CN111290440B - Double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking control and tracking method - Google Patents
Double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking control and tracking method Download PDFInfo
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Abstract
The invention discloses a multi-unmanned aerial vehicle formation standby off tracking control method based on a double virtual structure, which comprises the following steps: introducing a virtual UAV l As a virtual leader of the formation; introducing another virtual UAV b As a reference for formation target tracking control; and constructing a tracking parameter set to perform tracking control. The tracking control method characterizes UAV formation cooperative target standby off tracking by constructing a tracking parameter set, and converts tracking conditions into the design of the parameter set, so that the method is more visual and clear. On the basis of the tracking control method, the invention also discloses a tracking method, which can realize the standby off tracking of the target only by one control law, greatly simplifies the complexity of the tracking algorithm and has larger practical engineering value.
Description
Technical Field
The invention belongs to the field of unmanned aerial vehicle target tracking, and mainly relates to a control method for performing on-off tracking on a target by multi-unmanned aerial vehicle formation and a tracking method based on a corresponding control method, in particular to a multi-unmanned aerial vehicle formation on-off tracking control and tracking method based on a double virtual structure.
Background
Tracking of targets by drones (unmanned aerial vehicle, UAV) is one of the important tasks of drones. The standby off tracking is an important tracking mode of target tracking, and the method requires that the unmanned aerial vehicle keeps a certain distance from the target and the unmanned aerial vehicle makes fixed-distance spiral motion around the target. Along with the improvement of task degree of difficulty and the complicacy of environment for single unmanned aerial vehicle hardly satisfies actual combat demand, consequently research many unmanned aerial vehicles cooperation execution task is popular more and more.
Multiple UAVs cooperate with standby off tracking requires that each UAV track the same target and that each UAV maintain phase cooperation with the other UAV. Currently, the multi-UAV collaborative standby tracking method is mainly divided into two types, one type is that each UAV is directly guided to a standby tracking circle by a vector field, then phases among the UAVs are adjusted, and the other type is that UAV formation is generated before a target is tracked, and then guidance rules are designed to guide the formation to the standby circle. However, the two methods have respective disadvantages, and the former carries out the phase adjustment between the UAVs after all the UAVs reach the tracking circle, so that the time for realizing collaborative tracking is prolonged; the latter designs formation guidance laws between UAV and leader (virtual leader) tracking target guidance laws, respectively, based mainly on the leader-follower structure, and the algorithm design of this method is complicated.
For target tracking, a measurement method of the target information state is important for the research of the tracking method. The current unmanned aerial vehicle mainly relies on an onboard sensor for measuring the target state, and is combined by matching with a corresponding estimation algorithm. Meanwhile, it should be noted that the sensor performs measurement estimation on the target state at each sampling point, so the designed method must take this point into consideration to have more engineering value.
In summary, the main difficulties of the multi-UAV collaborative target standby off tracking problem are: firstly, how to convert the problem of the standby off tracking of multi-unmanned aerial vehicle formation into a simple tracking control description, and secondly, how to determine a method capable of shortening the multi-UAV phase coordination time and simplifying the guidance law design.
Disclosure of Invention
The invention aims to provide a multi-unmanned aerial vehicle formation standby off tracking control method based on a double virtual structure, so that difficulty in cooperative control of phases of multi-unmanned aerial vehicle formation is simplified; on the basis, the invention also aims to provide a multi-unmanned aerial vehicle formation standby off tracking method based on a double virtual structure, which not only can shorten the phase coordination time of a plurality of UAVs on target tracking, but also can simplify the guidance law.
The invention provides a double-virtual-structure-based multi-unmanned-plane formation standby off tracking control method, which comprises the following steps:
step S1, introducing a virtual UAV l Virtual leader as a team
The UAV (unmanned aerial vehicle) l Continuously approaching to the target until the target coincides with the target; p is p l For UAVs l V of (c) l For UAVs l Is a speed of (2);
step S2, introducing a virtual UAV b As a reference for formation target tracking control
UAV b Position p of (2) b ＝r s ·[cosθ b sinθ b ] T Wherein r is s Radius, θ for the Stardoff tracking b For UAVs b Is a phase of (2); and theta is theta b ＝θ 0 +ωt, where θ 0 For a set initial angle, the disc angular velocity,
ω 0 is a constant, t 0 The method comprises the steps of tracking the moment of an upper target for UAV formation, namely, the moment of forming a multi-UAV formation tracking situation; UAV (unmanned aerial vehicle) b The velocity of (2) is v b ；
S3, constructing a tracking parameter set for tracking control
Taking the ith UAV i As phase control factor R i I is {1,2, …, N }, N is the number of frames of the unmanned aerial vehicle in the formation;
then, a set of standby off tracking parameters S (N), S (N) = (p) l (t),p b (t),R 1 (t),R 2 (t),…,R N (t)) controlling the queued steady off trackingAnd (5) preparing.
Preferably, when each unmanned aerial vehicle rotates anticlockwise by a corresponding angle to perform phase adjustment, the R i The specific steps are as follows:
θ i for UAVs i Is used to determine the desired relative phase angle of the lens. Each unmanned aerial vehicle can be rotated clockwise by corresponding angles to carry out phase adjustment, and corresponding R is obtained i 。
Preferably, step S1 specifically includes:
step S11, p l According to the position p of N unmanned aerial vehicle i Determination of v l Is a determined constant;
step S12, determining the UAV according to the estimation of the target motion direction at the current moment l The motion direction at the current moment is
UAV l Control input of +.>
Wherein p is t (t+Δt) is the estimated position of the target at time t+Δt, Δt being the sensor sampling time interval.
Step S13, repeating step S12 until the UAV l Coincident with the target.
Preferably, specifically take
Here, the weighted average of the positions of the unmanned aerial vehicles is taken, and p can be determined by other methods l 。
Preferably, when the unmanned aerial vehicle is a fixed-wing unmanned aerial vehicle, in order to prevent the fixed-wing unmanned aerial vehicle from stalling, the unmanned aerial vehicle is specifically taken
Wherein v is min Is the minimum safe flying speed of the UAV, r s Radius is tracked for standby off.
The invention also provides a double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking method, which is used for tracking a target on the basis of the double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking control method:
during tracking, ith UAV i Control law u i The method comprises the following steps:
wherein χ is i ＝u l -R i u b ，
θ i For UAVs i Is>
a ij And a ib Representing UAVs respectively i Receiving information from a UAV j And UAV (unmanned aerial vehicle) b Ability to receive information, take a when information can be received ij ，a ib > 0, otherwise take a ij ，a ib ＝0；UAV i Velocity error e of (2) vi ＝v i -v l -R i v b ，UAV i Position error e of (2) pi ＝p i -p l -R i p b ，p i For UAVs i V of (c) i For UAVs i The speed of k 1 ,k 2 And > 0 is the control coefficient.
Preferably, when the multi-unmanned aerial vehicle formation performs cooperative standby off tracking on the target, the following conditions are required to be satisfied:
wherein lambda is q For q=l+a ib I N L is the directed graph G 1 Laplacian matrix and L.epsilon.R N ×N ，G 1 Is the communication topological relation among UAVs in formation.
Preferably, G 1 In particular G 1 ＝(V 1 ,ε 1 ) Wherein: v (V) 1 Representing a set of vertices, i.e., a set of UAVs; epsilon 1 Is a collection of edges, i.e., a collection of connected relationships between UAVs.
Preferably, L is specifically l=d-a, wherein: d=diag { D 1 ,d 2 ,…,d N }∈R N×N Is G 1 Is used for the weight input degree matrix of the (a),
for UAVs i Weight input value of (a) = [ a ] ij ]∈R N×N Is an adjacency matrix->
The invention relates to a double-virtual structure-based multi-unmanned aerial vehicle formation standby off tracking control method, which is based on combining a current airborne sensor to a target motion measuring and estimating method by introducing a virtual UAV (unmanned aerial vehicle) l Tracking the target motion trail, and realizing tracking trail guidance of UAV formation; and by introducing virtual UAVs b Controlling the spiral motion of the UAV formation after the formation generation and the tracking of the upper target in the tracking process; the UAV formation cooperative target standby off tracking is characterized by constructing the tracking parameter set, the tracking condition is converted into the design of the parameter set, the difficulty of phase cooperative control is simplified, and the phase cooperative time among multiple UAVs is shortened. The invention also carries out tracking on the basis of the tracking control method, can realize the standby off tracking of the target only by one control law under the contract of the tracking parameter set, greatly simplifies the complexity of the tracking algorithm and has larger practical engineering value.
Drawings
FIG. 1 is a flow chart of a multiple unmanned aerial vehicle formation standby off tracking method based on a double virtual structure;
FIG. 2 is a UAV l Tracking a target track schematic diagram;
FIG. 3 is a UAV at two moments l Schematic of relative position to the target; FIG. 4 is a multiple UAV platoon stand off heelA trace control schematic;
FIG. 5 is a diagram of the communication topology between all UAVs;
FIG. 6 is a trajectory diagram of a multiple UAV platoon performing a stand off tracking of a maneuver target;
FIG. 7 is a UAV i Distance error e of (2) pi Is a curve of (2);
FIG. 8 is a UAV l A track guiding schematic;
FIG. 9 is a UAV i With UAV l Schematic of the distance between the two parts over time;
fig. 10 is a phase change diagram.
Detailed Description
Embodiments of the present invention will now be described with reference to fig. 1 to 10.
As shown in fig. 1, the multi-unmanned aerial vehicle formation standby off tracking control method based on the double virtual structure mainly comprises 3 steps: introducing a virtual UAV l As a virtual leader of the formation; introducing a virtual UAV b As a reference for formation target tracking control; and constructing a tracking parameter set to perform tracking control.
The invention considers the problem that N-frame UAVs carry out the standby off tracking on targets, and can establish an unmanned aerial vehicle dynamic model based on a double-integral model:
wherein p is i ＝(x i ,y i ) T 、v i UAV respectively i Position and velocity of (c); u (u) i To control the amount.
In order to convert the problem of the standby off tracking of multi-unmanned aerial vehicle formation into a simple tracking control description needle, the invention provides a double-virtual-structure-based standby off tracking control method for multi-unmanned aerial vehicle formation, which specifically comprises the following steps:
step S1, introducing a virtual UAV l As a virtual leader of the formation, track guidance is provided for the movement of the entire formation.
Establishing a UAV l The model of (2) is:
wherein: p is p l ＝(x l ,y l ) T 、v l UAV respectively l Position and velocity of (c); u (u) l For UAVs l Is provided for the control input of (a).
As a virtual leader, UAV l The main function is to provide a reference for the UAV platoon to the kinematic location. UAV (unmanned aerial vehicle) command l The target is continuously tracked, and is continuously moved towards the target until the target coincides with the target. UAV (unmanned aerial vehicle) l Tracking the target track is a precondition for realizing accurate tracking of targets by multiple UAV formation, and a track guiding UAV tracking target track schematic diagram is shown in figure 2.
UAV l The method is continuously approaching to the target until the target is coincident with the target, and specifically can be adopted as follows:
step S11, p l According to the position p of N unmanned aerial vehicle i Determining i ε {1,2, …, N }; in the present embodiment, specifically take
v l For UAVs l Velocity magnitude, v l Is a determined constant;
step S12, determining the UAV according to the estimation of the target motion direction at the current moment l The motion direction at the current moment is
UAV l Control input of +.>
Wherein p is t (t+Δt) is the estimated position of the target at time t+Δt, Δt being the sensor sampling time interval; p is p l (t) is the time t UAV l Is a position of (c).
Step S13, repeating step S12 until the UAV l The target is caught up and coincides with the target.
To validate defined movement rules to enable UAVs l The upper target can be tracked and now demonstrated using geometric knowledge.
As shown in FIG. 3, A and B are UAVs at time t respectively l UAV at time t+Deltat for A 'and B' respectively corresponding to the position of the target l The position of the target is AB and A 'B' are t and t+Δt times UAV, respectively l The distance between the target and the target, AA 'and BB' are UAV in the delta t time period respectively l Distance to the target. Then to prove UAV l Can track the target, namely, the A 'B' is less than AB.
It is evident that AB-A 'B < AA', A 'B' -A 'B < BB' due to UAV l If the target track is to be tracked at a certain speed, the following of the target track is required to be ensured t ||＜||v l I i.e., AA '> BB'. Therefore, A 'B' -AB is less than AA ', A' B 'is less than AA' +AB is less than AB, and the evidence is obtained.
According to UAV l In the method convention of the invention, the UAV takes the measurement characteristics of the airborne sensor to the target into consideration l The motion trail of the target is formed by a plurality of tiny sub-paths, which also means that the target tracking algorithm provided by the invention meets the tracking problem when the target maneuvers, the UAV l The object approaching the object continuously can be realized by continuously adjusting the motion direction of the object according to the motion trend of the object at the sampling moment.
Step S2, introducing a virtual UAV b As a reference for formation target tracking control
Establishing a UAV b The model of (2) is:
wherein: p is p b ＝(x b ,y b ) T 、v b UAV respectively b Position and velocity of (c); u (u) b For UAVs b Is used for controlling the amount of the control of the (b).
In the invention, UAV is used as b As a reference for the cooperative control of multiple UAVs, the method is not only a reference for the cooperative control of phases among unmanned aerial vehicles, but also a reference for the multiple unmanned aerial vehicle formation to perform the stand off tracking.
UAV b Position pb=r of (2) s ·[cosθ b sinθ b ] T Wherein r is s Radius, θ for the Stardoff tracking b For UAVs b Is a phase of (2); UAV (unmanned aerial vehicle) b The velocity of (2) is v b 。
To achieve multi-UAV collaborative standby off tracking, θ is selected b ＝θ 0 +ωt, where θ 0 Is the initial angle set.
According to the characteristics of the stardoff tracking, the spiral angular velocity omega is selected as follows:
ω 0 to determine the constant, t 0 The moment of tracking the upper target for the UAV platoon, i.e. the moment of forming the multiple UAV platoon tracking situation.
When the unmanned aerial vehicle in the formation is a fixed wing unmanned aerial vehicle, it has clear constraints on the flight speed and turning radius, so the flight situation during the multi-UAV formation target tracking must be considered. In order to ensure flight safety and prevent stall and other problems, constraint conditions of hover motion in the standby off tracking can be obtained as follows:
wherein v is min Is the minimum safe flying speed of the UAV, r s Radius is tracked for standby off.
S3, constructing a tracking parameter set for tracking control
The tracking method is controlled by two virtual unmanned aerial vehicles, and the UAV can be known through the two steps b Is the basis for controlling formation generation and unmanned aerial vehicle hover motion control, and UAV l Then the motion trail of the multi-unmanned aerial vehicle formation is controlled.
To achieve multi-UAV collaborative target tracking, consider that the multi-UAVs form a phased collaborative formation. Each UAV uses UAVs b And (3) rotating the corresponding angles by taking the reference as the reference, and respectively maintaining corresponding phase intervals, thereby achieving the aim of phase coordination of multiple UAVs. According to the invention, each unmanned aerial vehicle rotates anticlockwise by a corresponding angle to perform phaseBit adjustment, using rotation matrix as formation parameter, recorded as phase control factor R i I.e.
Wherein θ is i For UAVs i Is relative to the UAV b As shown in fig. 4.
In addition, each unmanned aerial vehicle can also be rotated clockwise by a corresponding angle to carry out phase adjustment.
Further, the standby off tracking parameter set S (N) may be constructed as
S(N)＝(p l (t),p b (t),R 1 (t),…,R N (t))
Through the parameter set S (N), not only can the formation of the phase coordination of the multiple UAVs be satisfied, but also the control of the standby off tracking of the formation can be realized.
For any initial state, if it is satisfied
As shown in fig. 4, assuming that the number of UAVs in formation n=4,
it can be found that when p b And p is as follows l After the determination, all UAVs will follow the UAVs before they track the targets l Centered along the UAV b Anticlockwise rotation angle theta i To respective positions, form a phased formation, illustrating that the formation of the UAV formation may be formed by (p l (t),p b (t),R 1 (t),…,R N (t)) controlling formation; and after the UAV tracks the target, the UAV receives the target b All UAVs will be in communication with the UAV b A spiral motion with an angular velocity omega is performed.
Furthermore, in order to simplify the complexity of the tracking algorithm, the invention provides a double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking method based on the double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking control method, and the double-virtual-structure-based multi-unmanned-aerial-vehicle formation standby off tracking method can realize the standby off tracking of a target only by one control law.
The tracking method specifically comprises the steps of adding step S4 on the basis of the three steps, and determining a control law to realize tracking.
To achieve formation and standby tracking of UAV platoons, it is also critical to determine control laws.
The present invention utilizes directed graphs to represent the communication topology between UAVs.
In particular using directed graph G 1 ＝(V 1 ,ε 1 ) Representing communication topology between unmanned aerial vehicles within a formation, wherein V 1 Representing a set of vertices, i.e., a set of intra-formation UAVs; epsilon 1 Is a collection of edges, i.e., a collection of connected relationships between UAVs. If there is a directed graph edge (UAV i ,UAV j )∈ε 1 Then represent UAV i Capable of receiving information from a UAV j And the two are said to be contiguous. Defining an adjacency matrix a= [ a ] ij ]∈R N×N Wherein a is ij Representative edge (UAV) i ,UAV j ) Weights of (i.e. UAV) i Receiving information from a UAV j Ability to information, and
defining a directed graph G 1 Laplacian matrix L.epsilon.R N×N The method comprises the following steps: l= [ L ] ij ]=d-a, where d=diag { D } 1 ,d 2 ,…,d N }∈R N×N Is G 1 Is used for the weight input degree matrix of the (a),
for UAVs i Weight input value of (2).
In addition, using directed graph G 2 ＝(V 2 ,ε 2 ) Representing information transfer relationships between two virtual UAVs and each UAV, where V 2 Representing UAVs k With UAV i K e { l, b }; epsilon 2 Representing two virtual UAVs and UAVs i A set of connected relationships between. If there is a directed graph edge (UAV i ,UAV k )∈ε 1 Then represent UAV i Capable of receiving information from a UAV k Is a piece of information of (a). Definition matrix A 2 ＝[a ik ]∈R N×N Wherein a is ik Representing UAVs i Receiving information from a UAV k Ability to information, and
set up UAV i Position error e of (2) pi And speed error e vi The method comprises the following steps of: e, e pi ＝p i -p l -R i p b ，e vi ＝v i -v l -R i v b 。
For any UAV i And UAV (unmanned aerial vehicle) j If there is a certain bounded time t 0 So that t is greater than or equal to t 0 At the time, |e vi -e vj I.fwdarw.0 and i e pi -e pj I 0, then the desired multi-UAV formation may be said to be formed and maintained.
Taking into account that formation control depends mainly on the respective UAV position p in the formation i And velocity v i For this purpose, the speed u is designed separately vi And a position control law u pi ：
Ith UAV obtainable from the superposition of linear systems i Control law u i The method comprises the following steps:
wherein χ is i ＝u l -R i u b ，k 1 ,k 2 And > 0 is the control coefficient.
The UAV formation error dynamic equation is:
wherein:
Q＝L+a ib I N 。
in UAVs l And UAV (unmanned aerial vehicle) b There is at least one arrival at all UAVs i Directed information flow between UAVs about UAVs l And UAV (unmanned aerial vehicle) b In the case where the information transfer of (1) is the same, all eigenvalues λ of Q q All have a positive real part and are referred to as quotation marks 1 for convenience of subsequent reference.
For a quadratic polynomial f (λ) =λ 2 +(a 1 +ib 1 )λ+a 2 +ib 2 To have all feature roots of f (λ) =0 with negative real parts, it is necessary to satisfy:
for ease of subsequent reference, it is referred to as lemma 2.
To sum up, in UAV l And UAV (unmanned aerial vehicle) b There is at least one arrival at all UAVs i Directed information flow between UAVs about UAVs l And UAV (unmanned aerial vehicle) b If the information transfer is the same, if:
the contract and control law u at parameter set S (N) i Under the influence of (a) the multiple UAVs will achieve coordinated stand off tracking in accordance with the desired formation. Im (lambda) q ) Lambda is lambda q Imaginary part, re (lambda) q ) Lambda is lambda q Is a real part of (c).
To prove the conclusion, only the requirement is to prove
Stabilization is achieved by->
The characteristic polynomials of A available are:
and the characteristic root of the above formula has negative real part when the requirement is from e to 0.
As can be seen from the lemma 2, if all feature roots of the feature polynomial have negative real parts, it is necessary to satisfy:
as can be seen from the index 1, re (lambda) q ) > 0. If it meets
It can be ensured that the feature roots of the feature polynomials of a all have negative real parts, proving complete.
Examples:
in this embodiment, tracking of maneuver targets by a 4-frame UAV is taken as an example for verification.
Initial parameters for the 4 frame UAV are shown in table 1:
TABLE 1 unmanned simulation initial conditions
UAV l Initial velocity v of (1) l For (20, 0) T m/s；UAV b Is set to r s ＝50m，θ b ＝0，ω 0 ＝(20/r s ) rad/s; control coefficient k 1 ＝3，k 2 =2. The acceleration of the target at 0-12 s is [5sin t,5cos t] T m/s 2 Acceleration after 12s is [4cos t,4sin t] T m/s 2 . The communication topology between UAVs is shown in FIG. 5, i.e
The simulation results are shown in fig. 6 to 10.
FIG. 6 is a trajectory diagram of a multiple UAV platoon performing a stand off tracking of a maneuver target, 4 UAVs starting from respective initial positions, at the UAV l The target is tracked under the guidance of the system, and the requirement of the standby off tracking of the target is met. FIG. 7 is a UAV i Distance error e of (2) pi From the image, it can be seen that e is approximately 9s pi And 0, wherein the UAVs form a formation with cooperative phases, small jitter appears in an error curve at about 16-21 s, and the UAV formation tracks the target and starts to perform spiral motion, but the target speed is smaller than the UAV speed, so that small change of the error is caused by adjustment of the UAV speed. FIGS. 8-10 are illustrations of a dual virtual structure according to the present invention, wherein FIG. 8 illustrates a UAV l The function of (a) was verified, figures 9 and 10 vs. UAV b The effect of (2) was verified. FIG. 8 is a UAV l Tracking the curve of the target motion, from which it can be seen that the UAV l The track of the target is tightly tracked finally by continuously adjusting the motion direction of the target, so that the track guide is provided for UAV formation tracking of the target; FIG. 9 presents a UAV b Controlling the effect of a standby off tracking radius in a dual virtual structure as a reference UAV; FIG. 10 is a UAV b Is evident that each UAV is under UAV b Based on the reference, the phase coordination can be realized faster. Comprehensive simulation of the aboveThe result illustrates the effectiveness of the multi-unmanned aerial vehicle formation standby off tracking method based on the double virtual structure.
Finally, it should be noted that the foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but although the present invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that modifications may be made to the technical solutions described in the foregoing examples, or equivalents may be substituted for some of the technical features thereof. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. The multi-unmanned aerial vehicle formation standby off tracking control method based on the double virtual structures is characterized by comprising the following steps of:
step S1, introducing a virtual UAV l Virtual leader as a team
The UAV (unmanned aerial vehicle) l Continuously approaching to the target until the target coincides with the target; p is p l For UAVs l V of (c) l For UAVs l Is a speed of (2);
step S2, introducing a virtual UAV b As a reference for formation target tracking control
UAV b Position p of (2) b ＝r s ·[cosθ b sinθ b ] T Wherein r is s Radius, θ for the Stardoff tracking b For UAVs b Is a phase of (2); and theta is theta b ＝θ 0 +ωt, where θ 0 For a set initial angle, the disc angular velocity,
ω 0 to determine the constant, t 0 Tracking the time of the upper target for the UAV formation; UAV (unmanned aerial vehicle) b The velocity of (2) is v b ；
S3, constructing a tracking parameter set for tracking control
Taking the ith UAV i As a phase controlFactor R i I is {1,2, …, N }, N is the number of frames of the unmanned aerial vehicle in the formation;
then, a set of standby off tracking parameters S (N), S (N) = (p) l (t),p b (t),R 1 (t),R 2 (t),…,R N (t)) controls the queued steady off tracking.
2. The control method according to claim 1, wherein R i The specific steps are as follows:
θ i for UAVs i Is used to determine the desired relative phase angle of the lens.
3. The tracking control method according to claim 1 or 2, characterized in that step S1 is specifically:
step S11, p l According to the position p of N unmanned aerial vehicle i Determining i ε {1,2, …, N }; v l Is a determined constant;
step S12, determining the UAV according to the estimation of the target motion direction at the current moment l The motion direction at the current moment is
UAV l Control input of +.>
Wherein p is t (t+Δt) is the estimated position of the target at time t+Δt, Δt being the sensor sampling time interval;
step S13, repeating step S12 until the UAV l Coincident with the target.
4. A tracking control method according to claim 3, characterized by taking in particular
5. The tracking control method according to claim 1 or 2, characterized in that for a fixed-wing unmanned aerial vehicle, it is specifically taken
Wherein v is min Is the minimum safe flying speed of the UAV, r s Radius is tracked for standby off.
6. Double-virtual-structure-based multi-unmanned aerial vehicle formation standby off tracking method, which is characterized in that tracking is performed on the basis of the tracking control method as claimed in claim 1 or 2, and an ith UAV is used for tracking i Control law u i The method comprises the following steps:
wherein χ is i ＝u l -R i u b ，
a ij And a ib Representing UAVs respectively i Receiving information from a UAV j And UAV (unmanned aerial vehicle) b Ability to receive information, take a when information can be received ij ，a ib > 0, otherwise take a ij ，a ib ＝0；UAV i Velocity error e of (2) vi ＝v i -v l -R i v b ，UAV i Position error e of (2) pi ＝p i -p l -R i p b ，p i For UAVs i V of (c) i For UAVs i The speed of k 1 ,k 2 And > 0 is the control coefficient.
7. The tracking method of claim 6, wherein the multiple unmanned aerial vehicle formation performs coordinated standby off tracking on the target, and the following conditions are satisfied:
wherein lambda is q For q=l+a ib I N L is the directed graph G 1 Laplacian matrix and L.epsilon.R N×N ，G 1 Is the communication topological relation among UAVs in formation.
8. The tracking method of claim 7, wherein G 1 In particular G 1 ＝(V 1 ,ε 1 ) Wherein: v (V) 1 Representing a set of vertices, i.e., a set of UAVs; epsilon 1 Is a collection of edges, i.e., a collection of connected relationships between UAVs.
9. The tracking method of claim 7 or 8, wherein L is specifically L = D-a, wherein: d=diag { D 1 ,d 2 ,…,d N }∈R N×N Is G 1 Is used for the weight input degree matrix of the (a),
for UAVs i The weight input value of (a) and the adjacency matrix a= [ a ] ij ]∈R N ×N ，/>
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