtual target point falls in the blind area, the path is calculated in segments by adding a segment of circular arc on the threat circle as a part of the path and then using the classical Dubins method, and finally the flight trajectory of the projection coordinates of the unmanned aerial vehicle cluster to the virtual target point is obtained.
9. The method for planning and guidance of the collaborative path of the multiple unmanned aerial vehicles under the space-time constraint is characterized in that the flight trajectory is optimized to obtain the optimal flight trajectory corresponding to each unmanned aerial vehicle, specifically, the scheme data packet is globally searched based on the weighting functions of two distribution strategies of time-optimal collaboration and deviation-optimal collaboration, and the optimal distribution mode and the corresponding path group are obtained through calculation.
10. The method for planning and guiding the collaborative path of multiple unmanned aerial vehicles under the space-time constraint according to claim 1, wherein the terminal flight guidance is specifically the collaborative guidance of the unmanned aerial vehicle cluster reaching respective virtual target points by adopting a time collaborative guidance law.
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