CN102591358B - Multi-UAV (unmanned aerial vehicle) dynamic formation control method - Google Patents

Abstract

The invention discloses a multi-UAV (unmanned aerial vehicle) dynamic formation control method, and belongs to the technical field of flight control. The multi-UAV dynamic formation control method includes steps as follows: step 1, a formation keeping method; step 2, an obstacle avoidance method; and step 3, a behavior-based formation process, wherein the behavior-based formation process includes behavior decomposition and control realization. The method solves the defect that the traditional virtual structure manner formation control has higher communication quality requirement; the behavior-based formation control method is introduced to lower the requirement of formation wireless data link update rate and enhances the obstacle avoidance capability of the UAV group formation; and aiming at the defect that the traditional behavior-based manner formation control cannot keep good formation rigidity, a virtual structure is introduced for reference. On the premise of keeping the relatively stable formation, the capability of obstacle and threat avoidance of a microminiature UAV can be enhanced, and the method has a certain reference value for UAV group cooperation low-altitude penetration.

Description

A kind of dynamic formation control method of multiple no-manned plane

Technical field

The present invention relates to a kind of microminiature unmanned vehicle formation control, belong to technical field of flight control, be specifically related to a kind of dynamic formation control method of multiple no-manned plane.

Background technology

Current had nearly more than 30 countries to drop into research and the production that a large amount of manpower and financial resources is engaged in unmanned plane.Through vicennial development, this technology comparative maturity, play in the army and the people every field and act on, however, single rack unmanned plane also exists some problems when carrying out task, and such as single rack unmanned plane may be subject to the restricted number of sensor, can not observing target area from Multi-angle omnibearing, when facing wide area search task, can not effectively cover whole region of search; If what perform is rescue task, single rack unmanned plane is restricted in load, often affects the usefulness of whole rescue, brings larger loss, in addition, once single rack unmanned plane breaks down, must interrupt task return immediately, may incur loss through delay rescue opportunity.

For the shortcoming of single rack unmanned plane, proposed the concept of formation flight control in recent years and achieved and must achievement in research mainly comprise: configuration design, pneumatic coupling, formation dynamic conditioning, flight path coordinated planning, mobile ad-hoc network and formation flight control method etc.Formation control method generally includes the formation control of Behavior-based control mode, the formation control of " lead aircraft-wing plane " mode and virtual architecture mode formation control.

The formation control of Behavior-based control mode: in multiple no-manned plane close formation flight course, in a group of planes, each frame unmanned plane behavior to its sensor input information is corresponding is divided into following four kinds of situations: collision is avoided, obstacle avoidance, Target Acquisition and formation keep.The maximum feature of the formation control method of Behavior-based control mode is that the average weight controlled by means of behavior response determines any behavior response mode of each this employing of frame unmanned plane in formation, but the formation rigidity of the method is inadequate, is often loose formation.

The formation control of " lead aircraft-wing plane " mode: the feature of this formation strategy is the formation structure based on presetting, and by the course speed to lead aircraft, course angle and height tracing, adjusts wing plane, reaches the object keeping flight pattern.Because this control structure can be subject to very large disturbing effect, therefore for its feature, have employed the multiple technologies such as robust control method, extremum search control method, self-adaptation control method and variable structure control method, the shortcoming of this formation is that formation rigidity is too strong, Threat Avoidance scarce capacity.

Virtual architecture mode formation control: virtual architecture mode generally takes the method for virtual lead aircraft to coordinate other aircrafts, the interference problem of mode that this mode can be avoided " lead aircraft-wing plane ", but synthesize virtual lead aircraft position and transmit its position to each unmanned plane of formation, need with high communication quality and high computing power for cost, the node location of virtual architecture is fixed in addition, and barrier avoiding function is often very poor.

Except above-mentioned three kinds of formation control methods, the formation control method of unmanned plane also comprises the control of some other modes, as MPC Model Predictive Control strategy process, based on the formation control of fuzzy logic and nerual network technique and Robot dodge strategy method, these two kinds of method control structure more complicated, choose in fuzzy logic and neural network weight and need to do comparatively test of many times and could determine, holding time is more, and result does not have universality.

Summary of the invention

The object of the invention is to solve the microminiature unmanned vehicle formation control problem being convenient to through engineering approaches, a kind of dynamic formation control method of multiple no-manned plane is proposed, for the shortcoming that traditional virtual architecture mode formation control is higher to QoS requirement, introduce the formation control method of Behavior-based control, reduce the requirement to formation wireless data chain turnover rate, what enhance unmanned aerial vehicle group formation keeps away barrier ability; Formation control formation rigidity for traditional Behavior-based control mode keeps bad shortcoming, introduce virtual architecture as a reference, by the fusion of two kinds of formation methods, the advantage of respective method can be played: keeping rank under metastable prerequisite, strengthen the ability of Small and micro-satellite avoiding barrier and threat under circumstances not known, working in coordination with low-level penetration for unmanned aerial vehicle group has certain reference.And the dynamic formation control method of a kind of multiple no-manned plane of the present invention's proposition, under being particularly useful for threatening uncertain environment, unmanned plane was formed into columns in the past, and to carry out investigation or search and rescue the environment of task be generally mountain region or Plain, at this moment barrier is generally the natural object (such as mountain peak) that scale ratio is larger, such barrier is easily extracted by numerical map, has often been loaded in the numerical map of flight control computer before execution formation flight task.And for city investigation and search and rescue task, surface state is comparatively complicated, for ensureing that the investigation precision of images requires that formation flight is highly low, the lower unmanned plane of flying height easily and ground artificial barrier (such as housing-group, high-tension line tower and electric pole) collide, and cultural obstacle and natural object have very large difference, cultural obstacle yardstick is less, not easily extracts at numerical map, easily causes the larger risk of formation flight.

A dynamic formation control method for multiple no-manned plane, is characterized in that: comprise following step:

Step one: Keeping Formation;

(1) earth axes XOY is set up;

Set up earth axes XOY, wherein X-axis represents east orientation position, and Y-axis represents north orientation position, ML and MF represents formation leader and wing plane respectively, Ψ _land Ψ _frepresent the flight path drift angle of lead aircraft and wing plane respectively, MV represents the wing plane that virtual architecture sets, and referred to as virtual wing plane, L and a represents the Distance geometry view angle that virtual wing plane is expected lead aircraft, L respectively _land a _lrepresent the Distance geometry view angle of actual wing plane to lead aircraft respectively, the communication network existed postpones for Δ t, MVH and MFH represents virtual wing plane and the position of actual wing plane after Δ t moves respectively, MFH represents that the section distance that lead aircraft MF flies in communication network delay Δ t, MVH represent the section distance that virtual wing plane MV flies in communication network delay Δ t;

(2) each relation formula is set up;

Setting lead aircraft and wing plane displacement in communication cycle are l, set up the position relationship formula of lead aircraft ML and MVH according to the geometric relationship of lead aircraft, wing plane and virtual wing plane:

$\left\{\begin{array}{c}{x}_{\mathrm{MVH}}=x_{\mathrm{ML}}-L\cos ({\mathrm{\ψ}}_L-a)+l\cos {\mathrm{\ψ}}_L\\ y_{\mathrm{MVH}}=y_{\mathrm{ML}}-L\sin ({\mathrm{\ψ}}_L-a)+l\sin {\mathrm{\ψ}}_L\end{array}\right.---\left(1\right)$

Wherein, x _mVH, y _mVH, x _mL, y _mLrepresent the east orientation position of the virtual wing plane considering communication delay, north orientation position, the east orientation position of lead aircraft, north orientation position respectively, L represents the distance that virtual wing plane is expected lead aircraft, Ψ _lrepresent the flight path drift angle of lead aircraft, a represents that the view angle that virtual wing plane is expected lead aircraft, l represent lead aircraft wing plane displacement in communication cycle;

Set up the position relationship formula of wing plane MF and MFH:

$\left\{\begin{array}{c}{x}_{\mathrm{MFH}}=x_{\mathrm{MF}}+l\cos {\mathrm{\ψ}}_F\\ y_{\mathrm{MFH}}=y_{\mathrm{MF}}+l\sin {\mathrm{\ψ}}_F\end{array}\right.---\left(2\right)$

Wherein, x _mFH, y _mFH, x _mF, y _mFrepresent the east orientation position of the actual wing plane considering communication delay, north orientation position, the east orientation position of actual wing plane, north orientation position respectively, Ψ _frepresent the flight path drift angle of wing plane; Formula (2) subtracts the tracking error relation formula that formula (1) can set up MVH and MFH:

$\left\{\begin{array}{c}{e}_x=x_{\mathrm{MFH}}-x_{\mathrm{MVH}}=x_{\mathrm{MF}}+l\cos {\mathrm{\ψ}}_F-x_{\mathrm{ML}}+L\cos ({\mathrm{\ψ}}_L-a)-l\cos {\mathrm{\ψ}}_L\\ e_y=y_{\mathrm{MFH}}-y_{\mathrm{MVH}}=y_{\mathrm{MF}}+l\sin {\mathrm{\ψ}}_F-y_{\mathrm{ML}}+L\sin ({\mathrm{\ψ}}_L-a)-l\sin {\mathrm{\ψ}}_L\end{array}\right.---\left(3\right)$

Wherein, e _x, e _yrepresent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, north orientation position deviation respectively; Differentiate is carried out to the tracking error relation formula (3) of MVH and MFH, obtains:

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_x=V_F\cos {\mathrm{\ψ}}_F-l{\mathrm{\ω}}_F\sin {\mathrm{\ψ}}_F-V_L\cos {\mathrm{\ψ}}_L-L{\mathrm{\ω}}_L\sin ({\mathrm{\ψ}}_L-a)+l{\mathrm{\ω}}_L\sin {\mathrm{\ψ}}_L\\ {\stackrel{\·}{e}}_y=V_F\sin {\mathrm{\ψ}}_F+l{\mathrm{\ω}}_F\cos {\mathrm{\ψ}}_F-V_L\sin {\mathrm{\ψ}}_L+L{\mathrm{\ω}}_L\cos ({\mathrm{\ψ}}_L-a)-l{\mathrm{\ω}}_L\cos {\mathrm{\ψ}}_L\end{array}\right.---\left(4\right)$

Wherein, V _l, V _frepresent the speed of lead aircraft and wing plane respectively, ω _l, ω _fshow the yaw rate of lead aircraft and wing plane respectively, represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of north orientation position deviation, l represents lead aircraft wing plane displacement in communication cycle, and L represents the distance that wing plane is expected virtual lead aircraft, Ψ _lrepresent the flight path drift angle of lead aircraft, a represents the view angle that virtual lead aircraft is expected, Ψ _fthe flight path drift angle of wing plane;

By the e of earth axes _x, e _yproject to the velocity coordinate system of wing plane:

$\left\{\begin{array}{c}{\stackrel{\‾}{e}}_x=e_x\cos {\mathrm{\ψ}}_F+e_y\sin {\mathrm{\ψ}}_F\\ {\stackrel{\‾}{e}}_y=-e_x\sin {\mathrm{\ψ}}_F+e_y\cos {\mathrm{\ψ}}_F\end{array}\right.---\left(5\right)$

Wherein, e _x, e _yrepresent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, north orientation position deviation respectively, represent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, the projection of north orientation position deviation under wing plane velocity coordinate system respectively;

Differentiate is carried out to the formula (5) after coordinate transforming, obtains:

$\left\{\begin{array}{c}{\stackrel{\·}{\stackrel{\‾}{e}}}_x={\stackrel{\·}{e}}_x\cos {\mathrm{\ψ}}_F-e_x\sin {\mathrm{\ψ}}_F-{\stackrel{\·}{e}}_y\sin {\mathrm{\ψ}}_F-e_y\cos {\mathrm{\ψ}}_F\\ {\stackrel{\·}{\stackrel{\‾}{e}}}_y={\stackrel{\·}{e}}_x\sin {\mathrm{\ψ}}_F+e_x\cos {\mathrm{\ψ}}_F+{\stackrel{\·}{e}}_y\cos {\mathrm{\ψ}}_F-e_y\sin {\mathrm{\ψ}}_F\end{array}\right.---\left(6\right)$

Wherein represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of north orientation position deviation, represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of the projection of north orientation position deviation under wing plane velocity coordinate system;

Simultaneous formula (3), formula (4) and formula (6) obtain:

$\left\{\begin{array}{c}{\stackrel{\·}{\stackrel{\‾}{e}}}_x=V_F-V_L\cos ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)-L{\mathrm{\ω}}_L\sin ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F-a)+l{\mathrm{\ω}}_L\sin ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)+{\mathrm{\ω}}_F{\stackrel{\‾}{e}}_y\\ {\stackrel{\·}{\stackrel{\‾}{e}}}_y=l{\mathrm{\ω}}_F-V_L\sin ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)+L{\mathrm{\ω}}_L\cos ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F-a)-l{\mathrm{\ω}}_L\cos ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)-{\mathrm{\ω}}_F{\stackrel{\‾}{e}}_x\end{array}\right.---\left(7\right)$

When the yaw rate of wing plane and speed command are shown in formula (8), formula (7) can abbreviation be formula (9):

$\begin{array}{c}{V}_F=V_L\cos ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)+L{\mathrm{\ω}}_L\sin ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F-a)-l{\mathrm{\ω}}_L\sin ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)-k_1{\stackrel{\‾}{e}}_x\\ {\mathrm{\ω}}_F=(V_L\sin ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)-L{\mathrm{\ω}}_L\cos ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F-a)+l{\mathrm{\ω}}_L\cos ({\mathrm{\ψ}}_L-{\mathrm{\ψ}}_F)-k_2{\stackrel{\‾}{e}}_y)/l\end{array}---\left(8\right)$

Wherein, k ₁, k ₂represent control law coefficient to be adjusted in actual formation process;

$\left\{\begin{array}{c}{\stackrel{\·}{\stackrel{\‾}{e}}}_x=-k_1{\stackrel{\‾}{e}}_x+{\mathrm{\ω}}_F{\stackrel{\‾}{e}}_y\\ {\stackrel{\·}{\stackrel{\‾}{e}}}_y=-k_2{\stackrel{\‾}{e}}_y-{\mathrm{\ω}}_F{\stackrel{\‾}{e}}_x\end{array}\right.---\left(9\right)$

Consider Lyapunov function:

$\left\{\begin{array}{c}V={\stackrel{\‾}{e}}_x^2+{\stackrel{\‾}{e}}_y^2\\ \stackrel{\·}{V}=2{\stackrel{\‾}{e}}_x{\stackrel{\·}{\stackrel{\‾}{e}}}_x+2{\stackrel{\‾}{e}}_y{\stackrel{\·}{\stackrel{\‾}{e}}}_y\end{array}\right.---\left(10\right)$

Formula (9) substitutes into formula (10) and can obtain

$\stackrel{\&CenterDot;}{V}=2{\stackrel{\&OverBar;}{e}}_x{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_x+2{\stackrel{\&OverBar;}{e}}_y{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_y=-2(k_1{\stackrel{\&OverBar;}{e}}_x^2+k_1{\stackrel{\&OverBar;}{e}}_y^2)<0---\left(11\right)$

By Liapunov law, for given deviation adopt speed and the angular velocity instruction of formula (8), flight pattern deviation converges to 0, makes error expression converge to 0;

Final formation overload instruction with formation speed command for:

$\left\{\begin{array}{c}{n}_1^{*}={\mathrm{\&omega;}}_F{V}_F\\ V_1^{*}=V_F\end{array}\right.---\left(12\right)$

Step 2: barrier-avoiding method;

Ground obstacle is obeyed in space and is uniformly distributed, M is unmanned plane current location, V is unmanned plane velocity, r is the threat range of barrier, R is the distance of unmanned plane distance barrier, and threaten district for ensureing that unmanned plane does not enter, unmanned plane also can fly along right side flight path MB along left side flight path MA flight, if the threat source nearest apart from unmanned plane is center of circle O, desirable Threat Avoidance flight path is two circumscribed with circle O and tangent with velocity V circle O _l, O _rcircular arc MA and MB, definition point of contact A, B is Threat Avoidance navigation spots;

The method of radius of turn application solving a triangle is asked for, at Δ OO _lapply the cosine law in M to obtain:

$\cos (\&angle;{\mathrm{OMO}}_l)=\sin \left(b\right)=\frac{R^2+R_l^2-{(R_l+r)}^2}{2R{R}_l}---\left(13\right)$

Draw the radius of turn of unmanned plane Threat Avoidance:

$R_l=\frac{R^2-r^2}{2(r+R\sin b)}---\left(14\right)$

$R_r=\frac{R^2-r^2}{2(r-R\sin b)}---\left(15\right)$

The expression formula of corresponding side acceleration is:

$a_r=\frac{V^2}{R_r},$ $a_l=\frac{V^2}{R_l}---\left(16\right)$

Wherein a _r, a _lrepresent that unmanned plane carries out the side acceleration of keeping away required for barrier along circular arc MB, MA respectively;

Final keeps away the instruction of barrier overload

$n_2^{*}=\begin{array}{ccc}{a}_r& \mathrm{or}& a_l\end{array}---\left(17\right)$

Finally keep away barrier speed command to select and lead aircraft speed aligned instruction

$V_2^{*}=V_L---\left(18\right)$

Wherein V _lrepresent the speed of lead aircraft;

Step 3: the formation process of Behavior-based control;

(1) behavior decomposition process: being three sub-line parallel to each other by task behavior decomposition is: abnormal conditions process, Keeping Formation and Threat Avoidance method, be simultaneously each sub-line for giving corresponding importance, represent with weights; In Keeping Formation, unmanned plane obtains the information of lead aircraft by cordless communication network, specifically comprises lead aircraft speed V _l, yaw rate ω _lwith flight path drift angle Ψ _l; Unmanned plane obtains navigation information by self the machine navigator, specifically comprises speed V _f, angular velocity omega _fwith drift angle Ψ _f, generate according to step one formula (8) and formula (12) overload instruction of forming into columns with formation speed command the information that in barrier-avoiding method, unmanned plane obtains barrier by optical sensor comprises: the distance R of unmanned plane distance barrier, the angle of velocity and unmanned plane and barrier line is b, generates keep away the instruction of barrier overload according to step 2 formula (17) and formula (18) with keep away barrier speed command abnormal conditions process refers to that aircraft is when performing aerial mission, run into the reason that interrupted communication link etc. cannot maintain formation, UAV flight control enters abnormality processing state, abnormality processing to ensure unmanned plane according to the strategy execution task of unit optimum or fly away from region of search arrive assigned address prepare landing, abnormality processing is the highest at medium priority of executing the task, and the overload instruction that unmanned plane needs according to the strategy execution task of unit optimum and speed command are respectively

(2) control realization process refers to that unmanned plane is according to motion model and current motion state, the steering order of weighted calculation unmanned plane reality, and then input topworks: the jaw channel of unmanned plane produces yaw rudder partially, thus realizes the motion control to unmanned vehicle formation;

According to the Keeping Formation in step one and step 2 and barrier-avoiding method, be weighted according to formula (17) after the overload instruction that each sub-line is and speed command obtain:

$n^{*}=w_{n0}{n}_0^{*}+w_{n1}{n}_1^{*}+w_{n2}{n}_2^{*}$

$V^{*}=w_{V0}{V}_0^{*}+w_{V1}{V}_1^{*}+w_{V2}{V}_2^{*}---\left(17\right)$

Wherein w _n0+ w _n1+ w _n2=1.0, w _v0+ w _v1+ w _v2=1.0

Wherein, w _n0overload instruction weights, w during expression abnormality processing _v0represent abnormality processing hourly velocity instruction weights, w _n1overload instruction weights, w when representing that formation keeps _v1represent that formation keeps hourly velocity instruction weights, w _n2represent overload instruction weights, w when keeping away barrier _v2represent and keep away barrier hourly velocity instruction weights;

1) condition of abnormality processing is met: w _n0=w _v0=1.0, w _n1=w _v1=w _n2=w _v2=0.0, at this moment formation keep and barrier-avoiding method no longer valid, the mode that unmanned plane takes unit fly is executed the task, or edge appointment navigation spots enter landing phases;

2), when not meeting abnormality processing condition, according to optical sensor, whether Keeping Formation and barrier-avoiding method effectively, find that barrier carries out weight computing:

Wherein, w _n2, w _v2value depend on the ratio of ground obstacle yardstick and barrier threat range, w _n1=1.0-w _n2, w _v1=1.0-w _v2.

The invention has the advantages that:

(1) for the shortcoming that traditional virtual architecture mode formation control is higher to QoS requirement, introduce the formation control method of Behavior-based control, reduce the requirement to formation wireless data chain turnover rate, what enhance unmanned aerial vehicle group formation keeps away barrier ability;

(2) the formation control formation rigidity for traditional Behavior-based control mode keeps bad shortcoming, introduce virtual architecture as a reference, by the fusion of two kinds of formation methods, the advantage of respective method can be played: keeping rank under metastable prerequisite, strengthen the ability of Small and micro-satellite avoiding barrier and threat under circumstances not known, working in coordination with low-level penetration for unmanned aerial vehicle group has certain reference;

(3) for the formation strategy that actual Small and micro-satellite proposes, the mathematical model of employing is also actual Small and micro-satellite dynamics and kinematics model, not only algorithm is verified to also have very strong engineering significance.

(4) in order to verify formation method and Threat Avoidance strategy, develop the software of actual emulation group behavior, this software has the advantage of user friendly, convenient operation and demonstration, and the exploitation for formation simulation software has certain reference with production domesticization.

Accompanying drawing explanation

Fig. 1: lead aircraft, wing plane and virtual wing plane location diagram in earth axes in the present invention;

Fig. 2: do not adopt Keeping Formation unmanned aerial vehicle group initial position and distribution of obstacles vertical view in the present invention;

Fig. 3: access Keeping Formation unmanned aerial vehicle group formation control result figure in the present invention;

Fig. 4: unmanned plane and ground obstacle location diagram in the present invention;

Fig. 5: access in the present invention barrier-avoiding method impend avoid result figure;

Fig. 6: the schematic flow sheet of the formation process of Behavior-based control in the present invention;

Fig. 7: the result figure again formed into columns after Threat Avoidance in the present invention;

Fig. 8: the schematic diagram realizing the demoware that above-mentioned simulation result utilizes in the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The dynamic formation control method of a kind of multiple no-manned plane that the present invention proposes, comprises following step:

Step one: Keeping Formation;

(1) earth axes XOY is set up;

Set up earth axes XOY, as shown in Figure 1, wherein X-axis represents east orientation position, and Y-axis represents north orientation position.ML and MF represents formation leader and wing plane respectively, Ψ _land Ψ _frepresent the flight path drift angle of lead aircraft and wing plane respectively, MV represents the wing plane of virtual architecture setting, and referred to as virtual wing plane, L and a represents the Distance geometry view angle that virtual wing plane is expected lead aircraft respectively, L _land a _lrepresent the Distance geometry view angle of actual wing plane to lead aircraft respectively, the communication network existed postpones for Δ t, MVH and MFH represents virtual wing plane and the position of actual wing plane after Δ t moves respectively, so unmanned plane formation problem is equal to the tracking problem of MFH to MVH, also namely consider that the actual wing plane after network delay is to the tracking problem of virtual wing plane, wherein MFH represents that the section distance that lead aircraft MF flies in communication network delay Δ t, MVH represent the section distance that virtual wing plane MV flies in communication network delay Δ t.Require use unmanned plane longitudinally can be in stable height-lock control state, unmanned plane adopts yaw rudder to carry out side-slipping turn, so mainpiston area and flying speed are in flight course change not quite, the aircraft altitude loss caused that is coupled well can compensate with elevating rudder.

(2) each relation formula is set up;

High state is determined because the lead aircraft wing plane of forming into columns longitudinally all is in, the turning mode adopted is side-slipping turn, therefore lead aircraft wing plane velocity deviation is little, when general deviation is no more than 10m, so setting lead aircraft and wing plane displacement in communication cycle are l, set up the position relationship formula of lead aircraft ML and MVH according to the geometric relationship of lead aircraft, wing plane and virtual wing plane in Fig. 1:

$\left\{\begin{array}{c}{x}_{\mathrm{MVH}}=x_{\mathrm{ML}}-L\cos ({\mathrm{\&psi;}}_L-a)+l\cos {\mathrm{\&psi;}}_L\\ y_{\mathrm{MVH}}=y_{\mathrm{ML}}-L\sin ({\mathrm{\&psi;}}_L-a)+l\sin {\mathrm{\&psi;}}_L\end{array}\right.---\left(1\right)$

Wherein, x _mVH, y _mVH, x _mL, y _mLrepresent the east orientation position of the virtual wing plane considering communication delay, north orientation position, the east orientation position of lead aircraft, north orientation position respectively.L represents the distance that virtual wing plane is expected lead aircraft, Ψ _lrepresent the flight path drift angle of lead aircraft, a represents that the view angle that virtual wing plane is expected lead aircraft, l represent lead aircraft wing plane displacement in communication cycle.

The position relationship formula of wing plane MF and MFH is set up according to the geometric relationship of lead aircraft, wing plane and virtual wing plane in Fig. 1:

$\left\{\begin{array}{c}{x}_{\mathrm{MFH}}=x_{\mathrm{MF}}+l\cos {\mathrm{\&psi;}}_F\\ y_{\mathrm{MFH}}=y_{\mathrm{MF}}+l\sin {\mathrm{\&psi;}}_F\end{array}\right.---\left(2\right)$

Wherein, x _mFH, y _mFH, x _mF, y _mFrepresent the east orientation position of the actual wing plane considering communication delay, north orientation position, the east orientation position of actual wing plane, north orientation position respectively, Ψ _frepresent the flight path drift angle of wing plane.Formula (2) subtracts the tracking error relation formula that formula (1) can set up MVH and MFH:

$\left\{\begin{array}{c}{e}_x=x_{\mathrm{MFH}}-x_{\mathrm{MVH}}=x_{\mathrm{MF}}+l\cos {\mathrm{\&psi;}}_F-x_{\mathrm{ML}}+L\cos ({\mathrm{\&psi;}}_L-a)-l\cos {\mathrm{\&psi;}}_L\\ e_y=y_{\mathrm{MFH}}-y_{\mathrm{MVH}}=y_{\mathrm{MF}}+l\sin {\mathrm{\&psi;}}_F-y_{\mathrm{ML}}+L\sin ({\mathrm{\&psi;}}_L-a)-l\sin {\mathrm{\&psi;}}_L\end{array}\right.---\left(3\right)$

Wherein, e _x, e _yrepresent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, north orientation position deviation respectively.

Differentiate is carried out to the tracking error relation formula (3) of MVH and MFH, obtains:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{e}}_x=V_F\cos {\mathrm{\&psi;}}_F-l{\mathrm{\&omega;}}_F\sin {\mathrm{\&psi;}}_F-V_L\cos {\mathrm{\&psi;}}_L-L{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-a)+l{\mathrm{\&omega;}}_L\sin {\mathrm{\&psi;}}_L\\ {\stackrel{\&CenterDot;}{e}}_y=V_F\sin {\mathrm{\&psi;}}_F+l{\mathrm{\&omega;}}_F\cos {\mathrm{\&psi;}}_F-V_L\sin {\mathrm{\&psi;}}_L+L{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-a)-l{\mathrm{\&omega;}}_L\cos {\mathrm{\&psi;}}_L\end{array}\right.---\left(4\right)$

Wherein, V _l, V _frepresent the speed of lead aircraft and wing plane respectively, ω _l, ω _fshow the yaw rate of lead aircraft and wing plane respectively, represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of north orientation position deviation.L represents lead aircraft wing plane displacement in communication cycle, and L represents the distance that wing plane is expected virtual lead aircraft, Ψ _lrepresent the flight path drift angle of lead aircraft, a represents the view angle that virtual lead aircraft is expected, Ψ _fthe flight path drift angle of wing plane.

By the e of earth axes _x, e _yproject to the velocity coordinate system of wing plane, the velocity reversal that this coordinate system is defined as wing plane is X-axis, and clockwise select vertical with X turn 90 degrees as Y-axis.

$\left\{\begin{array}{c}{\stackrel{\&OverBar;}{e}}_x=e_x\cos {\mathrm{\&psi;}}_F+e_y\sin {\mathrm{\&psi;}}_F\\ {\stackrel{\&OverBar;}{e}}_y=-e_x\sin {\mathrm{\&psi;}}_F+e_y\cos {\mathrm{\&psi;}}_F\end{array}\right.---\left(5\right)$

Wherein, e _x, e _yrepresent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, north orientation position deviation respectively, represent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, the projection of north orientation position deviation under wing plane velocity coordinate system respectively.

Differentiate is carried out to the formula (5) after coordinate transforming, obtains:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_x={\stackrel{\&CenterDot;}{e}}_x\cos {\mathrm{\&psi;}}_F-e_x\sin {\mathrm{\&psi;}}_F-{\stackrel{\&CenterDot;}{e}}_y\sin {\mathrm{\&psi;}}_F-e_y\cos {\mathrm{\&psi;}}_F\\ {\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_y={\stackrel{\&CenterDot;}{e}}_x\sin {\mathrm{\&psi;}}_F+e_x\cos {\mathrm{\&psi;}}_F+{\stackrel{\&CenterDot;}{e}}_y\cos {\mathrm{\&psi;}}_F-e_y\sin {\mathrm{\&psi;}}_F\end{array}\right.---\left(6\right)$

Wherein represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of north orientation position deviation, represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of the projection of north orientation position deviation under wing plane velocity coordinate system.

Simultaneous formula (3), formula (4) and formula (6), obtain:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_x=V_F-V_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-L{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)+l{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)+{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_y\\ {\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_y=l{\mathrm{\&omega;}}_F-V_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)+L{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)-l{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_x\end{array}\right.---\left(7\right)$

As can be seen from formula (7), when the yaw rate of wing plane and speed command are shown in formula (8), formula (7) can abbreviation be formula (9)

$\begin{array}{c}{V}_F=V_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)+L{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)-l{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-k_1{\stackrel{\&OverBar;}{e}}_x\\ {\mathrm{\&omega;}}_F=(V_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-L{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)+l{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-k_2{\stackrel{\&OverBar;}{e}}_y)/l\end{array}---\left(8\right)$

Wherein, k ₁, k ₂represent control law coefficient to be adjusted in actual formation process, value magnitude and ω in actual formation _fapproximate positive number.

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_x=-k_1{\stackrel{\&OverBar;}{e}}_x+{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_y\\ {\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_y=-k_2{\stackrel{\&OverBar;}{e}}_y-{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_x\end{array}\right.---\left(9\right)$

Consider Lyapunov function:

$\left\{\begin{array}{c}V={\stackrel{\&OverBar;}{e}}_x^2+{\stackrel{\&OverBar;}{e}}_y^2\\ \stackrel{\&CenterDot;}{V}=2{\stackrel{\&OverBar;}{e}}_x{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_x+2{\stackrel{\&OverBar;}{e}}_y{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_y\end{array}\right.---\left(10\right)$

Formula (9) substitutes into formula (10) and can obtain

$\stackrel{\&CenterDot;}{V}=2{\stackrel{\&OverBar;}{e}}_x{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_x+2{\stackrel{\&OverBar;}{e}}_y{\stackrel{\&CenterDot;}{\stackrel{\&OverBar;}{e}}}_y=-2(k_1{\stackrel{\&OverBar;}{e}}_x^2+k_1{\stackrel{\&OverBar;}{e}}_y^2)<0---\left(11\right)$

By Liapunov law, for given deviation adopt speed and the angular velocity instruction of formula (8), flight pattern deviation can converge to 0.Make error expression converge to 0.

Final formation overload instruction with formation speed command

$\left\{\begin{array}{c}{n}_1^{*}={\mathrm{\&omega;}}_F{V}_F\\ V_1^{*}=V_F\end{array}\right.---\left(12\right)$

In application the present invention, Keeping Formation is formed into columns, do not adopt Keeping Formation unmanned aerial vehicle group initial position and distribution of obstacles vertical view as shown in Figure 2, formation result vertical view as shown in Figure 3, wherein 0,1,2,3,4 represent unmanned plane, No. 0 represents lead aircraft, No. 1-4 represents actual unmanned plane, the ellipse circle representative of solid line has certain region threatened, dotted ellipse circle represents unmanned plane investigative range, as can be seen from the figure, apply the Keeping Formation that step one of the present invention proposes, the formation task of Small and micro-satellite can be completed.

Step 2: barrier-avoiding method;

Unmanned plane is in the process of formation flight, often there is ground barrier, ground high-tension bus-bar such as during earth observation search and housing-group, if these barriers were known before executing the task, and in UAV Formation Flight process barrier do not move or the change in location of movement little, off-line routeing so can be leaned on before executing the task to avoid the known barrier in ground.In fact the barrier investigating region is generally unknown, so require that unmanned plane formation has certain avoidance ability for unknown or emergent barrier.

If ground obstacle is obeyed in space and is uniformly distributed, as shown in Figure 4, M is unmanned plane current location, and V is unmanned plane velocity, and r is the threat range of barrier, and R is the distance of unmanned plane distance barrier.Threaten district for ensureing that unmanned plane does not enter, unmanned plane also can fly along right side flight path MB along left side flight path MA flight, if the threat source nearest apart from unmanned plane is center of circle O, desirable Threat Avoidance flight path is two circumscribed with circle O and tangent with velocity V circle O _l, O _rcircular arc MA and MB, definition point of contact A, B is Threat Avoidance navigation spots.

The method of radius of turn application solving a triangle is asked for, at Δ OO _lapply the cosine law in M to obtain:

$\cos (\&angle;{\mathrm{OMO}}_l)=\sin \left(b\right)=\frac{R^2+R_l^2-{(R_l+r)}^2}{2R{R}_l}---\left(13\right)$

Draw the radius of turn of unmanned plane Threat Avoidance further:

$R_l=\frac{R^2-r^2}{2(r+R\sin b)}---\left(14\right)$

$R_r=\frac{R^2-r^2}{2(r-R\sin b)}---\left(15\right)$

The expression formula of corresponding side acceleration is:

$a_r=\frac{V^2}{R_r},a_l=\frac{V^2}{R_l}---\left(16\right)$

Wherein a _r, a _lrepresent that unmanned plane carries out the side acceleration of keeping away required for barrier along circular arc MB, MA respectively.

Final keeps away the instruction of barrier overload

$n_2^{*}=\begin{array}{ccc}{a}_r& \mathrm{or}& a_l\end{array}---\left(17\right)$

Under the prerequisite that barrier region is not very large, finally keep away barrier speed command and select and lead aircraft speed aligned instruction

$V_2^{*}=V_L---\left(18\right)$

Wherein V _lrepresent the speed of lead aircraft.

As shown in Figure 5, wherein the long curve of solid line represents unmanned plane during flying track to the result adopting the barrier-avoiding method in step 2 to impend to avoid, and the ellipse circle representative of solid line has certain region threatened, and dotted ellipse circle represents unmanned plane investigative range.1-4 unmanned plane can adopt the barrier-avoiding method in step 2 to impend avoidance plan, avoid the ground based threats that may exist, because the weights of forming into columns are not exclusively zero, so when avoiding threat, basic formation position also can maintain further, for the formation again after Threat Avoidance is ready.

Step 3: the formation process of Behavior-based control;

Step one and step 2 give formation method and the barrier-avoiding method of Small and micro-satellite, actual formation flight process is exactly the superposition of above-mentioned two situations, often require that aircraft carries out formation flight to obtain large area earth observation, often require that aircraft has the function temporarily hiding threat when aircraft runs into the not specified barrier of routeing in early stage, adopt the formation process of Behavior-based control, the process of step one and step 2 is combined, specifically be divided into two steps, as shown in Figure 6, behavior decomposition and control realization is respectively.

(1) in behavior decomposable process, unmanned plane is according to current environmental information and task character, being three sub-line parallel to each other by task behavior decomposition is: abnormal conditions process, Keeping Formation and Threat Avoidance method, being each sub-line for giving corresponding importance simultaneously, representing with weights.Keeping Formation refer step one, unmanned plane obtains the information of lead aircraft by cordless communication network, specifically comprises lead aircraft speed V _l, yaw rate ω _lwith flight path drift angle Ψ _l; Unmanned plane obtains navigation information by self the machine navigator, specifically comprises speed V _f, angular velocity omega _fwith drift angle Ψ _f, generate according to step one formula (8) and formula (12) overload instruction of forming into columns with formation speed command barrier-avoiding method refer step two, the information that unmanned plane obtains barrier by optical sensor comprises: the distance R of unmanned plane distance barrier, the angle of velocity and unmanned plane and barrier line is b, generates keep away the instruction of barrier overload according to step 2 formula (17) and formula (18) with keep away barrier speed command abnormal conditions process refers to that aircraft is when performing aerial mission, run into the reason that interrupted communication link etc. cannot maintain formation, UAV flight control enters abnormality processing state, abnormality processing to ensure unmanned plane according to the strategy execution task of unit optimum or fly away from region of search arrive assigned address prepare landing, abnormality processing is the highest at medium priority of executing the task, and the overload instruction that unmanned plane needs according to the strategy execution task of unit optimum and speed command are respectively such as linearly fly.

(2) control realization process refers to that unmanned plane is according to motion model and current motion state, the steering order of weighted calculation unmanned plane reality, and then input topworks, the jaw channel of unmanned plane produces yaw rudder partially, thus realizes the motion control to unmanned vehicle formation.

According to the Keeping Formation in step one and step 2 and barrier-avoiding method, the overload instruction that each sub-line is and speed command can be weighted after obtaining according to the following formula:

$n^{*}=w_{n0}{n}_0^{*}+w_{n1}{n}_1^{*}+w_{n2}{n}_2^{*}$

$V^{*}=w_{V0}{V}_0^{*}+w_{V1}{V}_1^{*}+w_{V2}{V}_2^{*}---\left(19\right)$

Wherein w _n0+ w _n1+ w _n2=1.0, w _v0+ w _v1+ w _v2=1.0

Wherein, w _n0overload instruction weights, w during expression abnormality processing _v0represent abnormality processing hourly velocity instruction weights, w _n1overload instruction weights, w when representing that formation keeps _v1represent that formation keeps hourly velocity instruction weights, w _n2represent overload instruction weights, w when keeping away barrier _v2represent and keep away barrier hourly velocity instruction weights.

1) condition of abnormality processing is met: w _n0=w _v0=1.0, w _n1=w _v1=w _n2=w _v2=0.0, at this moment formation keep and barrier-avoiding method no longer valid, the mode that unmanned plane takes unit fly is executed the task, or edge appointment navigation spots enter landing phases;

2), when not meeting abnormality processing condition, according to optical sensor, whether Keeping Formation and barrier-avoiding method effectively, find that barrier carries out weight computing:

Wherein, w _n1w _v1w _n2w _v2suitably can adjust according to actual conditions, w _n2, w _v2value depend primarily on the ratio of ground obstacle yardstick and barrier threat range, ratio large explanation barrier scale ratio is comparatively large, at this moment w _n2, w _v2value will strengthen, and prevents from colliding with barrier, otherwise w _n2, w _v2value reduces, w _n1=1.0-w _n2, w _v1=1.0-w _v2increase, strengthen the formation ability of unmanned plane.W _n2preferred value is w _n2=0.3, w _n1=0.7.Generation instruction n of the present invention ^*for overload instruction, therefore there is certain reference for the unmanned plane of the sensor that cannot install and measure flow angle.

As shown in Figure 7, when unmanned plane detection is less than threat, again flight pattern is recovered, carry out formation flight, wherein the long curve of solid line represents unmanned plane during flying track, and the ellipse circle representative of solid line has certain region threatened, and dotted ellipse circle represents unmanned plane investigative range.1-4 unmanned plane can adopt the formation method of the Behavior-based control in step 3 to carry out formation maintenance and Threat Avoidance, in the rigidity avoiding keeping rank under the prerequisite of the ground based threats that may exist.The schematic diagram of demoware of Fig. 8 for realizing above-mentioned simulation result and utilizing, domestic current existing group formation simulation software is often not easy to demonstration, and this software has the advantage of user friendly, convenient operation and demonstration, its software architecture has certain reference for the exploitation of formation simulation software with production domesticization.

Claims (1)

1. a dynamic formation control method for multiple no-manned plane, is characterized in that: comprise following step:

Step one: Keeping Formation;

(1) earth axes XOY is set up;

Set up earth axes XOY, wherein X-axis represents east orientation position, and Y-axis represents north orientation position, ML and MF represents formation leader and actual wing plane respectively, ψ _land ψ _frepresent the flight path drift angle of lead aircraft and actual wing plane respectively, MV represents the wing plane that virtual architecture sets, and referred to as virtual wing plane, L and a represents the Distance geometry view angle that virtual wing plane is expected lead aircraft, L respectively _land a _lrepresent the Distance geometry view angle of actual wing plane to lead aircraft respectively, the communication network existed postpones for Δ t, MFH represents that the section distance that actual wing plane MF flies in communication network delay Δ t, MVH represent the section distance that virtual wing plane MV flies in communication network delay Δ t;

(2) each relation formula is set up;

Setting lead aircraft and virtual wing plane displacement in communication cycle are l, set up the position relationship formula of lead aircraft ML and MVH according to the geometric relationship of lead aircraft, actual wing plane and virtual wing plane:

$\left\{\begin{array}{c}{x}_{\mathrm{MVH}}=x_{\mathrm{ML}}-L\cos ({\mathrm{\&psi;}}_L-a)+l\cos {\mathrm{\&psi;}}_L\\ y_{\mathrm{MVH}}=y_{\mathrm{ML}}-L\sin ({\mathrm{\&psi;}}_L-a)+l\sin {\mathrm{\&psi;}}_L\end{array}\right.---\left(1\right)$

Wherein, x _mVH, y _mVH, x _mL, y _mLrepresent the east orientation position of the virtual wing plane considering communication delay, north orientation position, the east orientation position of lead aircraft, north orientation position respectively; Set up the position relationship formula of actual wing plane MF and MFH:

$\left\{\begin{array}{c}{x}_{\mathrm{MFH}}=x_{\mathrm{MF}}+l\cos {\mathrm{\&psi;}}_F\\ y_{\mathrm{MFH}}=y_{\mathrm{MF}}+l\sin {\mathrm{\&psi;}}_F\end{array}\right.---\left(2\right)$

Wherein, x _mFH, y _mFH, x _mF, y _mFrepresent the east orientation position of the actual wing plane considering communication delay, north orientation position, the east orientation position of actual wing plane, north orientation position respectively; Formula (2) subtracts the tracking error relation formula that formula (1) can set up MVH and MFH:

$\left\{\begin{array}{c}{e}_x=x_{\mathrm{MFH}}-x_{\mathrm{MVH}}=x_{\mathrm{MF}}+l\cos {\mathrm{\&psi;}}_F-x_{\mathrm{ML}}+L\cos ({\mathrm{\&psi;}}_L-a)-l\cos {\mathrm{\&psi;}}_L\\ e_y=y_{\mathrm{MFH}}-y_{\mathrm{MVH}}=y_{\mathrm{MF}}+l\sin {\mathrm{\&psi;}}_F-y_{\mathrm{ML}}+L\sin ({\mathrm{\&psi;}}_L-a)-l\sin {\mathrm{\&psi;}}_L\end{array}\right.---\left(3\right)$

Wherein, e _x, e _yrepresent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, north orientation position deviation respectively;

Differentiate is carried out to the tracking error relation formula (3) of MVH and MFH, obtains:

$\left\{\begin{array}{c}{\stackrel{.}{e}}_x=V_F\cos {\mathrm{\&psi;}}_F-l{\mathrm{\&omega;}}_F\sin {\mathrm{\&psi;}}_F-V_L\cos {\mathrm{\&psi;}}_L-L{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-a)+l{\mathrm{\&omega;}}_L\sin {\mathrm{\&psi;}}_L\\ {\stackrel{.}{e}}_y=V_F\sin {\mathrm{\&psi;}}_F+l{\mathrm{\&omega;}}_F\cos {\mathrm{\&psi;}}_F-V_L\sin {\mathrm{\&psi;}}_L+L{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-a)-l{\mathrm{\&omega;}}_L\cos {\mathrm{\&psi;}}_L\end{array}\right.---\left(4\right)$

Wherein, V _l, V _frepresent the speed of lead aircraft and actual wing plane respectively, ω _l, ω _fshow the yaw rate of lead aircraft and actual wing plane respectively, represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of north orientation position deviation;

By the e of earth axes _x, e _yproject to the velocity coordinate system of actual wing plane:

$\left\{\begin{array}{c}{\stackrel{\&OverBar;}{e}}_x=e_x\cos {\mathrm{\&psi;}}_F+e_y\sin {\mathrm{\&psi;}}_F\\ {\stackrel{\&OverBar;}{e}}_y=-e_x\sin {\mathrm{\&psi;}}_F+e_y\cos {\mathrm{\&psi;}}_F\end{array}\right.---\left(5\right)$

Wherein, represent the east orientation position of virtual wing plane and the actual wing plane considering communication delay, the projection of north orientation position deviation under wing plane velocity coordinate system respectively;

Differentiate is carried out to the formula (5) after coordinate transforming, obtains:

$\left\{\begin{array}{c}{\stackrel{.}{\stackrel{\&OverBar;}{e}}}_x={\stackrel{.}{e}}_x\cos {\mathrm{\&psi;}}_F-e_x\sin {\mathrm{\&psi;}}_F-{\stackrel{.}{e}}_y\sin {\mathrm{\&psi;}}_F-e_y\cos {\mathrm{\&psi;}}_F\\ {\stackrel{.}{\stackrel{\&OverBar;}{e}}}_y={\stackrel{.}{e}}_x\sin {\mathrm{\&psi;}}_F+e_x\cos {\mathrm{\&psi;}}_F+{\stackrel{.}{e}}_y\cos {\mathrm{\&psi;}}_F-e_y\sin {\mathrm{\&psi;}}_F\end{array}\right.---\left(6\right)$

Wherein, represent respectively and consider the virtual wing plane of communication delay and the east orientation position of actual wing plane, the derivative of the projection of north orientation position deviation under wing plane velocity coordinate system;

Simultaneous formula (3), formula (4) and formula (6) obtain:

$\left\{\begin{array}{c}{\stackrel{.}{\stackrel{\&OverBar;}{e}}}_x=V_F-V_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-L{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)+l{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)+{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_y\\ {\stackrel{.}{\stackrel{\&OverBar;}{e}}}_y=l{\mathrm{\&omega;}}_F-V_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)+L{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)-l{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_x\end{array}\right.---\left(7\right)$

When the yaw rate of actual wing plane and speed command are shown in formula (8), formula (7) can abbreviation be formula (9):

$\begin{array}{c}{V}_F=V_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)+L{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)-l{\mathrm{\&omega;}}_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-k_1{\stackrel{\&OverBar;}{e}}_x\\ {\mathrm{\&omega;}}_F=(V_L\sin ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-L{\mathrm{\&omega;}}_L\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F-a)+l{\mathrm{\&omega;}}_L-\cos ({\mathrm{\&psi;}}_L-{\mathrm{\&psi;}}_F)-k_2{\stackrel{\&OverBar;}{e}}_y)/l\end{array}---\left(8\right)$

Wherein, k ₁, k ₂represent control law coefficient to be adjusted in actual formation process;

$\left\{\begin{array}{c}{\stackrel{.}{\stackrel{\&OverBar;}{e}}}_x=-k_1{\stackrel{\&OverBar;}{e}}_x+{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_y\\ {\stackrel{.}{\stackrel{\&OverBar;}{e}}}_y=-k_2{\stackrel{\&OverBar;}{e}}_y-{\mathrm{\&omega;}}_F{\stackrel{\&OverBar;}{e}}_x\end{array}\right.---\left(9\right)$

Consider Lyapunov function:

$\left\{\begin{array}{c}{V}^{\&prime;}={\stackrel{\&OverBar;}{e}}_x^2+{\stackrel{\&OverBar;}{e}}_y^2\\ {\stackrel{.}{V}}^{\&prime;}=2{\stackrel{\&OverBar;}{e}}_x{\stackrel{.}{\stackrel{\&OverBar;}{e}}}_x+2{\stackrel{\&OverBar;}{e}}_y{\stackrel{.}{\stackrel{\&OverBar;}{e}}}_y\end{array}\right.---\left(10\right)$

Formula (9) substitutes into formula (10) and can obtain

${\stackrel{.}{V}}^{\&prime;}=2{\stackrel{\&OverBar;}{e}}_x+2{\stackrel{\&OverBar;}{e}}_y{\stackrel{.}{\stackrel{\&OverBar;}{e}}}_y=-2(k_1{\stackrel{\&OverBar;}{e}}_x^2+k_2{\stackrel{\&OverBar;}{e}}_y^2)<0---\left(11\right)$

By Liapunov law, for given deviation adopt speed and the angular velocity instruction of formula (8), flight pattern deviation converges to 0, makes error expression converge to 0;

Final formation overload instruction with formation speed command for:

$\left\{\begin{array}{c}{n}_1^{*}={\mathrm{\&omega;}}_F{V}_F\\ {V_1}^{*}=V_F\end{array}\right.---\left(12\right)$

Step 2: barrier-avoiding method;

Ground obstacle is obeyed in space and is uniformly distributed, M is unmanned plane current location, V is unmanned plane velocity, r is the threat range of barrier, R is the distance of unmanned plane distance barrier, and threaten district for ensureing that unmanned plane does not enter, unmanned plane also can fly along right side flight path MB along left side flight path MA flight, if the threat source nearest apart from unmanned plane is center of circle O, desirable Threat Avoidance flight path is two circumscribed with circle O and tangent with velocity V circle O _l, O _rcircular arc MA and MB, definition point of contact A, B is Threat Avoidance navigation spots;

The method of radius of turn application solving a triangle is asked for, at Δ OO _lapply the cosine law in M to obtain:

$\cos (\&angle;{\mathrm{OMO}}_l)=\sin \left(b\right)=\frac{R^2+R_l^2-{(R_l+r)}^2}{2R{R}_l}---\left(13\right)$

Draw the radius of turn of unmanned plane Threat Avoidance:

$R_l=\frac{R^2-r^2}{2(r+R\sin b)}---\left(14\right)$

$R_r=\frac{R^2-r^2}{2(r-R\sin b)}---\left(15\right)$

The expression formula of corresponding side acceleration is:

$a_r=\frac{V^2}{R_r},a_l=\frac{V^2}{R_l}---\left(16\right)$

Wherein a _r, a _lrepresent that unmanned plane carries out the side acceleration of keeping away required for barrier along circular arc MB, MA respectively;

Final keeps away the instruction of barrier overload

$n_2^{*}=\begin{array}{ccc}{a}_r& \mathrm{or}& a_l\end{array}---\left(17\right)$

Finally keep away barrier speed command to select and lead aircraft speed aligned instruction

$V_2^{*}=V_L---\left(18\right)$

Wherein V _lrepresent the speed of lead aircraft;

Step 3: the formation process of Behavior-based control;

(1) behavior decomposition process: being three sub-line parallel to each other by task behavior decomposition is: abnormal conditions process, Keeping Formation and barrier-avoiding method, be simultaneously each sub-line for giving corresponding importance, represent with weights; In Keeping Formation, actual wing plane obtains the information of lead aircraft by cordless communication network, specifically comprises lead aircraft speed V _l, lead aircraft yaw rate ω _lwith lead aircraft flight path drift angle ψ _l; Actual wing plane obtains navigation information by self the machine navigator, specifically comprises actual wing plane speed V _f, angular velocity omega _fwith flight path drift angle ψ _f, generate according to step one formula (8) and formula (12) overload instruction of forming into columns with formation speed command ; The information that in barrier-avoiding method, unmanned plane obtains barrier by optical sensor comprises: the distance R of unmanned plane distance barrier, the angle of velocity and unmanned plane and barrier line is b, generates keep away the instruction of barrier overload according to step 2 formula (17) and formula (18) with keep away barrier speed command ; Abnormal conditions process refers to that aircraft is when performing aerial mission, run into interrupted communication link and cannot maintain formation, UAV flight control enters abnormality processing state, abnormality processing to ensure unmanned plane according to the strategy execution task of unit optimum or fly away from region of search arrive assigned address prepare landing, abnormality processing is the highest at medium priority of executing the task, and the overload instruction that unmanned plane needs according to the strategy execution task of unit optimum and speed command are respectively ;

(2) control realization process refers to that unmanned plane is according to motion model and current motion state, the steering order of weighted calculation unmanned plane reality, and then input topworks: the jaw channel of unmanned plane produces yaw rudder partially, thus realizes the motion control to unmanned plane formation;

According to the Keeping Formation in step one and step 2 and barrier-avoiding method, be weighted according to formula (19) after the overload instruction that each sub-line is and speed command obtain:

$n^{*}=w_{n0}{n}_0^{*}+w_{n1}{n}_1^{*}+w_{n2}{n}_2^{*}$

$V^{*}=w_{V0}{V}_0^{*}+w_{V1}{V}_1^{*}+w_{V2}{V}_2^{*}---\left(19\right)$

Wherein w _n0+ w _n1+ w _n2=1.0, w _v0+ w _v1+ w _v2=1.0

Wherein, w _n0overload instruction weights, w during expression abnormality processing _v0represent abnormality processing hourly velocity instruction weights, w _n1overload instruction weights, w when representing that formation keeps _v1represent that formation keeps hourly velocity instruction weights, w _n2represent overload instruction weights, w when keeping away barrier _v2represent and keep away barrier hourly velocity instruction weights;

1) condition of abnormality processing is met: w _n0=w _v0=1.0, w _n1=w _v1=w _n2=w _v2=0.0, at this moment formation keep and barrier-avoiding method no longer valid, the mode that unmanned plane takes unit fly is executed the task, or edge appointment navigation spots enter landing phases;

2), when not meeting abnormality processing condition, according to optical sensor, whether Keeping Formation and barrier-avoiding method effectively, find that barrier carries out weight computing:

Wherein, w _n2, w _v2value depend on the ratio of ground obstacle yardstick and barrier threat range, w _n1=1.0-w _n2, w _v1=1.0-w _v2.